Thermal stability of nanocrystalline Fe–Zr alloys

Thermal stability of nanocrystalline Fe–Zr alloys

Materials Science and Engineering A 527 (2010) 3572–3580 Contents lists available at ScienceDirect Materials Science and Engineering A journal homep...

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Materials Science and Engineering A 527 (2010) 3572–3580

Contents lists available at ScienceDirect

Materials Science and Engineering A journal homepage:

Thermal stability of nanocrystalline Fe–Zr alloys K.A. Darling a , B.K. VanLeeuwen b , C.C. Koch b , R.O. Scattergood b,∗ a b

U.S. Army Research Laboratory, Weapons and Materials Research Directorate, RDRL-WMM-B, Aberdeen Proving Ground, MD 21005-5069, USA Department of Materials Science and Engineering, NC State University, 911 Partners Way, Room 3000, Raleigh, NC 27695-7907, USA

a r t i c l e

i n f o

Article history: Received 5 January 2010 Received in revised form 10 February 2010 Accepted 11 February 2010

Keywords: Mechanical alloying Nanostructured materials Grain growth

a b s t r a c t Fe–Zr nanocrystalline alloys with an as-milled grain size less than 10 nm were synthesized by ball milling. The microstructure changes due to annealing were characterized using X-ray line broadening, microhardness, focused ion beam channeling contrast imaging, and transmission electron microscopy (TEM). Additions of 1/3 to 4 at.% Zr stabilized nanocrystalline grain sizes at elevated annealing temperatures compared to pure Fe. With 4 at.% Zr, a fully nanocrystalline microstructure with a TEM grain size of 52 nm was retained at temperatures in excess of 900 ◦ C. Alloys with lower Zr contents showed less stability, but still significant compared to pure Fe. Bimodal nano–micro grain size microstructures were also observed. © 2010 Elsevier B.V. All rights reserved.

1. Introduction A reduction of the excess grain-boundary free energy provides a very large driving force for grain growth in nanocrystalline metals. The effective pressure P that is the driving force for grain growth is based on the expansion of a curved boundary [1] P=

C r


C is a numerical constant of order 1,  is the grain-boundary free energy (hereafter referred to as grain-boundary energy) and r is the radius of curvature, which is proportional to the grain size. P will be very large as the grain size is reduced to the nanocrystalline size scale (<100 nm). It has been shown that pure nanocrystalline metals such as Al, Sn, Pb, Zn and Mg can exhibit extensive grain growth at room temperature [2–4]. Metals with higher melting points, such as Co, Ni and Fe, are not exceptions to this phenomenon and show rapid grain growth over moderate temperature ranges, resulting in grain sizes in the micron size range at annealing temperatures of 50% or less of melting temperature [5–7]. This thermally driven grain-size instability limits the processing and applications of nanocrystalline metals. Therefore, it is important to develop nanocrystalline alloys that are resistant to grain growth at elevated temperatures.

∗ Corresponding author at: Department of Materials Science and Engineering, NC State University, 911 Partners Way, Room 3000, Raleigh, NC 27695-7907, USA. Tel.: +1 919 515 7843; fax: +1 919 515 7747. E-mail addresses: [email protected] (K.A. Darling), [email protected] (B.K. VanLeeuwen), carl [email protected] (C.C. Koch), [email protected], ron [email protected] (R.O. Scattergood). 0921-5093/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2010.02.043

A number of investigations on the grain-size stability of nanocrystalline alloys have been conducted based on controlling the parameters in the equation for velocity v of a grain boundary undergoing grain growth [1,8]  = MP = Mo exp

 −Q  C m RT



M is the grain-boundary mobility and Qm is the activation energy. Two approaches have been used to reduce grain growth at higher temperatures. These are the kinetic mechanism that involves impediment of the boundary motion by pinning, and the thermodynamic mechanism that involves reducing  to zero by solute segregation. Grain-boundary pinning can be achieved using second phases [9], pores [10], chemical ordering [11] or solute drag [12]. Pinning can reduce grain growth at elevated temperatures. However, the mobility is thermally activated, and pinning forces resisting boundary motion can be overcome by thermal activation at higher temperatures [1]. If precipitates are not formed, the thermodynamic approach can be more effective at high temperatures because the reduction in  due to solute segregation is expected to have weaker temperature dependence [13]. Addition of solute atoms that segregate to the grain boundaries can lower the grain-boundary energy. Hondros and Seah [14] reported a decrease in  with solute additions for several binary alloys. The Gibbs interface equation [15] is the basis for the thermodynamic effect d = −s ds


 s is the segregated solute excess, which is the excess concentration relative to the bulk equilibrium of solute atoms per unit area of grain-boundary interface, and s is the solute chemical potential.

