Directionally solidified eutectic ceramic oxides

Directionally solidified eutectic ceramic oxides

Progress in Materials Science 51 (2006) 711–809 www.elsevier.com/locate/pmatsci Directionally solidified eutectic ceramic oxides Javier LLorca a a,* ...

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Progress in Materials Science 51 (2006) 711–809 www.elsevier.com/locate/pmatsci

Directionally solidified eutectic ceramic oxides Javier LLorca a

a,*

, Victor M. Orera

b

Departamento de Ciencia de Materiales, Universidad Polite´cnica de Madrid, E.T.S. de Ingenieros de Caminos, 28040 Madrid, Spain b Instituto de Ciencia de Materiales de Arago´n, CSIC/Universidad de Zaragoza, 50009 Zaragoza, Spain Received 2 August 2005; accepted 17 October 2005

Abstract The processing, structure and properties (mechanical and functional) of directionally solidified eutectic ceramic oxides are reviewed with particular attention to the developments in the last 15 years. The article analyzes in detail the control of the microstructure from the processing variables, the recently gained knowledge on their microstructure (crystallographic orientation, interface structure, residual stresses, etc.), the microstructural and chemical stability at high temperature, the relationship between the eutectic microstructure and the mechanical properties, and the potential of these materials as patterning substrates for thin films, templates to manufacture new composite materials, photonic materials and electroceramics. The review highlights the achievements obtained to date, the current limitations and the necessary breakthroughs.  2005 Elsevier Ltd. All rights reserved.

Contents 1. 2.

*

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Eutectic oxide systems and processing techniques . . . . . . . . . 2.1. Oxide eutectic systems . . . . . . . . . . . . . . . . . . . . . . . 2.2. Coupled eutectic growth . . . . . . . . . . . . . . . . . . . . . . 2.3. Eutectic range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Preparation techniques . . . . . . . . . . . . . . . . . . . . . . .

Corresponding author. Tel.: +34 91 336 5375; fax: +34 91 543 7845. E-mail address: [email protected] (J. LLorca).

0079-6425/$ - see front matter  2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.pmatsci.2005.10.002

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Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. DSE oxides microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Crystallography and interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Microstructural and chemical stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Microstructural stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Oxidation and chemical resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Residual stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Origins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Measurement techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1. Al2O3–YSZ system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2. Al2O3–YAG system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3. NiO–ZrO2 and Co1xNixO–ZrO2 systems . . . . . . . . . . . . . . . . . . . . . . . 5.4.4. Al2O3–YAG–YSZ ternary eutectic system . . . . . . . . . . . . . . . . . . . . . . . Mechanical behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Elastic modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1. Ambient temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2. High temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3. Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. Hardness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Fracture toughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5. Creep deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6. Subcritical crack growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Functional properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1. Substrates for thin film deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.1. YBCO in CaSZ/CaZrO3 (CZO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.2. LCMO in CaSZ/CZO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.3. YBCO in MgSZ/MgO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Structured Ni/YSZ and Co/YSZ composites . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3. Photonic materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1. Optical waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2. Effect of microstructure size on luminescence. . . . . . . . . . . . . . . . . . . . . 7.4. Electroceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5. Bioeutectics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction Eutectics are a paradigm of composite materials with a fine microstructure on the lm scale whose characteristics are controlled by the solidification conditions. These in situ composites have been studied for decades because of their excellent mechanical properties inherent to the reduced interphase spacing, homogeneous microstructure and large surface area of clean, strong interfaces. Attention in the past was mainly focused on metallic eutectics, and most of the advances in the comprehension of eutectic growth and microstructure were achieved in these materials [1]. Less effort was devoted to ceramic eutectics,

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notwithstanding the pioneer work on some oxide–oxide systems (such as Al2O3–ZrO2 or ZrO2–CaZrO3 [2]). These early studies demonstrated the outstanding mechanical properties and the thermal and microstructural stability of directionally solidified eutectic (DSE) ceramic oxides, as compared with conventional composites and monolithic ceramics [3]. Recently, interest in DSE ceramic oxides has been renewed by the synergistic effect of new developments in the processing and characterization techniques. From the point of view of processing, the key to obtaining a homogeneous microstructure is to keep flat solid–liquid interfaces during growth at microscopic and macroscopic level, and this requires large thermal gradients in the solidification direction. The Bridgman method used in the 1970s to grow DSE is limited to thermal gradients below 102 K/cm but new processing techniques developed recently can reach thermal gradients in the range 103–104 K/cm, providing more degrees of freedom to control the microstructure through changes in processing variables. This led to a better understanding of the physical mechanisms which control the microstructural development upon directional solidification [4]. In addition, the knowledge of the relationship between the eutectic microstructure and the properties has profited from the widespread use of better techniques of microstructural characterization. This includes high-resolution transmission electron microscopy of the interfaces, the determination of the orientation relationship between the eutectic phases [5], and the precise evaluation of residual stresses by X-ray diffraction [6] and piezospectroscopic techniques [21]. As a result of the advances in processing and characterization, DSE ceramic oxides with novel microstructures have been developed in the last 15 years. Al2O3-based DSE with minimum interphase spacing and free of large defects showed excellent mechanical properties up to temperatures very close to the melting point [7,8], as well as outstanding microstructural stability and corrosion resistance. This new generation of DSE ceramic oxides presents important advantages over conventional structural ceramics for high temperature structural applications. In addition, Galasso [9] showed nearly four decades ago the potential of some DSE for optical, electronic or magnetic applications. Regular eutectics with ordered microstructures of either single crystal rods embedded in a single crystal matrix or alternating lamellae behave as planar optical waveguides, as reported in ZrO2–CaO eutectics [10], while CaF2/MgO fibrous eutectics can be viewed as an array of micron-sized single crystalline optical fibers with a density of 40,000 fibers/mm2 [11]. From the point of view of optical spectroscopy, eutectics made from large optical band gap materials, such as insulator compounds, present the unusual characteristic of being at the same time a monolith and a multiphase material, and the optically active ions can be placed in different crystal field environments in the same material, as reported in ZrO2–CaO eutectics activated with Er3+ ions [12]. Finally, new applications have appeared recently in the areas of electroceramic and biomaterial engineering. These recent developments in processing, microstructural characterization and mechanical and functional properties of DSE ceramics oxides are reviewed in this paper, which is structured as follows. After the introduction, the Section 2 describes briefly the most important DSE ceramic oxide systems and analyzes in detail the mechanisms of coupled eutectic growth, necessary to understand the relationship between processing and microstructure. Section 3 shows the rich variety of eutectic microstructures found in these materials, and special attention is paid to the crystallographic orientation of the phases and interfaces. Section 4 analyzes the kinetics of phase coarsening in DSE ceramic oxides at high temperature and their chemical and oxidation resistance, while thermo-elastic residual stresses in DSE are studied in Section 5, which covers the origin, experimental

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techniques, and models to determine their magnitude. The main mechanical properties of these materials (elastic modulus, strength, hardness, toughness, creep resistance) and their relationship to the eutectic microstructure and composition are summed up in Section 6, while Section 7 explores new functional applications of DSE ceramic oxides as patterning substrates for thin films, templates to manufacture for new composite materials, photonic materials and electroceramics. The review ends with Section 8, where the achievements obtained to date, the current limitations and the necessary breakthroughs are considered. 2. Eutectic oxide systems and processing techniques DSE may be defined as composite materials with a complex and homogeneous microstructure which controls their properties. Hence, most of the research has been aimed at understanding the relationship between microstructure and properties, and at controlling the growth processes to obtain the desired microstructure for specific applications. In this framework, the first question to answer is how the properties of the eutectic depend upon those of their components. Broadly speaking, composite properties can be divided in two categories, namely additive and product properties [13]. The former depend only on the volume fraction and spatial distribution of the phases and their magnitude is limited by the maximum and minimum values of the composite phases. Examples of additive properties are elastic stiffness, electrical conductivity and mass density. Product properties are those that depend on the interaction between the composite phases and thus are controlled by structural factors such as periodicity or phase size. Of course, product properties are not bounded by the phase properties and may exist in the composite but not in the individual phases. Examples of product properties in DSE oxides are optical interference or hardness. Finally, it should be noted that the eutectic phases are usually solid solutions whose characteristics depart from those of the pure phases. In summary, the mechanical and functional properties of DSE are strongly dependent on the characteristics of the microstructure (morphology, phase shape and size), which can be controlled to some extent during the solidification process. This section describes the process of eutectic solidification from the melt after a brief description of the main DSE ceramic oxides systems which present interesting properties for engineering applications. 2.1. Oxide eutectic systems Several eutectic oxide systems have been studied in the past. The reviews from Minford et al. [3], Ashbrook [14] and Revcolevschi et al. [5] describe the investigations carried out until 1990 in DSE ceramic oxides. More recent efforts have been focused on Al2O3-based eutectics because the outstanding creep resistance of sapphire along the c-axis was combined with other oxide properties to create new families of compounds with exceptional thermo-mechanical properties. In particular, binary and pseudo-binary eutectics, ternary eutectics and even some off-eutectic compositions of the ternary system Al2O3–ZrO2–Y2O3 were explored in detail following the phase diagram for this system presented by Lakiza and Lopato [15]. This includes the Al2O3/Y3Al5O12 (YAG) system, extensively studied because of its exceptional creep resistance [16–19], and the Al2O3/ZrO2 system. The addition of Y2O3 to Al2O3/ZrO2 led to the pseudo-binary Al2O3/ZrO2(Y2O3) eutectic in which different zirconia polymorphs (monoclinic, tetragonal or cubic zirconia) could be obtained just by changing the yttria content. The presence of the zirconia polymorphs gave rise to a rich variety of microstructural

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morphologies and residual stress states, which controlled the mechanical properties [20,21]. More recently, attention has been paid to the oxide ternary compounds, such as Al2O3/ YAG/YSZ (yttria-stabilized zirconia), to further improve the excellent mechanical properties of their binary counterparts [22,23]. In addition, rare-earth aluminates–sapphire of the Al2O3/(RE)AlO3 (RE = rare earth) families are eutectic composites made up by sapphire in combination with either perovskite (in the case of the larger rare-earth ions as Sm, Eu, Gd) or garnet phases (in the case of the smaller rare-earth ions Sm, Lu, Y) [7,24]. Magnesium spinel (MgAl2O4) is another well-known oxide material with excellent thermal and chemical resistance and two different spinel-based eutectics were grown. MgO/ MgAl2O4 eutectic consisted of thin MgO crystalline fibers embedded into the spinel matrix [25]. Conversely, the fosterite-spinel eutectic is composed of MgAl2O4 fibers within a Mg2SiO4 matrix. Interestingly, it was reported that the silicate matrix could be removed in this eutectic to obtain isolated spinel fibers of 50 lm in length [26]. ZrO2-based eutectics make up a family of eutectic oxides, which is of interest because of their functional applications. For example, the microstructure of the NiAl2O4/YSZ eutectic is of highly ordered colonies of YSZ fibers in a hexagonal arrangement embedded in a NiAl2O4 single crystal matrix, and Ni nanoparticles were produced by chemical reduction of the Ni-spinel matrix [27]. The reduction from NiAl2O4to Ni took place throughout the sample as the YSZ fibers acted as channels for oxygen ion transportation from the external surface, thus producing a homogeneous reduction of the spinel domains. The same principle was used to produce very stable Ni (or Co) porous cermets from lamellar NiO/CaSZ (CaO stabilized-zirconia) or NiO/YSZ eutectics, which were envisaged as potential materials for fuel cell anodes or as catalysts [28]. In addition, CaSZ/CaZrO3 eutectics presented relatively large (several mm3) regions of well-aligned lamellae, which led to anisotropic ionic conductivity and light waveguide effects [27]. Fibrous MgO–MgSZ (MgO-stabilized ZrO2) eutectics present a structure formed by an almost hexagonal array of MgO fibers of 1 lm diameter embedded within a MgSZ single crystal matrix, and interesting optical effects were reported in CaF2/MgO and MgF2/MgO eutectics with a similar structure in which the light is transmitted through the MgO single crystalline fibers with a higher refractive index [29,11]. Moreover, Revcolevschi et al. [5] have reviewed in detail other eutectic oxide families of either MO (M = 3d ions) and/or RE2O3 (RE = rare-earth ions) oxides. These systems comprised lamellar NiO/CaO [30], NiO/Y2O3 [31] and NiO/Gd2O3 [32], and fibrous NiO in NiAl2O4 (Ni-spinel) [33]. The composition and the eutectic temperature of the most relevant DSE ceramic oxide systems is given in Table 2.1. Of course, there are other DSE oxide systems with potential interest for engineering applications but they are not addressed in this review because of the lack of information available. The only exception will be the CaSiO3/Ca3(PO4)2 eutectic composite, which presents two unconventional and interesting properties: firstly, the degenerated lamellar structure of the system favored the biological transformation of the tricalcium phosphate phase into hydroxiapatite, giving rise to a biological material with a microstructure similar to that of human bone [34]. Secondly, it is possible to form a eutectic glass of this composition with excellent optical properties [35]. 2.2. Coupled eutectic growth A crucial aspect of the study of eutectic systems is the understanding of the dynamics of eutectic growth. Since the pioneering ideas of Zener [36] and Tiller [37], a lot of excellent

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Table 2.1 Eutectic phases, eutectic temperature, TE, composition, and vk2 (v growth rate, k interphase spacing) of some oxide eutectics Eutectic phases

TE (K)

Composition (wt%)

% Volume (minor phase)

vk2 (lm3/s)

Reference

Al2O3/YSZa Al2O3/Y3Al5O12 Al2O3/Er3Al5O12 Al2O3/EuAlO3 Al2O3/GdAlO3 Al2O3/Y3Al5O12/YSZ Ca0.25Zr0.75O1.75/CaZrO3 Mg0.2Zr0.8O1.8/MgO YSZ/NiAl2O4 CaSZ/NiO CaSZ/CoO MgAl2O4/MgO CaF2/MgO

2135 2100 2075 1985 2015 1990 2525 2445 2270 2115 2025 2270 1625

42YSZ + 58Al2O3 33.5Y2O3 + 66.5Al2O3 52.5Al2O3 + 47.5Er2O3 46.5Al2O3 + 53.5Eu2O3 47Al2O3 + 53Gd2O3 54Al2O3 + 27Y2O3 + 19ZrO2 23.5CaO + 76.5ZrO2 27MgO + 73ZrO2 54NiAl2O4 + 46Zr0.85Y0.15O1.92 61NiO + 39Zr0.85Ca0.15O1.85 64CoO + 36Zr0.89Ca0.11O1.89 45MgO + 55Al2O3 90CaF2 + 10MgO

32.7ZrO2 45Al2O3 42.5Al2O3 45Al2O3 48Al2O3 18YSZ 41CaSZ 28MgO 39YSZ 44CaSZ 38.5CaSZ 23.5MgO 9MgO

11 100 60 – 6.3 70 400 50 8 32.5 25 150 68

[62] [16] [59] [24] [233] [22] [3] [3] [27] [234] [235] [25] [11]

a

Tetragonal or cubic yttria-stabilized zirconia.

work has been published on this topic. For instance, Hecht et al. [38] have recently reviewed the experimental and theoretical aspects of the solidification of multiphase materials, including the advances in phase field modeling. Kurz and Fisher [39] described the fundamentals of solidification including eutectic growth and rapid solidification from a very tutorial point of view, while Hunt and Lu [40] and Magnin and Trivedi [41] applied the current solidification theories to eutectic growth. Finally, Hogan et al. [42] focused on models to explain the development of eutectic microstructures. A characteristic of eutectic structures is the simultaneous growth of two or more phases from the melt, and a summary of the theoretical bases of coupled eutectic growth is presented in this section, as they elucidate the microstructural features found in DSE ceramic oxides. Regular lamellar growth is assumed for the sake of simplicity and a typical phase diagram is shown in Fig. 2.1(a) for a binary eutectic a/b with lamellar structure and lamellar spacing k. The relevant magnitudes of this diagram are the eutectic temperature, TE, the growth temperature T0, the eutectic composition CE (wt%), and the slopes of the liquidus lines ma and mb for the a and b phases, respectively. When T0 < TE (under-cooling), the reduction in the free energy of the liquid at CE is the driving force behind the growth of both a and b phases while the solid phases of compositions C sa and C sb are in equilibrium with the liquid at the growth temperature T0. The segregation phenomenon can be described by the partition coefficient defined as k a ¼ C sa =C la in equilibrium. A solute redistribution takes place because each solid phase rejects the other solute component and the concentration profile in the liquid ahead of the lamella tips is no longer a flat surface (see Fig. 2.1(b)). Extensive lateral mixing takes place as a consequence of this concentration gradient at the a–b interface, and a diffusion flux parallel to the solid–liquid interface reduces the concentration oscillation to values between C la and C lb , as depicted in Fig. 2.1(b). The concentration gradients across the solid–liquid interface, which are defined by DCC = C(z)  CE (both a and b phases), decrease exponentially with z in the growth direction along a boundary layer given by dC = 2D/v, D being the diffusion coefficient in the liquid and v the growth rate. The compensation between the lateral flux, scale

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Fig. 2.1. (a). Schema of a typical temperature–composition phase diagram of a binary eutectic with lamellar structure. The liquidus and solidus lines are assumed to be straight and thus the partition coefficients ka and kb are independent of the concentration. The tie line between the a and b solid solution fields at the eutectic temperature TE gives the equilibrium concentrations of the eutectic phases. (b) Concentration profile in the liquid ahead of the lamella tips, which determines the boundary layer.

length k, and the flux perpendicular to the growth front, scale length dC, produces the eutectic-coupled growth. The concentration gradient is equivalent to a temperature gradient according to the phase diagram, which is given for the phase i (=a, b) as DT C ¼ mi DC C

ð2:1Þ

in which mi is the liquidus slope (Fig. 2.2). The temperature at the interface also depends on other factors such as the interface curvature (also called capillarity effect), DTr and the kinetic under-cooling DTK. The curvature under-cooling is taken into account by the Gibbs–Thomson equation, and is given by

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Fig. 2.2. Contributions of solute under-cooling, DTC, and curvature under-cooling, DTr, to the total undercooling DT0. DTC is proportional to DC ¼ C la  C lb .

DT r ¼

2c rDS m

ð2:2Þ

for a sphere of radius r in which c is the solid–liquid surface energy and DSm the fusion entropy per unit volume. A positive under-cooling (decrease in melting point) produces a surface convex towards the liquid phase. The Gibbs–Thomson principle states that the higher the curvature radius of the solid–liquid interface the lower the solute concentration in the liquid phase in equilibrium. This contribution to the under-cooling is important for radii equal to or lower than 10 lm. The kinetic under-cooling increases with growth rate and is generally negligible in comparison with the other contributions in most metals but it can be large in systems with high entropy of melting, such as ceramic oxides, even at low growth rates. Hence the overall under-cooling, DT0, is obtained by adding the three contributions DT 0 ¼ T E  T 0 ¼ DT C þ DT r þ DT K

ð2:3Þ

and it can be nearly constant along the solid–liquid interface if the curvature of the solid– liquid interfaces in each phase varies along the interface to compensate for constitutional under-cooling (Fig. 2.2). Solidification is a surface reaction whose rate depends upon the degree of under-cooling that drives it. Steady-state solidification produces regular lamellar or fibrous eutectic structures where the flat interface moves at uniform and constant speed v. In a reference frame moving with the interface, z ! z  vt, the diffusion field equations are oT ; oz v oC r2 C ¼  ; D oz r2 T ¼ K

ð2:4Þ ð2:5Þ

K being the thermal diffusion coefficient and C ¼ C li (i = a, b). As explained by Davis [43], if solute diffusion in the solid phase is negligible (one sided model) and D  K (frozen temperature approximation, FTA), the temperature in both solid and liquid phase can be defined by a constant thermal gradient GT, T ¼ T E þ GT z.

ð2:6Þ

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If the densities of the a and b phases are equal, and the regular microstructure interspacing is given by k = ta + tb, the solution to Eq. (2.5) is [44,45]    1 X 2npx Bn exp xn z cos ; ð2:7Þ C ¼ CE þ k n¼0 in which " #  v 2 2np2 1=2 v þ þ . xn ¼ 2D 2D k

ð2:8Þ

It is worth noting in Eq. (2.7) the exponential decay along the z (growth) direction and the periodic fluctuation of the concentration in x. The coefficients Bn are determined by imposing the mass conservation law at the interface in Eq. (2.7). If the eutectic interface is assumed to be planar to simplify the problem, the average concentration C i and the average constitutional under-cooling DT C ¼ mi ðC E  C i Þ can be easily evaluated [45]. The second source of under-cooling is the curvature of the a  l and b  l interfaces (Fig. 2.3), which changes the equilibrium temperature. An average change in the liquidus temperature can be estimated from the average curvature, and the capillarity effect can be described from Eq. (2.2) as DT r;i ¼

2ai ti

with i ¼ a; b;

ð2:9Þ

in which ti is the thickness of the lamella of phase i and ai = Ci sin hi, where Ci = (TE/Li)ci is the Gibbs–Thomson coefficient, Li the heat of fusion per unit volume and ci the interfacial solid–liquid energy of phase i. The contact angle, hi, at the three contact points (Fig. 2.3) obeys the equilibrium relationships ca cos ha ¼ cb cos hb

and

ca sin ha þ cb sin hb ¼ cab ;

ð2:10Þ

cabbeing the solid–solid interfacial energy. Curvature under-cooling is clearly caused by the increase of interface energy. An insight into the physical meaning of this term can be obtained from energy arguments, considering that the energy necessary to create the solid–solid interface in the eutectic system is provided by the decrease in the Gibbs energy.

Fig. 2.3. Liquidus–solid interfaces in the lamellar eutectic. The mechanical equilibrium at the three-phase joint point is also shown.

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In particular, if ta = tb (50% in volume lamellar eutectic), the curvature under-cooling is clearly related to the interface solid–solid energy. In fact, the a–b interfacial area per unit volume is 2/k and the net Gibbs free energy change during the solidification process is given by DG ¼

LDT r 2cab .  TE k

ð2:11Þ

Obviously, the minimum under-cooling that leads to zero free energy change for a given spacing k is given by, DT r ¼

2cab T E ; Lk

ð2:12Þ

which is similar to expression (2.9). Coming back to Eq. (2.9) and neglecting the kinetic contribution, the average undercooling can be obtained by the addition of constitutional and curvature under-cooling as DT i ¼ mi ðC E  C i Þ þ

2ai . ti

ð2:13Þ

During coupled growth, the average under-cooling in front of each phase has to be about the same, DTa  DTb = DT, and the relationship between under-cooling DT and spacing k is given by [45] DT kv C 0 Pðk; k i Þ a ¼ þ .  m D fa fb k

ð2:14Þ

It is easily recognized that the first term on the right-hand side of Eq. (2.14) corresponds to the constitutional under-cooling DTC, and the second one to the capillarity effect DTr. C0 is the concentration difference, which can be obtained from the tie-line of the eutectic phase diagram, and P(k, ki) is a structure function defined in [45] which depends on the eutectic Peclet number Pe = k/dC = kv/2D, the volume fraction of the phases, and the seg and a are defined as a function of the liquidus slopes mi and regation coefficients, ki. m volume fractions fi as   jma jjmb j aa ab  þ m¼ and a ¼ 2 . ð2:15Þ ma þ mb fa jma j fb jmb j Similar expressions were obtained for fibrous structures [45]. Fig. 2.4 represents the under-cooling given by Eq. (2.14) as a function of the lamellar spacing k. The diffusiondriven term DTC increases while the capillarity term DTr decreases with spacing, giving rise to a minimum for the total under-cooling DT. At large values of the spacing, the limiting growth process is diffusion, while at lower ones it is capillarity. Zener [36], Tiller [37] and Jackson and Hunt (JH) [1] proposed that the eutectic grows precisely at this minimum interface under-cooling (growth at extremum). If it is assumed that P and C0 are independent of k, the relationships between spacing, thermal under-cooling and growth rate are given by aDf a fb ¼ K 1; PC 0 kDT ¼ 2ma ¼ K 2 ; vk2 ¼

ð2:16aÞ ð2:16bÞ

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0

TE

ΔTσ

Temperature

ΔT

ΔT ΔT C

Interlamellar spacing λ Fig. 2.4. Solute under-cooling DTC and curvature under-cooling DTr contributions vs. interlamellar spacing k at constant growth rate v. The sum of the contributions gives a minimum total under-cooling.

and the parameters and coefficients in Eq. (2.16) can be found in Table 1 of Ref. [45] for both lamellar and fibrous eutectic structures. Eq. (2.16a) is the well-known law which relates the interphase spacing to the solidification rate for coupled eutectic growth conditions. However, this equation implies the JH condition: the diffusion distance in the liquid is larger than the spacing in the eutectic, which is only valid at low growth rates. In principle, the structure function P(k, ki), C0 and even m and D depend on the growth rate. Moreover, at high growth rates there will not be enough time for the solute to undergo lateral diffusion before being trapped at the solid surface. Trivedi et al. (TMK theory) [46] studied eutectic growth at high solidification rates and established that coupled growth is unstable above a certain value of the solidification rate. In other words, the relation k2v = constant is only valid if the eutectic Peclet number Pe < 1. Experimental values of the phase interspacing, k, are plotted in Fig. 2.5 as a function of growth rate v for two important DSE ceramic oxides, Al2O3/YSZ and Al2O3/YAG. Typical spacings in both systems are in the range 0.2–10 lm, corresponding to growth rates

10

λ (μm)

Al 2O3 / YAG

1

Al2O3 / YSZ

0.1 10

100

1000

v (mm/h) Fig. 2.5. Log–log representation of the microstructural interspacing vs. growth rate for two irregular eutectics Al2O3/YSZ and Al2O3/YAG. The straight lines correspond to expression k2v = constant.

