Mo multilayers

Mo multilayers

Thin Solid Films 398 – 399 (2001) 397–404 Microstructure of superhard (Ti,Al)NyMo multilayers ` b, J. Pacaudb, H. Garemb, K. Pischowc, Z. Wangc C.J. ...

1MB Sizes 0 Downloads 31 Views

Thin Solid Films 398 – 399 (2001) 397–404

Microstructure of superhard (Ti,Al)NyMo multilayers ` b, J. Pacaudb, H. Garemb, K. Pischowc, Z. Wangc C.J. Tavaresa,*, L. Reboutaa, J.P. Riviere a

´ ´ 4800-058 Guimaraes, ˜ Departamento de Fısica, Universidade do Minho, Azurem, Portugal Laboratoire de Metallurgie Physique, Universite´ de Poitiers, 86960 Futuroscope, France c ¨¨ Savcor Coatings Oy, Insinoorinkatu 7, 50100 Mikkeli, Finland


Abstract Nanocomposite multilayers were fabricated by reactive magnetron sputtering with modulation periods of approximately 6 nm. The structure of the (Ti,Al)NyMo multilayers was studied by X-ray diffraction (XRD), both in the low and high angle regions, while the interface morphology was probed by high-resolution transmission electron microscopy (HRTEM). Particular attention has been directed to the evolution of the roughness with the bias voltage. It was shown that with a bias voltage of y100 V these structures were prepared with relatively flat and smooth interfaces, albeit a certain level of intermixing that can have an interdiffusion width of approximately 0.6 nm in the roughest samples. Furthermore, the reduction in grain size and change in direction of preferential growth as bias increases is clearly visible from the selected area diffraction (SAD) patterns in HRTEM experiments. The high-angle XRD scans confirmed the reduction in grain size for the higher bias voltages, while from the simulation of the low-angle scans the grain roughness was estimated. A correlation between the evolution of roughness and nanohardness is also given, featuring the smoothest films hardness values as high as 51 GPa. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Multilayers; Superhard coatings; Roughness; High-resolution transmission electron microscopy; X-Ray diffraction; Stress

1. Introduction There is an increasing interest in using physical vapour deposition techniques for the production of hard ceramic coatings on steel tools w1,2x. Once the specific deposition parameters are encountered, these coatings may be easily reproduced and applied for commercial purposes w3x. Multilayered structures are becoming a new category of coatings successfully used for improving the surface mechanical properties of materials such as hardness and wear resistance. However, for specific engineering applications, there is an important need for modelling in order to find the optimum conditions for the individual components of the bilayer, which is not straightforward. Deposition parameters such as working and reactive gas partial pressure, ion current density and relative thickness of the multilayer material constituents, to name just a few, are crucial for the overall perform* Corresponding author. Tel.: q351-253-510154; fax: q351-253510153. E-mail address: [email protected] (C.J. Tavares).

ance. Hence the design aspects of the coating architecture in the initial stage of development require systematic experimental investigations and are extremely time consuming, which is only surpassed by the relative ease of the subsequent reproducibility. Nitrideymetal superlattice coatings have attracted considerable attention w1,4x because they combine properties of both hardness and elasticity; it has also been shown that their hardness can be higher than that of the individual layers of the superlattice. Therefore nitrideymetal multilayers represent a promising category of coatings for improving surface mechanical properties. High resolution transmission electron microscopy (HRTEM) is an important tool for the study of the structural quality within the layers and at the interfaces since the microstructure is imaged with fine detail w5x. Atomic scale information on the structure of both the layers and the interfaces can be obtained as well as general features like columnar growth, grain size and orientation and grain boundaries. The diffusion between adjacent layers and waviness of the interfaces are also readily monitored and compared with the structural data available from the X-ray diffrac-

0040-6090/01/$ - see front matter 䊚 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 6 0 9 0 Ž 0 1 . 0 1 3 4 9 - 9

