X光是目前最精確也最常使用於非破壞性薄膜材料分析的工具，其中蘊含豐富的結晶相結構資訊與準確的平面間距。然而多晶薄膜材料因為其特殊微結構與厚度限制，準確的應力與應力梯度仍然是目前機械性質研究中的一大挑戰。在此研究中，我們提出平均X光應變法用應用
cos2sin2 X光技術量測應變於不同的平面轉角()，藉此改善X光應力與X光彈性常數的量測精確度。此方法的主要概念是通過多個平面轉角()測量X光應變，進而增加有效取樣體積。此外通過調整X光入射角度，應力於不同X光穿透深度可被測得。然而以上述方法所測得X光應力是試片表面至該深度之加總平均，非實際的分層應力，因次本研究採取分層法用以解析分層應力梯度。氮化鈦硬膜於矽(100)基材作為量測模型系統，用以驗證不同的應力測量技術之取樣體積與統計意涵，包含雷射曲率法、sin2、cos2sin2及高能量X光繞射法。當足夠的取樣體積可供量測，X光應力精確度可降至3% 相較於光學曲率所測得的宏觀應力，。藉由比較X光應力與X光彈性係數，使用平均應變法之薄膜厚度限制約在350奈米上下。本研究因應薄膜厚度低於160奈米之應力測量需求，開發了一個新的多繞射平均應變法。利用正確的X光應力量測於不同的穿透深度與分層法解析，我們成功的量測應力梯度分別於三個不同的氮化鈦厚度，從1.5、2.7到3.9微米，所得應力梯度結果可關聯至薄膜微結構與內應力所造成的破裂形貌。

For polycrystalline films, X-Ray diffraction (XRD) is the most common nondestructive technique for measuring residual stress because of its excellent phase selective capability and precise interplanar distance determination. However, the measurement of accurate stress and stress gradient on thin films is challenging and critical mainly due to confined thickness and unique microstructure. In this study, we proposed an average X-ray strain (AXS) method by using cos2sin2 XRD technique at several rotational () angles to improve the accuracy of the measurement of X-ray stress (XRS) or X-ray elastic constants (XECs). The major concept was to increase sampling volume by measuring X-ray strain at multiple rotational angles. In addition, by adjusting the grazing incident angle of X-ray the variation of stress with thickness could be measured. Since the resultant stress was an integrated magnitude from the surface to the penetration depth, a layer-by-layer method was adopted to resolve the real layer stress at different penetration depth. TiN hard coating on Si (100) substrate was selected as the model system, where the residual stress was determined by laser curvature, sin2, cos2sin2 and high energy XRD methods, from which the influence of sampling volume was revealed and the corresponding statistical meanings of each method were discussed. When sufficient sampling volume was obtained, the accuracy of AXS method could be reduced to 3% comparing to macrostress acquired from laser curvature method. The thickness limitation of AXS methods was about 350 nm by comparing the XRS and XECs to other techniques and literature data. For ultra-thin film less than 160 nm, a new multiple (hkl) diffraction AXS method was developed. With the correct XRS’s measured at different penetration depths, the stress gradients on TiN coatings with thickness 1.5, 2.7 and 3.9 μm were successfully acquired and the results were correlated to the film structure and fracture morphology in our previous study.