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between 1 mm/h and 1500 mm/h [22]. It is worth to noting that the k2v = constant law holds for binary oxide eutectics with different microstructures and also for ternary eutectics with few exceptions limited to the regions of extreme low or high growth rates (see Table 2.1). Eq. (2.16a) can also be used to estimate the interfacial surface energy and the diffusion coefficient of solute in the liquid. Bourban et al. [47] compared the measured eutectic spacing in Al2O3/ZrO2 eutectic laser remelted surfaces with values calculated by Eq. (2.16a) but with thermo-physical constants obtained from literature. The growth rate was quite high in this case (up to 10,000 mm/h) and the observed spacing was four times larger than calculated. The discrepancy was attributed to the inaccuracy in the estimation of D. Conversely, they obtained a diffusion coefficient of D  5.0 · 1010 m2/s using k as a data. Minford et al. [3] also used Eq. (2.16a) and parameters taken from literature, including a value of D  2.0 · 109 m2/s, to obtain an interfacial energy of 8.5 · 101 J/m2 for the MgO/MgAl2O4 system from v–k experimental data, which was in good agreement with other independent estimations. It is interesting that in both cases the eutectic Peclet number was low, which assures the validity of the analysis. The growth of DSE oxides usually takes place with a low Peclet number, and in principle, the coupled regime could be attained even at very fast growth rates. Then, fast solidification could be used to produce nanometric sized ordered microstructures but, as will be shown below, a new effect hinders the production of very fine microstructures in this regime. 2.3. Eutectic range Coupled growth produces regular eutectics growing near the extremum conditions. The structure can self-adapt to local growth instabilities by branching, which is a mechanism in which lamellae or rods can change the growth direction or branch to recover the minimum under-cooling conditions and coupled growth dynamics. Two material characteristics hinder this adaptation. The first one occurs when one or both phases show a marked tendency to grow in preferred directions, which makes changes in growth direction very difficult and impedes the soft microstructure adaptation to front instabilities, leading to irregular spacing. This is fairly common in DSE oxides. A second difficulty arises when the material composition departs from the exact eutectic composition, which produces the growth of single-phase dendrites or cells. The presence of dendrites or cells depends strongly on the growth rate, the solidification thermal gradient, and the concentration gradient. In fact v, GT, and DC are the three parameters that control planar growth. It has been found that for a given GT and DC, the planar front is stable up to a certain critical growth rate v = vC, where shallow cells start to appear as a secondary phase. If v keeps increasing one-phase dendrites appear. Dendrites become deep cells and eventually a planar front is established again at higher v values. This evolution is illustrated in Fig. 2.6 with several scanning electron microscope (SEM) images of an Al2O3/YSZ eutectic grown at increasing rate [48]. The transition from coupled to cellular and then to shallow cells with increasing growth rate is evident. One simple way to understand this behavior uses the concept of ‘‘competitive growth’’. Dendrites instead of coupled eutectics grow when the temperature at the dendrite tip is above the eutectic growth temperature [49]. Burden and Hunt [50] proposed the following phenomenological equation for the under-cooling at the b-dendrite tip

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Fig. 2.6. SEM micrographs showing the microstructure of an Al2O3/YSZ DSE grown by the laser-heated floating-zone method at different growth rates: (a) 10 mm/h, (b) 100 mm/h, (c) 300 mm/h, and (d) 1500 mm/h. (Reprinted by permission of Elsevier from [48].)

DT D ¼ T l  T D ¼

GT D þ K 3 v1=2 v

ð2:17Þ

where Tl is the liquidus temperature, TD the dendrite tip temperature, and K3 is a constant given by (for the b phase)  1=2 2=3 ma C L ð1  k b ÞCb K3 ¼ 2 ; D where CL is shown in Fig. 2.7, and the under-cooling for coupled growth is obtained from Eq. (2.16) as K2 DT E ¼ T E  T 0 ¼ pffiffiffiffiffiffi v1=2 K1

ð2:18Þ

TD and T0 are plotted in Fig. 2.7 as a function of the growth rate according to Eqs. (2.17) and (2.18) for an irregular eutectic with different growth kinetics of the a and b primary phases. Dendrites grow if TD > TE, which can occur at intermediate v values. The results are superimposed into the eutectic phase diagram in order to show the skewed region of coupled eutectic growth for irregular eutectics, while the coupled eutectic growth region in the case of a regular eutectic is shown in Fig. 2.8. The coupled-growth region extends

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Fig. 2.7. The skewed coupled eutectic growth zone associated with irregular eutectics. The plot at the right-hand side shows the under-cooling as a function of the growth rate; b-dendrites grow at higher temperatures than adendrites. TDb and TDa stand for the temperatures at the tip of the dendrites of phases b and a, respectively (Eq. (2.17)).

TE

0

Planar Eutectic

α-dendrites -dendrites + Coupled Eutectic

Cells coupled eutectic

β-dendrites -dendrites + Coupled Eutectic

ΔT T or v1/2

Faceted eutectic dendrites

CE

C

Fig. 2.8. The symmetric eutectic-coupled zone projected over the phase diagram for a regular binary eutectic.

towards compositions departing from the true CE eutectic composition at low growth rates. The mixed primary dendrite–eutectic zone is attained even for small departures from eutectic compositions at high growth rates. Thermal gradient and growth rate are entangled magnitudes. In fact, the thermal gradient term dominates in the low growth rate region and Eqs. (2.17) and (2.18) can be combined to give the following constitutional under-cooling: mi DC ¼ T l  T E ¼

GT D þ ðT D  T 0 Þ; v

ð2:19Þ

mi being the liquidus slope of the phase in excess. Dendrites could be avoided if mi DC GT  . D v

ð2:20Þ

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725

Coupled-growth implies either low growth rates or high growth gradients. For instance, thermal gradients above 105 K/m are needed to obtain a planar front at v > 20 mm/h for eutectic oxides with m  10 K/%, D  1010 m2/s and DC > 0.1%. Trivedi and Kurz [51] extended the TMK theory to the case of cellular growth during fast solidification and obtained qualitatively similar results except that their theory predicted a critical growth rate above which coupled growth is not possible. This implies that the second planar growth regime at very high growth rates may not always be attainable even if the coupled eutectic zone is symmetric (see Fig. 2.8), and eutectic glass can be formed at very high growth rates. 2.4. Preparation techniques As shown in the previous section, the key rule for regular homogeneous growth is to keep micro- and macroscopically flat solid–liquid interfaces during growth, thus preventing constitutional under-cooling and cellular growth. This in turn requires large thermal gradients. These conditions are essentially the same as those required for the growth of single crystals from the melt, and consequently similar directional solidification procedures are used to grow ceramic eutectics. The growth methods can be classified in two groups, (i) unidirectional solidification in a container, (ii) pulling of a solid from a melt meniscus. Among the former methods, the Bridgman–Stockbarger technique is suitable for growing bulk samples of large size, the ingot volume being limited only by crucible size. Melt oxide eutectics are usually contained in molybdenum, tungsten or iridium crucibles heated by resistance heaters or more frequently, by radio frequency (RF) induction through a graphite susceptor. Unidirectional solidification is achieved by slowly pulling the crucible off the hot region [25]. Schmid and Viechniki used this procedure to grow Al2O3/ZrO2 DSE [52,53] and Echigoya et al. [54] produced various DSE oxides and reported melt temperatures up to 2600 C. The apparent thermal gradients in the Bridgman method are generally below 102 K/cm and consequently the growth rates have to be relatively low to avoid cellular growth, usually v < 100 mm/h, and interphase spacing is large according to Eq. (2.16a), usually k > 10 lm. In the Czochralski method, a container for the melt is also needed but direct contact between crucible and grown material is avoided since the eutectic is pulled out from the melt pool. Thick rods of about 6 cm diameter can be grown by this method. For the high melting point oxide eutectics the melt is heated by RF in a self-container ‘‘skull’’ of the same material [55]. The oxide powder has to be preheated to couple with the RF radiation, so heating is initiated by introducing some chips of metal or graphite into the oxide powders. Larger thermal gradients, and consequently faster growth rates, can be attained in the melt zone methods. Rudolph and Fukuda [56] published an excellent review in which the fundamentals of fiber crystal growth from free melt meniscus, i.e., the melt zone, are well described. Fig. 2.9 shows three diagrams illustrating the most commonly used melt zone methods. The processing techniques based on floating zone (FZ) or on pedestal growth (PG) are crucibleless methods in which a relatively small amount of sample volume is melted by the action of lasers, radiofrequency or lamp mirror furnaces (Fig. 2.9(a)). Growth thermal gradients of up to 104 K/cm can be obtained, and Al2O3/YSZ and Al2O3/YAG DSE oxides grown by laser-heated floating-zone method (LFZ) presented interphase spacings that could be smaller than 1 lm [57–60,48]. Other growth-from-meniscus methods are based on solid pulling from a wetting shaper as in the Stepanov or

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Fig. 2.9. Solid–melt interfaces during directional solidification from meniscus showing the growth angle at the interface /. (a) Floating zone method, (b) edge-defined film-growth method, (c) micropulling down method. The arrows indicate the growth direction. The eutectic rod diameter is R, and the feeding rod diameter in (a) or the wetting shaper diameter in (b) and (c) is R0. The liquid region is marked by horizontal broken lines.

edge-defined film-growth (EFG) and micro-pulling down (l-PD) methods (Fig. 2.9(b) and (c)). These methods can give thermal gradients of the order of 103 K/cm and the solidified sample is obtained by pulling out at high growth rates (up to m/h) from a liquid pool feed by capillaries through the shaping dies. Sample width is limited by meniscus stability and can vary from several microns to several centimeters. l-PD methods have been used intensively by the Fukuda group to grow sapphire-based DSE oxides [56,61,62] while Borodin et al. produced cylinders of Al2O3/YSZ DSE up to 12 mm diameter using the Stepanov method and molybdenum dies [63]. Establishing capillary stable growth conditions is a crucial issue in the growth-frommeniscus methods. For a uniform rod cross section, the growth angle at the solidus-melt interface / (Fig. 2.9) has to be kept constant and equal to a certain angle /0 determined not from growth conditions such as growth rate, diameter or zone length, but from thermodynamic equilibrium conditions at the liquid–solid–vapor three phase interface [64]. /0 has been experimentally determined for some simple materials such as YAG {1 0 0} (8)

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and Al2O3 {1 0 0 0} (17). There is also a limit to the melt zone length lm for stable growth, lm = 2pR for floating zone and lm = 3(R + R0)/3 for pedestal growth. Similar simple relationships between the fiber diameter and the melt zone length are found in the case of growth from dies [56]. The rod radii and the pulling rate are also related by the mass conservation law (qS = qL), R2 v ¼ R20 v0 ;

ð2:21Þ

where R, v and R0, v0 stand, respectively, for the radius and velocities of the grown fiber and the feeding rod or shaper. It should be borne in mind that there is a maximum attainable DSE rod diameter due to the heat transfer through the section. For example, since the absorption coefficient of molten oxides for CO2 laser radiation is high [65], most of the energy is absorbed within the first 0.1 mm near the exposed surface. Heating of the internal volume takes place via thermal diffusion, which competes with radiation losses. Consequently, the melt zone is limited to a few cubic millimeters and the feed rod to less than 2 mm in diameter with a CW-laser of about 100 W. With RF heating, the radiation is absorbed in the bulk rather than at the surface and the melting of large sample volumes is not a problem. However, the large thermal stresses generated during growth as a consequence of the high axial thermal gradients at the liquid–solid interface often lead to fracture in thick samples. During eutectic growth the thermal gradients can be directly measured in situ using non-contact optical methods [66] but this gives only the surface temperature given the high absorption of molten oxides. Thus, the growth thermal gradient along a growing rod of radius R has to be calculated from, for example, the following expression proposed by Brice [67]. hr2 "   # 1=2 2h 2R T ðr; zÞ ¼ T ext þ ðT E  T ext Þ exp  z ; ð2:22Þ hR R 1 2 where the origin of the cylindrical reference frame is taken at the rotation axis in the liquid–solid interface. h is a cooling constant, given by the ratio between thermal losses by radiation to the ambient and by conductivity along the rod (equal to 1.1 cm1 for YSZ and 0.65 cm1 for sapphire [68]), and Text is the ambient temperature. Pen˜a et al. [48] measured the surface temperature profile during solidification of an Al2O3/YSZ eutectic rod grown by the LFZ method and obtained a cooling constant of h = 0.5 cm1 and an axial gradient dT/dz = GT = 6.0 · 105 K/m by fitting the experimental data to Eq. (2.22). Due to the heating constraint discussed above, the rod diameter is relatively small, R < 0.1 cm and hR  1. Then, the axial gradient is  1=2 2h GT ðz ¼ 0Þ  ðT E  T 0 Þ; ð2:23Þ R which is essentially independent of r and decreases as the rod diameter increases. The radial thermal gradient is related to the axial thermal gradient by    1=2 dT h r GT ð2:24Þ dr z¼0 2R 1

which is linearly dependent on r. The through-the-thickness thermal gradients lead to thermal stresses and limit the axial gradient to avoid sample failure. According to the Brice model [67], GT is limited to

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GT <

4e ; ah1=2 R3=2

ð2:25Þ

where a stands in Eq. (2.25) for the thermal expansion coefficient and e is the failure strain. In conclusion, thermal stresses associated with large axial thermal gradients limit the sample diameter in the meniscus-driven eutectic growth methods, although eutectic rods thicker than single crystal rods can be processed thanks to the good thermo-mechanical properties of DSE. For instance, the maximum rod diameter in the Al2O3/YSZ eutectics is about 2 mm, assuming a failure strain of 103 and using the values of h and GT given above, and this value is in agreement with the experiments. It should be noted, however, that the Brice theory, originally developed for Czochralski growth, does not predict correctly the liquid–solid profiles observed in the LFZ experiments although it gives a reasonable picture of the temperature gradient in the solid and a good estimation of the maximum radius. The solid–liquid interface in a transparent melt is shown in Fig. 2.10: the front is convex towards the melt. The melt is highly absorbent in most DSE oxides, which impedes visualization of the growth front. However, the profile of the solid–liquid interface is shown in Fig. 2.11 in the longitudinal section of a Al2O3/YAG/YSZ ternary eutectic grown by the LFZ method. The rod was obtained by switching off the laser, and the differences in the microstructure between the quenched region (top) and the grown rod (bottom) delineate the solidification front. The isotherms as a function of z (calculated from Eq. (2.22)) are plotted in the same figure. Those predicted by the Brice model in the solid are concave towards the melt while the solidification front presents the opposite curvature. Basically, the heat distribution in the melt is not uniform, not only because of the absorption of the heating source but also due to the convention and thermal flow in the molten liquid. As a consequence, the equations governing crystal growth are complex and the solution has to be approached by numerical simulations. Equations and solution methods, as well as some simulations illustrating the details of crystal growth from melt, are found in the book of Kou [69].

Fig. 2.10. Solid–liquid interface of a CaSiO3/Ca3(PO4)2 (wollastonite-three calcium phosphate) glass growth by the LFZ method. The solid phase is transparent and the solidification front can be observed.

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Fig. 2.11. Longitudinal section of an Al2O3/YAG/YSZ ternary eutectic in which the solidification front is clearly observed. The rod was obtained by switching off the laser and the differences in the microstructure between the quenched region (top) and the grown rod (bottom) delineate the solidification front. The 50 C isotherms calculated from Eq. (2.22) are superimposed.

Recently, two interesting variations of the FZ method have been applied to DSE oxide growth. One is rapid solidification, which was applied to Al2O3/YAG/YSZ ternary systems melted in an arc-image furnace. Of course, the enormous thermal stresses induced by quenching limited the sample size to a few mm3 so the interphase spacing was extremely small, about 50 nm [70]. Balasubramaniam et al. [71] also produced powders with nanometer interphase spacing of Al2O3/ZrO2(Y2O3) eutectics by arc plasma spraying followed by rapid quenching. Subsequent hot-forging of the powders yielded dense ceramics of nanometric microstructural size. Interestingly, the densification of these nanosize powders was controlled by the microstructural dimensions rather than by the particle size. Rapid solidification of some eutectic systems also opens up the possibility of fabricating glass. In fact, glass is formed if the kinetic under-cooling brings the system below the glass transition temperature Tg (Fig. 2.1(a)). In addition, the low melting point of the eutectic composition helps glass formation and minimizes evaporation from the melt at the same time [72,35]. The CaSiO3/Ca3(PO4)2 eutectic is a good example of a binary glass made from eutectic composition with excellent optical properties and resistance to corrosion [35]. The second variation exploited the favorable geometry of the narrow line laser spots or of diode laser arrays to solidify the surface of an eutectic ceramic oxide plate directionally. Surface melting was very useful for DSE cladding on metals [73] and in DSE surface

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processing [74]. Fig. 2.12 shows the experimental set-up. The spot line sweeps over the precursor eutectic ceramic and a melt pool is created when the laser fluence exceeds a certain threshold determined by radiation thermal losses, heat of fusion and diffusion according to the principles of laser surface melting, which are given elsewhere [75]. Basically, the melt pool depth depends on laser power, sweep speed, optical properties and thermal diffusivity, and hence on the substrate properties. The melt pool section is symmetric at low growth rates but becomes asymmetric at high growth rates. Of course, thermal stresses through the thickness are also a problem during surface melting and sample failure are avoided by using porous ceramic substrates and/or preheating the system. The transverse section of an NiO/YSZ DSE oxide processed by this method is shown in Fig. 2.13. The

Fig. 2.12. Schema of the experimental set-up for laser surface melting used to process in-plane Al2O3/YSZ eutectics. The CO2 laser beam is transformed into a line beam and sweeps over the precursor ceramic surface as shown. (Reprinted by permission of Elsevier from [74].)

Fig. 2.13. SEM micrograph of the transverse cross section of a NiO/YSZ eutectic ceramic processed by surface melting. The successive melt front lines and growth directions are indicated. The inset shows a photograph of the upper surface after laser treatment.

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microstructure of the DSE plate depended on the melt front geometry. The phases grew with a depth-dependent orientation, and the growth rate v varied from the sweep speed v0 at the surface to 0 at the bottom of the melt pool. Then, the relationship k2v0 sin a = constant (where a is the angle between the normals to the solidification front and to the plate surface) was found in all surface melt eutectics following Eq. (2.16a) [74]. This technique efficiently produces large surfaces of DSE oxides with improved wear and erosion resistance. In conclusion, several useful methods are available for growing DSE oxides with a homogeneous microstructure, although the relationships between thermal gradient, growth rate and microstructure size established in Sections 2.2 and 2.3 impose some limits to the sample dimension and/or microstructural characteristics, and different growth methods have to be found for each need. For example, Bridgman methods are optimum if large volume samples are desired, although the relatively modest thermal gradients inherent to this method imply low growth rates and consequently large interface spacing, which may not be the best in terms of strength and hardness. On the contrary, the growthfrom-meniscus methods induce large thermal gradients and admit high growth rates, leading to eutectics of small interphase dimensions, but the large thermal stresses associated with steep thermal gradients impose a limit to the macroscopic sample size. In practice, a compromise between processing method and microstructure variables must be established for each requirement. 3. Microstructure Eutectic solids show not only a lower melting temperature than their constituent phases but also a very fine microstructure with clean interface and a rich variety of microstructure morphologies that control their structural and functional properties. Much has been done to study their microstructure by the latest methods of structural analysis: X-ray or electron diffraction, image analysis, synchrotron radiation, high-resolution electron microscopy, and spectroscopic techniques (Raman and electron probe microanalysis) in conjunction with recent improvements in theoretical modeling to provide an ever more precise characterization of DSE microstructures and interfaces. In a multiphase eutectic material, it is especially interesting to evaluate the homogeneity of the microstructure. Homogeneous microstructures are produced in coupled eutectic growth conditions (as discussed in Section 2.2) while uncoupled growth leads to the development of colonies or dendrites. Other important aspects are the grain size, the size and shape of the eutectic domains, and the relative crystallographic orientation, as well as the morphology and nature of the interfaces between the eutectic domains. The presence of eutectic grains is ubiquitous in regular eutectic structures, as illustrated in Fig. 3.1. These grains are a consequence of the adaptation of the eutectic structure to small instabilities in the solidification front, and the grain size is governed by both the growth conditions and the eutectic ability to accommodate growth fluctuations. Although directional solidification imposes an orientation of the grains preferably in the growth direction, the lateral dimensions can be rather small. Larger grain sizes can be obtained by using single crystals as growth seeds, but even then the longitudinal dimension rarely exceeds 0.5 mm and the lateral one 100 lm in most eutectic oxides. The small size of the eutectic grains imposes limits in applications that need phase continuity extended in space, such as those involving light or electrical transport. Interestingly, eutectic grains seem to be absent in

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Fig. 3.1. SEM micrograph of the transverse section of a lamellar NiO/YSZ DSE grown by the LFZ, showing the distribution of eutectic grains.

irregular eutectic structures. The problem of the small dimensions of the grains in regular eutectics has not yet been solved satisfactorily. 3.1. DSE oxides microstructure The microstructure and crystallography of some oxide eutectics was reviewed by Minford et al. [3], Stubican and Bradt [76], Revcolevschi et al. [5] and Ashbrook [14]. This previous work is taken into account here, but the discussion is focused on more recent results. The microstructure morphology of some DSE oxides grown with different solidification methods is summarized in Table 3.1. Regular structures which consist of non-faceted phases, either single crystal rods or lamellae, embedded in a single crystal matrix are found in some DSE oxides. In the simplest case of isotropic surface energy, rods are predicted when the volume fraction of the minority phase is lower than 28% and lamellae when it is above 28%. This crossover between lamellar and fibrous microstructures can be explained using interfacial energy arguments similar to those described in Section 2.3. The interfacial energy in isotropic media is proportional to the interface surface per volume unit, which is equal to 2/k for lamellae and to 2(2pf)1/2/1.31k for a hexagonal distribution of rods (Fig. 3.2) where f is the volume fraction of the rods. This rule is nearly always followed by regular oxide eutectics, as shown in Table 3.1. However, simple regular microstructures are the exception rather than the rule in DSE oxides due to the strong tendency of most oxide crystals to grow along certain crystallographic planes, for example to faceting. This highly anisotropic growth behavior was quantified by the Jackson interface roughness parameter defined as a  DSf/R where DSf is the entropy of fusion and R the gas constant. According to Jackson’s criterion, if a > 2 for one of the phases, its growth is limited by the rate of nucleation and facets are easily produced. As a rule of thumb, the growth is coupled if phases possess low melting entropy but the microstructure is irregular when the fusion entropy of one or both components is high because the growth interface cannot easily deviate from certain crystal orientations and faceted phases are produced [1]. Although the Jackson parameter is not known for many of the oxide systems discussed in this review, oxide phases have in general

Table 3.1 Microstructure and crystallography of DSE oxides Microstructure

YSZ/Al2O3

TDI

YSZ/Al2O3

CR, YSZ fibers

Growth direction  2 O3 kð1 1 0ÞYSZ ð1 1 0 2ÞAl [0 0 0 1]Al2O3 k [0 0 1]YSZ ½0 1 1 0Al2 O3 k½0 0 1YSZ [0 0 0 1]Al2O3 k h0 1 1iYSZ

Orientation relationships or interface planes  2 O3 k  ð1 1 0ÞYSZ ð1 1 0 2ÞAl ½0 2 2 1Al2 O3 k  ½1 1 1YSZ

References

ð2 1 1 0ÞAl2 O3 kð1 0 0ÞYSZ ð2 1 1 0ÞAl2 O3 kð1 0 0ÞYSZ

[5,81] [59]

[74]

Al2O3/Y3Al5O12

TDI

½1 1 0 0Al2 O3 k½1 1 1YAG ½1 1 0 0Al2 O3 k½1 1 1YAG

ð0 0 0 1ÞAl2 O3 kð1 1 2ÞYAG ½1 1 0 0Al2 O3 k½1 1 1YAG ½1 1 0 0Al2 O3 k½1 1 1YAG

[236]

CaZrO3/CaSZ

R, Lamellar

[1 1 2]CaSZ k [1 0 1]CaZO

[86]

[1 1 0]CaSZ k [0 1 1]CaZO [1 1 0]CaSZ k [0 1 1]CaZO [1 1 2]CaSZ k [1 0 0]CaZO

(1 0 0)CaSZ k (0 1 1)CaZO (0 1 0)CaSZ k (1 0 0)CaZO ð1 1 0ÞCaSZkð1 0 0ÞCaZO (1 0 0)CaSZ k (1 0 0)CaZO (1 1 1)CaSZ k (1 0 0)CaZO

[81] [76] [76]

MgO/MgSZ

R, MgO fibers

[1 1 1]MgO k [1 1 1]MgSZ ½1 1 0MgOk½1 1 0MgSZ ½1 1 0MgOk½0 1 0MgSZ

(hkl)MgO k (hkl)MgSZ (1 1 1)MgO k (1 1 1)MgSZ (1 1 1)MgO k (1 0 0)MgSZ

[76] [80] [80]

Al2O3/GdAlO3

TDI

½0 1 1 0Al2 O3 k½0 1 0GdAlO3  h1 0 1 4iAl2 O3 k  h1 1 1iGdAlO3

½2 1 1 0Al2 O3 k½1 1 2GdAlO3 –

[81] [237]

MgAl2O4/MgO

R, MgO fibers

[1 1 1]MgO k [1 1 1]MgAl2O4

(hkl)MgO k (hkl)Spinel

[76]

R, lamellar

½1 0 0YSZk  ½1 1 0NiO ½1 1 0YSZk  ½1 1 0NiO

(0 0 2)YSZ k (1 1 1)NiO (0 0 2)YSZ k (1 1 1)NiO

[238] [85]

YSZ/NiO (or CoO)

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Eutectic

Abbreviations describing microstructure are: R, regular; CR, complex regular; TDI, irregular three-dimensional interpenetrating network.