C.J. Tavares et al. / Thin Solid Films 398 – 399 (2001) 397–404


tion experiments. The origin of the hardness enhancement in multilayered structures is not completely understood but appears to be the combination of different effects such as the image dislocation force at the interfaces and the difference in shear modulus between the two constituents w6x. In this paper the authors report advances made on the deposition of (Ti,Al)NyMo multilayers. X-Ray diffraction (XRD) and HRTEM measurements have been performed on these films in order to study their structural parameters with the aid of modelling. Furthermore, the misorientation of the textured grains was probed through XRD asymmetric experiments. Nanohardness experiments yielded both the hardness and the Young’s modulus of these coatings. A correlation between the structural and the mechanical properties is given. 2. Experimental details The (Ti,Al)NyMo multilayer coatings were deposited on high-speed steel (AISI M2) substrates and Si(100) wafers using a custom made sputtering system. An Ary N2 atmosphere was present in the chamber with a reactive nitrogen partial pressure of 0.1 Pa for growing (Ti,Al)N, while the working Ar partial pressure to grow (Ti,Al)N and Mo was set to 0.35 Pa and 0.5 Pa, respectively. Pure 200 mm=100 mm=6 mm TiAl (50:50) and Mo targets were used with a current density applied to both magnetrons of approximately 0.01 Ay cm2. Substrate bias voltages from y40 to y100 V were applied while the target-to-substrate distance was kept at 65 mm for all depositions. The base pressure was approximately 5=10-5 Pa, with a substrate temperature during deposition of 2508C. Before deposition the substrates were sputter etched in situ in an argon atmosphere of 7 Pa with a dc power of 100 W for 20 min. For the XRD scans a classical two-circles diffractometer with the standard Bragg–Brentano geometry working with CuKa radiation was used for both low-angle and high-angle diffraction experiments w7x. In the symmetric low-angle regime, the length scales that are probed are greater than the lattice spacing of the constituent layers. Therefore, the scattering solely arises from the chemical modulation of the structure. The modulation period can be assessed through the position of the small angle Bragg diffraction peaks w8x: ns

2L ycos2Žuc.ycos2Žun. l


where n represents the order of diffraction related to the Bragg peak positioned at un; L is the modulation period of the multilayer; l corresponds to the radiation wavelength; uc is the critical angle (;0.48 for our samples) below which all radiation is totally reflected. By modelling the low-angle XRD patterns with SUPREX w9,10x structural information regarding the relative thickness of

each material in a bilayer, inter-diffusion at the interface and the interfacial roughness is accessed w7x. An estimate for the average rms roughness present at the interfaces (sTotal) w9,11x, which is, however, limited by the coherence length of the probing radiation, is given by: 2 2 sTotalsysDW qsc2qtiyd qŽsTiAlN=dTiAlN. 2qŽsMo=dMo. 2


In this last equation the modelled parameters from the SUPREX program includes the width of the interdiffusion zone at the interface (ti-d), a Debye–Waller (sDW) coefficient that accounts for the waviness of the interfaces and the width of the continuous distribution of the layer thickness (sc). In the asymmetric mode (a-2u scans) the incident angle a is fixed for a particular value while the detector probes a specific 2u region. The diffraction vector q has a misorientation angle given by CsayuB with respect to the surface normal. uB is the Bragg position for the particular family of (hkl) planes to be investigated and C the angle between the normal to the sample surface and the whklx direction. By this method, fibre texture phenomenon may be probed when plotting the maximum intensity corresponding to uB as a function of C w12x. Transmission electron microscopy (TEM) observation was performed in high-resolution mode using a JEOL 3010 equipment with accelerating voltages of 300 kV. All samples were prepared by the cross-section technique, which consists of gluing together two mirrorfaced parts of the sample and then grinding a dimple into the cross-section and further eroding it by ion milling until achieving transparency. Coating hardness was determined from the loading and unloading curves carried out with an ultra low load depth sensing Nano Instruments Nanoindenter II w13x. The indenter was operated in the constant displacement rate of 5 nmys until a depth of 100 nm was reached. Indentation depths of approximately 100 nm were required to keep them within the recommended value of approximately 10–20% of the film thickness w14x; for indentation depths lower than 100 nm a contribution from the (softer) substrate affects the experiments. The unload segment is load controlled with an unloading rate equal to 50% of the loading rate, at the end of the previous load segment, then unloading continues until 90% of the previous load has been removed from the indenter, ending with a hold segment and a final unload segment in which 100% of the load is removed. Young’s modulus of the films (E) was determined by the measurement of the film stiffness. These measurements were calibrated using a fused silica sample. For the hardest samples, the hardness value was obtained from the average of at least 20 measurements taken at different positions. The technique used for residual stress measurement was based on the associated curvature deflection of a thin substrate.