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The initial slope of the  vs. solute concentration curves in [14] was more negative the greater the difference in atomic size between an oversize solute atom and the solvent atom. This suggests that the enthalpy change due to size-misfit elastic strain energy will cause solute segregation to grain boundaries. Weissmuller [15,16] derived a thermodynamic model for grain-size stabilization. The free energy change in a closed system due to a change in grainboundary area dA is dG = dA, therefore, a decrease dA < 0 (grain growth) with  > 0 will decrease the free energy [17,18]. However, the segregated solute excess  s dA must be transferred into the grains and the corresponding change ds > 0 will decrease  according to Eq. (3). This reasoning leads to the equation  = o + s [Hseg − T Sseg ]


 o is the non-segregated (intrinsic) grain-boundary free energy,  s is the segregated solute excess and Hseg and Sseg are the enthalpy and entropy changes, respectively, associated with the segregation of a solute atom from a matrix site into a grainboundary site. Thus, when [Hseg − TSseg ] < 0, solute segregation to grain boundaries is favored and  decreases. This is the basis of the thermodynamic mechanism for grain-size stabilization. If the condition  = 0 is achieved, then a metastable equilibrium is reached and there is no longer a driving force for grain growth. In order to achieve this thermodynamic stabilization effect, solute segregation must take precedence over competing processes such as precipitation of solute-containing second phases. A thermodynamic mechanism for grain-size stabilization was proposed by Weissmuller [15,16], Liu and Kirchheim [17], Kirchheim [18], Millett et al. [19] and Beke et al. [20]. The general consensus arrived at in these studies is that a metastable equilibrium grain size can exist in alloy systems due to solute segregation to grain boundaries. This was concluded based on the intrinsic grain-boundary energy and the segregation enthalpy change due to a solute excess in the form of a grain-boundary monolayer. There are a number of experimental studies that demonstrate stabilization of a nanocrystalline grain size by solute additions [21]. This has been reported for Nb–Cu [22], Ni–P [23], RuAl–Fe [24], Ti–Cu [25], Y–Fe [26], TiO2 –Ca [27] and Ni–W [28] and Pd–Zr [8]. Krill et al. [8] reported nanocrystalline grain-size stabilization in ball-milled Pd–Zr alloys up to annealing temperatures in excess of 90% of the melting temperature. Malow and Koch [7,29] showed that grain growth in ball-milled nanocrystalline pure Fe takes place rapidly during isothermal annealing. In addition, a large change in the grain size occurs for annealing temperatures above about 500 ◦ C. This temperature is a threshold temperature for extensive grain growth in pure nanocrystalline Fe, and it is a baseline for improvement of grain-size stability for nanocrystalline Fe-based alloys. Darling et al. [30] reported that Fe 1 and 4 at.% Zr alloys produced by ball milling are resistant to grain growth up to annealing temperatures of 1373 ◦ C, which is in excess of 90% of the melting temperature. The motivation for this initial Fe–Zr study followed from the stabilization effects reported earlier by Krill et al. [8] for Pd–Zr alloys. Zr solutes in Fe have a size misfit of +28% and a segregation enthalpy Hseg = −Eel = −92 kJ/mol where Eel is the elastic misfit strain energy for Zr solutes in Fe. This can be compared to a +11% size misfit and Hseg = −Eel = −31 kJ/mol for Zr solutes in Pd [31]. Furthermore, Zr has very limited equilibrium solubility in Fe up to high temperatures (less than 0.5 at.% at 1300 ◦ C), whereas the solubility of Zr in Pd increases from 12 at.% at low temperatures to 16 at.% at high temperature. The X-ray grain size for Fe–Zr showed a gradual increase up to about 800 ◦ C followed by stabilization at a 50 nm grain size up to 1373 ◦ C for alloys with 1 and 4 at.% Zr. The general trends followed those reported for Pd–Zr alloys [8]. Definitive microstructure characterization of the grain-size distributions was not done in the previous work reported by Krill