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(a)

(b)

λ

λ

Fig. 3.2. Schema of the two simplest regular microstructures found in DSE oxides.

a high fusion entropy and a strong tendency to faceting (see Table 3.2). The tendency of a given phase to develop facets can be experimentally established by looking at the morphology of the primary phases in off-eutectic compositions. In particular, primary oxide phases of Al2O3, YAG, and RE-aluminates always show facets, an indication of their high entropy of fusion. The strong tendency of these oxides to develop facets generally leads to irregular eutectic structures. A special case of irregular microstructure was found in DSE oxides where the phases were continuously entangled in a three-dimensional interpenetrating network (TDI), like the one shown in Fig. 3.3 in a transverse section of an Al2O3/YAG DSE. A TDI microstructure is a homogeneous and fine dispersion of phases, free of grain boundaries, that appears under eutectic coupled-growth conditions. The absence of grains and other larger scale irregularities, together with excellent bonding between phases, leads to structures with extraordinary mechanical properties [20] as well as high temperature stability and corrosion resistance [17]. In contrast to metallic eutectics, where this microstructure is observed only in non-faceted/non-faceted composites, TDI microstructures are also found in faceted/non-faceted Al2O3/YSZ DSE grown at very low growth rates, and in faceted/faceted Al2O3/YAG DSE over a wide range of growth rates. The domains exhibit sharp angle facets in the latter, and this morphology is referred to in the literature as Chinese Script (CS) microstructure. Recently, three-dimensional observations of eutectic structures in Al2O3/YAG DSE using high resolution X-ray tomography revealed their truly entangled morphology [77]. In spite of their obvious practical interest, theoretical models of the generation of these irregular eutectic structures are still embryonic. Kaiden et al. [78] worked out a simple model for irregular CS microstructures based on a cellular automata representation of the growth interface, which took into account the state of the neighboring cells and the anisotropic growth rates. Although the foundations of the model are not sufficiently clear, it apparently reproduces quite well the microstructural features of some Al2O3/RE2O3 eutectics (RE = rare earth ions). Table 3.2 Melting entropy of some ceramic oxides Compound

DHm/RTm

Al2O3 ZrO2 MgO NiO CoO MgAl2O4 CaF2

5.74 3.55 3.01 2.94 3.15 9.82 2.11

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735

Fig. 3.3. SEM micrograph of the transverse section of an Al2O3/YAG DSE grown by the LFZ method showing the continuous three-dimensional interpenetrating (TDI) microstructure, also known as Chinese Script.

As stated in previous sections (see Fig. 2.5), the interphase spacing of DSE oxides with the irregular TDI microstructure is growth-rate dependent, generally following Eq. (2.16a). The accurate evaluation of the interphase spacing in the case of irregular microstructures was solved by Mizutami et al. [79] using the relationship between the interfacial length per unit area, S, in the CS microstructure and the spacing for the equivalent lamellar microstructure k (S = 2/k). The interfacial length was estimated numerically from SEM micrographs of transverse sections in Al2O3/YAG DSE and the corresponding effective lamellar spacing was compatible with that predicted by different methods. As in most oxide eutectics, the compositional range for eutectic coupled growth in both Al2O3/YAG and Al2O3/YSZ DSE oxides was narrow, and small deviations from eutectic composition promoted precipitation of the primary phase in excess [77]. However, there were some interesting differences in the growth behavior of these two DSE oxides with TDI microstructure. Firstly, Al2O3/YSZ eutectics presented curved smooth interfaces rather than the planar sharp interfaces of Al2O3/YAG. Secondly, the TDI structure in Al2O3/YAG eutectic survived even up to quite high growth rates while the TDI microstructure of Al2O3/YSZ persisted only up to relatively low growth rates before entering into the cellular growth regime (Fig. 2.6). In fact, the Al2O3/YSZ eutectic underwent a transition on increasing the growth rate from the planar to the cellular growth regime and then to faceted cells consisting of a triangular dispersion of embedded, orderly zirconia fibers of about 0.3 lm diameter in the Al2O3 matrix (named complex-regular microstructure). At the highest growth rates the colony structure merged into a nearly homogeneous cell structure with lamellae, which resembles that obtained at low growth rates. This behavior is in close agreement with the theoretical predictions for eutectic coupled growth, and the different growth regimes follow those depicted in Fig. 2.8. However, the actual growth rates for the transition from a growth regime to the next one depend on the growth procedure. This is illustrated by Fig. 3.4 where the evolution of the

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GT 2 1000

100

λ

v (mm/h)

3

Cells

10

Planar growth 0.1

Cells 1

10

Dendrites 100

R (mm) Fig. 3.4. Evolution of the microstructure as a function of the growth rate v and sample radius R for Al2O3/YSZ DSE grown by different methods (see text for details).

microstructure with growth rate is presented in log–log plot of the growth rate vs. the sample radius R for Al2O3/YSZ DSE grown under different methods (thermal gradient GT and sample radius R). The experimental data in Fig. 3.4 correspond (in order of increasing sample size) to Al2O3/YSZ grown by the l-PD [62], FZ [54], LFZ [48], Bridgman [53] and EFG [63] methods, respectively. The growth thermal gradients decrease from the left to the right and the broken lines which delimit the different growth regimes follow the inequality: R3=2 v 6 constant,

ð3:1Þ

which derives from the relationship between thermal gradient and growth rate for eutectic planar growth in Eq. (2.20) and between the maximum sample radius and the thermal gradient in Eq. (2.25). The plot in Fig. 3.4 indicates that a similar inequality could hold for the transition from cellular to dendrite growth regime. It was demonstrated in the previous section that the relationships between growth parameters and microstructure size imposed limits to the eutectic growth. In addition, these results show that not only the microstructure size but also the microstructure morphology strongly depend on the growth procedure in DSE oxides. However, comprehensive models to simulate and control the development of the different eutectic morphologies are not available for these materials and the search for a given microstructure in a particular sample has to rely on experimental expertise. 3.2. Crystallography and interfaces The single crystal phases in eutectics often grow preferentially along well-defined crystallographic directions that are not necessarily the directions of easy growth of the components but which correspond to structures with minimum interfacial energy (see Eq. (2.11)). In fact, eutectic stability and most of the properties of the structures depend on the interface properties since the interfacial surface is very large. A complete characteriza-

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737

tion of DSE oxides clearly needs a deep knowledge of the orientation relationships between the phases and the characteristics and quality of their interfaces. Interfaces are determined by two crystallographic relations: the interfacial plane defined as parallel to the (hkl)A and (hkl)B planes, and the growth direction defined as in the [hkl]A and [hkl]B directions. The preferred growth direction and orientation relationships between phases can be obtained by X-ray or transmission electron microscopy diffraction. The interfaces can also be observed on an atomic scale using high resolution electron microscopy (HREM) in the most favorable cases of perfect orientation between eutectic phases with well-defined atomic lines [5,55,80]. The solidification directions and orientation relationships in most of the DSE oxides were measured years ago [3,5]. Mazerolles et al. [81] have recently performed a detailed study of the orientation relationships, interface planes and interface structure using HREM methods in some eutectic oxides; some of these results are presented in Table 3.1. As indicated by Stubican and Bradt [76], the orientation relationships of oxide eutectics should follow the general rules of metallic systems where the interface is determined by the minimization of lattice misfit between the component phases and the balance of the ionic charge, or better charge neutrality at the interface. These conditions can usually be handled by the near coincidence site lattice (NCLS) model as described by Bonnet and Cousineau [82], the atomic misfit and the charge density on the two planes being the parameters defining the interface. The following rules are of general application in most of the DSE oxides studied so far [5,81]: • Eutectic growth axes correspond to well-defined crystallographic directions and crystallographic relations between phases, which are unique in most systems. • Perfectly aligned lattices produce well-defined interface planes. Interfaces usually correspond to dense atomic arrangements in the component phases. • Growth habit is generally imposed by the major phase. However, a mistilt between the growth directions and the orientation relationships of the component phases is observed in most eutectic oxides. In addition, spatial variations of these magnitudes along the sample transverse sections are frequently found [236,87] because the surface energy, which determines interface morphology, has to compete with the growth anisotropy in order to stabilize the optimum structural configuration. Curved and planar interfaces coexist in some cases, such as the CaF2/MgO fibrous eutectic [11]. The fibers are semifaceted, with exact epitaxial relationships between both phases, which build two orientation relationships in two growth directions OR1 [1 0 0]CaF2 k [2 1 1]MgO and OR2 [0 0 1]CaF2 k [1 1 0]MgO, the planar interface (1 0 0)CaF2 k (1 1 1)MgO and two curved ones ½1 0 0CaF2 k½0 1  1MgO and ½1 0 0CaF2 k½1 1 2MgO, as shown in Fig. 3.5. The coincidence of the cation sublattices is plotted in Fig. 3.6 and is characterized by the parameters RCaF2 ¼ 2 and RMgO = 4 with misfits of 5.7% for OR1 and 8.7% for ˚ 2 for {1 0 0}CaF2 and 0.126 A ˚ 2 for OR2. The charge densities were +0.135 A {1 1 1}MgO and the curved interfaces correspond to a much worse mismatch and charge balance. A related case is that of the MgO/MgSZ fibrous eutectic. The MgO fibers are generally well-aligned with growth directions [hkl]MgO k [hkl]MgSZ and show well defined facets corresponding to several sets of planar interfaces. As established by HREM, the poor lattice mismatch is accommodated by an array of periodic misfit dislocations, leading to semicoherent interfaces [5,80].

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Fig. 3.5. (a) Transmission electron micrograph of a MgO fiber into the CaF2 matrix. (b) Diagram of the orientation relationships found in the CaF2/MgO eutectic grown by Bridgman method. (Reprinted by permission of the Materials Research Society from [11].)

These examples show the rich variety of phenomena encountered in the DSE oxide interfaces. Nevertheless, it should be noted that the observed crystallographic orientation relationships do not correspond to surfaces of minimum interfacial energy in some DSE oxides. As explained above, it could be argued that growth kinetics also play an important role in the control of the interface formation due to the large fusion entropy and growth anisotropy of some oxides, such as Al2O3. With strong growth anisotropy, interfaces should minimize not only the contribution to the surface energy but also that of the solidification process, and the interface orientation has to be compatible with the directions of favorable growth. In favor of this interpretation is the fact that multiple orientation relationships have been reported for some of these systems, which can be modified to some

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Fig. 3.6. Coincidence of the cationic sublattices at the (0 1 0)CaF2 k (1 1 1)MgO interface. (Reprinted by permission of the Materials Research Society from [11].)

extent by appropriate changes of the growth parameters. This is the case of Al2O3/YAG where the corundum-garnet structures grow with different interface orientations (see Table 3.1). The same is true for Al2O3/YSZ where at least two different interface orientation sets, the (0 0 0 1)Al2O3 k (0 1 0)YSZ and the [0 0 0 1]Al2O3 k [0 1 0]YSZ interfaces [5] were observed by HREM. Recently, Mazerolles et al. [81] performed new HREM studies on these interfaces and proved that the residual lattice mismatch is accommodated by misfit dislocations or steps, as shown in Fig. 3.7. In both Al2O3/YAG and Al2O3/YSZ eutectics, it is evident that growth parameters play an important role in determining not only the microstructure morphology but also the crystallography. Another example is given in Fig. 3.8 for an Al2O3/YSZ DSE grown by LFZ at high rates. The microstructure is complex regular and consists of elongated Al2O3 cells growing along the c-axis with three-fold symmetric sets of ZrO2 fibers [48]. The orientation relationships and growth habits found in this case are found neither in TDI microstructures nor in colonies by other authors (see Table 3.1). Some lamellar DSE oxides such as (CaSZ or YSZ)/NiO, (CaSZ or YSZ)/CoO and CaSZ/CaZrO3 were able to adapt to growth fluctuations by smoothly changing the interphase spacing leading to relatively large, well-aligned eutectic grains (Fig. 3.9). Additionally, the fluorite–rocksalt coupled structures in CaSZ/NiO and CaSZ/CoO eutectics present perfect planar interfaces, and this allows the detailed study of the interface by HREM [83]. It was found that the phases are well bonded by low energy interface planes in both YSZ/NiO and YSZ/CoO: (1 1 1)NiO or CoO k (0 0 2)YSZ with periodic steps for the accommodation of the near coincidence. This interface is that of the lowest energy studied up to now in DSE oxides [84]. However, at least two different growth directions have also been found in this case: [1 0 0]YSZ k [1 1 0]NiO and [1 1 0]YSZ k [1 1 0]NiO [85],

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Fig. 3.7. HREM micrograph of the transverse section of an [0 0 0 1]Al2O3 k [0 1 0]YSZ interface. The arrows indicate the phase steps. (Reprinted by permission of Elsevier from [81].)

Fig. 3.8. Transverse and longitudinal sections and orientation relationships in an Al2O3/YSZ DSE grown at 300 mm/h by the LFZ. The transverse cross-section is the sapphire c-plane. (Reprinted by permission of Elsevier from [48].)

and the zone axes of these phases are not exactly parallel. There was a typical misorientation angle in the range 2 and 12 between adjacent lamellae. This lack of an exact orientation relationship pattern also occurs in the CaSZ/CaZrO3 lamellar eutectic. In LFZ

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Fig. 3.9. Optical transmission microscope micrograph of a CaSZ/CaZrO3 lamellar DSE. The light is guided by the CaSZ phase, which is the highest refractive index phase.

grown CaSZ/CaZrO3 samples, X-ray diffraction pole figures point to the following orientation relationships: (1 0 0)CaSZ approx. k (0 1 1) pseudocubic CaZrO3 and (0 1 0)CaSZ approx. k (1 0 0) pseudocubic CaZrO3 [86], while diffraction experiments in the TEM showed that there is a misorientation of up to 12 between adjacent lamellae [87]. These observations support the hypothesis that in some DSE oxides competition between interface energy and growth anisotropy break down the uniqueness of the crystallographic relation between phases, and several sets of crystallographic orientations at the interface can be found in the same eutectic system. 4. Microstructural and chemical stability Oxide-based materials are always attractive because of their inherent thermochemical stability in oxidizing environments at high temperature, so the development of DSE oxides has been partially driven by the need of new structural materials which have to withstand high temperatures for long periods of time [88,89]. This is the case, for instance, of gas turbine components which operate at temperatures above 1000 C for thousands of hours in an oxidizing environment which contains significant amounts of water vapor. Si-based ceramics deteriorate rapidly in moisture-rich atmosphere above 1200 C [90–92] and cannot be used without expensive protective coatings. Oxides present better environmental resistance and, for instance, hot-pressed polycrystalline Al2O3 shows good corrosion resistance up to 1600 C even in wet Ar atmosphere [93]. However, samples tested in water vapor above 1600 C showed evidence of grain boundary etching, weight gains and grain growth, which affected the mechanical properties. Moreover, subcritical crack growth— which has been detected in single crystal Al2O3 [94] and tetragonal ZrO2 [95] in air at temperatures above 600 C—rules out their application as structural materials. These precedents have motivated the study of the microstructural stability of DSE oxides after long-term exposure at high temperature as well as their resistance to oxidation and chemical attack. The main conclusions of these investigations are presented below. 4.1. Microstructural stability Eutectic microstructures present a large area of interfaces and tend to release the excess of surface energy by coarsening when the temperature is high enough to allow the diffusion

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of atoms. The microstructural stability of eutectic microstructures has been analyzed primarily in metallic systems, where it was found that the mechanisms controlling the homogeneous coarsening depended on the eutectic morphology [96,97]. In fibrous eutectics, thicker fibers can grow at the expense of thinner ones by a process similar to the Ostwald ripening of precipitates in matrix where the ‘‘concentration gradient’’ for diffusion between fibers arises from the different fiber radii. However, this mechanism is normally hindered by the uniform fiber diameter distribution produced by eutectic growth, and coarsening is normally controlled by fault migration [98]. Faults are instabilities that develop during eutectic growth in both fibrous and lamellar microstructures; they consist of one pair of a termination and a branch (Fig. 4.1(a)). Branches are expected to fill in, and the termination to shrink backwards as shown in Fig. 4.1(b) since the curvature is maximum at the termination and minimum (negative) at the branch, leading to the formation of a thicker bulge (Fig. 4.1(c)). The thickening of lamellae at the expense of thin ones cannot operate in lamellar eutectics where both phases form alternating sheets, because the chemical potential at the interface is constant in the absence of any curvature. Graham and Kraft [99] showed that coarsening in lamellar eutectics was due to fault migration and involved the diffusive transport of matter from the curved edge of a lamellar termination to a curved bulge in an adjacent lamella. However, the interpretation of the coarsening mechanisms in eutectics is often more difficult as they cannot be always classified as perfect fibrous or lamellar eutectics. TDI microstructures (also named CS) made up of a threedimensional interpenetrating network of irregular lamellae are found in many directionally solidified eutectics and no coherent theory to explain coarsening in these systems has been developed. Experimental results on metallic eutectics with this microstructure

Fig. 4.1. Schema of microstructure coarsening by fault migration in rod eutectics. (a) Initial fault geometry, (b) progressive termination shrinkage and branch growth, (c) bulge formed by fault migration.

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are consistent with an Ostwald ripening mechanism but no definitive conclusions can be drawn from the limited amount of data [100]. The investigations of the microstructural evolution at high temperature of DSE oxides are limited although the experimental data show that these materials present an excellent stability even at temperatures approaching the eutectic point. For instance, Waku et al. [18,101] did not find any coarsening after 100 h at 1700 C in Al2O3–YAG and Al2O3– GAP DSE manufactured by the Bridgman method. Both materials presented a CS microstructure with the average domain thickness t, as measured in 2D cross-sections, of 30 lm, and the only change detected was a rounding of the sharp domain corners. Al2O3–YSZ eutectics with a cellular microstructure showed coarsening of the submicron fiber [48] or lamellar [102] structures within the cells after a few hundred hours at 1500 C. Coarsening was, however, limited: the rod and lamella dimensions remained in the micron range (Fig. 4.2) and the cell size did not change with the heat treatment.

Fig. 4.2. Coarsening of YSZ rods in a cell of an Al2O3–ZrO2 (9 mol% Y2O3) eutectic grown at 300 mm/h by the laser-heated floating zone method. (a) SEM of the as-received material, (b) Idem after 100 h at 1500 C in air, (c) Idem after 300 h at 1500 C in air. YSZ stands as the white phase. (Reprinted by permission of Elsevier from [48].)

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The homogeneous degradation of the ordered trigonal fiber structure within the cell is compatible with a fiber thickening induced by Ostwald ripening and this would explain the excellent microstructural stability as the initial fiber distribution is very uniform in diameter (Fig. 4.2). The most comprehensive study of the microstructural stability of DSE oxides was carried out by Park et al. [103] in Al2O3–YAG fibers manufactured by the EFG technique. The fibers presented a CS microstructure and were heat treated in air at 1360 C, 1410 C, and 1460 C (0.8Tm) for 50–200 h. The evolution of k (average interphase spacing) and S (interface length per unit area)1 as a function of time and temperature was measured using an image analysis program on SEM micrographs formed with back-scattered electrons. The as-received microstructure was homogeneous and k was between 0.4 and 0.5 lm throughout the fiber. Coarsening was more pronounced at the fiber surfaces and k reached 2.5 lm and 1.2 lm at the fiber surface and center, respectively, after 200 h at 1460 C. The kinetics of the microstructural change was modeled following the Graham and Kraft model [99] for lamellar eutectics under the assumptions that the geometry of the lamella does not change (except in size), leading to   1 1 Q t  ¼ K 0 exp ; ð4:1Þ S S0 RT T where S0 stands for the initial interface length per unit area, t the time, T the absolute temperature, K0 a proportionality constant and Q the activation energy of the process. The experimental results were in excellent agreement with the model predictions, as shown in Fig. 4.3(a), which indicates that the homogeneous coarsening of pseudo-lamellar DSE follows the same mechanisms as those discovered in metallic eutectics. Moreover, the activation energy for the diffusion process was estimated from Arrhenius-type plots of the logarithm of (1/S  1/S0) vs. the reciprocal of the absolute temperature (Fig. 4.3(b)). The lower activation energy of the surface data (262 ± 42 kJ/mol) was responsible for the higher coarsening rate at the surface and indicated that surface diffusion dominated over interface and volume diffusion. The activation energy at the bulk (308 ± 103 kJ/mol) suggested that the rate-controlling processes for the coarsening of the Al2O3–YAG fibers were the diffusion of O2 ions through the YAG phase and of Y3+ ions through the Al2O3 phase. These results show that the resistance of DSE oxides to homogeneous coarsening is very good, but other investigations have detected heterogeneous or localized coarsening at the surface of Al2O3–YAG [104–106] and Al2O3–YSZ [107] fibers. They appear as large blotches on the fiber surface, and fiber fracture was nucleated very often at these surface defects, which were responsible for the degradation of the mechanical properties after long term annealing. Discontinuous coarsening in eutectic fibers was normally associated with the presence of impurities in the coarsened region [105,107] and Matson and Hecht [106] developed a model to explain this phenomenon by the reaction of the eutectic fiber constituents with silicates deposited on the fiber surface from dust and dirt.

1

The product kS is constant for a given microstructure and was approximately equal to 3.6 for the CS morphology of the Al2O3–YAG fibers.

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745

(a) 1460°C

0.1

1410°C

1/S - 1/S0 (μm)

1360°C 0.08

0.06

0.04

0.02

0

0

50

100

150

200

250

Time (hours) 0.2

(b)

Bulk, Q = 308 ± 103 kJ/mol

1/S - 1/S0 (μm)

Surface, Q = 262 ± 42 kJ/mol

0.1 0.09 0.08 0.07 0.06 0.05 0.04 0.03

0.02 0.56

0.58

0.6

0.62

0.64

1000 / T (1/K) Fig. 4.3. Coarsening kinetics of Al2O3–YAG fibers during high temperature exposure in air. (a) Evolution of the interface length per unit area, S, and fitting to the predictions of the Graham and Kraft model. (b) Arrhenius plot of log(1/S  1/S0) vs. (1/T) to estimate the activation energy of diffusion at the surface and in the bulk. (Reprinted by permission of the American Ceramic Society from [103].)

Discontinuous coarsening in the absence of impurities has been reported in metallic eutectics with a lamellar microstructure. Instead of a continuous increase in the thickness or spacing of the lamellae with high temperature exposure, discontinuous coarsening occurs by the consumption of the original fine lamellae by cells of new lamellae with spacings several times larger than the original ones [100]. This phenomenon is associated with the presence of high angle grain boundaries and it was reported by Jenecek and Pletka in a directionally solidified, polycrystalline NiO–CaO lamellar eutectic heat treated at 1422 C [108]. The coarsening reaction is initiated at the grain boundaries and proceeds by boundary migration into the adjacent eutectic grain whose lamellae are oriented most nearly normal to the boundary. The coarsened lamellar interfaces are also oriented normal to the

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advancing grain boundary and Livingston and Cahn [109] developed a theory to compute the speed of the advancing grain boundary v as a function of the original (k1) and coarsened (k2) interphase spacings by assuming that the discontinuous coarsening movement was controlled by the diffusion along the grain boundary. The theory predicted that v was proportional to ðk2  k1 Þ=k1 k32 and the experimental data of Jenecek and Pletka as well as data from metallic eutectics followed this trend but quantitative comparisons between theory and experiments are not yet possible as v and k2/k1 cannot be predicted independently [109]. 4.2. Oxidation and chemical resistance DSE oxides present an excellent resistance to oxidation at elevated temperature owing to the inherent stability of the eutectic oxides and to the absence of impurities at the interfaces. For instance, no change in weight or in volume was detected in 6 · 6 · 6 mm3 prismatic bars of Al2O3–YAG after 1000 h at 1700 C in laboratory atmosphere, whereas the shape of Si3N4 and SiC specimens collapsed after 10–20 h under the same conditions due to oxidation [110]. Further studies in the Al2O3–YAG system did not measure any variation in weight or volume after 20 h at 1800 C in Ar or dry air, even though the eutectic temperature was 1826 C, and these results agree with fundamental studies on the stability of the compounds in the Al2O3–Y2O3 binary system, which showed that they are intrinsically stable in oxygen atmosphere up to very high temperature [111]. The most common corroding species is water vapor, and the effect of moisture on the high temperature stability was studied in Al2O3–YAG, Al2O3–GAP, and Al2O3–YAG– YSZ DSE [112,113]. The changes in weight at 1500 C in humid Ar atmosphere (total pressure 0.6 MPa, partial pressure of water vapor 0.15 MPa) are plotted as function of

0

Weight change (mg/cm 2)

YAG -0.2

A l2O3 -0.4

-0.6

SiC

Al2O3 - YAG - YSZ

-0.8

Al2O3 - YAG

Si3N 4 -1

0

50

Al2O3 - GAP 100

150

200

250

300

350

Time (hours) Fig. 4.4. Weight change as function of time exposure at 1500 C in a humid Ar atmosphere (partial pressure of water 0.15 MPa). The weight changes in Si3N4 and SiC in a similar environment are shown for comparison. (Reprinted by permission of the American Ceramic Society from [113].)