C.J. Tavares et al. / Thin Solid Films 398 – 399 (2001) 397–404


Table 1 Structural and mechanical results relative to the wTi0.4Al0.6Ny Mox=250 multilayers Sample Bias (V)

L lTiAlN ylMo sTotal s HV E (nm) (nm) (GPa) (GPa) (GPa)

H40 H60 H80 H100

5.9 5.7 6.0 6.2

y40 y60 y80 y100

1.2 1.2 1.3 1.4

0.9 0.8 0.4 0.4

y2.7 y3.7 y4.1 –

28"2 30"3 51"4 45"3

382"35 404"22 554"36 460"22

Bias is the negative polarization in the substrate holder, L the modulation period calculated using Eq. (1), lTiAlN ylMo is the relative thickness between the TiAlN and the Mo layer, sTotal is the calculated interfacial roughness extracted from the simulation of the low-angle XRD profiles and calculated using Eq. (2), s is the residual stress, HV is the nanohardness and E is Young’s modulus. Fig. 1. Low-angle XRD scans taken for two wTi0.4Al0.6NyMox=250 multilayer samples grown with different bias voltages; sample H40 (y40 V) and sample H80 (y80 V).

3. Results and discussion Previous work on RBS w15x experiments and corresponding simulations extracted the composition and areal atomic density (atomsycm2) of (Ti,Al)N and Mo thick samples. From this result it was assumed that the (Ti,Al)N layers consist of 30 at.% of aluminum, 20 at.% of titanium and approximately 50 at.% of nitrogen, hence Ti0.4Al0.6N. According to the literature w16x, and from the XRD analysis of a thick sample, this stoichiometry evidences a B1 NaCl type structure. Molybdenum is bcc type and has an out-of-plane lattice mismatch of ;8% relative to the bulk (Ti,Al)N. In both Figs. 1 and 2 low-angle XRD patterns are presented, regarding Ti0.4Al0.6NyMo multilayers modulated with 250 periods of ;6 nm each, leading to a final thickness of approximately 1.5 mm. Fig. 1 is very

important in illustrating the evolution of the interfacial sharpness with increasing bias voltage. Sample H80 was grown with a bias voltage of y80 V while H40 was grown with y40 V (see Table 1). It is clearly visible that the Bragg peaks on H80 are better resolved and hence yielded from stronger constructive interference between the surface of the multilayer and its interfaces. In Fig. 2 a model is presented for sample H80. There is a good agreement between the experimental profile and the corresponding simulation with SUPREX. In order to take the most advantage from the refinements and ensure trustworthy fits some structural parameters must be accessed beforehand through other techniques so that the number of variables is reduced. TEM observations are a useful partner regarding the XRD scans, since a reasonable approximation for individual layer thickness and modulation period can be collected as well as a qualitative control on the fluctuation in the number of layers that are grown. Some of these calculated parameters such as the relative thickness between the

Fig. 2. Low-angle XRD scan and corresponding SUPREX refinement for sample H80 consisting of a 250-bilayer Ti0.4Al0.6NyMo structure with a period of 6 nm.