et al. [8], or by Darling et al. [30]. The results and conclusions were based entirely on X-ray grain-size data with the exception of one TEM micrograph in [8]. This does not necessarily identify the true nature of the grain-size distributions. In the present study, detailed microstructure characterization in annealed Fe–Zr alloys will be presented using X-ray diffraction, microhardness, optical microscopy, focussed ion beam channeling contrast imaging and transmission electron microscopy. 2. Experimental procedure Ball milling was used to produce non-equilibrium solid solution Fe–Zr alloys containing 0, 0.33, 1 and 4 at.% Zr. Limited results were also obtained for Fe–10 at.% Zr. Hardened steel vials and 440C stainless steel balls were used with a Spex 8000 shaker mill and Alpha Aesar Fe and Zr powders (−325 mesh, 99.9 and 98.5% purity, respectively) to produce the alloys. The ball to powder mass ratio was maintained at 10:1. Vials were sealed in an argon atmosphere (O2 <1 ppm) prior to milling. Milling took place for 20 h at room temperature. Powders with a particle-size range of 20–100 ␮m and a nanocrystalline grain size on the order of 5–10 nm resulted. Xray diffraction analysis of the ball-milled and annealed powders was performed using Cu K␣ radiation and a Rigaku DMax/A X-ray diffractometer with a nominal instrumental broadening of 0.1◦ . Cu K␣2 peak stripping and background subtraction were accomplished by using the Xpowder software ( The average grain size was calculated from diffraction line broadening using the Scherrer equation [32]. This is an approximation and does not include the effect of lattice strain to the broadening if it is present. Hereafter, this will be denoted the X-ray grain size. Disk specimens were prepared by uniaxial cold pressing as-milled powders at 3.5 GPa in a 6.35 mm diameter tungsten carbide die. These were subsequently heat treated in groups at 530, 700, 828, 870, 913 and 1173 ◦ C for 60 min under an Ar/2%H atmosphere. A few selected heat treatments were done at 1373 ◦ C. The heat-treated samples were mounted in Epothin, a room-temperature curing epoxy. Samples were polished to a mirror finish for Vickers hardness tests performed using a Buehler Micromet II. Hardness tests were performed on individual particles within the compacts using loads appropriate to avoid influences of the indentation plastic zone with particle boundaries. A particle diameter-to-indent depth of at least 10:1 was maintained for the hardness tests. Optical microscopy samples were polished to a mirror finish and then etched for approximately 45 s at room temperature in a Nitol solution containing 98% ethanol and 2% nitric acid. Samples were imaged using a Zeiss inverted microscope and Axio Vision LE software. Image J software was used to analyze optical images for average grain size and percent area of micron-size grains. Focused ion beam channeling contrast imaging was done on individual powder particles using a FEI Quanta 200 3D FIB system. Transmission electron microscopy samples were obtained using focused ion beam machining and Hbar film lift-outs from the individual power particles. The H-bar technique is described in [33]. The extracted TEM samples were examined in a Hitachi HF2000 electron microscope operating at 200 kV. 3. Results Fig. 1 shows X-ray grain size vs. isochronal (1 h) annealing temperature for pure Fe and Fe–0.33, 1 and 4 at.% Zr alloys. The plots include data reported for pure Fe and Fe–1 and 4 at.% Zr in the previous study [30]. Fig. 1 shows that at approximately 700 ◦ C, the grain size for pure Fe has reached a value of 6 ␮m (determined in this case using optical microscopy). By comparison, the Fe–Zr alloys are nanocrystalline at 700 ◦ C. At 800 ◦ C, grain growth for the Fe–1


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Fig. 1. The X-ray grain size vs. isochronal annealing temperature for 1 h anneals with data for pure Fe and Fe–1 and 4 at.% Zr taken from [30]. Data for Fe–0.33, 1 and 4 at.% Zr obtained in the current investigation is included and data for Fe–Ni and Fe–Cr has been added from [33]. The pure Fe data includes is a compilation from the literature.

and 4 at.% Zr alloys ceases altogether at a grain size of 50 nm, while the grain size for Fe–0.33 at.% Zr reaches 75–100 nm. Based on the X-ray diffraction results, the grain sizes of the Fe–1 and 4 at.% Zr alloys remain nanocrystalline up to a temperature of 1373 ◦ C. This remarkable thermal stability was attributed to Zr segregation to grain boundaries and the thermodynamic stabilization mechanism [30]. For comparison, data for Fe–1 at.% Ni and Fe–10 at.% Cr [33] are included in Fig. 1. Since both Ni and Cr have atomic sizes very close to Fe, significant grain-boundary segregation and thermodynamic stabilization due to elastic strain energy is not expected. Consistent with this, Fig. 1 indicates no effect of Ni and only a smaller effect of Cr on stabilization. Isothermal annealing curves (not presented here) for Fe–Zr alloys containing 0.33, 1, 4 and 10 at.% Zr showed that the X-ray grain size increases rapidly and then approaches a limiting value as a function of annealing time. At 500 ◦ C, there is a monotonic decrease in the limiting grain size with increasing Zr content. At 700 ◦ C, precipitation occurred in the Fe–10 at.% Zr alloy and the limiting grain size was larger than that for the 1 or 4 at.% Zr alloys. Loss of thermal stability as a result of precipitate formation is often observed for nanocrystalline alloys, and no further results will be given for the Fe–10 at.% Zr alloy. Fig. 2 shows the Vickers microhardness change vs. isochronal annealing temperature for pure Fe and the Fe–Zr alloys. The roomtemperature values are the as-milled hardness. The hardness for all compositions shows a distinct downward trend above 530 ◦ C.