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exposure time in Fig. 4.4. The results obtained on single-crystal Al2O3 and YAG are also plotted for comparison, and they show that the eutectic weight reduction occurred between those of the single-crystals. Other DSE oxides presented slightly greater weight changes during high temperature exposure, but these variations are negligible when compared with those of Si3N4 and SiC in a similar environment (1500 C and 33 kPa of water vapor partial pressure) reported in [114]. In the three DSE oxides tested, corrosion in humid environments at high temperature produced localized thermal grooving at the interface between Al2O3 and the other phase (YAG, YSZ or GdAlO3). Moreover, roughness of the surface increased due to the recession of the Al2O3 domains by approximately 2 lm after 300 h of thermal exposure, and the new Al2O3 surfaces were faceted. These results can be explained by the decomposition of Al2O3 into Al(OH)3(g), particularly at the higher-energy phase boundaries. Nevertheless, the chemical attack did not progress into the specimens and the materials retained most of the flexure strength [112]; both facts demonstrate their excellent corrosion resistance in the presence of water. The chemical resistance of DSE oxides at high temperature in environments containing other chemical species has not been studied in detail, to the authors’ knowledge. However, Mah et al. [111] showed that compounds in the Al2O3–Y2O3 system suffered a severe degradation at 1500 C in air containing CO or in the vicinity of SiC under vacuum due the carbothermal reduction of Al2O3 and Y2O3 and the loss of Al-containing gaseous species into the atmosphere. However, Al2O3–Y2O3 DSE exposed to combustion gases in a burner-rig test did not undergo any chemical degradation and X-ray photoelectron spectroscopy revealed that Y and Al atoms were bonded to oxygen without traces of other bondings [115], and it was concluded that this eutectic is stable even in fuel-rich combustion gas at 1500 C. No degradation was observed when single crystal YAG specimens were placed in close proximity, but not in contact, with SiO2 powders at 1650 C. Finally, the reactivity of DSE oxides with metals was studied by Farmer et al. [107] to asses the potential of these materials as reinforcement of metallic matrices. They manufactured a composite made up of Al2O3–YAG eutectic fibers in a FeCrAlY high temperature metallic matrix, and the fibers were removed from the composite by etching the matrix with a mixture of equal parts of H2O, HNO3 and HCl. The fibers extracted from the composite showed a 50% reduction in strength, and extensive depletion of YAG from the fiber surface was produced during composite fabrication. They concluded that protective coatings were necessary when using DSE oxides as reinforcements of metallic matrices. 5. Residual stresses 5.1. Origins DSE oxides are grown directly from the melt at very high temperature, and the eutectic reaction leads to the nucleation of two phases with strong interfacial bonding and different thermal expansion coefficients. The thermal expansion mismatch between the phases induces thermal strains as the material cools down, which cannot be relaxed because plastic deformation in ceramics is limited, giving rise to large thermal residual stresses. The accurate estimation of the thermal residual stresses is a complex (and important) problem, which depends not only on the thermal expansion mismatch but on the cooling rate from the eutectic temperature, the morphology of the eutectic microstructure and the development of stress relaxation mechanisms. Tensile residual stresses can induce microcracking

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throughout the material upon cooling, as it was shown in MgO–MgAl2O4 [157] and Mg– CSZ [116] DSE, but their effects are not always undesirable and, for instance, controlled residual stresses in laminated materials can be used to increase the toughness by enhancing crack deflection at the interface. In ZrO2-containing DSE, residual stresses are also influenced by tetragonal to monoclinic martensitic phase transformation (which occurs at 900 C) which is associated with a volume increase of 4.67%. In fact, the magnitude of the residual stresses in each phase can be tailored to some extent by controlling carefully the amount of transformed ZrO2, which depends on the dopant content and its nature [21]. Similar control was reported in Co1xNixO/ZrO2(CaO) DSE where Co1xNixO is a solid solution of CoO and NiO whose thermal expansion coefficient changes with the Co/Ni ratio [117]. 5.2. Measurement techniques Residual stresses in DSE oxides have been measured using X-ray diffraction [117,118,6], neutron diffraction [117], and piezospectroscopy techniques [21,119–122]. X-ray and neutron diffraction are well-established methods based on the fact that residual stresses modify the interplanar spacings in the crystalline lattice. The actual spacing can be determined from the angular position of the diffraction peaks, and the lattice strains can be computed from the strain-free lattice parameter. This latter parameter is not necessary in the study of monolithic materials by X-ray diffraction because it can be assumed that the normal stresses at the surface vanish. This hypothesis is not valid in neutron diffraction (which measures stresses within the bulk of the sample) and it cannot be applied in either case to DSE because they are made up of two (or more) phases and the normal residual stresses in each phase do not converge to zero at the surface: only the integral over both phases has to be zero. Moreover, DSE are usually single crystals (or coarse-grained materials) and strain measurements have to be carried out with a goniometer diffractometer. A given family of planes (hkl) is selected to measure the strains in each phase taking into account that it is interesting to have as many reflecting planes as possible (although only six are strictly necessary) and that high angular positions for diffraction increase the strain sensitivity. The sample is rotated to bring into the diffraction plane a particular diffraction vector corresponding to one plane of the (hkl) family, and the interplanar lattice spacing dhkl is determined from the angular position of the diffraction peaks. The corresponding normal strain ehkl can be computed as ehkl ¼

d hkl  d 0 ; d0

ð5:1Þ

where d0 is the unstressed lattice spacing. This normal strain is related to the strain tensor eij by ehkl ¼ ai aj eij ;

ð5:2Þ

where ai and aj stand for the direction cosines between the diffraction plane and the bicrystal coordinate system which defines the orientation of the strain tensor eij for the phase considered. Although only six measurements are necessary to compute the six independent components of the symmetric strain tensor e, the accuracy is improved if the system of equations resulting from (5.2) is overdetermined and the eij components are normally computed by fitting the tensor components to as many data as possible using the generalized

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least squares method. Once the strain tensor is known, the actual stress tensor r can be computed as2 r ¼ C : e;

ð5:3Þ

where C is the crystal stiffness tensor of the phase considered. The most critical source of error in these measurements comes from the determination of the unstressed lattice spacing in each phase because small errors in d0 can greatly affect the accuracy of the strain measurement. In the measurements of residual stresses in DSE oxides reported in the literature [117,118], d0 was determined from crushed powders of the eutectic material. Crushing the material to powder reduces most of the interfacial constraint and relaxes the residual stresses but it cannot ensure that they have been completely removed and the error in d0 introduces an uncertainty in the absolute magnitude of the stresses in each phase. However, if the stresses measured in each phase verify the equilibrium force equation, it is likely that the independently measured d0, and hence the calculated strains and stresses, are reasonably accurate. Information about the stresses and strains can also be obtained through the shift of some spectroscopic bands (emission or Raman lines) due to the action of stress, the socalled piezo-spectroscopic effect [123]. Among the different piezospectrocopic effects, the fluorescence of Cr-doped sapphire has been extensively used to measure residual stresses in DSE oxides using an optical microprobe [21,119–122]. This non-contacting technique is very simple, does not require any specimen preparation, has an excellent lateral spatial resolution (of up to a few microns) and provides good precision in the stress measurement. As is well known, the majority of ceramics are optically transparent because of their large band gaps but the presence of impurities (mainly transition metal and rare earth ions) can cause intense fluorescence resulting from the electronic transitions of the dopant ions. For instance, the O2 ions in sapphire are arranged in a hexagonal closed-packed lattice structure, with the Al3+ ions occupying 2/3 of the octahedral sites. Small amounts of Cr3+ impurities are currently present in the sapphire, and they substitute the Al3+ ions in the octahedral sites leading to a small trigonal distortion of the lattice. The resulting sequence of the electronic Cr3+ levels is characterized by two states, whose energy differences with the ground state are 14,403 cm1 and 14,433 cm1 at ambient temperature for small Cr3+ concentrations and in absence of stress. This leads to the presence of two very narrow radiative emission bands in the optical spectrum of ruby (Cr-doped sapphire) denominated R1 and R2 at the 14,403 cm1 and 14,433 cm1 wavenumbers, respectively. These characteristic lines are extremely sensitive to the local ionic environment, as described by the ligand field theory, and externally applied strains change the Cr3+ ion position within the octahedron of O2 ions, modifying the energy differences with the ground state of the two energy levels. This is the piezospectroscopic effect which results in the shift of the position of R1 and R2 lines in the spectra. Forman et al. [124] suggested the use of the R1 line shift to monitor pressure in diamond anvil cells, and subsequent developments by Clarke et al. [125,126] have taken advantage of this phenomenon to measure residual stresses in polycrystalline and single crystal alumina and alumina-containing ceramics.

2 Throughout this section, bold lowercase roman and Greek letters stand for second rank tensors, and bold capital letters for fourth rank tensors. In addition, the different products are expressed as (A : a)ij = Aijklakl, and b : a = bklakl. Finally,  a represents the volumetric average of a.

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A phenomenological relationship between the line shift and the applied stress was first presented by Grabner [127], where the frequency shift of a fluorescence line, Dm, could be expressed as a linear function of the stress state given by Dm ¼ p : r;

ð5:4Þ

where r is the applied stress tensor and p is second rank piezospectroscopic tensor. Grabner proposed that this latter tensor is symmetric, following the symmetry of the stress tensor. Hence the piezospectroscopic tensor for spectra of single, isolated dopant ions, such as Cr3+ R lines, should follow the instantaneous point symmetry of the dopant ion in the crystalline lattice during deformation, and this assumption implies that the piezospectroscopic tensor is diagonal (pij = 0 if i 5 j) if the reference frame for the piezospectroscopic tensor is defined by the three crystallographic a, m and c axes of hexagonal lattice. Following these hypotheses, He and Clarke [128] determined experimentally the three piezospectroscopic constants for the R1 and R2 fluorescence lines of ruby (0.05 wt% of Cr3+) at 20 C from uniaxial compression tests, which are given by Dm1 ¼ 2:56r11 þ 3:50r22 þ 1:53r33 ; Dm2 ¼ 2:65r11 þ 2:80r22 þ 2:16r33 ;

ð5:5Þ

where the shift is expressed in cm1 and the stresses in GPa. Moreover, the results of shear tests showed that the off-diagonal components of pij, if non-zero, are less than 10% of the diagonal components. These piezospectrocopic coefficients are rather insensitive to the Cr3+ content and thus can be used to measure stresses in all kind of alumina-containing materials. In addition, extrapolation of these coefficients to the tensile range is sensible if the elastic strains are moderate, and they have been used to monitor the tensile stresses in bundles of alumina fibers [126]. The details of the experimental set-up to measure accurately residual stresses in DSE using this technique can be found in Refs. [21,119–122] and are not repeated here. The volume of material analyzed was 1 lm in diameter and 4 lm in depth, and luminescence was measured with a spectral resolution of 0.15 cm1, while R-line positions and width were obtained by fitting the spectra to a pseudo-Voigt function. It should be mentioned that besides the shift in the peak, the R lines in DSE oxides were broader than in unstressed ruby due to inhomogeneous distribution of residual stresses among the alumina domains in the eutectic microstructure. This inhomogeneity in the stress distribution within the sapphire phase was clearly detected in measurements at 77 K, where the thermal broadening of R lines is minimum [120]. 5.3. Modeling The experimental measurement of the residual stresses has to be accompanied by the micromechanical modeling of their development upon cooling to ascertain the actual mechanisms (thermal expansion mismatch, stress-free temperature, phase transformation, microcracking, etc.) controlling the residual stresses, and the influence of the microstructural factors (volume fraction, shape and spatial distribution of each phase) on their magnitude. Moreover, accurate micromechanical models can supply guidelines for the design of eutectic structures with optimized residual stress fields for specific applications. The classical micromechanical models provide the thermo-mechanical response (also denominated effective) of a representative volume element of the material which is much

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larger than the heterogeneities in the microstructure from the rigorous description of the volume fraction, shape and spatial distribution of the various phases in the material and of their corresponding constitutive equations. Detailed descriptions of these techniques are beyond the scope of this review and can be found in the literature [129,130]. DSE oxides are formed by a dispersion of two ceramic phases whose deformation is well represented by a thermo-elastic solid; the following discussion will be focused on the two approximations widely used to describe the behavior of two-phase thermo-elastic solids with perfectly bonded interfaces: the Mori–Tanaka [131,132] and the self-consistent models [133]. Extensions of these models to three-phase materials (which may be of interest in the case, for instance, of Al2O3–YSZ–YAG ternary eutectics) are straightforward and can be found in [134,23]. The thermo-elastic response of a representative volume element of the eutectic twophase material subjected to a uniform overall stress and strain, expressed by the corresponding tensors r and e, and to a uniform change in temperature h is given by r ¼ C : e þ lh

and

e ¼ S : r þ mh;

ð5:6Þ

where C and S, are the effective stiffness and compliance tensors of the eutectic composite and l and m stand for the corresponding second rank thermal strain and stress tensors. For consistency, they must satisfy C = S1 and l = C : m. Mean-field approximations (such as the Mori–Tanaka and the self-consistent method) assume that the stress and strain i and fields in each phase i (=1, 2) are well represented by the volume-averaged values, r ei , which can be computed by integration over the representative volume element V as Z Z 1 1 i ¼ r ri dV and ei ¼ ei dV ; ð5:7Þ V i Vi V i Vi where Vi is the volume of phase i and V1 + V2 = V. In turn, the composite stress and strain are obtained by integration of the corresponding stresses and strains in each phase within V. This operation, called homogenization, is expressed as X X i and e ¼ r¼ fi r fiei ; ð5:8Þ i

i

where fi stands for the volume fraction of phase i. The effective stress and strain in the composite eutectic are related to the average stress and strain in each phase through the respective mechanical and thermal stress and strain concentration tensors,  i ¼ B i : r þ bi h r

and ei ¼ Ai : e þ ai h

which clearly satisfy the following relationships X X X fi Ai ¼ I; fi B i ¼ I; fi ai ¼ 0; i

i

i

ð5:9Þ X

fi bi ¼ 0;

ð5:10Þ

i

where I is the unit tensor of fourth rank. To determine the average stresses induced in phase i by an external stress r and/or by a temperature change h, it is only necessary to know the expressions for the mechanical (Bi) and thermal (bi) stress concentration factors. They are given by [134] B i ¼ ðC i : Ai Þ : C 1 ; h i 1 1  C Þ : ðm  m Þ bi ¼ ðI  B i Þ : ðC 1 2 1 ; 1 2

ð5:11Þ

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and depend on the elastic stiffness tensors (C1 and C2) and thermal stress tensors (m1 and m2) of each phase and on the elastic stiffness C of the two-phase eutectic composite, which can be obtained easily from (5.6)–(5.10) as X C¼ fi C i : Ai ¼ C 1 þ f2 ðC 2  C 1 Þ : A2 . ð5:12Þ i

Obviously, the effective composite stiffness depends on the elastic properties and volume fraction of both phases as well as on the strain concentration tensors which, in turn, depend on the volume fraction, shape, and constitutive equation of each phase. Their simplest form is given by A1 = A2 = I, the well-known isostrain model, which leads to a very poor approximation in most microstructures. More realistic values of the strain concentration tensors can be obtained following various methods. The simplest one, within the framework of linear elasticity, is based on the pioneer work of Eshelby [135] who analyzed the stress distribution in an elastic and isotropic ellipsoidal inclusion embedded in an elastic, isotropic and infinite matrix which is subjected to a remote strain e. Eshelby showed that the strain field within the inclusion, ein, was constant and was expressed by [133,135]

1 ein ¼ Adil : e where Adil ¼ I þ ðE in : C 1 ; m Þ : ðC in  C m Þ

ð5:13Þ

where Cm and Cin stand for matrix and inclusion stiffness tensors, respectively, and Ein is the Eshelby’s tensor for the inclusion, whose components depend on the inclusion shape as well as on the matrix elastic constants. The superscript dil indicates that this expression is only valid when the volume fraction occupied by the inclusion is very small (for practical purposes, below 10%). There are many extensions of Eshelby’s method to account for a higher volume fraction of inclusions and the most popular are the Mori–Tanaka and the self-consistent model. The Mori–Tanaka approximation is better suited to heterogeneous materials with a topology characterized by inclusions dispersed in a continuous matrix, which is found in fibrous eutectics as well as in degenerated lamellar microstructures formed by the dispersion of irregular platelets of one eutectic phase into the higher volume fraction phase. Under these conditions, the connected phase acts as the matrix and the strain concentration tensor of phase 2 (the dispersed one) is given by [131,132] 1

A2 ¼ Adil : ½ð1  f2 ÞI þ f2 Adil  .

ð5:14Þ

The self-consistent method, which was developed to compute the effective elastic properties of polycrystalline solids, is particularly appropriate when the various phases are distributed forming an interpenetrating network, as found in many DSE oxides with CS microstructure. Both phases in the composite are assumed to be embedded in an effective medium, whose properties are precisely those of the composite, which are sought. The corresponding strain concentration tensor for each phase, Asc i , is obtained from Eshelby’s dilute solution (Eq. (5.12)) substituting the matrix elastic constants by those of the effective medium, C. Mathematically [133]

1 1 Asc . ð5:15Þ i ¼ I þ ðE i : C Þ : ðC i  CÞ

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Introducing Eq. (5.15) in (5.12), it leads to 1

C ¼ C 1 þ f2 ðC 2  C 1 Þ : ½I þ ðE 2 : C 1 Þ : ðC 2  CÞ ;

ð5:16Þ

where Eq. (5.15) stands for a non-linear set of equations for the components of C which can be solved numerically to obtain the elastic constants of the heterogeneous solid. It should be noted that Eshelby’s tensor depends on the inclusion shape as well as on the elastic constants of the effective medium given by C. Both Mori–Tanaka and the self-consistent model can be used to determine the residual stresses generated upon cooling in DSE from the elastic constants of each crystal, their volume fraction and the shape of the eutectic domains. In addition, it is necessary to know the ‘‘stress-free’’ temperature, at which the build-up of elastic stresses begins. The elastic strains generated by the thermal expansion mismatch above this temperature are smoothed out by the plastic deformation of one (or both) phases. An approximate value of this temperature can be estimated from the minimum temperature necessary to activate the slip systems in the eutectic crystals, or from experimental data of the residual stresses along one direction in one phase. Finally, it should be noted that this methodology can also include the residual stresses induced by phase transformations upon cooling or heating [21,119]. The volumetric strain in one phase due the phase transformation is mathematically equivalent to a thermal strain and can be added to the thermal strains in Eq. (5.9). The mean-field models described above provide very powerful tools to compute the residual stresses in DSE with a complex microstructure formed by fibers, colonies or degenerated lamellae. However, the residual stresses in perfect lamellar eutectics can be computed more easily due to the symmetries of the problem and even analytical expressions can be obtained. In a first approximation, lamellar eutectics can be viewed as a stack of isotropic, elastic slabs of phases A and B perfectly bonded at the interface. The deformation perpendicular to the lamella is not constrained and the thermal residual stresses along this axis are zero. The in-plane stresses in both phases are isotropic and can be computed imposing the isostrain and the force equilibrium conditions. This leads to 1 tA EA tA  rA ¼ DaEA h 1 þ and rB ¼  rA ð5:17Þ tB EB tB where rA and rB are the in-plane residual stresses in the lamellae of phase A and B, tA and tB stand for the corresponding lamella thicknesses, EA and EB are the elastic lamella constants expressed in terms of the elastic modulus and the Poisson’s coefficient of each phase as E/(1  v), and Da is the average mismatch in the thermal expansion coefficient of both phases. More complex expressions can be obtained from the same hypotheses if the eutectic lamellae are orthotropic in the lamella plane (as it is often the case because the eutectic domains are single crystals which grow in well defined crystallographic directions) and they can be found in laminate theory textbooks [136]. 5.4. Results The development of residual stresses has been studied in a number of eutectic systems using the experimental and analytical tools described above, and the main results are

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Table 5.1 Elastic constants and thermal expansion coefficients of single crystal Al2O3 [137,138], ZrO2 [139], NiO [117,140], and YAG [23] Constanta

Al2O3 YSZ (tetragonal/cubic)c ZrO2 (monoclinic)c NiO Y3Al5O12

C11 (GPa)

C12 (GPa)

C13 (GPa)

C33 (GPa)

C44 (GPa)

m1b (C1 · 106)

m3b (C1 · 106)

495 288 288 270 334

160

115

497

125 111.2

125 111.2

270 334

146 85.3 85.3 105 115.1

8.0 12.65 7.5 16.7 8.0

9.2 12.65 7.5 16.7 8.0

a

The Al2O3 single crystal is transversally isotropic in the basal x1–x2 plane and the c-axis corresponds to direction x3. b Average values between 1150 C and 25 C. c All the ZrO2 polymorphs are assumed to be elastically isotropic to compute the thermal residual stresses and only two elastic constants are given.

presented in the following sections. The corresponding thermo-elastic constants of the eutectic phases can be found in Table 5.1 [119,137–140]. 5.4.1. Al2O3–YSZ system Al2O3–YSZ DSE oxides are formed by dispersion of YSZ domains within a continuous single crystal Al2O3 matrix with the c-axis parallel to the solidification direction. The respective volume fractions of YSZ and Al2O3 are 30% and 70%, and Y2O3 is always found in solid solution within the ZrO2. The residual stresses in this system have been measured at ambient temperature [21,119–122] and down to 196 C [120] using the shift in the R1 and R2 lines of the fluorescence spectrum of sapphire, which contained small amounts of Cr3+ impurities, and these analyses were completed with simulations using the self-consistent model [21,119]. These detailed investigations have shown that the residual stresses depend on three factors: the nucleation (or not) of the tetragonal to monoclinic martensitic transformation in the ZrO2 domains upon cooling, the mismatch in the thermal expansion coefficients between Al2O3 and the various ZrO2 polymorphs (either monoclinic, tetragonal or cubic) which may coexist in the eutectic, and the morphology and spatial distribution of the ZrO2 domains within the Al2O3 matrix. This latter factor depends on the solidification rate, which may lead to very different microstructures, as shown in Section 2. The influence of the martensitic transformation on the residual stresses was carefully analyzed by Harlan et al. [21], who grew Al2O3–ZrO2 eutectic rods containing 0– 12.2 mol% of Y2O3 (in relation to ZrO2) using the LFZ method. Processing conditions were chosen to achieve a homogeneous CS microstructure in all the rods. The resulting materials were formed by a dispersion of irregular, elongated ZrO2 platelets of 2 lm in thickness and oriented along the solidification axis, with an aspect ratio of 3. The proportion of monoclinic ZrO2 in the rods with low yttria content (<3.5 mol%) was determined from the relative intensity of the 177 cm1 and 260 cm1 peaks in the Raman spectra of ZrO2, which are shown in Fig. 5.1(a), according to the expression [141] xt I 260 ¼ xm 1:8I 177

and

xm þ xt ¼ 1

ð5:18Þ

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(a)

755

Y (%)

a

12.2

t

8.6

Raman intensity

7.5 5.2 3.3

m

2.0 1.5 0.9 0.44 0 100

200

300

400

500

600

700

-1

Wavenumber (cm ) (b)

Volume fraction (%)

100

80

60

x

m

x +x t

c

40

20

0 0

2

4

6

8

10

12

Y (%) Fig. 5.1. (a) Ambient temperature Raman spectra of Al2O3–ZrO2(Y2O3) DSE as a function of the yttria content (Y) expressed by the mol% of Y2O3 dissolved into the ZrO2. The alumina peaks are marked with an ‘‘a’’, the tetragonal and monoclinic zirconia peaks used to quantify the volume fraction of each phase are marked with ‘‘t’’ and ‘‘m’’. (b) Volume fraction of monoclinic (xm) and tetragonal plus cubic (xt + xc) phases in the ZrO2 as a function of the yttria content Y. (Reprinted by permission of the American Ceramic Society from [21].)

where xt and xm stand for the volume fraction of tetragonal and monoclinic ZrO2 in the eutectic (Fig. 5.1(b)). The spectrum shows that Raman peaks of monoclinic ZrO2 are not present when the yttria content is above 3.3 mol% and that tetragonal ZrO2 is progressively substituted by the cubic phase as the yttria content increases. However, this latter

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fact is not important in our case because both cubic and tetragonal ZrO2 contribute equally to the residual stresses as they have very similar elastic constants and thermal expansion coefficients. The average residual stresses in alumina, parallel (rk, along the solidification direction) and perpendicular (r?) to the rod axis, were determined assuming that the residual stress state was transversally isotropic, a sensible hypothesis taking into account that the Al2O3 continuous phase kept this symmetry and that the contribution of the ZrO2 crystals was isotropic as they were oriented in various directions. They are plotted as a function of the yttria content in Fig. 5.2, and were compressive, composition independent and isotropic in the absence of monoclinic ZrO2 (Y > 3.5%). The presence of monoclinic ZrO2 changed the sign of the residual stresses in Al2O3 from compressive to tensile, and induced a marked anisotropy with longitudinal stresses much higher than the transverse ones. Moreover, the variability in the residual stresses increased as the yttria content decreased, as shown by the error bars in Fig. 5.2, and this reflects the variability of the stress values in different regions of the sample. Finally, there was a marked relaxation of the longitudinal residual stresses in the sample without yttria. Simulations using the self-consistent scheme were fundamental to understanding the complex behavior depicted in Fig. 5.2. The eutectic microstructure was represented by a dispersion of ZrO2 ellipsoids with an aspect ratio of 3 oriented along the solidification axis. The Al2O3 matrix was modeled as a transversally isotropic thermoelastic solid around the c-axis and their five independent elastic constants as well as the two average thermal expansion coefficients (parallel and perpendicular to the c-axis) are shown in Table 5.1. The contribution of the ZrO2 crystals was assumed to be isotropic in the absence of a well-defined growth habit and the elastic constants and thermal expansion coefficients of monoclinic, tetragonal and cubic ZrO2 are also given in Table 5.2. The elastic constants of monoclinic ZrO2 were taken as equal to those of the tetragonal polymorph due to the

Residual stress (MPa)

2000

σII σ⊥

1600 1200 800 400 0 -400 -800

0

2

4

6

8

10

12

Y (%) Fig. 5.2. Residual stresses in Al2O3 parallel (rk, along the solidification direction) and perpendicular (r?) to the rod axis as a function of the yttria content Y in Al2O3–ZrO2(Y2O3) DSE. (Reprinted by permission of the American Ceramic Society from [21].)