C.J. Tavares et al. / Thin Solid Films 398 – 399 (2001) 397–404

Fig. 3. High-angle XRD spectra taken for different bias voltage conditions. All samples consist of a 250-bilayer Ti0.4Al0.6NyMo structure with a period of ;6 nm.

Ti0.4Al0.6N and the Mo layer (lTiAlN ylMo) and the calculated interfacial roughness (sTotal) are presented in Table 1. One must not forget that the listed roughness values have a depth validity that is related with the coherency length of the X-rays; which in the case of these samples is of the order of a few grains. A main factor in the evolution of roughness is the inter-diffusion width at the interfaces that decreases from 0.6 to 0.3 nm as the bias increases from y40 V to y100 V; hence the decrease of roughness from 0.9 to 0.4 nm, with the same evolution of bias. Regarding lTiAlN ylMo, the development with bias of the Mo fraction is accounted for by the decrease in uncertainty of the number of atomic planes that are deposited in one layer as the bias increases, which was favouring the nitride layer. In the case of sample H40 it was extremely difficult to determine this relative thickness because of the inter-diffusion and waviness present at the interfaces (which can be observed further into this review on the HRTEM micrograph of Fig. 5). The high-angle patterns presented in Fig. 3 show the evolution of the multilayer modulation at a constant modulation period (Lf 6 nm) with increasing bias voltage. In samples H40 (y40 V) and H60 (y60 V) four distinct peaks associated with the modulation that was induced by the scattering powers of both Ti0.4Al0.6N an Mo, and the interference between them, result in a

central peak at approximately 2uf408 sided by two orders of satellites peaks (one on the left and two on the right). The fiber texture is predominantly (111) up to a bias of –60 V, changing to (100) for higher values. Associated with this change in texture is the complete disappearance of satellite peaks. Instead a broad peak is resolved hinting the possibility of reduced-grain size effect and strain gradients, if we rule out stacking faults w17x; from the observation of the HRTEM micrographs no relevant rigid lattice displacements have been noticed. Dashed lines corresponding to the texture of bulk Ti0.4Al0.6N and Mo are also displayed. Fig. 4 shows the variation of the fibre axis diffraction peak as a function of C, obtained from the asymmetric measurements (a-2u) made on samples H40 and H100 in the diffraction region of Ti0.4Al0.6N (111) and Ti0.4Al0.6N (200). From this, it was possible to conclude that the misorientation level of both fibre axes with respect to the growth direction is important. The value deduced from the Gaussian width of the curves in Fig. 4 is equal to "8.48 around w111x for H40 and "7.58 around w200x for H100. The level of interfacial disorder, which in a large scale is interpreted as waviness, explains the reason for such a large tilt in the Ti0.4Al0.6N textured grains. Thus, an increase in roughness at the interfaces correlates with a greater tilt of the grains. However, and since it is relative to different textures, this difference in tilt for both samples is not really substantial, which in the case of H100 indicates that another phenomenon is responsible for the level of misorientation of the grains. Since the out-of-plane interplanar distances are slightly strained in the case of molybdenum (0.228 nm), compared with bulk values (0.222 nm), and since the relative thickness of a Mo layer is always greater than the corresponding Ti0.4Al0.6N in the bilayer system, the conjunction of

Fig. 4. Variation of the Ti0.4Al0.6N fibre axis diffraction peak intensity as a function of c. The width of the Gaussian profile yields a misorientation of "8.48 for w111x and "7.58 for w200x for samples H40 (y40 V) and H100 (y100 V), respectively.