Abstract I
摘要 II
致謝 III
Content I
Figure Caption V
Table Caption X
Symbols XII
Abbreviations XV
Chapter 1 Introduction 1
Chapter 2 Literature Review 3
2.1 Residual Stress in Thin Films and Coating 3
2.1.1 Origins of Residual Stress in Thin Film and Coatings 3
2.1.2 Types of Stress in Thin Films and Coatings 8
2.2 Stress Measurement by X-ray Diffraction Methods 10
2.2.1 Basic Concept of X-ray Stress Measurement 10
2.2.2 X-ray Elastic Constants (XECs) and Mechanical Elastic Constant 14
2.2.3 Traditional X-ray Stress Measurement on Thin Films using sin2ψ Method 17
2.2.4 Stress Measurements using Grazing Incident X-ray Diffraction (GIXRD) 24
2.3 Measurement of Stress Gradient for Thin Film Materials Using XRD Methods 30
2.4 Selection of Model System: TiN coating 38
Chapter 3 Theoretical Basis 41
3.1 Average X-ray Strain (AXS) Method 41
3.1.1 Statistical Meaning of X-ray Stress Measurement 41
3.1.2 Effective X-ray Diffraction Volume 44
3.1.3 Determination of Average X-ray Strain (AXS) using cos2αsin2ψ XRD Method 46
3.1.4 Measurement of Young’s Modulus and Poisson’s Ratio 51
3.2 Measurement of Stress Gradient using Layer-by-layer Method 55
3.3 Evaluation of Fracture Toughness of Hard Coatings using Internal Energy Induced Cracking (IEIC) Method 57
Chapter 4 Experimental Procedures 59
4.1 Deposition Details of TiN/Si Coating 59
4.2 Structure and Composition 62
4.2.1 X-ray diffraction (XRD) and Grazing incident X-ray diffraction (GIXRD) 62
4.2.2 X-ray Photoelectron Spectroscopy (XPS) 63
4.2.3 Field-Emission Gun Scanning Electron Microscopy (FEG-SEM) 64
4.3 Properties 65
4.3.1 Hardness and Young’s modulus 65
4.3.2 Macrostress by laser curvature method (LCM) 66
4.4 X-ray Stress and Stress Gradient 69
4.4.1 AXS from cos2αsin2ψ XRD method 69
4.4.2 AXS using Multiple (hkl) diffractions 71
4.4.3 XRS and XECs Measurements by Conventional sin2ψ XRD Method 73
4.4.4 AXS from High Energy Synchrotron XRD 77
4.4.5 Measurements of Young’s Modulus (E) and Poisson’s () Ratio 79
4.4.6 Stress Gradient and Internal Energy Distribution 81
Chapter 5 Results 83
5.1 Composition and Structure 83
5.2 Mechanical Properties 88
5.3 Strain Anisotropy 91
5.3.1 X-ray Strain Distribution using cos2sin2 XRD method 91
5.3.2 X-ray Strain Distribution using High Energy Synchrotron X-ray (HEXRD) 95
5.3.3 XRS from Traditional sin2 XRD and AXS methods 99
5.4 Thickness limitation of AXS Method 100
5.4.1 AXS vs. Thickness 100
5.4.2 XRS vs. Thickness 103
5.4.3 AXS using Multiple (hkl) Diffractions 105
5.5 Determination Young’s Modulus and Poisson’s Ratio 110
5.5.1 Average Effective X-ray Elastic Constants (AEXEC) vs. XECs 110
5.5.2 Poisson’s Ratio Measurement using AXS and Nanoindentation Methods 113
5.5.3 AEXEC of Thin TiN Films 115
5.6 Stress Gradient 116
5.6.1 Influence of Strain Anisotropy 116
5.6.2 Using AXS method to determine in-depth stress gradient 118
5.6.3 Internal Energy Induced cracking (IEIC) 120
Chapter 6 Discussion 125
6.1 Accurate stress Measurement using Effective Diffraction Volume 125
6.2 Thickness Limitation of AXS Method 128
6.3 Stress Gradient 135
Chapter 7 Conclusion 145
Appendix A 147
A.1 Internal energy induced Cracking method 147
A.1.1 Fracture Toughness of TiN Coating (Г) 147
A.1.2 Energy Release Rate (G) 148
A.1.3 Griffith Theory and Critical Film Thickness (hc) 151
Appendix B 155
B.1 X-ray Stress Fitting of samples A to F 155
B.2 X-ray Stress Fitting for Stress gradient on Sample E, M and L 160
B.3 High Energy XRD for sample M and L 164
Reference 168
Publication List 179

[1] S.L. Jin, D. Gruber, H. Harmuth, Determination of Young's modulus, fracture energy and tensile strength of refractories by inverse estimation of a wedge splitting procedure, Eng. Fract. Mech., 116 (2014) 228-236.