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lack of experimental data. The model also included the effect of the volumetric strain of 4.67% associated with the martensitic transformation in the samples with low yttria content, and the amount of transformed material was given by the data in Fig. 5.1(b). Finally, the stress-free temperature of the eutectic composite was taken as 1150 C, which is in agreement with the minimum temperature necessary to activate plastic deformation in YSZ (1200 C [142]), while slip in single crystal Al2O3 occurs at 900 C in the basal plane and at 1150 C in prismatic and pyramidal planes [143]. The model predictions for the residual stresses in Al2O3 at ambient temperature are plotted in Fig. 5.3(a). They show that, in the absence of the martensitic transformation

2000

(a)

σII σ⊥

Residual stress (MPa)

1600

no relaxation by basal slip

1200 800 400 0 -400 -800 0

2

4

6

8

10

12

Y (%)

Residual stress (MPa)

2000

(b)

σII σ⊥

1600

relaxation by basal slip

1200 800 400 0 -400 -800

0

2

4

6

8

10

12

Y (%) Fig. 5.3. Self-consistent simulations of the residual stresses in Al2O3 in the parallel and perpendicular directions as a function of the yttria content Y in Al2O3–ZrO2(Y2O3) DSE. (a) Without relaxation in the alumina basal plane, (b) with relaxation in the alumina basal plane. (Reprinted by permission of the American Ceramic Society from [21].)

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(Y > 3%), the residual stresses are controlled by the thermal expansion mismatch between Al2O3 and YSZ, which led to the development of compressive stresses in the former and tensile (0.9 GPa) in the latter. The longitudinal stresses were slightly higher due to the anisotropy in the thermal expansion coefficients of Al2O3 but the stress state was predominantly hydrostatic. The residual stresses changed from compressive to tensile as the volume fraction of transformed ZrO2 increased, indicating that they were controlled by the volumetric strain associated with the martensitic transformation. Although the parallel stresses in Al2O3 were similar to the experimental results in the range 0.45% < Y < 3.3%, the computed transversal component was significantly higher. A very likely explanation of this behavior was the relaxation of volumetric strains resulting from the martensitic transformation along the perpendicular direction by basal slip in ZrO2 because the temperature at which the martensitic transformation occurs (950 C) is very close to that necessary to activate dislocation motion in the Al2O3 basal planes. This mechanism was accounted for in the second simulations, which assumed that the volumetric strains generated by the martensitic transformation did not contribute to the generation of residual stresses in the transversal direction. The results are plotted in Fig. 5.3(b), and the agreement with the experimental data in the transverse direction is much better than in Fig. 5.3(a). In fact, the results in Fig. 5.2 fall between those plotted in Fig. 5.3(a) and (b) in the range 0.45% < Y < 3.3%, and the actual mechanisms of deformation in the eutectic should involve some degree of stress relaxation by basal slip upon cooling. The biggest discrepancy between the self-consistent simulations and the experimental data was found in the eutectic without yttria. While the model predicted tensile residual stress in Al2O3 in the range 1.2–1.6 GPa along the rod axis, the experimental data only reached 0.4 GPa. This difference was due to the development of microcracking in the eutectic, as shown in Fig. 5.4. These defects were nucleated at the Al2O3–ZrO2 interface to accommodate the twinning of the ZrO2 grains resulting from the tetragonal-to-monoclinic martensitic transformation (Fig. 5.5) and they grew driven by high tensile residual stresses induced in the Al2O3 phase by the volumetric change associated with the martensitic transformation to form the defects in Fig. 5.4. These defects appeared in all the samples with Y < 3% and were responsible for the large variability in the residual stresses indicated by the large error bars in Fig. 5.2. Moreover, they were nor present in the materials with Y > 3% because no microcracks were nucleated at the ZrO2/Al2O3 interface in the absence of the martensitic transformation and the propagation of interface cracks generated by any other cause was impeded by the compressive residual stresses in the continuous Al2O3 phase. The influence of the morphology and spatial distribution of the ZrO2 domains on the residual stresses was studied in [119,121] in eutectics with Y = 0% and 9%. Residual stresses in the Al2O3 phase were measured in Al2O3–ZrO2 eutectics with three different microstructures: a regular dispersion of monoclinic ZrO2 fibers of 0.3 lm in diameter and >60 lm in length, and two materials formed by a homogeneous dispersion of degenerated lamellae (as in Fig. 5.4) of different thicknesses. The experimental values of the residual stresses are presented in Table 5.2 together with the average lamella (or fiber) spacing t. They show that anisotropy between rk and r? (which appears as a result of the martensitic transformation and the stress relaxation by basal slip) is enhanced if the ZrO2 domains have the shape of elongated fibers. In addition, the residual stresses in microstructures formed by a dispersion of disordered lamellae decreased rapidly as the lamellae size

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Fig. 5.4. Secondary-electron micrograph of the Al2O3–ZrO2 DSE showing microcracking. (a) General view, (b) detail showing cracks and defects at the interface. Monoclinic ZrO2 stands as the white phase. Growth axis is vertical. (Reprinted by permission of the American Ceramic Society from [21].)

(and the spacing) increased. Analysis of the microstructures in the SEM showed residual stress relaxation by microcracking in the material with t  1.8 lm but not in the other two, and points to a size effect induced by the ability of very fine microstructures to withstand large tensile residual stresses without damage. The effect of the microstructure on the residual stresses was not important, however, in the case of Al2O3–ZrO2 eutectics with Y = 9% [119]. The residual stresses were very similar in the parallel and perpendicular directions regardless of whether the cubic or tetragonal ZrO2 domains were elongated fibers or irregular lamellae, and the experimental results were confirmed by self-consistent simulations. While in the absence of yttria the residual stresses are mainly controlled by the martensitic transformation, the anisotropy in the residual stresses comes from two sources in materials with YSZ: the elongated shape of the ZrO2 domains (either lamellae or fibers) and the anisotropy in the Al2O3 thermal expansion coefficients. These two factors operate in opposite directions and lead to a hydrostatic residual stress state. Moreover, the nucleation and growth of defects is impeded in these materials by the compressive residual stresses in the continuous Al2O3

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Fig. 5.5. TEM micrograph of a monoclinic ZrO2 lamella within the Al2O3 in an Al2O3–ZrO2 DSE showing the nucleation of interfacial cracks as a result of twinning associated with the martensitic transformation in ZrO2. (Reprinted by permission of Elsevier from [74].)

Table 5.2 Residual stresses at ambient temperature in the longitudinal (growth) and perpendicular directions in the Al2O3 phase of Al2O3–ZrO2 eutectics with different microstructure Shape of the ZrO2 domains

t (lm)

rk (GPa)

r? (GPa)

Ordered rods Disordered lamellae Disordered lamellae

0.6 0.75 1.8

2.0 ± 0.4 1.1 ± 0.4 0.5 ± 0.15

0.7 ± 0.2 0.5 ± 0.2 0.19 ± 0.03

phase and the effect of lamella size on the residual stresses observed in materials without yttria was not present. 5.4.2. Al2O3–YAG system Al2O3–YAG DSE present a microstructure formed by an interpenetrating network of Al2O3 and YAG in the proportion 55/45. The residual stresses in this system were expected to be low because the thermal expansion coefficient of YAG (8 · 106 C1) is very close to that of the Al2O3 (see Table 5.1). This hypothesis was confirmed by Dickey et al. [6], who measured residual stresses in both phases by X-ray diffraction in eutectic crystals processed by the LFZ method and found values below 100 MPa in both phases, in agreement with the predictions provided by the self-consistent simulations. 5.4.3. NiO–ZrO2 and Co1xNixO–ZrO2 systems NiO–ZrO2 DSE present a regular lamellar microstructure made up of cubic NiO (56%) and cubic ZrO2 (44%) crystals which grow with specific crystallographic orientations ½ 1 1 0NiO k½0 1 0ZrO2 and ð1 1 1ÞNiO kð1 0 0ÞZrO2 [144]. Cubic ZrO2 was obtained by adding

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9 mol% of Y2O3 as stabilizer to the eutectic powders and the resulting material presented a strong, clean, abrupt interface between the two phases, which was able to withstand the large thermal residual stresses generated upon cooling from the eutectic temperature (1700 C) owing to the strong interfacial bonding which stems from the electrostatic bonding between the polar cation sheets (Ni2+ in the {1 1 1} plane and Zr4+ in the {1 0 0} plane) by an interfacial sheet of O2. Residual stresses at ambient temperature were measured in each phase by X-ray diffraction [118] and the results are shown in Table 5.3, where directions 1 and 2 are parallel to the interfaces and direction 3 is perpendicular to the lamellae. The stresses perpendicular to the lamellae should be zero in a perfect bicrystal and the reduced values measured by X-ray (as compared to the in-plane stresses) could be attributed to surface effects and irregularities in the microstructure (faults and curved lamellae). The in-plane stresses were very similar in directions 1 and 2 and they fulfilled the force balance condition (Eq. (5.17)) along each axis with r33(NiO)  0.79 r33(ZrO2). However, the actual prediction of the residual stresses in both phases using Eq. (5.17) and the elastic constants and thermal expansion coefficients in Table 5.1 is hindered because the stress free temperature is not known and may be influenced up to a large extent by the onset of plastic deformation in NiO at intermediate temperatures (Guiberteau et al. [145] have reported the activation of the {1 0 0}h1 1 0i slip system in NiO at 500 C), which in turn depends on the residual stresses themselves and on the plastic constraint induced by the small lamella thickness. An interesting study of the effect the thermal expansion coefficient mismatch on the residual stresses was carried out by Brewer et al. [117], who measured the residual stresses by X-ray and neutron diffraction in Co1xNixO–ZrO2(CaO) DSE with x = 0.5, 0.6 and compared the results with those measured in NiO–ZrO2(CaO). Co1xNixO–ZrO2(CaO) is a solid-solution DSE which is isostructural with NiO–ZrO2(CaO) possessing a lamellar morphology and the same interfacial stacking sequence involving the {1 1 1} planes of Co1xNixO and the {1 0 0} planes of cubic ZrO2. The thermal expansion coefficient of Co1xNixO at high temperature (1300–1400 C) is 20.4 · 106 C for 0.3 < x < 0.6, significantly higher than that of CoO and NiO [146], and this enhances the generation of thermal residual stresses upon cooling. The experimental values of the residual stresses in both phases are presented in Table 5.4 for materials with x = 0.5, 0.66 and 1. They are in agreement with those measured by neutron diffraction in the Co1xNixO phase, and this shows that surface relaxation of stresses does not influence significantly the residual stresses measured by either X-ray diffraction or piezospectroscopic techniques. As expected, the residual stresses in Co1xNixO–ZrO2 eutectics were enhanced, as compared to NiO–ZrO2, due to the higher thermal expansion mismatch. However, they should be much larger according to Eq. (5.17), which predicted values around 1.7 GPa in each phase assuming a stress

Table 5.3 Residual stresses at ambient temperature in the NiO–cubic YSZ eutectics with lamellar microstructure [118] Phase NiO Cubic YSZ a b c

r11 (GPa)a

0.91 ± 0.02 1.1 ± 0.1 Direction 1 corresponds to the ½1 1 2 in NiO and [0 0 1] Direction 2 corresponds to the ½1 1 0 in NiO and [0 1 0] Direction 3 corresponds to the [1 1 1] in NiO and [1 0 0]

r22 (GPa)b

r33 (GPa)c

0.88 ± 0.02 1.1 ± 0.1

0.21 ± 0.02 0.16 ± 0.10

in ZrO2. in ZrO2. in ZrO2.

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Table 5.4 In-plane residual stresses at ambient temperature in the Co1xNixO–cubic ZrO2(CaO) eutectics with lamellar microstructure [117] Composition

x = 0.5

Phase

Co1xNixO

r11 (GPa)a r22 (GPa)b

1.0 ± 0.09 1.1 ± 0.13

a b

x = 0.66 ZrO2

Co1xNixO

x=1 ZrO2

0.93 ± 0.08 1.4 ± 0.1 1.70 ± 0.04 1.6 ± 0.1 1.4 ± 0.1 1.34 ± 0.05 Direction 1 corresponds to the ½1 1 2 in Co1xNixO and [0 0 1] in ZrO2. Direction 2 corresponds to the ½1 1 0 in Co1xNixO and [0 1 0] in ZrO2.

NiO

ZrO2

0.93 ± 0.02 0.93 ± 0.02

1.05 ± 0.06 0.84 ± 0.05

free temperature of 1200 C. This demonstrates the important role played by the stress relaxation mechanisms upon cooling. In particular, the stress necessary to promote plastic slip decreases as the Co content increases in this material [147], and this phenomenon was responsible for the difference in the residual stresses of the eutectics with x = 0.5 and x = 0.66. 5.4.4. Al2O3–YAG–YSZ ternary eutectic system More recently, the residual stresses have been measured in ternary Al2O3–Y2O3–ZrO2 [23] eutectic rods grown by the LFZ method. They presented a CS microstructure formed by an interpenetrating network of Al2O3 and YAG domains with respective volume fractions of 40% and 42%. The remainder (18%) was formed by smaller cubic YSZ domains, normally located at the Al2O3/YAG interfaces. Compressive residual stresses were measured in Al2O3 by piezospectrosocopy, and their absolute value increased from 160 MPa in the rods grown at 1000 mm/h to 300 MPa in those grown at 10 mm/h. Self-consistent simulations carried out with the thermo-elastic constants and stress-free temperatures of Al2O3–YSZ and Al2O3–YAG eutectics predicted compressive residual stresses in Al2O3 of 200 MPa, in excellent agreement with the experimental results and a confirmation of the thermo-elastic origin of these residual stresses in this ternary eutectic. The self-consistent results also showed that YAG and YSZ were subjected to tensile residual stresses of 295 MPa and 1130 MPa, respectively. It is worth noting that no interface cracks were observed in the microstructure, an indication of the excellent interfacial strength in these eutectics. 6. Mechanical behavior The mechanical properties of DSE oxides are dictated by the ionic bonding between the atoms and by the peculiar characteristics of the eutectic microstructure, which shares many similarities with single-crystal oxides and ceramic composites. Ionic bonding leads to hard and brittle materials with high elastic modulus and high melting point, and where plastic deformation is impeded up to very high temperature. DSE oxides have well defined crystallographic orientations and do not present grain boundaries (or are coarse-grained, as compared with sintered counterparts), and hence their creep resistance is comparable to that of single-crystal oxides. In addition, their microstructure is formed by the dispersion of two (or more) phases and presents a large surface fraction of clean, strong interfaces between the eutectic domains. The size of the defects which control the strength is related to the morphology of the phases in the microstructure and the thermo-elastic residual

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stresses and domain interfaces interact with propagating cracks leading sometimes to crack arrest and deflection, as in ceramic composites. In the following sections, the relationship between the mechanical properties of DSE oxides and their composition and microstructure is analyzed, with results up to very high temperatures where DSE oxides present a unique behavior. 6.1. Elastic modulus Ceramic oxides are always very stiff as a result of the strong ionic bonding between anions and cations. The mismatch in the elastic modulus between the phases in the eutectic is always limited and never above a factor of two or three. Under these circumstances, the micromechanical models for the thermo-elastic behavior of heterogeneous materials (see Section 5.3) predict that the elastic constants are a function of the elastic properties of each phase and their respective volume fractions, while the effect of the spatial distribution of the phases is negligible. For instance, self-consistent estimations (Eq. (5.15)) of the longitudinal modulus of Al2O3–YSZ eutectics predicted a difference of just 5% if the cubic ZrO2 phase was dispersed in the form of spheres or long fibers oriented in the solidification direction. Hence theoretical predictions for the elastic modulus can be made for each DSE from the elastic constants of each phase as the phase volume fraction is fixed for each eutectic composition (Table 5.1) assuming perfect bonding between the phases. Representative results obtained with the self-consistent approximation are presented in Table 6.1 for the elastic modulus in the longitudinal (growth) direction of Al2O3–YSZ and Al2O3–YAG. Experimental data on the elastic modulus of DSE oxides are scarce due to the limited availability of samples large enough to carry out the measurement and to the high stiffness of the material, which requires non-standard techniques to measure the strain. Pastor et al. [20,148] determined the dynamic longitudinal modulus of Al2O3–YSZ and Al2O3–YAG samples from the resonance frequency of simple supported beams excited in bending, and the results are shown in Table 6.1. They are in perfect agreement with the theoretical predictions in the case of Al2O3–YAG, and slightly below in that of Al2O3–YSZ. This discrepancy may be attributed to irregularities in the diameter of the small rods along their length and to the presence of internal pores or cracks in the microstructure. Ochiai et al. [149] studied the elastic anisotropy of Al2O3–YAG eutectics using the wave pulse echo method along the longitudinal and transverse directions and found differences of around 1%. In addition, Farmer ad Sayir [57] measured the elastic modulus with an optical extensometer in hypoeutectic Al2O3–ZrO2 fibers which contained 77 vol.% of Al2O3 (7% above the eutectic composition). The modulus of the fibers containing tetragonal YSZ was 370 GPa and decreased to 310 GPa as the yttria content increased due to the formation of crack-like shrinkage cavities. The modulus of Al2O3–ZrO2(m) fibers was only 270 GPa due to microcracking induced by the martensitic transformation upon cooling.

Table 6.1 Self-consistent estimates and experimental results for the longitudinal elastic modulus of DSE at ambient temperature DSE oxide

Theoretical (GPa)

Experimental results (GPa)

Al2O3–YSZ Al2O3–YAG

370 340

343 ± 7 [20] 340 ± 3 [148]

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1

E / E25°C

0.8

0.6

Tm

0.4

0.2

Load-deflection curves Wave pulse echo

0 0

300

600

900

1200

1500

1800

Temperature (°C) Fig. 6.1. Evolution of the longitudinal elastic modulus of Al2O3–YAG DSE as a function of temperature. Data from load–displacement curves [148] and from wave pulse echo method [149].

Pastor and LLorca [148] determined the evolution of the elastic modulus with temperature in Al2O3–YAG eutectics processed by the Bridgman method. Parallelepipedic beams were loaded in three-point bending and the modulus was obtained from the slope of the load-midspan deflection register in several loading and unloading cycles at each temperature, where accurate values of the midspan deflection were obtained with a laser extensometer. The results are plotted in Fig. 6.1 and show that the elastic modulus remained practically constant up to 1300 C, and then started to decrease as the eutectic temperature of 1826 C was approached. These results are in reasonable agreement with those obtained by Ochiai et al. [149] with the wave pulse echo method from 25 C up to 1500 C. They measured a constant reduction in modulus with temperature rather than from 1300 C. Nevertheless, the moduli determined by both techniques at 1500 C were very similar. 6.2. Strength 6.2.1. Ambient temperature The mechanical strength of DSE oxides follows the behavior expected for stiff and brittle materials with low fracture toughness and is controlled by the defects in the material, which act as stress concentrators and lead to the nucleation of cracks. This has been demonstrated by fractographic studies in DSE oxides tested in tension and bending, which identified the critical surface defects by the convergence of the river line patterns found on the fracture surface (Fig. 6.2) [104,105,107,20,57,150,4,151]. The size and shape of these flaws depends mainly on the processing conditions and inhomogeneities, banding, and the generation of pores and shrinkage cavities3 reduces significantly the strength and increases 3 Shrinkage cavities appear when there is not enough liquid to flow into the intercellular regions, which are the last to solidify, because they are too far away from the solidification front. The volumetric shrinkage on cooling leads to the development of shrinkage cavities with a crack-like morphology.

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Fig. 6.2. SEM micrograph showing the fracture nucleation defect on Al2O3–YAG rods broken in three-point bending at ambient temperature. (Reprinted by permission of the American Ceramic Society from [150].)

the scatter [151]. However, if these defects are removed by careful processing conditions, the critical flaws which control the strength are a function of the eutectic microstructure, which can be modified by the growth rate. The effect of growth rate on the strength is evident in the Al2O3–YAG system. The microstructure of this eutectic is always formed by an interpenetrating network of both phases in a proportion 55/45, and higher growth rates only reduce the average domain thickness without modifying the shape of the domains (Figs. 2.5 and 6.3). Several studies [106,150,152] have measured the ambient temperature strength of Al2O3–YAG eutectics grown at different rates whose domain thicknesses, t, were in the range 0.2–25 lm; their results are compiled in Fig. 6.4. Small diameter monofilaments were tested in tension while rods and bulk specimens were fractured in three-point bending. The figure also includes one result corresponding to an Al2O3–Er3Al5O12 (EAG) eutectic, whose microstructure pffi is equivalent to that of Al2O3–YAG. The eutectic strength was proportional to 1= t, indicating that the critical defects responsible for brittle fracture depend on the size of the eutectic domains. In fact, if the critical flaws are approximated by semicircular surface cracks with a radius equal to t, the eutectic strength, ru, is given (according to fracture mechanics) by pffiffiffi p KC pffi ; ru ¼ ð6:1Þ 2 t where KC stands for the fracture toughness. p The linear fit to the experimental results in Fig. 6.4 is obtained with KC = 1.6 MPa m. This value is only marginally lower than p the ambient temperature fracture toughness of Al2O3–YAG, 2 MPa m, which is independent of the orientation and domain size [148,153]. More recent tests on Al2O3–YAG fibers of 130 lm in diameter grown between 150 mm/h and 1500 mm/h by the EFG method have shown the same linear dependence of the tensile strength with t0.5 [154]. Reduction in the domain thickness can also be achieved by adding a third phase to form a ternary eutectic composite, Al2O3–YAG–YSZ [22,23,155]. The resulting microstructure is comprised by an interpenetrating network of Al2O3 and YAG domains (40% and 42% in volume, respectively) while cubic YSZ (18%) is found as small rounded domains mainly at

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Fig. 6.3. Back-scattered SEM micrograph of the transverse section of the Al2O3–YAG rods showing the interpenetrating network of Al2O3 (black) and YAG (white) domains. (a) Growth rate of 25 mm/h, (b) growth rate of 750 mm/h. (Reprinted by permission of the American Ceramic Society from [150].)

the Al2O3/YAG interfaces. Ternary eutectics showed higher room temperature strength than binary ones grown at the same rate [22,156] and their flexure strength followed the trend dictated by Eq. (6.1), as shown in Fig. 6.4, although this ternary eutectic exhibited higher toughness and was not free from residual stresses (see [23]). This indicates that as in the Al2O3–YAG binary eutectics with CS microstructure, the defect size was controlled by the lamella thickness. The growth rate controls the strength of the Al2O3–YAG through the domain size but this conclusion is not applicable to other DSE oxides. For instance, the flexure strength of MgO–MgAl2O4 [157], ZrO2–MgO [158] and ZrO2–CaZrO3 [2] eutectics was independent of the solidification rate, while several studies in Al2O3–YSZ eutectics found the highest strength at intermediate growth rates [107,8,159]. The complex effect of the solidification rate on the strength in this latter system was systematically studied by Pastor et al. [151], who measured the flexure strength of Al2O3–YSZ rods grown from 20 mm/h up to 1000 mm/h by the LFZ method. The microstructure of the rods grown at lower rates was formed by a homogeneous dispersion of micron-sized irregular YSZ platelets within the Al2O3 matrix. At intermediate growth rates this microstructure was substituted by

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3.0

Strength (GPa)

2.5

2.0

1.5

1.0 Bending Al 2 O3 -YAG Tension Al 2 O3 -YAG Bending Al 2 O3 -EAG Bending Al 2 O3 -YAG-YSZ

0.5

0

0

0.5

1

1.5

2

2.5

1/¦t (μm-0.5) Fig. 6.4. Ambient temperature strength of Al2O3–YAG [106,150,152], Al2O3–EAG [152] and Al2O3–YAG–YSZ [23,156] DSE as a function of the average thickness of eutectic domains, t. Rods and bulk specimens were tested in three-point bending, while monofilaments were broken in tension.

colonies oriented perpendicularly to the solidification front. The colony core (formed by a dispersion of submicron YSZ platelets embedded in the Al2O3 matrix) was surrounded by a thick intercolony region containing coarse YSZ particles of irregular shape. The rods grown at 1000 mm/h presented very long cells oriented along the growth axis. The cells were formed by a dispersion of very fine YSZ lamellae and were separated by thin intercellular boundaries with coarser microstructure. The flexure strength of the rods is plotted in Fig. 6.5 as a function of a characteristic length of each microstructure, which was taken as the average dimension of the feature which defined the morphology of the microstructure perpendicularly to the tensile stress. This length was the colony or cell diameter perpendicular to the growth axis in rods with cellular and colony microstructure. The selection of the characteristic length of the rods formed by a homogeneous distribution of YSZ platelets was not so obvious, and various candidates (platelet width or separation) could be chosen. Both were of the order of 1 lm, and selecting one instead of the other does not change the plot significantly. The data in Fig. 6.5 showed that the highest strength was found in the eutectics formed by a homogeneous dispersion of small YSZ platelets, which were grown at the lowest rate. Moreover, the strength of eutectics with colony and cell microstructure tended to increase as the colony or cell diameter decreased. This trend follows the behavior found in metallic eutectics and it is supported by the flexure strengths measured by Bates [160] on Al2O3– YSZ eutectic fibers prepared by the edge defined-film fed-growth method. Moreover, Kennard et al. fabricated MgO–MgAl2O4 [157] and MgO–CSZ [116] DSE of constant colony size but with different spacing (by a factor of 4) between the MgO fibers within the colonies by changing the growth rate. The flexure strength of these eutectics was independent of the growth rate and it was concluded that the colony size controlled the eutectic strength. However, as suggested in several publications [107,146,8], this relation holds good so long as the thickness of the intercolony/intercell region is below a critical value. Above this, the