Fig. 2. Vickers hardness (25 g load for 15 s) vs. 1 h isochronal annealing temperature for pure Fe and Fe–Zr alloys.

This is most dramatic for pure Fe, which undergoes extensive grain growth as seen in Fig. 1. The hardness for the alloys is elevated with respect to pure Fe throughout the annealing temperature range. At the 1173 ◦ C annealing temperature, the hardness for all alloys drops to less than 3 GPa. The progressive decreases in hardness with increasing annealing temperatures in Fig. 2 are not consistent with retention of a nanocrystalline grain size on the order of 50 nm up to 1373 ◦ C, as was presumed based on the X-ray grainsize data in Fig. 1 [30]. More definitive characterization of the microstructure, described next, is needed to reveal the nature of these changes. Fig. 3 shows optical micrographs of the microstructure evolution in the Fe–0, 0.33 and 1 at.% Zr alloys annealed at the temperatures indicated. The large cracks in the samples are due to incomplete bonding between the powder particles. After etching, contrast in the form of dark gray regions and white regions was observed. Micron-scale grains could be distinguished in the white regions whereas no grain structure could be resolved in the darker regions. The latter were assumed to be submicron and/or nano-scale regions where the high density of etched grain boundaries produce darker contrast. This was verified by the subsequent focused ion beam contrast images. The optical micrographs are useful for revealing bimodal grain-size distributions over large areas. Fig. 3A and B show micrographs for pure Fe. At 530 ◦ C (Fig. 3A), no large micron-scale grains are present. At 700 ◦ C, large grains are present throughout the microstructure and an average grain size of 6 ␮m was obtained. The grain size was determined using software (Image J) that profiles the grain boundaries and determines the average area per grain. The grain size is taken as the radius of an equivalent circle. Fig. 3C shows a micrograph for the Fe–0.33 at.% Zr alloy annealed at 700 ◦ C where micron-size grains are evident in a background of submicron/nanograins. Fig. 3D and E show micrographs for the Fe–1 at.% Zr alloy annealed at 700 and 913 ◦ C, respectively. No micron-size grains are present at 700 ◦ C. At 913 ◦ C, isolated regions of micron-size grains (white area in the upper right of Fig. 3E) can be observed. Fig. 3F shows a portion of the microstructure for the Fe–1 at.% Zr alloy annealed at 870 ◦ C, where several large grains can be isolated from the background region. Low-load Vickers indentations made in a large grain and in the background region in Fig. 3F (insets) gave values of approximately 3.5 and 7 GPa, respectively, consistent with a bimodal distribution of large and small grain sizes. The background was about 85% of the observed area, and the area-average hardness is 6.5 GPa, in reasonable agreement with Fig. 2. High-resolution microscopy described in the next sections is needed to identify details of these bimodal grain-size microstructures. Fig. 4A (inset) is a low magnification focused ion beam channeling contrast imaging (FIBCCI) micrograph of the etched surface of the Fe–0.33 at.% Zr alloy annealed at 913 ◦ C. Fig. 4B is a higher magnification FIBCCI micrograph taken from a focused ion beam (FIB) machined cross-section trench made within the shaded bar in Fig. 4A. The FIBCCI micrographs are images obtained using backscattered electrons produced by the ion beam. The FIBCCI contrast mechanism is due to changes in the grain orientations that cause variations in ion channeling efficiency, i.e., the light vs. dark contrast grains. It is clearly evident from Fig. 4B that a bimodal distribution of grain sizes is present wherein submicron-scale grains are layered between large micron-scale grains. Micro-porosity associated with incomplete particle bonding is also present in Fig. 4B. A notable feature of FIBCCI imaging is that it also allows for site-specific TEM sample preparation using the FIB machining lift-out technique. Fig. 5A and B are FIBCCI micrographs of Fe–1 and 4 at.% Zr alloys, respectively, annealed at 913 ◦ C. A large micron-size grain (dark) is evident in Fig. 5A surrounded by a distribution of much smaller grains that are in the nano-scale range. The large grain captured in this micrograph indicates the onset of abnormal grain growth

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Fig. 3. Optical micrographs for pure Fe and Fe–Zr alloys with the at.% Zr indicated, after annealing 1 h at the temperatures indicated.