[2] W.J. Chou, G.P. Yu, J.H. Huang, Mechanical properties of TiN thin film coatings on 304 stainless steel substrates, Surf. Coat. Technol., 149 (2002) 7-13.
[3] M.P. Manoharan, A.V. Desai, M.A. Haque, Fracture toughness characterization of advanced coatings, J. Micromech. Microeng., 19 (2009) 115004.
[4] M. Sebastiani, E. Bemporad, F. Carassiti, N. Schwarzer, Residual stress measurement at the micrometer scale: focused ion beam (FIB) milling and nanoindentation testing, Philos. Mag., 91 (2011) 1121-1136.
[5] W. Fang, J.A. Wickert, Determining mean and gradient residual stresses in thin films using micromachined cantilevers, J. Micromech. Microeng., 6 (1996) 301-309.
[6] N. Sabate, D. Vogel, J. Keller, A. Gollhardt, J. Marcos, I. Gracia, C. Cane, B. Michel, FIB-based technique for stress characterization on thin films for reliability purposes, Microelectron. Eng., 84 (2007) 1783-1787.
[7] L.E. Koutsokeras, G. Abadias, Intrinsic stress in ZrN thin films: evaluation of grain boundary contribution from in situ wafer curvature and ex situ x-ray diffraction techniques, J. Appl. Phys., 111 (2012) 093509.
[8] I.C. Noyan, T.C. Huang, B.R. York, Residual stress/strain analysis in thin films by X-ray diffraction, Crit. Rev. Solid State Mater. Sci., 20 (1995) 125-177.
[9] A. Saeren, P. Van Houtte, B. Meert, C. Quaeyhaegens, Assessment of different X-ray stress measuring techniques for thin titanium nitride coatings, J. Appl. Cryst., 33 (2000) 312-322.
[10] G. Abadias, Y.Y. Tse, P. Guérin, V. Pelosin, Interdependence between stress, preferred orientation, and surface morphology of nanocrystalline TiN thin films deposited by dual ion beam sputtering, J. Appl. Phys., 99 (2006) 113519.
[11] A. Debelle, G. Abadias, A. Michel, C. Jaouen, Stress field in sputtered thin films: Ion irradiation as a tool to induce relaxation and investigate the origin of growth stress, Appl. Phys. Lett., 84 (2004) 5034-5036.
[12] C.E. Murray, Invariant X-ray elastic constants and their use in determining hydrostatic stress, J. Appl. Phys., 110 (2011) 123501.
[13] G. Abadias, Diffraction stress analysis in fiber-textured TiN thin films grown by ion-beam sputtering: Application to (001) and mixed (001)+(111) texture, J. Appl. Phys., 95 (2004) 2414-2428.
[14] J.-D. Kamminga, T.H. de Keijser, R. Delhez, E.J. Mittemeijer, A model for stress in thin layers induced by misfitting particles: an origin for growth stress, Thin Solid Films, 317 (1998) 169-172.
[15] G.G. Stoney, The tension of metallic films deposited by electrolysis, Proc. R. Soc. Lond. A, 82 (1909) 172-175.
[16] J.A. Thornton, D.W. Hoffman, Stress-related effect in thin films, Thin Solid Films, 171 (1989) 5-31.
[17] J.H. Van Der Merwe, Crystal interfaces. part II. finite overgrowths, J. Appl. Phys., 34 (1963) 123-127.
[18] J.W. Matthews, A.E. Blakeslee, Defects in epitaxial multilayers, J. Cryst. Growth, 29 (1975) 273-280.