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Flexure strength (GPa)

1.6

Y = 3%

1.4

1.2

1

0.8 Y = 12%

Al2O3-YSZ 0.6 0

5

10

15

20

25

30

35

Characteristic length (μm) Fig. 6.5. Flexure strength of Al2O3–YSZ eutectic rods as a function of the average characteristic length of each microstructure. Data from [151,159]. See text for details.

weak intercolony regions, which contain pores and microcracks, act as the stress concentrators which nucleate the crack. An example is found in the two materials with similar colony diameter (18–19 lm) and different yttria content (Y = 3% and 12%), whose strength is plotted in Fig. 6.5. Because of yttria segregation during solidification [161], the intercolony region was thicker in the eutectic with Y = 12%, and the flexure strength of this latter material was dictated by the coalescence of pores and microcracks at the intercolony region (Fig. 6.6), leading to a much larger critical defect and thus reducing the flexure strength by a factor of 2. This mechanism explains why the highest strength has been found at intermediate growth rates in eutectics with cellular microstructure [8,107,159]: increasing the growth rate reduces the colony size but also increases the thickness of the intercolony region, and this latter parameter (and not the colony diameter) controls the strength above a critical solidification rate. An important issue in the strength of brittle materials is the variability, which is normally characterized through the Weibull modulus. This parameter was measured by a number of investigators in Al2O3–YAG [58] and Al2O3–YSZ [57,102,150] eutectics. High Weibull moduli in the range 13–15 were measured in materials with a homogeneous microstructure throughout the sample in both types of eutectics, but processing-related defects (such as shrinkage cavities [105,150] or banding [57]) led to a marked reduction of up to 3– 6. Moreover, localized surface coarsening during a high temperature annealing due to contact with impurities (see Section 4.1) reduced significantly the Weibull modulus in fibers, which have a high specific surface and are very susceptible to the nucleation of these defects [104,105]. Finally, the sign and distribution of residual stresses is also an important factor and this has been systematically studied in the Al2O3–ZrO2(Y2O3) system, where the presence of yttria controls the residual stress distribution, as explained in Section 5. This effect was analyzed in [122,57] in fiber and rods and the strength (in bending for rods and in tension for fibers) is plotted in Fig. 6.7 as a function of the yttria content in the ZrO2 phase, given

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Fig. 6.6. Fracture surface of Al2O3–YSZ eutectic rod (Y = 12%) broken at 0.52 GPa. (a) Low magnification, (b) high magnification, showing the surface defect formed by the coalescence of pores and cavities at the intercolony region, which nucleated the fracture. (Reprinted by permission of Elsevier from [151].)

by Y. The lowest strength was always found in the yttria-free samples, where zirconia has transformed from tetragonal to monoclinic upon cooling from the processing temperature. The transformation nucleates microcracks at the interface (Fig. 5.4) and large tensile residual stresses in the Al2O3 continuous phase, which facilitated the propagation of the cracks and impaired the eutectic strength. Tetragonal ZrO2 was found in the eutectics with Y  3% as the tetragonal to monoclinic transformation was completely suppressed by yttria. As a result, the thermo-elastic residual stresses were compressive in the Al2O3 phase and the strength was almost twice that of the yttria-free materials. Further increase in the yttria content leads to the stabilization of the cubic ZrO2 phase in the eutectic, without significant changes in the residual stresses. However, higher yttria contents favor the formation or cracks and cavities at the intercolony regions and lead to a slight reduction in strength, which is consistent with the results reported by other investigators [161]. 6.2.2. High temperature The outstanding strength retention of DSE oxides at high temperature was reported in the first investigations [4,2,146,157,159] and follows the microstructural characteristics of

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900

600 ZrO2 (m)

Strength (MPa)

1200

300

Rods, flexure strength Fibers, tensile strength 0 0

5

10

15

20

25

Yttria content, Y (mol %) Fig. 6.7. Ambient temperature strength of Al2O3–ZrO2(Y2O3) eutectic fibers [57] and rods [122] as a function of the Y2O3 content, expressed by Y = mol% Y2O3/(mol% Y2O3 + mol% ZrO2).

these materials. In addition to the microstructural stability and oxidation resistance (see Section 4), which limits the development of surface defects, the high temperature strength of DSE oxides benefits from the clean and strong interfaces between the eutectic domains. Conventionally sintered oxide and non-oxide polycrystalline ceramics always present a glassy phase at the grain boundaries, and high temperature deformation occurs by grain boundary sliding, as opposed to the dislocation motion in DSE. The effect of both mechanisms on the strength is shown in Fig. 6.8(a), where the flexure strength in Ar up to 1700 C is plotted for Al2O3–YAG eutectics processed by conventional hot-press sintering and directional solidification. The strength of the polycrystalline material obtained by sintering drops very quickly above 800–1000 C due to the flow of the glassy phase at the grain boundaries (Fig. 6.8(b)). On the contrary, the DSE oxides retained the ambient temperature strength up to 1700 C because the domain boundaries were free of amorphous phases, Fig. 6.8(c), and the resistance to deformation was controlled by the activation of plastic slip, as has been shown in a number of DSE such as Al2O3–YAG, Al2O3–EAG and Al2O3–GAP [152,162,7]. Single crystal oxides normally present higher ambient temperature strength than the DSE owing to smaller defect sizes but their high strength retention is poorer. In some cases, the strength of single crystal oxides, such as sapphire [94,107,8] and ZrO2(Er2O3) [95], experiences a noticeable reduction at intermediate and high temperatures due to the thermally activated slow crack growth or stress corrosion cracking whereas DSE oxides do not undergo this degradation. Moreover, the domain boundaries in the eutectics act as barriers to dislocation motion at high temperature and can improve the resistance to plastic deformation. The best high temperature strength among DSE oxides has been found in the Al2O3– YAG system. Due to the interpenetrated structure of both phases in the eutectic microstructure and to the excellent resistance to dislocation motion of YAG, the strength of these materials remains constant up to 1400 C and very little degradation is observed

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Fig. 6.8. (a) High temperature flexure strength (in Ar) of Al2O3–YAG eutectics processed by directional solidification or sintered by hot pressing. (b) Transmission electron micrograph showing the presence of an amorphous phase at the grain boundary in the sintered Al2O3–YAG eutectic. (c) Transmission electron micrograph showing the clean interface between Al2O3 and YAG domains of the directionally solidified material. (Reprinted by permission of Elsevier from [162] and of Springer [152].)

up to 1600 C, Fig. 6.9(a) and only in the materials with smaller domain thickness. The analysis of the fracture surfaces of the specimens of t 6 1 lm broken at 1627 C showed that the faceted interfaces between Al2O3 and YAG had become rounded and the average domain thickness had increased, Fig. 6.9(b), and the reduction in strength was attributed to the homogeneous coarsening of the microstructure [150]. Al2O3–YAG eutectics tested in tension or bending showed a brittle/ductile transition in the fracture mode around

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Fig. 6.9. (a) Effect of the temperature on the flexure strength of Al2O3–YAG eutectics with different domain thickness (t) tested in Ar [152] and air [150]. (b) Secondary electron micrograph of the fracture surface of the Al2O3–YAG eutectics with t = 0.6 lm broken at 1627 C showing the homogeneous coarsening of the microstructure after short term exposure to high temperature. (Reprinted by permission of the American Ceramic Society from [150].)

1600 C, which was attributed to the different deformation mechanisms in Al2O3 and YAG. Elastic deformation is dominant in both phases up to 1200 C but above this temperature plastic deformation begins to occur in Al2O3 while YAG remains elastic up to 1550 C. As a result of the interpenetrating nature of the microstructure, the plastic deformation of Al2O3 is constrained by the elastic deformation of YAG in the range 1100–1550 C and the overall eutectic behavior is elastic although the crack path tends to follow the brittle YAG phase and the fraction of YAG in the fracture surface is higher [153]. Above 1550 C, both phases can deform plastically and the behavior shows a nonlinear stress–strain curve, although the overall strength is maintained or even improved as a result of the increase in toughness associated with the plastic deformation around

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notches and defects. Of course, the amount of plastic deformation in this regime is very sensitive to the strain rate and to the domain size, and the ductile/brittle transition temperature depends on both factors [153,163]. Similar behavior in terms of the plastic deformation and strength retention (or even improvement) has been reported in Al2O3–GAP DSE [101,7] but it is worth noting that polycrystalline Al2O3–YAG eutectics which were not processed by directional solidification suffered a marked reduction in strength above 1000 C [164]. Good strength retention at high temperature was also reported in the 1970s in the Al2O3–YSZ eutectic system [2] but more systematic studies to ascertain the effect of yttria content and microstructure on the high temperature strength were carried out more recently [107,122,20,8]. The results of these investigations are plotted in Fig. 6.10, where the flexure strength of Al2O3–ZrO2(Y2O3) DSE with an yttria content in the range 0.5% < Y < 9% is plotted between ambient temperature and 1427 C. Eutectics with either cubic or tetragonal YSZ showed a mild reduction in strength up to 1427 C and no evidence of macroscopic plastic deformation was observed in the load–displacement curves, which were linear until failure. In addition, the fracture surfaces created at elevated temperature could not be distinguished from those of the ambient temperature tests: fracture was nucleated at surface defects which were also found in the specimens broken at 25 C. Thus, the short term exposure to elevated temperature did not introduce new defects in their microstructure, in agreement with the investigations on the microstructural stability of these eutectics up to 1500 C [48]. The reduction in strength with temperature was attributed to two causes: the release of the thermal residual stresses in the microstructure at high temperature, which could reduce the fracture toughness of the material (see Section 6.4), and the activation of plastic deformation mechanisms at the microscopic level in the ZrO2 phase above 1200 C. Similar arguments can be used to explain the limited

1200

Flexure strength (MPa)

1000

800

Y = 9%

600

Y = 3% Y= 0.5%

400

200

0 0

300

600

900

1200

1500

Temperature (˚C) Fig. 6.10. Influence of the temperature on the flexure strength of Al2O3–ZrO2(Y2O3) eutectic rods processed by the laser-heated floating-zone technique with different yttria content, as indicated by Y = mol% Y2O3/(mol% Y2O3 + mol% ZrO2). Data compiled from [122,20].

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degradation (30%) in the flexure strength of MgO–MgAl2O4 DSE between 25 C and 1500 C [157]. The eutectics containing monoclinic ZrO2 (Y = 0.5% in Fig. 6.10) showed a much more marked reduction in strength with temperature, which dropped below 200 MPa at 727 C, and then remained practically constant. The analysis of the fracture surfaces of rods tested at high temperature showed extensive microcracking caused by the propagation of the interfacial microcracks present in the material (Figs. 5.4 and 5.5). The inversion of the martensitic transformation of ZrO2 at temperatures in the range 700–900 C (now from monoclinic to tetragonal) was accompanied by a volume reduction of 4%, which generated large tensile stresses in the ZrO2 and drove the propagation of the cracks. The high temperature strength retention was also studied in ternary Al2O3–YAG–YSZ eutectics [22,23], which showed better ambient temperature strength than did the binary counterparts, as explained above. The results of flexure tests on rods and of tensile tests on fibers are plotted in Fig. 6.11. Although the absolute values are very different (owing to the differences in test and specimen geometry), both investigations showed that the ternary eutectics presented good strength retention up to 1200 C. However, the strength dropped very rapidly above this temperature: for instance, the flexure strength at 1427 C was only one half of that at ambient temperature. This sudden degradation in strength was attributed to several factors, including the release of residual stresses, the plastic deformation of cubic ZrO2 and the proximity of the eutectic temperature (1715 C), which may activate diffusion-assisted plastic deformation in these eutectics whose average domain thickness was just 0.3–0.4 lm. The two former factors were also operating in Al2O3–YSZ eutectics which presented, however, higher melting temperature (1860 C) and thicker domains and thus the strength degradation at 1427 C was limited.

2500

Strength (MPa)

2000

1500

1000

Tm = 1715˚C

500

Rods tested in bending Fibers tested in tension

0 0

300

600

900

1200

1500

1800

Temperature (˚C) Fig. 6.11. Effect of the temperature on the flexure strength of Al2O3–YAG–YSZ ternary eutectics. Rods processed by the LFZ method were tested in three-point bending [23] while fibers manufactured by the l-PD technique were broken in tension [22].

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6.2.3. Anisotropy Directionally solidified materials tend to present anisotropic properties. Kennard et al. [157], Ochiai et al. [153] and Nakagawa et al. [101] studied the effect of orientation on the flexure strength of MgO–MgAl2O4, Al2O3–YAG and Al2O3–GAP bulk eutectics, respectively, manufactured by the Bridgman method. The bending strength parallel to the growth axis was slightly higher than in the perpendicular direction from ambient temperature up to 1600–1750 C but the differences were not significant, and indicated that the strength of bulk DSE oxides is fairly isotropic. Studies on rods and fibers grown at higher rates were only carried out by Pastor et al. [20,150] using the diametral compression test (also known as the Brazilian test). Circular disks sliced from the rods were subjected to diametral compression between two rigid ceramic plates. Although the compressive stresses in the load direction are much higher than the transverse tensile stresses, the disk fails by splitting across the compressed diameter in ceramic materials, in which the compressive strength is significantly higher than the tensile one. The transverse tensile strength of the rods was approximately one order of magnitude lower than the longitudinal one measured is three-point bending. The differences were attributed to the presence of elongated voids oriented along the growth axis in the rods. These defects, which did not affect significantly the longitudinal strength, were responsible for the reduced transversal strength. 6.3. Hardness The hardness of DSE oxides is primarily a function of the hardness of the single crystal oxides in the eutectic, and the highest values reported in the literature were measured in the Al2O3–YSZ, which reached 18–20 GPa [122,161]. Al2O3–ZrO2 eutectics without yttria [122,62,165] presented much lower hardness (around 11–14 GPa) and this reduction was mainly attributed to the presence of microcracks in the material, which were nucleated at the domain interfaces during the martensitic transformation and grew driven by the tensile residual stresses in the Al2O3 matrix, as detailed in Section 5.4.1. Al2O3–YAG eutectics presented hardness in the range 13–16 GPa [150,166], while ternary Al2O3–YAG–YSZ [22,23] eutectics showed intermediate values between Al2O3–YAG and Al2O3–YSZ. It is worth noting that the hardness of DSE is often higher than that of single crystal oxides in the eutectic. This was first reported in MgO–MgAl2O4 eutectics [157], and it has been normally found in the systems mentioned the previous paragraph. Moreover, the microhardness of Al2O3–YAG [150,166], Al2O3–YSZ [62] and Al2O3–YAG–YSZ [22,23] DSE with a lamellar microstructure increased with growth rate, or in other words, as the domain size decreased, and this effect was attributed to the strengthening induced by the presence of interface domains, which act as dislocation barriers. The relationship between the microstructure and the hardness in eutectics with colony microstructure is more difficult to assess, but higher growth rates, which decreased the size of the fibers or lamellae within the colonies, improved the microhardness [151,157,161]. 6.4. Fracture toughness Ceramics are brittle materials and this characteristic imposes serious limitations on their application as structural materials. Hence, toughening of ceramics has been an active research area in recent decades and, as the resistance to crack initiation was very difficult to improve significantly, the strategy was focused in increasing the resistance to crack

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propagation. This was achieved in transformation-toughened ceramics [167], fiber-reinforced ceramics [168,169], particle-reinforced ceramics [170,171], and laminates [172] by designing microstructures in which the crack propagation is hindered by obstacles. The microstructure of DSE oxides, as opposed to that of single crystal oxides, is likely to present these mechanisms on account of the large area fraction of interfaces, the presence of fluctuating residual stress fields and the elastic mismatch between the eutectic phases; significant improvements in toughness in relation to the single crystal oxides were found in CaF2–MgO [11], PbO–Nb2O5 [2] and CoO–YSZ [147] DSE in which crack deflection at the interface (rather than crack penetration) was the main fracture mechanism (Fig. 6.12). The behavior of a crack impinging on an interface between dissimilar elastic materials was studied by He and Hutchinson [173], who provided a criterion for crack deflection in the worst scenario of a crack growing perpendicular to the interface. Under such conditions, crack deflection will occur if the ratio between the interface fracture energy Ci and the fracture energy of the phase which has to be penetrated by the crack, C2, is below a critical value which depends on the elastic mismatch between both phases. The critical ratio Ci/C2 is of the order 0.2–0.4 for the typical elastic mismatch between the phases in DSE oxides and this condition was fulfilled in CaF2–MgO [11] and PbO–Nb2O5 [2]. It should be noted, however, that this behavior is unusual in DSE due to the excellent interfacial bonding between the phases and they rarely show extended delamination during crack propagation [105,150,153,23,163,174–178]. The fracture mechanisms of DSE oxides with the best mechanical properties (Al2O3– YSZ, Al2O3–YAG) have received particular attention in the literature. Several studies of the fracture toughness of Al2O3–YAG p [105,150,153,163,176] have reported similar values at ambient temperature (2 MPa m), and this brittle behavior is in agreement with the fracture micromechanisms observed experimentally (Fig. 6.13(a)). The crack propagated through the Al2O3 and YAG eutectic domains and the crack path was straight, not deflected at the interface. Hence, the crack did not interact with the microstructure and the crack propagation resistance was independent of the domain size [150] and orientation (perpendicular or transverse to the growth direction) [153]. This was the result of the

Fig. 6.12. Back-scattered scanning electron micrograph showing crack deflection at the CaF2–MgO interface. (Reprinted by permission of the Materials Research Society from [11].)

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Fig. 6.13. Back-scattered electron micrograph showing the propagation of a crack through the microstructure. (a) Al2O3–YAG eutectic rod. The Al2O3 phase is dark and the YAG phase white. (Reprinted by permission of the American Ceramic Society from [150].) (b) Al2O3–YSZ eutectic rod. The Al2O3 phase is dark and the YSZ phase white. (Reprinted by permission of Elsevier from [20].)

brittle nature of both Al2O3 and YAG, the strong interfacial bonding between them, and the absence of thermal residual stresses which could promote crack deflection at the interface or crack arrest in one phase. Slightly higher toughness was obtained in Al2O3–YAG eutectics doped with CeO2 [175] and it was suggested that it was due to the deflection of the cracks along the Al2O3–CeAlO3 interfaces, but no definitive conclusions could be obtained from observation of the crack path. p The fracture toughness of Al2O3–YSZ at ambient temperature was 4–5 MPa m [75,20,165,176], more than twice that of Al2O3–YAG, and this difference was echoed in the crack propagation pattern. Several cracks often emerged from the corner of the Vickers indentations (Fig. 6.13(b)) and propagated in parallel for a certain distance until one of them became dominant and the others were arrested. In general, crack arrest followed by the development of another parallel crack a few microns above or below the first crack tip was observed throughout the crack path. This led sometimes to the development of elastic bridges behind the main crack tip during crack propagation, which increased the toughness. These fracture mechanisms, not found in Al2O3–YAG, cannot be attributed to

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transformation toughening. No traces of monoclinic ZrO2 were found in the broken samples, and in addition, any transformable tetragonal ZrO2 in the eutectics rods should undergo a spontaneous transformation into the monoclinic phase prior to the application of any load, given the large tensile residual stresses which develop upon cooling. This phenomenon was observed in Al2O3–ZrO2 eutectics with low yttria content and led to the microcracking of the microstructure [122]. The higher toughness of Al2O3–YSZ was attributed to the presence of thermo-elastic residual stresses. The crack front will prefer to arrest in regions of compressive stress during crack propagation through a fluctuating residual stress field, and the applied stress intensity factor will have to be increased by an amount equal to the shielding effect induced by the compressive residual stresses at the crack tip to resume the crack propagation. A first order estimation of the effect of the residual stresses on the toughness can be obtained from the model developed by Taya et al. [171] by ignoring the contribution of all residual stresses other than those around the crack tip. The microstructure of the eutectic composite is idealized as a two-dimensional sandwich of alternative layers of Al2O3 and YSZ perfectly bonded. The crack propagates perpendicularly to the layers, and lies at the end of an Al2O3 layer. Assuming that the total crack length is much longer that the Al2O3 layer thickness, tA, the increase in fracture toughness, DKC, can be computed as [171] rffiffiffiffiffiffiffi 2tA DK C ¼ 2rr ; ð6:2Þ p p which leads to DKC = 2 MPa m for tA = 10 lm, and rr = 400 MPa, the average compressive residual stress along the rod axis in Al2O3. These findings of the effect of residual stresses on the toughness of DSE oxides are in agreement with more recent data on ternary Al2O3–YSZ–YAG eutectics [23,177,89]. p The toughness of Al2O3–YSZ–YAG was found to vary between 4.2 and 2.7 MPa m [23], and the samples with higher toughness presented higher compressive residual stresses in Al2O3 and domain thicknesses (300 MPa and 5–10 lm). The minimum toughness was found in rods grown at higher rates where the domain thickness was 0.3 lm and the compressive residual stresses in Al2O3 only reached 180 MPa. Finally, it should be noted that the high temperature toughness of Al2O3–YAG eutectics was measured by Ochiai et al. [153] up to 1750 C. The p ambient temperature values were maintained up to 1500 C and reached up to 4 MPa m above this temperature in samples tested at low rates due to the plastic deformation at the notch tip. This behavior is superior p to that ofpsapphire along the (0 0 0 1) planes, whose p toughness decreased from 4 MPa m to 5 MPa m at ambient temperature to 1 MPa m at 1000 C [89]. 6.5. Creep deformation The creep resistance of DSE oxides is superior to that of the sintered counterparts due to the absence of glassy phases at the interfaces, and the strain has to be accommodated by plastic deformation within the domains rather than by interfacial sliding. The interfacial bonding of DSE oxides is further increased in many oxide eutectic systems by the presence of homopolar surfaces, where they share a common oxygen plane. This leads to electrostatic bonding across the boundary, which retains the strength even at very high temperature. In the absence of relative sliding at the domain boundaries, compatibility of

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deformation between the eutectic phases is compulsory, and the overall strain rate is controlled by the eutectic morphology and the creep resistance of both phases. The creep resistance of DSE oxides has been studied mainly in two systems: Al2O3–YSZ and Al2O3–YAG. The first one is made up by a continuous creep resistant phase (Al2O3), which covers 70% of the eutectic volume and grows with the c-axis parallel to the solidification direction. This phase embeds a fine dispersion of a YSZ, an oxide with poor creep resistance. The creep behavior of the eutectic is controlled by that of the continuous Al2O3 phase, whose resistance to creep deformation is highly anisotropic, being maximum along the c-axis and decreasing by orders of magnitude as it is loaded just 15 from this axis [8]. Hence, creep resistance of Al2O3–YSZ DSE is one order of magnitude above that of Al2O3 single crystals oriented 45 off the c-axis, and of single crystal YSZ of equivalent composition [8,59] but it is inferior to that of c-oriented single crystal Al2O3 because the alignment of the Al2O3 domains within the eutectic is not perfect. The steady-state creep rates in this eutectic were measured between 1200 C and 1520 C at stresses ranging from 60 to 300 MPa [59,179] and the minimum creep rate, e_ , followed a power-law relationship as   Q n ; ð6:3Þ e_ ¼ Ar exp  RT where the stress exponent n was in the range 4–6, and the activation energy Q = 300 kJ/ mol. These results are compatible with a creep deformation controlled by the climb of pyramidal dislocations in Al2O3 with the O diffusion in Al2O3 as the rate controlling mechanism, where the somewhat low value of Q could be explained by the limited number of experimental data available. The role played by the YSZ domains during creep deformation was assumed to be secondary, as they merely remained dormant or underwent stress-relaxation while the topologically continuous Al2O3 phase deformed. Moreover, the global back stress in Al2O3 induced by the stress relaxation of YSZ is not important as the creep ductility of DSE oxides is low [179]. However, it should be noted that YSZ fibers and lamella found at the colony and cell center in eutectics with a cellular microstructure have dimensions in the submicron range and the mean spacing between them is of a few hundred nm. These submicron domains present a much higher resistance to plastic deformation on account of their small size, and in addition, they act as obstacles to the motion of dislocations in the continuous Al2O3 phase. As homogeneous phase coarsening is limited in DSE, they effectively strengthen the DSE oxide as compared to single crystal Al2O3, and creep deformation tends to localize in Al2O3–YSZ with cellular microstructure along the cell boundaries, where the size of the YSZ domains is larger (Fig. 6.14). This can offset the beneficial effects of the dispersed submicron YSZ domains, particularly in tension, because voids are nucleated in the intercolony regions, enhancing the creep rate and limiting the tensile creep ductility of cellular eutectics [76]. The creep deformation of Al2O3–YAG DSE oxide presents different characteristics from those of Al2O3–YSZ as its microstructure is made up of an interpenetrating network of both phases. This imposes an isostrain condition on the deformation of Al2O and YAG as strain accommodation by interface sliding is inhibited by the strong bonding at the interface domains. As YAG stands among oxides with highest creep resistance and its behavior is fairly isotropic [180,181], the creep resistance of Al2O3–YAG DSE oxides is superior to that of most single crystal oxides. Moreover, plastic deformation by basal,

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Fig. 6.14. Microstructure of Al2O3–YSZ eutectics after tensile creep deformation at 1400 C, showing the nucleation and growth of cavities at the intercolony regions. (Courtesy of A.R. Pinto Go´mez, A.R. de Arellano and J. Martı´nez-Ferna´ndez, University of Seville.)

prismatic and pyramidal slip in single crystal Al2O3 can start at 1000–1200 C while YAG remains elastic up to 1400–1500 C. This leads to two different creep regimes depending on the main deformation mechanism in YAG. The creep resistance in the high temperature regime (P1600 C) was measured in several investigations [110,162,182,183] along the solidification direction in air. The minimum creep rate, e_ , is plotted in Fig. 6.15 as a function of the applied stress, r, for Al2O3–YAG DSE with single crystal [182] and coarse-grained [183] microstructure. The behavior of both materials follows the typical power-law relationship given by Eq. (6.3) with a stress exponent of 5, which was normally found in these eutectics above 1600 C. The activation

-4

10

5 -5

Strain rate (s-1)

10

1

10-6

Temperature CG, 1650˚C

-7

10

CG, 1600˚C SC, 1650˚C SC, 1600˚C 10-8 100

200

300

400

500

Stress (MPa) Fig. 6.15. Minimum creep rate as a function of the applied stress for Al2O3–YAG DSECO manufactured by the Bridgman technique and tested at 1600 C and 1650 C. The open symbols correspond to single-crystalline materials [182] and the full symbols to coarse-grained (2–3 mm wide and several cm long) materials [183]. All the samples were tested in compression in the solidification direction.