Fig. 4. (A) Lower magnification FIBCCI micrograph for the Fe–0.33 at.% alloy annealed at 913 ◦ C for 1 h. The surface is etched. (B) Higher magnification FIBCCI micrograph from a FIB machined cross-section taken within the shaded bar in A.

(secondary recrystallization) in the Fe–1 at.% Zr alloy. In contrast, the microstructure in Fig. 5B is finer than that in Fig. 5A and is more uniform in appearance with no evidence of abnormal grain growth. These results, taken in conjunction with Figs. 2 and 3, indicate that thermal stabilization of a uniform nanocystalline grain structure in Fe–Zr alloys is possible, and that the stabilization effect will be promoted by increasing the Zr content at a given annealing temperature. Fig. 6A–C shows high magnification FIBCCI micrographs (near the resolution limit) for Fe–0.33, 1 and 4 at.% Zr alloys, respectively, annealed at 913 ◦ C. In Fig. 6A the tip of a nanocrystalline region of elongated grains protrudes into a micron-scale grain. The major and minor axes of the nano-grains are approximately 300 and 100 nm, respectively. Fig. 6B is a nanocrystalline region within a bimodal nano–micro grain distribution with elongated nano-grains having major and minor axes measuring approximately 250 and 75 nm, respectively. Fig. 6C shows a finer, uniform nanocrystalline region compared to Fig. 6A and B, with equiaxed grains measuring approximately 50–100 nm. No abnormal grain growth was observed in the Fe–4 at.% Zr alloy. Transmission electron microscopy (TEM) samples were prepared by first obtaining FIBCCI micrographs from FIB machined planar trench sections, and then selecting a suitable area for prepar-


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Fig. 5. FIBCCI micrographs for alloys annealed at 913 ◦ C for 1 h. (A) Fe–1 at.% Zr and (B) Fe–4 at.% Zr. The dark region in the center is a microvoid.

Fig. 10 is a Z-contrast TEM micrograph of the Fe–4 at.% Zr alloy annealed at 913 ◦ C. This was taken with a high angle annular dark field detector. The image contrast intensity is proportional to the atomic number, although channeling effects are possible [34]. The bright amorphous region is a Pt cap deposited to protect the underlying microstructure. Low atomic number phases would appear dark and high atomic number phases would appear bright. The micrograph in Fig. 10 does not show any sharp dark/light contrast regions that would be indicative of low-Z (oxide) or high-Z (Zr rich) phases. The inset in Fig. 10 is the X-ray diffraction pattern. X-ray diffraction scans taken from annealed Fe–7 and 10 at.% Zr alloys in [30] indicate that the precipitated phase is Fe2 Zr. None of the fundamental peaks for this phase or other equilibrium phases were present in the X-ray diffraction pattern in Fig. 10. The X-ray pattern, combined with the Z-contrast micrograph, provides evidence against the formation of grain boundary or lattice second phases in the Fe–4 at.% Zr alloy annealed at 913 ◦ C. Fig. 11A is a FIBCCI micrograph of the Fe–4 at.% Zr alloy annealed at 1173 ◦ C. Three large micron-scale grains with different orientation contrast meet at a triple point. The microstructure does not contain nanocrystalline regions. This shows that the hardness values in Fig. 2 for the Fe–Zr alloys annealed at 1173 ◦ C are determined by grain-size distributions with micron grain sizes. Based on optical micrographs, the average grain size for the Fe–Zr alloys annealed at 1173 ◦ C was 40 ␮m. Dispersed within the large grains in Fig. 11A are nano-scale precipitates shown in the bright field TEM micrograph in Fig. 11B. The precipitates are approximately spherical in shape with sizes ranging down to 50 nm or less. Fig. 11B also captures a large precipitate on the order of 400 nm in size. In situ energy dispersive spectroscopy (EDS) was done on this precipitate and in the adjacent matrix region, as indicated by the circles. The EDS results showed that the precipitate composition was nominally 57 at.% Fe and 42 at.% Zr, which is close to the composition for the equilibrium phase Fe2 Zr. The surrounding matrix composition was nominally 96 at.% Fe and 3 at.% Zr.