C.J. Tavares et al. / Thin Solid Films 398 – 399 (2001) 397–404


Fig. 5. HRTEM micrograph from the cross-section of sample H40 grown with a bias voltage of y40 V. The inset shows a selected area diffraction (SAD) pattern for the main reflections. Also on the inset, and corresponding to the Ti0.4 Al0.6 N (111) and (200) Debye–Scherrer diffraction rings, respectively, are two dark-field images that illustrate the morphology of the respective grains.

reduction of grain growth and strain effect explains the loss of modulation in the high-angle patterns. From the residual stress measurements performed on these multilayers (displayed in Table 1), it was found that these thin films possess an in-plane compressive stress, hence the out-of-plane strain. The stress values were calculated using Stoney’s equation w18,19x. HRTEM was used to image the fine structure of the coatings. Figs. 5–7 correspond to cross-section micro-

graphs of three different samples grown with increasing bias. The lamellar structure is evident, being the darker layers associated with Mo due to the higher scattering factor of this constituent. Upon studying the mentioned figures it can be noticed that the layers become better defined as the bias increases from y40 to y80 V. In particular for sample H80, grown with y80 V, there is evidence of planar layers that suggest a layer-by-layer growth mechanism, as reported elsewhere w20x.

Fig. 6. HRTEM micrograph from the cross-section of sample H60 grown with a bias voltage of y60 V. The inset shows a selected area diffraction (SAD) pattern for the main reflections.


C.J. Tavares et al. / Thin Solid Films 398 – 399 (2001) 397–404

Fig. 7. HRTEM micrograph from the cross-section of sample H80 grown with a bias voltage of y80 V. The inset shows a selected area diffraction (SAD) pattern for the main reflections.

In Fig. 5 the microstructure of sample H40, grown with a bias of y40 V, is probed in the middle of its stacking of 250 bilayers. The amount of roughness is considerable since a lower ion energy (which is a function of the bias voltage) induces slower adatom mobility, thus the disordered island growth is enhanced. In the main inset picture of Fig. 5 a selected area diffraction (SAD) pattern from the viewed cross-section is presented. An analysis of the Debye–Scherrer rings indicates a preferential growth from (111) and (200) Ti0.4Al0.6N planes, revealing also that the (200) reflections are associated with more misorientated grains than the corresponding (111) reflections, the latter having a preferred orientation that coincides with the multilayer stacking growth. From XRD asymmetric experiments the degree of misorientation from the (200) layers can reach "12.58, compared with to "8.48 from the (111) planes. Also in the inset of Fig. 5 there are two darkfield images that illustrate the size of (111) and (200) grains, and with a joint analysis from the cross-section micrograph the diameter of the grains can be estimated between 20 and 30 nm. After a close inspection of the micrograph from sample H60 in Fig. 6, grown with a bias voltage of y 60 V, it is reasonable to assume that the columnar structure is better resolved and larger in diameter when comparing to sample H40. At this cross-section, quite near the interface with the substrate, grains with diameters between 10 and 20 nm are viewed (in other micrographs with higher magnification), while the SAD pattern on the inset distinguishes both Ti0.4Al0.6N (111) and (200) reflection rings and also, contrary to the SAD inset on Fig. 5, the (110) reflection corresponding to Mo. The reason why the Mo(110) ring is not distinguished in the SAD in Fig. 5 has to do with the nonisostructural nature between (Ti,Al)N (fcc) and Mo (bcc) and the fact that when accommodating the lattice

mismatch between the two materials the deposit at the interface is elastically strained in order to have the same interatomic spacing; therefore the interface would be coherent with atoms. This coherency is easily observable in some grains where close inspection reveals that there is an out-of-plane alignment across an average of five layers, after which the termination of planes within a layer is associated with a lattice misfit dislocation that tends to deviate the mentioned alignment with a tilt of ;58. However, upon checking other SAD patterns along the whole thickness of sample H60, as we move away from the interface, it is apparent that the Mo (110) reflection ring disappears, suggesting that a strain gradient within the Mo layers hinders this observation. These strain gradients result from the adjusting of the mismatch between Ti0.4Al0.6N and Mo, and have a core of atomic planes within the Mo layer where the strain is annihilated. Since the Mo layer thickness (see Table 1) increases with bias, this core also increases and hence the better resolution of the Mo SAD rings for higher bias voltages. The micrograph in Fig. 7 corresponds to sample H80 grown with a substrate bias of y80 V. Here the columnar growth has been suppressed by the enhancement of the bias voltage. This intense bombarding causes densification and reduction of grain size in the growing film and contributes also to the flattening of the interfaces, thus lowering the surface roughness. From the inset SAD image it is possible to conclude that the points in the (200) ring are broader than the corresponding ones from the (111) planes, which is in accordance with the texture change from (111) to (200) observed in the high-angle XRD pattern for this same sample. According to some authors w21,22x, this change in preferred orientation resulting from increasing the ion bombardment is in agreement with the fact that for B1 NaCl structures such as (Ti,Al)N the w111x direction