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energies were 650–800 kJ/mol in the coarse grained material and slightly higher (800– 1000 kJ/mol) in the single crystal eutectic. These results are compatible with creep deformation controlled by dislocation motion in each phase induced by lattice diffusion in the single crystal eutectic, and this assumption was supported by transmission electron microscopy studies that showed evidence of dislocation activity in both phases, particularly in Al2O3 (Fig. 6.16). Final fracture of the eutectic materials under creep was dictated by the nucleation of damage at the domain interfaces as a result of the differences in creep rate between the phases and the lack of stress relaxation by interfacial sliding, which led to the progressive build up of stresses during deformation. The creep resistance of the directionally solidified Al2O3–YAG eutectics at 1600 C was several orders of magnitude higher than that of polycrystalline sintered materials with the same eutectic composition [110,162]. The creep exponent of the latter was very close to 1 and the analysis of the deformed specimens by transmission electron microscopy did not show any evidence of dislocation motion in either phase, Fig. 6.16(c), because inelastic deformation was controlled by grain boundary sliding rather than by plastic slip. In fact, the resistance to creep deformation of single crystal Al2O3–YAG DSE oxide at 1600 C along the solidification was in between that of YAG and c-axis sapphire, and was significantly better than a-oriented sapphire [182,183]. Moreover, a first-order approximation of the creep rates in the eutectics could be obtained from the creep rates of both phases assuming an isostrain approach, which is supported by the interpenetrated microstructure and the strong interfacial bonding. This simple isostrain model successfully explained the anisotropy in the creep rates between the specimens tested at 0 and 90 from the solidification axis, which came about as a result of the anisotropy in the creep deformation of the Al2O3 single crystal within the eutectic [182,184]. The creep curves of Al2O3–YAG [106,154,182,183] and Al2O3–Er3Al5O12 (EAG) [185] in the low temperature regime (1400–1600 C) did not always reach the steady-state secondary creep region because of premature failure triggered by the defects in the microstructure [106] or because the creep rate decreased below the detection limit and it was

Fig. 6.16. Transmission electron microscopy micrographs showing the dislocation structure in (a) Al2O3 phase and (b) YAG phase of a directionally solidified Al2O3–YAG eutectic, and (c) Al2O3 and YAG phases of a sintered Al2O3–YAG eutectic. The specimens were plastically deformed up to 14% in compression at 1600 C and the initial strain rate was 105 s1. (Reprinted by permission of Elsevier from [162].)

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necessary to increase the stress [183]. The minimum creep rate in the samples which reached stationary conditions followed the power-law relationship of Eq. (6.3), although the stress exponents were very high (in the range 5–10) and dislocation activity in the YAG domains was very weak [106,154] or not found [185]. Hence, the high stress exponents could be explained by the development of a backstress as a result of the formation of dislocation pile-ups in the sapphire in presence of the more creep resistant single crystal YAG domains. Following this argument, Matson and Hetch [106] recovered the stress exponent of 5 by introducing a threshold stress for creep in Eq. (6.3). They found that the threshold stress decreased with temperature and increased with the thickness tA of the Al2O3 domains in the eutectic microstructure [106,154], and these experimental results could be rationalized with an extremely simple model. If the far field backstress is generated by a mechanism similar to that of the Orowan bowing mechanism during creep of metals, the threshold stress, rth, can be roughly estimated as rth ¼ aG

b ; tA

ð6:4Þ

where a = 0.5 is a geometrical factor, G is the shear modulus of Al2O3 at the test temperature and b the burgers vector. Eq. (6.4) predicts that the threshold stress should approach to zero and provide no strengthening at 1500 C for tA = 5 lm, in agreement with the experimental data in [183]. Moreover, the threshold stress tended to zero above 1550–1660 C [154], a temperature at which dislocation motion occurs readily in YAG. The progressive build-up of elastic stresses in YAG during deformation at 1400 C was also supported by the evidence of elastic strain recovery in specimens deformed by creep after unloading [185]. Structural components for gas-turbines are one of the potential applications of DSE oxides, and Harada et al. [186,187] measured the creep rates in Al2O3–YAG and Al2O3–GAP DSE in moist environments at 1400 C, 1500 C and 1600 C as combustion gases may contain as much as 10% water vapor. They found that the presence of water vapor increased the steady state creep rates by a factor of 1.4–4 for H2O vapor partial pressures of 0.06 MPa and by a factor of 5–7 for partial pressures of 0.4–0.6 MPa, as compared with specimens tested in air. The stress exponents were consistent with those measured in air at the same temperature but the activation energy was lower (500–650 kJ/mol) and independent of the water vapor partial pressure. Analysis of the deformation mechanisms by transmission electron microscopy suggested that the higher creep rates in moist environments could be due to the enhanced dislocation mobility induced by the absorption of protons, but more work is necessary to find out the actual physical mechanisms. 6.6. Subcritical crack growth Subcritical crack growth has been found responsible for the degradation of the mechanical properties of several single-crystal oxides, such as sapphire [94] and tetragonal ZrO2 [95], in air at temperatures above 600 C. As they are constituents of important DSE oxides, evidence of subcritical crack growth was studied by Sayir [188]. The tensile strength of Al2O3–YAG monofilaments at 1100 C at strain rates spanning four orders of magnitude was constant, while sapphire monofilaments oriented along the c-axis showed a marked dependence of strength on strain rate (Fig. 6.17). The reduction of strength in sapphire at lower strain rates has been well correlated to the slow propagation of a crack, although

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Tensile strength (MPa)

2000

1500

1000

500 Sapphire (c axis) Al2 O3 /YAG eutectic 0 10-6

10-5

10-3

10-4

10-2

-1

Strain rate (s ) Fig. 6.17. Influence of the strain rate on the tensile strength of Al2O3–YAG DSE and c-axis oriented sapphire at 1100 C in air [188].

there is discussion on the actual mechanisms of crack propagation. On the contrary, DSE oxides did not present any fractographic evidence of crack propagation at high temperature [150] and their strength was independent of the loading rate, an indication that subcritical crack growth was not present in these materials. 7. Functional properties The outstanding mechanical performance and chemical stability of DSE oxide has been the main driving force for the recent developments in this area. However, DSE oxides also present an interesting role as functional materials. At first glance, the mere enhancement in mechanical properties, corrosion resistance and thermal stability, as compared with single crystals and conventional ceramics, supports their application as functional materials in devices. Additionally, their multi-component character is a stimulus to search for synergistic effects resulting from the combination of complementary functional properties into a single material. This would be the case of materials with mixed properties such as ferromagnetic and insulator, conductor and insulator, etc. Moreover, the unique microstructure of regular eutectics made up of ordered arrays of alternating lamellae or fibers with sharp and clean interfaces induces interesting functional properties, such as directional transport of light and electricity. The recent research efforts in DSE oxides from the point of view of the functional applications are summarized below, including the attempts to use DSE oxides as structured substrates for patterned thin films, ionic conductor composites, structured porous cermets, and optical waveguides [27,189]. 7.1. Substrates for thin film deposition The deposition of high-quality patterned epitaxial oxide thin films is noteworthy among a number of nanotechnologies. The periodic microstructure arrangement found in DSE

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can be used as a template to manufacture highly structured substrates for patterned oxide thin films [190]. Many of the applications envisaged for high-TC superconductors (HTSC) or ferromagnetic metals showing a colossal magnetoresistance (CMR) are based on the preparation of artificial grain boundary junctions (GBJ). For example, weak-link and Josephson effects shown by high-angle grain boundaries could be used to produce superconducting quantum interference devices (SQUID) with YBa2Cu3O7 (YBCO) films [191]. The most reproducible GBJ have been obtained so far in films epitaxially grown on bicrystal substrates in which the artificial GBJ is directly induced by the substrate biorientation and the film is obtained in a single deposition step [192]. The main limitation of this technology for practical applications is the small number of active junctions achievable along a single grain boundary and the difficulties of producing bicrystals of good quality [193]. Regular binary DSE are monolithic two-phase composites structured either in the form of alternating parallel lamellae or of cylinders of one phase embedded in a crystalline matrix of the other phase. They could be considered similar to bicrystal substrates but present thousands of grain boundaries per linear cm instead of just one. DSE oxides also show very sharp, atomic-scale interfaces which separate phases with different relative orientations, and substrate surfaces with the desired phase orientation relationships can be obtained by cutting the bulk eutectic along the appropriate crystallographic planes. The only attempt so far to grow thin films on DSE oxide substrates has led to the production in a single deposition step of biepitaxial films of YBCO and La2/3Ca1/3MnO3 (LCMO) with a regular array of GBJ [190,86]. The films deposited on these substrates reproduced the pattern of the eutectic surface, and hence films with different arrangements of two well-defined orientations could be prepared. The best result was obtained in special surface substrates cut from well-ordered lamellar CaSZ/CaZrO3 and fibrous MgSZ/MgO DSE oxides. CaSZ and MgO are among the best substrates for both YBCO and LCMO film deposition because of their chemical inertness and good lattice matching [194]. In addition, CaZrO3 presents a very stable orthorhombic perovskite with a pseudocubic cell ˚ ) close to that of YBCO and LCMO (see Table 7.1). The substrate parameter (4.005 A surfaces were prepared from CaSZ/CaZrO3 and MgSZ/MgO DSE rods of 2 mm in diameter grown by the LFZ technique [195]. The former presented relatively large areas (several mm2 size) of a well-ordered structure consisting of non-faceted alternating CaSZ (Ca0.25Zr0.75O1.75) and CaZrO3 (CZO) single crystal lamellae with a thickness of a few microns. The lamellae showed the orientation relationships described in Section 3.1. Two different types of substrate plates with different relative phase orientations, namely A and B, were cut longitudinally to the rod axis. The plates were approximately aligned with (2 0 0)CSZ k (2 0 0), (1 2 1), (0 0 2)CZO in substrate A and (2 0 0)CSZ k (2 0 2), (0 4 0)CZO in substrate B. In the fibrous MgSZ/MgO DSE, the substrate surface was

Table 7.1 Crystal structure and lattice parameters of some ceramic oxides Compound

Crystal structure

˚) Cell parameters (A

CaSZ, MgSZ CZO MgO YBCO LCMO [239]

Fluorite (Fm3m) Orthorhombic (Pnma) Cubic (Fm3m) Orthorhombic (Pnma) Orthorhombic (Pbnm)

5.15 5.756, 8.010, 5.593 4.213 3.825, 3.886, 11.660 5.472, 5.457, 7.711

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aligned with (2 0 0)MgSZ k (2 0 0)MgO [190]. YBCO and LCMO films about 400 nm thick were deposited on these substrates by different techniques, such as metal-organic chemical vapor deposition, pulsed-laser deposition, and sputtering [86,190]. 7.1.1. YBCO in CaSZ/CaZrO3 (CZO) The parallel strip pattern of biepitaxial YBCO in CaSZ/CZO on substrate A is shown in Fig. 7.1 together with the X-ray diffraction (XRD) pole figures corresponding to different reflections of the film and the substrate [86]. The film surface was smooth and uniform on the CaSZ domains (dark strips). Pole diagrams (Fig. 7.1(b)) indicated that the YBCO

Fig. 7.1. (a) SEM image of a YBCO film deposited on the surface of a well-aligned CZO/CaSZ DSE (substrate A). (b) XRD pole figures showing the different reflections of the phases in the film and the substrate. (Reprinted by permission of Wiley-VCH [86].)

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film grew epitaxially with c-axis orientation following the so-called cube-on-cube or 0 epitaxy. The film also grew epitaxially on the CZO domains (bright strips in Fig. 7.1(a)) with a (1 0 3) orientation, and presented a rough surface consisting of aligned triangular-shaped crystallites, typical of (1 0 3)-oriented films. The relative orientations of both c-axis and (1 0 3)-oriented strips in the YBCO film defined a single and unique type of grain boundary where the CuO2 planes of the YBCO structure meet together with a 45 rotation around their common b-axis parallel to the surface (Fig. 7.2(a)). The YBCO films deposited on substrate B showed two YBCO domains with a flat morphology, typical of c-axis oriented growth. The texture analysis confirmed the c-axis orientation of both film phases but with a 45 in-plane rotation, as depicted in Fig. 7.2(b). Electrical resistance measurements along (k) or perpendicular (?) to the strips were performed on the YBCO films grown on substrate A using the direct current four-contact method [86]. The temperature dependence of the electrical resistance is shown in Fig. 7.3. The resistive transition temperature (TC) and transition width (DTC) were 88 K and 2 K, respectively, along the strips, and 85 K and 5 K, respectively, perpendicular to the strips. The resistivity of the normal state was anisotropic, q?(300 K)/ qk(300 K) = 2.4, and the anisotropy was stronger of the critical current density, jCk ð77 KÞ=jC? ð77 KÞ ¼ 13 with jCk ¼ 4 kA=cm2 [86]. The high sensitivity to the magnetic field, which produced a shift to lower temperatures of the low TC in the transverse measurements, proves the weak-link nature of these GBJ. The low values of the critical currents and the high resistance at 0 K were possibly a consequence of the discontinuities in the films caused by defects in the substrate.

Fig. 7.2. Schemes of the orientation relationships between films and substrates. (a) YBCO film in substrate A: caxis oriented YBCO on CaSZ and (1 0 3)-oriented YBCO on CZO. (b) YBCO film in substrate B: both c-axis oriented but 0 and 45 in plane alignment on CaSZ and CZO strip phases, respectively. (c) LCMO film on substrate B showing epitaxial growth on CZO but polycrystalline growth on CaSZ. (d) YBCO film on MgO/ MgSZ substrates with c-orientation on the MgSZ matrix and polycrystalline dots on MgO fibers. (Reprinted by permission of Elsevier [190].)

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Fig. 7.3. Normalized resistance superconducting transitions along (k) or perpendicular (?) to the YBCO strips of Fig. 7.1 for different applied magnetic fields of 0, 10, 25, 50, 75, and 100 mT. Arrow indicates the region where weak-linked GBJ manifest. Inset shows the measured resistivity curves [240].

7.1.2. LCMO in CaSZ/CZO The surface morphology of the LCMO films was smooth in both substrates. The pole figures showed that the film grew epitaxially on the CZO domains, with a high (1 0 0)-orientation. LCMO grew in the form of a randomly oriented polycrystalline material [190] on the CaSZ phase, as depicted in Fig. 7.2(c). This difference could be explained by the lower mismatch in LCMO/CZO (4%) than in LCMO/CaSZ (11%) (see Table 7.1). 7.1.3. YBCO in MgSZ/MgO The YBCO films deposited on transverse sections of the MgSZ/MgO eutectic also reproduced the fibrous pattern of the substrate. The growth habit depicted in Fig. 7.2(d) could be explained by the lattice mismatch between YBCO with MgO, higher than that between YBCO and MgSZ. An array of micron-sized polycrystalline YBCO islands grew on the MgO substrate phase. The islands were regularly distributed in a smooth YBCO film grown on the MgSZ substrate phase with a c-axis orientation and a 45 in-plane rotation [190]. In conclusion, the preliminary findings presented in the previous paragraphs show that DSE oxides can be used as substrates for patterned oxide thin films growth, and exotic film configurations can be produced in one preparation step by choosing the proper substrate orientation. It should be noted, however, that the small size of the eutectic grains makes it difficult to obtain large areas (above several mm2) of perfectly and continuously ordered lamellae. Moreover, the choice of possible substrates is limited to the eutectic compositions available because off-eutectic compositions tend to develop disordered microstructures. 7.2. Structured Ni/YSZ and Co/YSZ composites DSE oxides can be used as precursor materials to obtain new composites, which may find applications in the fields of heterogeneous catalysis and in fuel cell technology. Fuel

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cells are envisaged as a clean, efficient alternative energy source to fossil fuel combustion, and porous cermets of Ni/YSZ are commonly used as anodes [196,197] in solid oxide fuel cells (SOFC). The durability and efficiency of the materials and the manufacturing costs stand among the most important factors in this technology [198], and it is well established that both improve if the cell operation temperature is below 700 C. However, the poor ionic conductivity of most common electrolyte materials at low temperatures limits the electrolyte thickness, while keeping at the same time the gas tightness across it. Moreover, the efficiency of the anodes is strongly dependent on their microstructure. In particular, the length and number of triple phase boundaries (TPB) where fuel, ions and electrons meet plays a crucial role in the anode performance, and new anode technologies tend to increase the number of pores and Ni particles while keeping the good connectivity necessary for gas and charge flow. Another matter of concern arises from the strong tendency of the Ni particles to agglomerate into larger particles at the operating temperatures, the effect being accelerated by the poor wetability between metallic Ni and YSZ ceramics [199]. Ni coarsening decreases the number of TPB and the electrical conductivity of the anodes, deteriorating the long-term stability of the SOFC under operation. An alternative to the conventional processes to manufacture of SOFC anodes has recently been proposed. The initial step is the growth of NiO/YSZ DSE oxides [200,201], which present a well-ordered lamellar microstructure with strongly bonded interfaces between the phases [202]. A subsequent reduction treatment produces the desired porous Ni/YSZ cermet where the metallic Ni remains well-aligned crystallographically with the YSZ phase [84]. The formation of these low energy interfaces prevents the coarsening of the Ni particles during cell operation. Additionally, the lamellar structure is appropriate for easy gas flow and ionic and electronic transport. The porous cermet also presents a thermal expansion coefficient very similar to that of the YSZ phase, which favors electrolyte thermo-mechanical integration. The half-cell preparation steps using this new concept are sketched in Fig. 7.4. The method starts with a precursor pellet of NiO/YSZ with the eutectic composition (70mol% NiO–30mol%YSZ) manufactured by standard ceramic procedures, but highly porous (around 65%). The ceramic pellets are processed by directional laser-surface melting, a method that achieves a good homogenization, densification and texturing of a surface layer without modification of the rest of the piece [87]. The thickness of the melt layer can be varied from 50 to 500 lm (see Fig. 2.13) and the lamellar morphology (Fig. 7.5) is similar to that obtained in rods grown by LFZ [189,234] but—as stated in Section 2.4—the interphase spacing changes from the surface to the substrate as a result the gradient in the solidification rate. For instance, the interphase spacing varied from 0.4 lm at the surface to 1.6 lm near to the unmelted substrate at a typical growth speed of 500 mm/h [74]. The porous Ni/YSZ cermet is subsequently prepared by reduction of the precursor oxide eutectic in a reducing atmosphere. The volume fraction of the YSZ phase is 43 and 33.5 vol.% of Ni and 23.5 vol.% of porosity is expected after reduction of NiO to metallic Ni. Due to the lamellar microstructure, the cermet can be visualized as alternating channels for oxygen ion diffusion (YSZ) and porous metallic Ni with a pore concentration of 40%, large enough for gas permeation and Ni content for electronic conduction (Fig. 7.5(b)). Percolation requirements are now restricted to a two phase material (porous Ni-channels) instead of three (Ni, pores and YSZ) as in conventional ceramics and this is why better connectivity between the Ni particles, pores and YSZ, and an improved anode yield, are expected.

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Fig. 7.4. Scheme illustrating the production of a SOFC half-cell from NiO/YSZ DSE.

The reduction kinetics in NiO/YSZ as well as in CoO/YSZ was studied in rod samples prepared by the LFZ method by gravimetric methods and the progression of the reduction front indicated that reduction took place via a diffusion-limited process [201,28]. It is interesting to notice that the cermets produced from the reduction of perfectly ordered lamellar precursors cannot sustain the enormous stresses derived from the 40% volume shrinkage associated with NiO and CoO reduction, and the lamellae tend to collapse in well-ordered samples [203]. On the contrary, the small size of the eutectic domains improved the mechanical properties and helped the stabilization of the pores, which leads to a better material for anodes provided there is good macroscopic connectivity between the component phases. The electrical conductivity of these channeled cermets has been determined to be around 9000 S/cm, which is twice as high as that of other ceramic cermets [28,204,205]. It was reported in Section 3.2 that the phases in DSE NiO/YSZ presented well-defined orientation relationships with an interface (1 1 1)NiO k (0 0 2)YSZ. The crystallographic orientation of NiO is maintained during reduction, i.e., {hkl}NiO k {hkl}Ni, and (1 1 1)Ni k (0 0 2)YSZ interfaces are established. These are presumably low-energy interfaces, which determine the good microstructure stability during cell operation. In fact, it was shown that the microstructure, conductivity, and open pore distribution remained constant after 300 h at 900 C in a reducing atmosphere [85]. The coefficients of thermal expansion of Ni/YSZ and Co/YSZ porous cermets produced from NiO or CoO/YSZ DSE were 10.8 · 106 K1, equal to that of YSZ [28]. Consequently, a tight thin layer of YSZ deposited at 800 C presents a good thermo-mechanical integration with the cermet [206]. The excellent cermet–electrolyte integration is shown in the fracture cross-section depicted in Fig. 7.5(a). Thus Ni and Co/YSZ channeled cermets produced from DSE precursors are very promising electrochemical materials owing to their microstructural stability and good electrochemical performance.

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Fig. 7.5. (a) SEM micrograph of the fracture cross-section of a SOFC showing the anode–electrolyte system. A thin film of YSZ of 3 lm was deposited on top of the anode–electrolyte system to ensure gas tightness [201]. (b) Channeled Ni/YSZ anodes for SOFC produced by reduction of NiO/YSZ DSE.

In addition to porous cermets, porous ceramics with applications in filters, gas burners, bio-ceramics, membranes, etc. can be produced by acid leaching of the reduced NiO and CoO/YSZ eutectics [207] (Fig. 7.6). Porous YSZ (with 57% porosity) produced from DSE are made up of tangled single crystal lamellae and its mechanical strength is enough for handling and processing [208]. It is also worth noting that the existence of oxygen diffusion paths through the YSZ phases is very convenient for attaining the desired in-depth homogeneous oxidation–reduction process in the materials. This avoids, for example, the usually deleterious layer-by-layer process in most oxidation–reduction experiments. The potential of these porous ceramics manufactured from DSE oxide structures is depicted in Fig. 7.7, which shows a NiAl2O4/YSZ fibrous eutectic in which the Ni-spinel has been

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Fig. 7.6. Optical microscope image of a porous lamellar YSZ obtained by leaching of a Ni/YSZ porous cermet.

Fig. 7.7. SEM micrograph of a NiAl2O4/YSZ DSE after thermo-reduction at 900 C. The Ni spinel has been partially reduced to Ni, and the Ni nanoparticles can be seen between the YSZ fibers [27].

partially reduced to Ni nanoparticles by the transport of oxygen through the YSZ fibers of the eutectic structure. 7.3. Photonic materials Although eutectic structures have been known for nearly a century, very few studies of their optical properties can be found in the literature. However, the structure of alternate lamellae or cylinders embedded in a matrix and the good bonding between the constituent phases is very interesting for the development of optical devices. In fact, the step index profiles and the absence of lattice mismatch defects—both characteristic of eutectic systems—are favorable to a decreasing light losses when they are used as optical waveguides and an ordered eutectic system is essentially a monolith of planar or fiber waveguides. Additionally, optically active ions (rare-earth or transition metal ions), needed for active optical operation, can be easily introduced into the eutectic materials by addition to the

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precursor powders before crystal growth. Impurities are expected to be homogeneously distributed in each phase during the solidification process owing to their respective partition coefficients. Preliminary studies on optical properties were performed several decades ago in some regular fibrous fluoride eutectics. These materials were proposed for fiber optic faceplate or microchannel plate components [29]. In fact, a fiber eutectic composed of a high refractive index dielectric compound embedded in a dielectric matrix of lower refractive index acts as a monolithic bundle of optical fibers. Another option is to etch out one of the phases, leaving a microchanneled matrix that can be filled up with a liquid or solid phase. Alternatively, the matrix can be chemically removed leaving behind a bundle of long single crystal fibers of micron section, as was done in the LiF/NaCl eutectics (Fig. 7.8) [209]. A similar technique was used several years ago to obtain single crystal spinel fibers from the MgAl2O4/Mg2SiO4 DSE but the colony structure of the eutectic impeded the growth of long fibers [26]. In addition, the favorable conditions of eutectic mixtures to produce glasses with a low number of components are also remarkable from the point of view

Fig. 7.8. NaCl/LiF DSE. (a) SEM image of the transverse section. The LiF single crystal fibers (black circles) are embedded in the NaCl matrix. (b) Optical microscope image of a single crystal LiF fiber obtained by removing the NaCl matrix.