4. Discussion ing TEM samples by the FIB H-bar film lift-out technique. This was necessary for obtaining TEM samples that include both the nanoscale and micro-scale grain regions in bimodal microstructures. TEM samples were obtained using non-compacted, heat-treated Fe–Zr alloy powders, and selecting a single particle (about 50 ␮m in diameter) for FIBCCI imaging and subsequent site-specific TEM sample preparation using H-bar lift-outs. Fig. 7A is a bright field TEM micrograph of the Fe–0.33 at.% Zr alloy annealed at 913 ◦ C. Consistent with the optical and FIBCCI images, the microstructure consists of micro-grains and elongated nano-grains. The diffraction pattern (inset) corresponds to a bcc crystal structure and the pattern shows spots with diffuse arcs suggestive of texturing. The inset Fig. 7B is a higher magnification bright field image of the elongated nano-grains in Fig. 7A. These have major and minor axes measuring approximately 60 and 200 nm, respectively. Fig. 8 is a bright field TEM micrograph of the Fe–4 at.% Zr alloy in the as-milled condition before annealing. The X-ray grain size was 5.4 nm, while the grain distribution in Fig. 8 shows a range of sizes up to about 20 nm. Fig. 9 is a bright field TEM micrograph of the Fe–4 at.% Zr alloy annealed at 913 ◦ C. The grains are equiaxed and polyhedron in nature. The grain-size distributions shown by the insets in Fig. 9 are relatively narrow, indicating that only a small fraction of the microstructure is made up of grains larger than 100 nm for either the number average or the volume average distributions. The average TEM grain size was 52 nm by number fraction, and 57 nm by volume fraction, as indicated in Fig. 9.

In the previous study on Fe–Zr alloys [30], the characterization method used to reveal the grain-size stabilization effect for Zr additions was the grain size derived from X-ray line broadening. Based on X-ray grain-size data like that shown in Fig. 1 for the Fe–Zr alloys, it was concluded in [30] that retention of a 50 nm nanocrystalline grain size is possible for annealing temperatures up to 1373 ◦ C with additions of only 1 at.% Zr. This remarkable behavior was attributed to Zr segregation to grain boundaries and thermodynamic stabilization. However, the microstructure characterization results obtained in the work reported here show that bimodal grain-size distributions are present at 913 ◦ C in the Fe–0.33 and 1 at.% Zr alloys, while nanocrystalline regions are not retained in any of the alloys at 1173 ◦ C. The relationship between hardness, grain size and development of bimodal grain-size distributions obtained in the current work is summarized using a Hall–Petch (HP) plot in Fig. 12. The solid line is the HP correlation for pure nanocrystalline Fe reported by Shen et al. [35], and the dashed lines indicate the range of scatter in their data. The Fe–Zr nanocrystalline grain sizes used in Fig. 12 are X-ray grain sizes in the lower annealing temperature regime where they are valid, or grain sizes derived from micrographs at higher annealing temperatures. The AM-Fe data point (cross) is the as-milled hardness for pure Fe obtained here and the remaining AM points correspond to the as-milled alloys indicated. For the initial 530 ◦ C anneal (encircled points), the grain size of the alloys increases without a corresponding drop in hardness. At higher annealing temperatures, the grain size increases and the

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Fig. 6. High magnification FIBCCI micrographs for Fe–Zr alloys annealed at 913 ◦ C for 1 h. (A) Fe–0.33 at.% Zr, (B) Fe–1 at.% Zr and (C) Fe–4 at.% Zr.

Fe–Zr hardness decreases. The latter follows the general trend of the HP correlation for Fe, with higher hardness values for increasing Zr content. The numbers next to selected data points are the esti-

Fig. 7. (A) Bright field TEM micrograph for Fe–0.33 at.% Zr annealed at 913 ◦ C for 1 h. Inset is the diffraction pattern. (B) High magnification of a nanocrystalline region in (A).

mated area percentages of nanocrystalline regions in the bimodal microstructures obtained from optical micrographs. Large grains are not included in the nano-scale grain sizes plotted in Fig. 12. The exception is the grains for samples annealed at 1173 ◦ C where only micron-size grains in the range 40 ␮m were present. At 700 and 913 ◦ C (encircled points) the hardness drops more steeply than the HP trend would suggest due to increasing fractions of micronscale grains in bimodal distributions. At 1173 ◦ C (encircled points)

Fig. 8. Bright field TEM micrograph for the as-milled Fe–4 at.% Zr alloy. Inset shows the diffraction pattern.