C.J. Tavares et al. / Thin Solid Films 398 – 399 (2001) 397–404


GPa when the substrate bias increases from y40 to y 80 V. An increase in bias corresponds to another in ion bombardment, where the collisional cascade effects enhance film densification and void annihilation w25x, thus the strengthening of the film. 4. Conclusions

Fig. 8. Magnified portion of the cross-section shown on Fig. 7 from sample H80. The angle between the coherent (111) planes confirms the (100) texture that prevails in the high-angle XRD scans of Fig. 3 for this range of bias voltages. The thickness of a bilayer period is ;6 nm.

possesses the densest array of atom columns while the w001x is the most open in the channelling direction. Moreover, the lowest surface energy for fcc (Ti,Al)N is (200) w23x, therefore the preferred orientation should be along w001x when the ion bombardment is enhanced, and also the adatom mobility, to sufficient levels that permit the formation of crystallites bounded by lowenergy planes. When growing Ti0.4Al0.6N and as the bias was increased from y40 V to y80 V the ratio of the accelerated-ion to deposited-thermal-particles fluxes incident at the growing film (Ji yJa) increased from 1 to 1.6. In Fig. 8 a magnification from the cross-section of the sample (H80) shown in Fig. 7 is illustrated. The angle between the coherent Ti0.4Al0.6N and Mo (111) planes (;708) confirms the w001x multilayer preferred orientation. It is also possible to verify the coherency that exists at the interfaces and lattice misfit dislocations. In Table 1 some data regarding nanoindentation tests and stress measurements are presented. The hardness values (and corresponding Young’s modulus) increase with bias voltage up to y80 V reaching 51"4 GPa (554"36) and then decreases at y100 V. It seems that the ion bombardment at y100 V is already in excess, incorporating too many defects, therefore not enhancing the mechanical properties of the growing film. After studying the hardness values in Table 1 and correlating them with the bias voltage, such a big leap from 30 GPa (y60 V) to 51 GPa (y80 V) is not entirely new in polycrystalline multilayer films; Chu et al. w24x had already obtained such strong variation in the TiNyNbN system for modulation periods in the same range. The factor that is behind the high elastic modulus is intrinsically related with the compressive residual stress. This state of compression is enhanced from y2.7 to y4.1