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of the photonic applications of the eutectics. A good optical quality glass can be produced by fast directional solidification of the CaSiO3/Ca3(PO4)2 binary eutectic system [35] (Fig. 7.9). Most of the DSE oxides considered in this paper are formed by phases transparent in the 0.2–10 lm optical spectral intervals and therefore suitable for optical applications. The relatively large (several mm long) ordered regions that can be found in most regular oxide eutectics, such as the lamellar CaSZ/CZO or the fibrous MgO/CaF2, can be used as single crystalline stacks of planar optical waveguides or optical fibers, respectively. In other cases, a phase dimension of the order of light wavelength adds to the refractive index contrast between phases to produce diffraction, interference, polarization effects, etc., which can be used in optical systems [210,211]. 7.3.1. Optical waveguides Research into active optical waveguides gained attention in the past because of the enormous success of the erbium-doped fiber amplifier. Optical gain with relatively low pump powers can be achieved with optical waveguides [212]. Furthermore, efforts were made to look for crystalline materials, instead of glassy, for waveguides. Compared with the glass fibers currently used in optical technologies [213], single crystal fibers offer some potential advantages: a wider transparency window, greater resistance to radiation damage, better mechanical, chemical and thermal stability, non-linear effects, and narrower emission bands. Crystalline composites are also suitable for integration of active and passive media, which can increase the potential applications of the guides [214]. A wide variety of fabrication and processing techniques and host materials are being investigated. The optical active ions and the required refractive index profiles are usually implemented by ion implantation, ion in-diffusion, co-deposition and ion exchange techniques, and several wave-guide lasers and amplifiers have been demonstrated in oxide materials such as YAG, LiNbO3, BGO, Al2O3, etc. In optical waveguides, light is guided by transparent phases, which are surrounded by a phase of lower refractive index. The effect is governed by the waveguide parameter V defined as [215]

Fig. 7.9. Wollastonite/TCP eutectic glass rod of 2 mm in diameter grown downwards at high rate by the LFZ method.

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V ¼

1=2 2p 2 d ni  n2o ; k

ð7:1Þ

where k is the light wavelength in vacuum, d the guide size parameter (the fiber radius for cylindrical fibers and one half of the lamella thickness for planar waveguides), and ni and no stand for the refractive indexes of the waveguide and the surrounding medium, respectively. The number of modes propagating in the guide also depends on V. The most favorable situation in terms of light propagation is obtained when V < p/2 for planar guides and V < 2.405 for fibers in the single-mode operation. For a given waveguide (characterized by d, ni and no), the cut-off wavelength kc, the most energetic light propagating in single-mode form, can be defined as

1=2 for lamellae, ð7:2aÞ k P kc ¼ 4d n2i  n2o  2pd 2 1=2 n  n2o for fibers. ð7:2bÞ k P kc ¼ 2:405 i Table 7.2 compiles the waveguide parameter in some DSE oxides. Light guiding effects are expected in the CaSZ lamellae of the CaSZ/CaZrO3 eutectic, in the ZrO2 fibers of the ZrO2/Al2O3 system and in the MgO fibers of the CaF2/MgO eutectic. It can be concluded that single-mode operation in the second optical window is predicted for CaZrO3/CaSZ and CaF2/MgO eutectics. For the ZrO2/Al2O3 system, the cut-off wavelength decreases down to the visible optical range. Preparation of active planar waveguides using the CaZrO3/CaSZ lamellar eutectic has recently been demonstrated [10]. The CaZrO3/CaSZ DSE samples consist of alternate lamella of 2 lm in thickness of cubic CaSZ and orthorhombic perovskite CaZrO3 single crystals [195]. Ordered grains extending over several mm in length and up to 100 lm in width were produced by the LFZ growth method. The component crystals are transparent from 0.3 lm to 15 lm and the refractive index contrast in this composite is 2.5%, enough to allow visible light guiding. The most refractive material, CaSZ, accommodates large amounts of rare-earth doping. In particular, Er3+ active ions can be easily introduced in both phases but at a higher concentration in the most refractive CaSZ phase. Merino et al. [12] studied the absorption and emission spectra and the corresponding oscillator strengths, radiative transition probabilities and emission lifetimes of the electronic transitions of Er3+ ions in this eutectic. Another interesting feature of the CaZrO3/CaSZ:Er material is the two photon green emission from the Er3+ ion 4S3/2 level at 545 nm, under excitation with a diode laser in the 4I15/2 ! 4I11/2 absorption band at 980 nm. This up-conversion was used to study the wave-guide effect in this material. As shown in the image sequence of Fig. 7.10, light from a 980 nm laser diode is focused on one polished transverse face of a 1.1 mm thick disk of the eutectic crystal whereas the other surface of the disk is focused by a 40· microscope objective into a charge coupled device (CCD) detecTable 7.2 Waveguide parameter V (calculated for light of wavelength k = 0.5 lm) and cut-off wavelength kc of some DSE oxides DSE

Guiding phase

Shape

Phase thickness (lm)

V

kc (lm)

CaZrO3/CaSZ Al2O3/ZrO2 CaF2/MgO

Ca0.25Zr0.75O1.75 ZrO2 MgO

Planar Fiber Fiber

2 0.3 1.2

5.2 2.45 7.5

1.7 0.5 1.6

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Fig. 7.10. CCD images obtained using the up-conversion effect demonstrating light guiding by CaSZ lamellae. Excitation on the opposite face of a CaZrO3/CaSZ: Er lamellar DSE with a k = 980 nm diode laser and end-fire detection at k = 545 nm. (a, b) Excitation spot of 1.8 lm centered in a CaSZ and a CaZrO3 lamellae, respectively, (c) spot of 3.2 lm, (d) excitation spot of 7.6 lm. (Reprinted by permission of the American Institute of Physics [10].)

tor, which detects the green light. Fig. 7.10(a) and (b) correspond to images taken by exciting the sample with a spot centered at a CaSZ and a CaZrO3 lamella, respectively. The planar waveguide effect is clearly demonstrated because the light emission is only detected at the CaSZ lamellae. This wave-guide effect is corroborated by Fig. 7.10(c) and (d) obtained by defocusing the exciting beam. Light guiding has also been demonstrated in the CaF2/MgO fibrous eutectics [11]. An optical micrograph taken in the transmission mode through a slab of 300 lm cut with the MgO fibers perpendicular to the film surface is shown in Fig. 7.11. Light is guided by the highest refractive index MgO fibers giving a density of about 40,000 pixels/mm2. A complete characterization of the optical properties of these eutectic materials is still lacking but it is advanced that large benefits can be obtained from the extraordinary stability, good crystalline and monolithic characteristics of DSE of wide electronic gap materials. The main constraint for optical applications is the difficulty of growing materials with large grains for phase continuity through the sample and phase alignment, and the present application of these materials in waveguides should be restricted to submillimeter size devices. 7.3.2. Effect of microstructure size on luminescence Periodic dielectric structures with interphase spacings of the order of the visible and near-infrared light wavelength, named photonic crystals, have experienced significant development in the last decade [216]. An important property of these structures is the

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Fig. 7.11. Optical transmission micrograph of a [0 0 1] k CaF2 plate of 300 lm thickness from an MgO/CaF2 DSE grown by the Bridgman method. (Reprinted by permission of the Materials Research Society [11].)

modification of the luminescence efficiency of atoms or molecules in strong or weak confining structures [217]. The luminescence at certain wavelengths can either be suppressed or forced to radiate in definite directions of the periodic structure in photonic crystals. The usual technique to manufacture photonic crystals is based on the packing of uniform-size particles from a colloidal suspension of SiO2 or polystyrene (3D) or in the stacking of alternating layers of Si and SiO2 (2D), and the main concern is the mechanical stability of these structures. The periodic microstructures found in regular DSE oxides with lamellar or fibrous phase arrangement present excellent structural integrity and could behave as 1D and 2D photonic crystals, but these latter effects have not yet been definitively proved. An effect which is related to photonic crystals has been recently reported on DSE oxides. The radiative lifetime of the 4I13/2 level of Er3+ was modified up to 15% by changing the microstructure size of the Al2O3/ZrO2 DSE [218]. Erbium in this system only enters in the higher-refractive-index ZrO2 phase, whose volume fraction is 30%. As shown above, the refractive index contrast produces efficient light guiding but it is not enough to produce a full band gap in terms of the photonic crystal theory. Consequently, the weak confinement or weak coupling range of the luminescent ion to the electromagnetic field leads to only feeble effects on the luminescence properties. The lifetimes of the 4S3/2 (545 nm) and 4 I13/2 (1520 nm) Er3+ levels were measured in Al2O3/ZrO2 DSE samples grown by LFZ method at various rates, which presented large differences in the microstructure (Fig. 7.12). The sample in Fig. 7.12(a) shows an interpenetrating degenerate lamellae structure where the average thickness of the ZrO2 degenerate lamellae was 0.6 lm. The sample in Fig. 7.12(b) presents a colony structure with a triangular arrangement of ZrO2 cylinders with average diameter 0.36 lm embedded in the Al2O3 matrix. The sample in Fig. 7.12(c) also presents a colony structure but the ZrO2 phase within the colonies is arranged in the form of lamellae of 0.05 lm in thickness. The luminescence lifetime varied from one

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Fig. 7.12. SEM micrographs of transverse sections of Al2O3/YSZ DSE grown by LFZ method at (a) 10 mm/h, (b) 150 mm/h, (c) frozen by switching off the laser [218].

sample to another as depicted in Table 7.3. It is clear that the 4S3/2 (545 nm) lifetime remains unchanged, whereas that of the 4I13/2 (1520 nm) level increases by about 15% at ambient temperature and 10 K as the ZrO2 phase size decreased. This weak but meaningful effect was explained as a result of the change in the density of states (DOS) of the electromagnetic radiation at the luminescent wavelength taking place near to the interfaces [219,220]. In a homogeneous dielectric medium, the electric dipole radiative deexcitation probability varies linearly with the refractive index n (apart from local field corrections). The small size of the ZrO2 phase (either lamellae or cylinders), which is comparable to the wavelength of the emitted radiation, makes the DOS a function of the distance to the boundary between the different dielectrics. According to the calculations of Snoeks et al. [221], the average DOS is proportional to the refractive index of the hosting dielectric Table 7.3 Lifetime of the 4I13/2 Er3+ emission as a function of the ZrO2 phase size Al2O3/ZrO2:Er Sample

ZrO2 particle size (nm)

Lifetime (300 K) ±0.1 ms

Lifetime (10 K) ±0.1 ms

Fig. 7.12(a) Fig. 7.12(b) Fig. 7.12(c)

600 360 50

3.4 3.6 4.0

4.8 5.2 5.4

798

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at a distance far away from the interface, and the local DOS decreases down to values that are proportional to the refractive index of the surrounding medium near to the interface and at distances below 0.7k/2p (k being the wavelength in vacuum). Consequently, more Er3+ ions will perceive a lowered density of states in the thinner phases than in the thicker ones, and the lifetime will be longer, as experimentally observed. Hence the variation of the luminescence lifetime with the interphase spacing is due to the change of the available electromagnetic modes at 1520 nm, which is observable in the fine microstructure obtained in DSE oxides grown at high rates. The main limitation of DSE oxides as photonic crystals is the small-refractive-index contrast. This handicap might be eliminated in the near future by the selective dissolution of one phase, to be replaced with a different phase of higher refractive index. In short, although still in their infancy, the photonic DSE materials constitute an alternative for the fabrication of periodic dielectric structures and they deserve an in-depth study. 7.4. Electroceramics Most of the research on the electric properties of DSE oxides has been carried out in ZrO2-based eutectics. Cubic zirconia is the oxygen electrolyte most widely used as an oxygen sensor (k-probe) [222] and in high temperature furnaces [223] because of its excellent chemical stability and oxygen-ion conductivity at high temperatures. However, the thermo-mechanical stresses associated with high temperature operation as well as the environmental degradation are limiting factors in terms of durability, which can be overcome to some extent by using DSE oxides if the overall eutectic conductivity is not drastically reduced by the presence of phases with lower conductivity than ZrO2. This latter property depends on the morphology of the eutectic microstructure, as was shown by Merino et al. [224] and by Cicka et al. [225], who measured the ionic conductivity in CaZrO3/CaSZ and MgO/MgSZ DSE, respectively. The domain size did not modify the eutectic conductivity but the effect of microstructure was clearly revealed by the strong anisotropy observed in some well-aligned DSE oxides. For instance, the ionic conductivities at 1000 K of lamellar CaZrO3/CaSZ and fibrous MgO/MgSZ eutectics are presented in Table 7.4 in the lamella or fiber direction (rk) or perpendicular to them (r?). The ionic conductivity along the lamellae plane of the CaZrO3/CaSZ DSE was higher than that of a CaZrO3/CaSZ eutectic manufactured by conventional sintering which presented a granular microstructure, whereas the conductivity perpendicular to the lamellae was significantly lower. The differences in conductivity between granular and lamellar CaZrO3/CaSZ eutectics and the anisotropy of the latter could be easily understood from the predictions of meanTable 7.4 Experimental and theoretical predictions of DC conductivity at 1000 K of some DSE oxides containing stabilized-zirconia phase Material

Processing

E (eV)

rk (X1 cm1) Experiment

Al2O3/YSZ MgO/MgSZ CaZrO3/CaSZ CaZrO3/CaSZ

DSE DSE DSE Sintered

1.04 1.5 1.3 1.3

3

2.0 · 10 1.5 · 103 1.5 · 104 5.0 · 105

r? (X1 cm1) Theory

Experiment 3

4.0 · 10 2.8 · 103 1.45 · 104 4.1 · 105

rT activation energies E in the low temperature range are also shown.

3

2.0 · 10 1.5 · 103 2.0 · 105 5.0 · 105

Theory 4.0 · 103 3.5 · 103 0 4.1 · 105

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field approximations, whose foundations are similar to those presented in Section 5.3. The conductivities of the CaZrO3/CaSZ eutectic produced by directional-solidification followed the predictions for a simple microstructure consisting of an ordered stacking of oxygen-conducting (cubic CaSZ) whose conductivity at 1000 K is 3.5 · 104 X1 cm1 at 1000 K [224] and non-conducting (CaZrO3 with a conductivity of 1.7 · 109 X1 cm1 at 1000 K [226]) phases. This representation leads to predictions of effective conductivity for the aligned eutectic given by the direct and inverse ‘‘rule of mixtures’’ when the electric field is parallel or perpendicular to the lamellae, respectively, which stand in good agreement with the experimental results parallel to the lamella (Table 7.4). The differences between the model and the experimental data in the perpendicular direction were attributed to some misorientation in the lamellae, as discussed in [224]. The conductivity of the sintered eutectic with a granular microstructure computed with the effective medium approximation [227] was very close to the experimental one (Table 7.4) although the model assumed a simple microstructure formed by a 41 vol.% random dispersion of conducting spherical particles of CaSZ embedded in a continuous insulating CaZrO3 matrix. Predictions based in the effective medium approximation for fibrous MgO/MgSZ eutectics showed a weak anisotropy [228,229], but this was not found experimentally (Table 7.4), and these differences were again explain by the microstructural disorder associated with the eutectic grains. Some potential applications of DSE as a result of the good thermo-mechanical properties, corrosion resistance and ionic conductivity are micron-size thin electrolytes for intermediate temperature SOFC, Nerst glower elements, and high temperature heating elements [27,225,230]. YSZ Nerst lamps are stable to very high temperatures (incandescence temperatures) in air but porous ceramics have to be used due to the poor thermal shock resistance of ZrO2. However, dense rods of YSZ/Al2O3 DSE fabricated by the LFZ method have been proved to glow at 1600 C for long periods without any deterioration of their conductivity or mechanical properties. Microstructural coarsening was observed after 160 h of operation but the rods retained their structural integrity [27]. The better mechanical and thermal shock resistance of DSE oxides may compensate for the lower operation temperature of the eutectics. Ionic conductivity was measured in Al2O3/YSZ DSE rods with TDI microstructure over the temperature range of 300–1650 C [27]. The results are given in Fig. 7.13, which shows the typical behavior of conducting YSZ with lower activation energy (0.8 eV) above 900 C and higher activation energy (1.04 eV) at lower temperatures (see also Table 7.4). It is important to realize that the conductivity of Al2O3/YSZ DSE is only one order of magnitude lower than that of YSZ and that it could be improved by a factor of two (reaching the theoretical values of the mean-field approximation) if the connectivity between the YSZ domains were improved. In conclusion, the conductivity of some directionally solidified eutectics based on YSZ, which possess excellent mechanical properties and corrosion resistance, has been characterized in recent years. Unfortunately, an improvement in conductivity associated with small size effects has not yet been found in these composites whose conducting properties can be explained by a mean-field approximation. A highly anisotropic DC conductivity has been reported for the lamellar CaZrO3/CaSZ eutectic, but the high stabiliser content in the zirconia phase and its low volume fraction leads to ionic conductivity along the growth axis which is about two orders of magnitude lower than the best YSZ ceramics. The fibrous MgO/MgSZ eutectic shows better electrical conduction but it has yet to be

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Fig. 7.13. Ionic conductivity of YSZ/Al2O3 DSE in the as-grown condition and after a thermal treatment at 1600 C [27].

proven that the improvement in mechanical strength introduced by the MgO fibers leads to a material suitable for thin film electrolyte production. Best achievements were obtained in the Al2O3/YSZ eutectics with TDI microstructure grown by LFZ methods. The ionic conductivity of these compounds was good enough to consider applications such as electrolytes for SOFC. For example, the maximum required area specific resistance for electrolytes of 0.15 X cm2 for these devices could be achievable with electrolyte layers of about 5 lm, a goal that seems not too difficult to reach. 7.5. Bioeutectics A new procedure was developed to obtain strong macroporous bioactive ceramics for human bone replacement. The material (Bioeutectic) was prepared by slow solidification

Fig. 7.14. SEM micrograph showing the colony microstructure of the wollastonite–tricalcium phosphate eutectic. (Reprinted by permission of Elsevier [232].)

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of the wollastonite–tricalcium phosphate eutectic system [231] and is composed of two phases, the pseudowollastonite and the a-tricalcium phosphate, which presents a morphology of eutectic colonies, as depicted in Fig. 7.14. This compound is reactive in simulated body fluid [34] and in human parotid saliva [232] and transforms into apatite and carbonate-hydroxiapatite-like phases, respectively. The transformed material is a macroporous bioactive material, which is expected to promote new bone ingrowth. 8. Concluding remarks The comprehensive review of the recent developments in DSE ceramic oxides presented in these pages has shown that they are highly structured composite materials with a dense and homogeneous microstructure, which determines the mechanical and functional properties. Several areas of remarkable successes were achieved, particularly in the last 15 years, and a number of key issues remain open. Both the achievements and the shortcomings are briefly discussed in the last section of the review, and the necessary breakthroughs as well as the emerging areas of research are noted. Until the late 1970s, most DSE oxides were grown by the Bridgman method, which is still optimum for large volume samples. The modest thermal gradients inherent in this method limited, however, the growth rate and the types of microstructure, which could be achieved with a given eutectic composition. Since the early 1990s, axial thermal gradients several orders of magnitude higher were obtained with new processing techniques based on the growth-from-meniscus methods (such as LFZ, EFG, and l-pD) where either lamps, lasers of RF were used as heating sources. These methods are nowadays readily available for growing DSE oxides whose microstructures have been tailored for specific applications by controlling the growth rate. However, the relationships between thermal gradients, growth rate and phase size imposed some limitations on sample processing and different growth methods have to be found for each particular need. Moreover, recent developments in processing have opened new possibilities for DSE oxides. They include the use of fast quenching methods to manufacture nanoeutectic oxides, i.e., eutectics with phase dimensions in the nm range, and the application of diode-laser technologies to the surface processing of large plates at high growth rates. The manufacturing of new microstructures was coupled with the detailed characterization of the growth habits of each eutectic phase and the nature of the interfaces, which play a dominant role in the eutectic properties as a result of their large area fraction. The crystallographic directions of eutectic growth and the crystallographic relations between phases are nowadays well established in most of the eutectic systems (and microstructures) of interest. In addition, the thermo-elastic residual stresses which develop upon cooling after solidification were determined by sophisticated measurement techniques (Xray, neutron diffraction and piezospectroscopy) and by simulation tools based on meanfield methods, which provided a complete picture of their origin and development. New developments in processing and microstructural characterization have led to a deeper knowledge of the relationship between the microstructure and the mechanical behavior and, as a result, DSE oxides with optimized microstructures for structural applications have been manufactured. In particular, the strength Al2O3–YAG DSE with submicron interphase spacing can reach 2 GPa at ambient temperature, and most of the strength is retained up to 1900 K, while Al2O3–YAG and Al2O3–EAG DSE with large interphase spacing made up of a single-crystal network of both eutectic phases stand

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among the oxides with best creep resistance at 1900 K. More modest (although still outstanding) ambient temperature strength, creep resistance and strength retention at high temperature were reported for Al2O3–YSZ DSE, whose toughness was approximately twice that of Al2O3–YAG. In addition, these eutectic microstructures showed very limited homogeneous phase coarsening even at temperatures approaching the eutectic point, excellent resistance to chemical attack in moist environments, and their mechanical strength was not impaired by subcritical crack growth at high temperature, as observed, for instance, in single-crystal Al2O3. As a result of this combination of properties, DSE oxides stand as the best available structural materials for applications at very high temperature (>1400 C), and feasibility investigations are under way to use these materials in a new generation of gas turbines which operate at 1700 C [89]. Examples of combustor liners and hollow turbine nozzles machined from directionally solidified ingots are shown in Fig. 8.1.

Fig. 8.1. Al2O3–YAG components for gas turbines mechanized from a directionally solidified ingot. (a) combustor liners, (b) hollow turbine nozzle. (Courtesy of Prof. Y. Waku.)

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Of course, there are still important restrictions on the widespread application of DSE oxides as structural materials. From the processing viewpoint, the relationships between thermal gradient, growth rate and microstructure size impose limitations of the sample dimension and/or microstructural characteristics. Bridgman methods are optimum if large volume samples are desired although the relatively modest thermal gradients inherent in this method imply low growth rates and consequently large interface spacing, which may not be the best in terms of strength and hardness. On the contrary, the growthfrom-meniscus methods induce large thermal gradients and admit high growth rates, leading to eutectics with small interphase dimensions, but the large thermal stresses associated with steep thermal gradients limit the specimen thickness to a few mm. In addition, the Achilles heel of DSE oxides for structural applications is their low toughness. DSE oxides are prone to catastrophic failure and their strength is very sensitive to the nucleation of defects (for instance, by localized coarsening of the microstructure at high temperature as a result of the reaction with Si-containing species in the environment). Increasing the toughness of DSE can only be attained by engineering the interface between domains to promote crack arrest and deflection as the eutectic components are brittle oxides with low toughness. However, any reduction of the interface strength will compromise their outstanding strength and microstructural stability at high temperature. Another option for DSE in structural applications is in coatings. DSE coatings may provide their excellent corrosion and abrasion resistance as well as strength, while the ductile substrate imparts the structural integrity. The deposition of DSE oxide coatings by laser surface melting on ceramic and metallic substrates has been demonstrated recently, and this technology is a promising research line. Functional applications of DSE oxides are still in the infancy in comparison with structural ones, and research efforts in this area are still very recent. The excellent chemical and thermal stability of DSE oxides, together with the good mechanical properties described above, are very important for many functional applications and they are added to the advantages provided by the synergistic combination of different phases within the same material. For instance, channeled Ni–YSZ and Co–YSZ cermets produced from DSE oxide precursors have been proposed for use in SOFC. The lamellar microstructure and the strong bonding between the YSZ and the metal prevent the coarsening of the metal particles in working conditions, and improve the efficiency and long-term stability of SOFC under operation. Promising attempts at using DSE oxides as structured substrates for patterned thin films, ionic conductor composites, and optical waveguides have been reported but comprehensives studies of the feasibility of these developments is lacking. In particular, applications, which need phase continuity extended in space, such as those involving light or electrical transport, are limited by the small grain size in DSE oxides with regular microstructure to applications in microdevices. However, the problem of the small grain size of regular eutectics, induced by eutectic ability to accommodate growth fluctuations, has not yet been solved satisfactorily. Although the basic principles controlling directional solidification of eutectic structures are well known, further improvements should be guided by numerical simulations of the eutectic growth process. This complex task, which requires the coupling of different physical phenomena (solid and fluid mechanics, heat conduction and radiation, phase change), is essential to produce eventually large samples at high growth rates (and hence with small domain size) and regular microstructures without grain boundaries, where phase continuity can be ensured throughout the eutectic samples.

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Many other functional applications of DSE oxides are being explored. For instance, soft magnetic materials with high initial permeability, low coercive field and high electrical resistance can be produced from lamellar ferromagnetic and insulating eutectic composites with possible applications as magnetic flux concentrators in transformers, generators, motors, dynamos and switches and microwave technology. Another area of research is the manufacture of pseudoeutectic materials by removing one of the eutectic phases in TDI microstructures. This leads to a single crystalline microstructure of one eutectic phase with interconnected porosity, which can be infiltrated with another phase with different properties to create new materials with an eutectic microstructure. Acknowledgements The authors are indebted to their colleagues of the Departamento de Ciencia de Materiales (Universidad Polite´cnica de Madrid) and of the Instituto de Ciencia de Materiales de Arago´n (CSIC-Universidad de Zaragoza) for their help during this work. The useful discussions with J.Y. Pastor, C. Gonza´lez, A. Martı´n, J. Segurado from the Polytechnic University of Madrid and with R.I. Merino, J.I. Pen˜a and A. Larrea from the ICMA in the course of this work are especially appreciated. Some of the results reported in this paper were obtained in research projects financed by the Spanish Government under grants MAT1997-673, MAT2000-1533, MAT2003-6085, and MAT2003-1182, and by the Comunidad de Madrid through the grant GR/MAT/357/2004. Their support is gratefully acknowledged. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]

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