[19] J.W. Matthews, Defects associated with the accommodation of misfit between crystals, J. Vac. Sci. Technol., 12 (1975) 126-133.
[20] P. Chaudhari, Grain growth and stress relief in thin films, J. Vac. Sci. Technol., 9 (1972) 520-522.
[21] G. Abadias, W.P. Leroy, S. Mahieu, D. Depla, Influence of particle and energy flux on stress and texture development in magnetron sputtered TiN films, J. Phys. D: Appl. Phys., 46 (2013) 055301.
[22] E. Chason, A kinetic analysis of residual stress evolution in polycrystalline thin films, Thin Solid Films, 526 (2012) 1-14.
[23] E. Chason, J.W. Shin, S.J. Hearne, L.B. Freund, Kinetic model for dependence of thin film stress on growth rate, temperature, and microstructure, J. Appl. Phys., 111 (2012) 083520.
[24] R. Koch, Stress in evaporated and sputtered thin films – a comparison, Surf. Coat. Technol., 204 (2010) 1973-1982.
[25] G.C.A.M. Janssen, Stress and strain in polycrystalline thin films, Thin Solid Films, 515 (2007) 6654-6664.
[26] M.M.M. Bilek, D.R. McKenzie, A comprehensive model of stress generation and relief processes in thin films deposited with energetic ions, Surf. Coat. Technol., 200 (2006) 4345-4354.
[27] M. Birkholz, C. Genzel, T. Jung, X-ray diffraction study on residual stress and preferred orientation in thin titanium films subjected to a high ion flux during deposition, J. Appl. Phys., 96 (2004) 7202-7211.
[28] G. Abadias, Y.Y. Tse, Diffraction stress analysis in fiber-textured TiN thin films grown by ion-beam sputtering:Application to (001) and mixed (001)+(111) texture, J. Appl. Phys., 95 (2004) 2414-2428.
[29] P.R. Guduru, E. Chason, L.B. Freund, Mechanics of compressive stress evolution during thin film growth, J. Mech. Phys. Solids, 51 (2003) 2127-2148.
[30] L.B. Freund, S. Suresh, Thin film materials : stress, defect formation, and surface evolution, Cambridge University Press, Cambridge, England ; New York, 2003, pp. 358-363.
[31] E. Chason, B.W. Sheldon, L.B. Freund, J.A. Floro, S.J. Hearne, Origin of compressive residual stress in polycrystalline thin films, Phys. Rev. Lett., 88 (2002) 156103.
[32] J.A. Floro, E. Chason, R.C. Cammarata, D.J. Srolovitz, Physical origins of intrinsic stresses in Volmer-Weber thin films, MRS Bull., 27 (2002) 19-25.
[33] J.-D. Kamminga, M. Leoni, U. Welzel, P. Lamparter, E.J. Mittemeijer, Stress in thin layers; grain interaction, elastic constants and diffraction response, Mater. Sci. Forum, 347-349 (2000) 42-47.
[34] J.D. Kamminga, T.H. de Keijser, R. Delhez, E.J. Mittemeijer, On the origin of stress in magnetron sputtered TiN layers, J. Appl. Phys., 88 (2000) 6332-6345.
[35] S.C. Seel, C.V. Thompson, S.J. Hearne, J.A. Floro, Tensile stress evolution during deposition of Volmer-Weber thin films, J. Appl. Phys., 88 (2000) 7079-7088.
[36] R. Nowak, F. Yoshida, J. Morgiel, B. Major, Postdeposition relaxation of internal stress in sputter-grown thin films caused by ion bombardment, J. Appl. Phys., 85 (1999) 841-852.
[37] H. Oettel, R. Wiedemann, Residual stresses in PVD hard coatings, Surf. Coat. Technol., 76-77 (1995) 265-273.
[38] R.C. Cammarata, Surface and interface stress effects in thin-films, Prog. Surf. Sci., 46 (1994) 1-38.