In this paper the authors report the successful production by PVD of polycrystalline multilayered Ti0.4Al0.6N yMo superhard coatings in the nanometer scale with diverse conditions of ion bombardment during growth. By selecting the appropriate bias voltage the roughness levels present at the interfaces can be controlled, so that the atomic layers will be flat and the interfaces sharp. This increase in bias has also the effect of creating smaller grains that enhances the overall strength of the multilayer, elevating the hardness to levels exceeding 50 GPa and enhancing the elasticity of the material. A good correlation was obtained between the hardness data and the residual compressive stress values, being related with the ion bombardment during growth. The highangle XRD scans revealed a texture change from (111) to (200) as the bias is increased, which is in accordance with the HRTEM and SAD experiments. Acknowledgements The authors gratefully acknowledge the financial support from the FrenchyPortuguese CNRSyICCTI institutions (program no. 8856y2000) and from the FCTy MCT pluri-annual program. References w1x J. Musil, Surf. Coat. Technol. 125 (2000) 322. w2x P.Eh. Hovsepian, D.B. Lewis, W.-D. Munz, ¨ Surf. Coat. Technol. 133y134 (2000) 166. w3x L.A. Donahue, W.-D. Munz, ¨ D.B. Lewis, J. Cawley, T. Hurkmans, T. Trinh, I. Petrov, J.E. Greene, Surf. Coat. Technol. 93 (1997) 69. w4x A. Matthews, A. Leyland, K. Holmberg, H. Ronkainen, Surf. Coat. Technol. 100y101 (1998) 1. w5x M. Chladek, ´ ´ J. Grim, J. Appl. V. Valvoda, C. Dorner, C. Holy, Phys. Lett. 69 (1996) 1318. w6x X. Chu, S.A. Barnett, J. Appl. Phys. 77 (1995) 4403. w7x C.J. Tavares, L. Rebouta, B. Almeida, J. Bessa e Sousa, Surf. Coat. Technol. 100y101 (1998) 65. w8x Y.S. Gu, W.P. Chai, Z.H. Mai, J.G. Zhao, Phys. Rev. B 50 (1994) 6119. w9x E.E. Fullerton, I.K. Schuller, H. Vanderstraeten, Y. Bruynseraede, Phys. Rev. B 45 (1992) 9292. w10x E.E. Fullerton, J. Pearson, C.H. Sowers, S.D. Bader, X.Z. Wu, S.K. Sinha, Phys. Rev. B 48 (1993) 17432. w11x K. Temst, M.J Van Bael, B. Wuyts, C. Van Haesendonck, Y. Bruynseraede, D.G. de Groot, N. Koeman, R. Griessen, Appl. Phys. Lett. 67 (23) (1995) 3429. w12x B.D. Cullity, Elements of X-Ray Diffraction, third ed, AddisonWesley, Menlo Park, CA, 1978, p. 103. w13x M.F. Doerner, W.D. Nix, J. Mater. Res. 1 (1992) 397.


C.J. Tavares et al. / Thin Solid Films 398 – 399 (2001) 397–404

w14x G.M. Pharr, W.C. Oliver, MRS Bull. 17 (7) (1992) 28. w15x C.J. Tavares, L. Rebouta, E. Alves, A. Cavaleiro, P. Goudeau, ` J.P. Riviere, A. Declemy, Thin Solid Films 377y378 (2000) 425. w16x F. Vaz, L. Rebouta, M.F. da Silva, J.C. Soares, J. Eur. Ceram. Soc. 17 (1997) 1971. w17x B.D. Cullity, Elements of X-Ray Diffraction, second ed, Addison-Wesley, Menlo Park, CA, 1978, p. 286. w18x G.G. Stoney, Proc. R. Soc. London A 82 (1909) 172. w19x C.J. Tavares, L. Rebouta, M. Andritschky, F. Guimaraes, ˜ A. Cavaleiro, Vacuum 60 (2001) 339.

w20x A. Madan, X. Chu, S.A. Barnett, Appl. Phys. Lett. 68 (16) (1996) 2198. w21x I. Petrov, F. Adibi, J.E. Greene, L. Hultman, J.-E. Sundgren, Appl. Phys. Lett. 63 (1) (1993) 3. w22x J.E. Greene, J.-E. Sundgren, L. Hultman, I. Petrov, D.B. Bergstrom, Appl. Phys. Lett. 67 (20) (1995) 2928. w23x L. Hultman, J.-E. Sundgren, J.E. Greene, Appl. Phys. Lett 66 (1989) 536. w24x X. Chu, S.A. Barnett, M.S. Wong, W.D. Sproul, Surf. Coat. Technol. 57 (1993) 13. w25x I. Petrov, L. Hultman, J.-E. Sundgren, J.E. Greene, J. Vac. Sci. Technol. A 10 (1992) 265.