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Fig. 9. Bright field TEM micrograph of the Fe–4 at.% Zr alloy annealed at 913 ◦ C for 1 h. The insets show the volume average (left) and number average (right) grain-size distributions determined using 400 grains from multiple micrographs.

nanocrystalline regions are not retained and the hardness would follow an HP correlation for conventional micron-scale grains. The origin of the incorrect nano-scale X-ray grain size values derived for the Fe–Zr alloys after high-temperature annealing is not resolved. Residual elastic strain is a possibility, although this would not be expected after high-temperature annealing. The transition from fcc to bcc Fe when cooling from higher temperature might modify and possibly enhance effects of Zr-induced elastic strains. In addition, when bimodal grain-size distributions are present X-ray line broadening captures only the contribution from the finest grain-size nanocrystalline regions. This was conclusively demonstrated in the work reported by He et al. [36]. The apparent discrepancies in the physical significance of the X-ray grain-size data obtained for the annealed Fe–Zr alloys reinforces the need to provide more definitive microstructure characterization when addressing phenomena such as thermal stabilization. As a final point of discussion, we concluded earlier [30] that thermodynamic stabilization is the mechanism responsible for high-temperature grain-size stabilization in nanocrystalline Fe–Zr alloys. Although the results presented here show that the conclusions based only on X-ray grain-size data in [30] are not correct at higher temperatures, there is nothing inconsistent with a ther-

Fig. 10. Z-contrast TEM micrograph of the Fe–4 at.% Zr alloy annealed at 913 ◦ C for 1 h. The inset shows the X-ray diffraction scan.

Fig. 11. Micrographs for the Fe–4 at.% Zr alloy annealed at 1173 ◦ C for 1 h. (A) FIBCCI micrograph. (B) Bright field TEM micrograph. The circles show the location for EDS spectra.

Fig. 12. Hall–Petch plot for pure Fe and annealed Fe–Zr alloys as described in the text. Annealing temperatures in ◦ C for the sets of encircled points are indicated.

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Table 1 Values from [31] and [41]. Solute

AS (J/m2 )

Eel (kJ/mol)

Zr Hf Ni Ta Cr Y

2.0 2.15 2.45 3.15 2.3 1.12

92 92 1 61 0 95

Hmix (kJ/mol) −25 −21 −2 −15 −1 −1

modynamic grain-size stabilization mechanism for Zr solutes in Fe. The micrographs in Fig. 11 indicate that extensive grain growth has occurred after annealing Fe–4 at.% Zr at 1173 ◦ C while at the same time nano-scale precipitates are present. This argues against a kinetic stabilization effect due to precipitate particles. A direct confirmation for Zr segregation on grain boundaries, concomitant with stabilization of the grain size at higher temperatures, will require analysis of the grain-boundary structure and chemistry at the atomic scale. This remains as a challenge for future studies. However, additional justification for a thermodynamic stabilization mechanism in Fe–Zr alloys can be obtained using a thermodynamic model. The Wynblatt–Ku (WK) model [37,38] used for solute segregation to free surfaces is based on a nearest-neighbor regular solution model, and the parameters needed for evaluation are available in the literature. Based on this approach, we derived a modified version of the WK model by replacing the single interface layer for a free surface by double interface layers where the out-of-plane interfacial bonds account for the grain-boundary energy [39]. The result for the segregation enthalpy includes both a chemical term Hchem and the elastic size-misfit term Eel > 0

Fig. 13. Grain-boundary energy vs. Zr solute atom fraction segregated to the grainboundary interface for the solutes indicated. The intrinsic grain-boundary energy for pure Fe at xA∗ = 0 is  o = 0.83 J/m2 [41].

Table 1 shows values from [31] for selected solutes in pure Fe. Fig. 13 is a plot using Eq. (6) for the solute-segregated grainboundary energy  vs. the atom fraction of solute xA∗ segregated on the grain-boundary interface layers. Curves for the oversize Zr, Ta and Y solutes are shown. The trends in such model results are

Hseg = Hchem − Eel Hchem = (As − Bs )(1 − ˛) −

8Hmix [zin (xA∗ − xA ) − zout (xA − 0.5) + ˛zout (xA∗ − 0.5)] z

A or B denote solute or solvent atoms,  s is surface energy,  is the molar interfacial area, z, zin and zout are coordination numbers for bulk, in-plane and out-of-plane interface bonds (z = zin + 2zout ), xA or xA∗ are the equilibrium bulk or interfacial solute atom fractions, Hmix is the equimolar (xA = xB ) enthalpy of mixing in the liquid state, and ˛ is the ratio of interface/bulk bond strengths (˛ = 0 is the WK model). For evaluation purposes we assume that the intrinsic grain-boundary energy  o =  s /3, which requires ˛ = 5/6 with 2/3 zin = z/2.  = vB NAVG where vB is the atomic volume and NAVG is the Avogadro number. Only nonequilibrium, oversize solutes at low bulk concentration in pure Fe (xA ≈ 0) will be considered. Eq. (5) can be combined with Eq. (4) using s = 2xA∗ / (double monolayer) to give  = o + s Hseg = o +


 s − s 6


Hmix (17xA∗ + 0.5) − Eel 3


The segregation entropy Sseg from Eq. (4) is not included in Eq. (6). Sseg includes entropy changes for solute in the matrix and in the grain boundary. The configurational entropy change for the matrix is on the order of RlnxA (dilute solution) and this can reduce the stabilization effect at higher temperatures. The grain-boundary interfacial entropy changes can compensate for the matrix configurational entropy change [37,38], but the details can be difficult to evaluate and will be discussed elsewhere [39]. For the cases of interest here where Eel is large, Hseg is a dominant effect at lower and intermediate temperatures. Moreover, the important effect of Hmix has mostly been ignored and our aim is to introduce this effect, which will be relevant over the entire temperature range.