[39] C.A. Davis, A simple-model for the formation of compressive stress in thin-films by ion-bombardment, Thin Solid Films, 226 (1993) 30-34.
[40] H. Windischmann, Intrinsic stress in sputter-deposited thin films, Crit. Rev. Solid State Mater. Sci., 17 (1992) 547-596.
[41] O. Knotek, R. Elsing, G. Kramer, F. Jungblut, On the origin of compressive stress in PVD coatings - an explicative model, Surf. Coat. Technol., 46 (1991) 265-274.
[42] A.J. Perry, The state of residual stress in TiN films made by physical vapor deposition methods; the state of the art, J. Vac. Sci. Technol., A, 8 (1990) 1351-1358.
[43] D.S. Rickerby, Internal stress and adherence of titanium nitride coatings, J. Vac. Sci. Technol., A, 4 (1986) 2809-2814.
[44] F.M. Dheurle, Aluminum films deposited by Rf sputtering, Metall Trans, 1 (1970) 725-732.
[45] H. Köstenbauer, G.A. Fontalvo, M. Kapp, J. Keckes, C. Mitterer, Annealing of intrinsic stresses in sputtered TiN films: The role of thickness-dependent gradients of point defect density, Surf. Coat. Technol., 201 (2007) 4777-4780.
[46] A. Debelle, G. Abadias, A. Michel, C. Jaouen, V. Pelosin, Growth stress buildup in ion beam sputtered Mo thin films and comparative study of stress relaxation upon thermal annealing or ion irradiation, J. Vac. Sci. Technol., A, 25 (2007) 1438.
[47] F. Brunner, V. Hoffmann, A. Knauer, E. Steimetz, T. Schenk, J.T. Zettler, M. Weyers, Growth optimization during III-nitride multiwafer MOVPE using real-time curvature, reflectance and true temperature measurements, J. Cryst. Growth, 298 (2007) 202-206.
[48] J.A. Floro, E. Chason, S.R. Lee, R.D. Twesten, R.Q. Hwang, L.B. Freund, Real-time stress evolution during Si1-xGex heteroepitaxy: Dislocations, islanding, and segregation, J. Electron. Mater., 26 (1997) 969-979.
[49] D. Ngo, X. Feng, Y. Huang, A.J. Rosakis, M.A. Brown, Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part I: Analysis for obtaining film stress from non-local curvature information, Int. J. Solids Struct., 44 (2007) 1745-1754.
[50] M.A. Brown, A.J. Rosakis, X. Feng, Y. Huang, E. Üstündag, Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions. Part II: Experimental validation of the non-local stress/curvature relations, Int. J. Solids Struct., 44 (2007) 1755-1767.
[51] G.C.A.M. Janssen, A.J. Dammers, V.G.M. Sivel, W.R. Wang, Tensile stress in hard metal films, Appl. Phys. Lett., 83 (2003) 3287-3289.
[52] F.A. Doljack, R.W. Hoffman, The origins of stress in thin nickel films, Thin Solid Films, 12 (1972) 71-74.
[53] V. Vasechko, B. Huang, Q. Ma, F. Tietz, J. Malzbender, Thermomechanical properties of Y-substituted SrTiO3 used as re-oxidation stable anode substrate material, J. Eur. Ceram. Soc., 34 (2014) 3749-3754.
[54] R.C. Cammarata, Surface and interface stress effect in thin films, Prog. Surf. Sci., 46 (1994) 1-38.
[55] R.C. Cammarata, T.M. Trimble, D.J. Srolovitz, Surface stress model for intrinsic stresses in thin films, J. Mater. Res., 15 (2000) 2468-2474.
[56] R.W. Hoffman, Stresses in thin-films - relevance of grain-boundaries and impurities, Thin Solid Films, 34 (1976) 185-190.
[57] W.D. Nix, B.M. Clemens, Crystallite coalescence: a mechanism for intrinsic tensile stresses in thin films, J. Mater. Res., 14 (1999) 3467-3473.
[58] L.B. Freund, E. Chason, Model for stress generated upon contact of neighboring islands on the surface of a substrate, J. Appl. Phys., 89 (2001) 4866-4873.
[59] C.V. Thompson, Grain-growth in thin-films, Annu. Rev. Mater. Sci., 20 (1990) 245-268.
[60] Z.H. Xu, L. Yuan, D.B. Shan, B. Guo, A molecular dynamics simulation of TiN film growth on TiN(001), Comput. Mater. Sci., 50 (2011) 1432-1436.
[61] D.G. Sangiovanni, D. Edstrom, L. Hultman, I. Petrov, J.E. Greene, V. Chirita, Ti adatom diffusion on TiN(001): Ab initio and classical molecular dynamics simulations, Surf. Sci., 627 (2014) 34-41.
[62] V. Hauk, H. Behnken, Structural and residual stress analysis by nondestructive methods : evaluation, application, assessment, Elsevier, Amsterdam ; New York, 1997, pp. 59-63.
[63] J.M. Pureza, M.M. Lacerda, A.L. De Oliveira, J.F. Fragalli, R.A.S. Zanon, Enhancing accuracy to Stoney equation, Appl. Surf. Sci., 255 (2009) 6426-6428.
[64] E. Macherauch, P. Mtiller, Das sin2ψ Verfahren der r6ntgenographischen Spannungsmessung, Z. Angew. Phys., 13 (1961) 305-312.
[65] B.D. Cullity, S.R. Stock, Elements of X-ray Diffraction, 3rd Ed., Prentice Hall 2001.
[66] U. Welzel, J. Ligot, P. Lamparter, A.C. Vermeulen, E.J. Mittemeijer, Stress analysis of polycrystalline thin films and surface regions by X-ray diffraction, J. Appl. Cryst., 38 (2005) 1-29.
[67] P.O. Renault, E. Le Bourhis, P. Villain, P. Goudeau, K.F. Badawi, D. Faurie, Measurement of the elastic constants of textured anisotropic thin films from x-ray diffraction data, Appl. Phys. Lett., 83 (2003) 473-475.
[68] M. Ferrari, L. Lutterotti, Method for the simultaneous determination of anisotropic residual stresses and texture by x-ray diffraction, J. Appl. Phys., 76 (1994) 7246-7255.
[69] I.L. Chang, S.-H. Chang, J.-C. Huang, The theoretical model of fcc ultrathin film, Int. J. Solids Struct., 44 (2007) 5818-5828.
[70] T. Gnäupel-Herold, A.A. Creuziger, M. Iadicola, A model for calculating diffraction elastic constants, J. Appl. Cryst., 45 (2012) 197-206.
[71] J.-M. Zhang, Y. Zhang, K.-W. Xu, V. Ji, Anisotropic elasticity in hexagonal crystals, Thin Solid Films, 515 (2007) 7020-7024.
[72] J.-M. Zhang, Y. Zhang, K.-W. Xu, V. Ji, Anisotropic elasticity in a textured cubic film plane, Physica B, 403 (2008) 3379-3383.
[73] M. Barral, J.M. Sprauel, G. Maeder, Stress measurements by X-ray diffraction on textured material characterized by its orientation distribution function (ODF), In: Eigenspannungen, eds.: E. Macherauch, V. Hauk. Deutsche Gesellschaft f'tir Metallkunde e.V., 1 (1983) 31-47.
[74] P.S. Theocaris, The limits of Poissons ratio in polycrystalline bodies, J. Mater. Sci., 29 (1994) 3527-3534.
[75] P.H. Mott, C.M. Roland, Limits to Poisson's ratio in isotropic materials, Phys. Rev. B, 80 (2009) 132104.
[76] Bollenra.F, V. Hauk, E.H. Muller, On calculation of polycrystalline elasticity constants from single crystal data, Z. Metallkd., 58 (1967) 76-82.