the significant point since quantitative accuracy is not expected. Cr and Ni added to Fe have negligible size misfit in Fe and very small Hmix values, therefore these solutes would not be candidates for thermodynamic stabilization (Fig. 1 also shows that Cr and Ni have a minimal stabilization effect in Fe). A negative enthalpy of mixing can result in a minimum in the curves and the relative magnitudes of Eel and Hmix determine whether or not the  = 0 intersection occurs, i.e., complete thermodynamic stabilization is achieved. The plots in Fig. 13 are master curves for the stabilization effect in that increasing the amount of solute xA added to the solvent in small amounts does not significantly change the xA∗ intersection point at zero. It does however determine the minimum grain size at stabilization, and this follows directly from a solute mass balance. For the cases shown in Fig. 13, Zr and Y produce stabilization whereas Ta does not. The most favorable case occurs for a large Eel and a small or positive Hmix . If the solute and solvent are immiscible, a positive Hmix will result. While Y would be a very favorable choice for a solute that produces thermodynamic stabilization in Fe, grain-boundary embrittlement would be a concern based on Seah’s correlation [40]. Using these model-based predictions, Zr and Hf in Table 1 are equally good candidates as solutes to achieve thermodynamic stabilization in pure Fe. 5. Conclusions The thermodynamic grain-size stabilization mechanism is consistent with the strong thermal stabilization effects observed for ball-milled nanocrystalline Fe–Zr alloys. The bimodal grain-size distributions that form consist of nanocrystalline regions inter-


K.A. Darling et al. / Materials Science and Engineering A 527 (2010) 3572–3580

mixed with micron-scale grain regions that are produced by abnormal grain growth. X-ray grain-size estimates were found to be unreliable for Fe–Zr samples annealed above about 800 ◦ C. The grain-size stabilization effect can be significant, and a relatively narrow nanocrystalline grain-size distribution with a 52 nm TEM average grain size and no abnormal grain growth can be retained in a Fe–4 at.% Zr alloy after annealing at 913 ◦ C. In comparison, pure Fe would have a 12 ␮m grain size. The thermal stabilization effects observed have potential to facilitate high-temperature consolidation of ball-milled Fe-based alloy powders doped with Zr, as well as applications of consolidated nanocrystalline Fe-based alloys at elevated temperature. Acknowledgements The authors are indebted to the National Science Foundation for support of this research work (DMR Grant no. 0504286). The authors thank Ryan Chan and Jonathon Semones for assistance with the experimental work and discussion on the results. References [1] F.J. Humphreys, M. Hatherly, Recrystallization and Related Annealing Phenomena, Elsevier Science, Inc., Tarrytown, 1996, p. 289. [2] H. Gleiter, Prog. Mater. Sci. 33 (1989) 223. [3] R. Birringer, Mater. Sci. Eng. A 33 (1989) 117. [4] B. Gunther, A. Kumpmann, H.D. Kunze, Scr. Mater. 833 (1992) 27. [5] G. Hibbard, K.T. Aust, G. Palumbo, U. Erb, Scr. Metall. 44 (2001) 513. [6] U. Klement, U. Erb, A.M. ElSherik, K.T. Aust, Mater. Sci. Eng. A 203 (1995) p. 177. [7] T.R. Mallow, C.C. Koch, Acta Mater. 45 (1997) 2177. [8] C.E. Krill, H. Ehrhardt, R. Birringer, Z. Metallkd. 96 (2005) 1134. [9] K. Boylan, D. Ostrander, U. Erb, G. Palumbo, K.T. Aust, Scr. Metall. Mater. 25 (1991) 2711. [10] H.J. Hofler, R.S. Averback, Scr. Metall. Mater. 24 (1990) 2401. [11] Z. Gao, B. Fultz, NanoStruct. Mater. 4 (1994) 939. [12] A. Michels, C.E. Krill, H. Eharhardt, R. Birringer, D.T. Wu, Acta Mater. 47 (1999) 2143.

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