[77] Stickfor.J, On Stress-Strain Relation of Macroscopic Elastic Stresses and Lattice Strains Observable by X-Ray Diffraction Methods, Tech Mitt Krupp Fors, 24 (1966) 89-102.
[78] W. Voigt, Lehrbuch der Kristallphysik (mit ausschluss der kristalloptik), B G Teubners sammlung von lehrbüchern auf dem gebiete der mathematischen wissenschaften, B.G. Teubner, Leipzig, Berlin,, 1910, pp. 964-965.
[79] A. Reuss, Account of the liquid limit of mixed crystals on the basis of the plasticity condition for single crystal, ZAMM, 9 (1929) 49-58.
[80] H. Neerfeld, Zur Spannungsberechnung aus rontegenographische Dehnungsmessungen In: Mitt. Kaiser Wilhelm Inst. Eisenforsch. , 24 (1942) 61-70.
[81] E. Kroener, Berechnung der elastischen Konstanten des Vielkristalls aus des Konstanten des Einkristalls, Z. Phys., 151 (1958) 504-518.
[82] S.J. Skrzypek, A. Baczmanski, W. Ratuszek, E. Kusior, New approach to stress analysis based on grazing-incidence X-ray diffraction, J. Appl. Cryst., 34 (2001) 427-435.
[83] G. Cornella, S.H. Lee, W.D. Nix, J.C. Bravman, An analysis technique for extraction of thin film stresses from x-ray data, Appl. Phys. Lett., 71 (1997) 2949-2951.
[84] G. Abadias, L.E. Koutsokeras, A. Siozios, P. Patsalas, Stress, phase stability and oxidation resistance of ternary Ti-Me-N (Me = Zr, Ta) hard coatings, Thin Solid Films, 538 (2013) 56-70.
[85] B.L. Ballard, P.K. Predecki, T.R. Watkins, K.J. Kozaczek, D.N. Braski, C.R. Hubbard, Depth profiling biaxial stresses in sputter deposited molybdenium films; use of the cos²ϕ method, Adv. X-Ray Anal., 39 (1997) 363-370.
[86] M. Klaus, C. Genzel, X-ray residual stress analysis on multilayer systems: an approach for depth-resolved data evaluation, J. Appl. Cryst., 46 (2013) 1266-1276.
[87] V. Hauk, W.K. Krug, R.W.M. Oudelhoven, L. Pintschovius, Calculation of lattice strains in crystallites with an orientation corresponding to the ideal rolling texture of iron, Z. Metallkd., 79 (1988) 159-163.
[88] J.D. Kamminga, T.H. de Keijser, E.J. Mittemeijer, R. Delhez, New methods for diffraction stress measurement: a critical evaluation of new and existing methods, J. Appl. Cryst., 33 (2000) 1059-1066.
[89] B. Kania, P. Indyka, L. Tarkowski, E. Beltowska-Lehman, X-ray diffraction grazing-incidence methods applied for gradient-free residual stress profile measurements in electrodeposited Ni coatings, J. Appl. Cryst., 48 (2015) 71-78.
[90] R. Delhez, T.H. de Keijser, E.J. Mittemeijer, Role of X-ray diffraction analysis in surface engineering: investigation of microstructure of nitrided iron and steels, Surf. Eng., 3 (1987) 331-342.
[91] W.C. Marra, P. Eisenberger, A.Y. Cho, X-ray total-external-reflection–Bragg diffraction: A structural study of the GaAs-Al interface, J. Appl. Phys., 50 (1979) 6927.
[92] C.H. Genzel, X-ray residual stress analysis in thin films under grazing incidence – basic aspects and applications, Mater. Sci. Technol., 21 (2005) 10-18.
[93] A.J. Perry, V. Valvoda, D. Rafaja, X-Ray residual-stress measurement in TiN, ZrN and HfN films using the Seemann-Bohlin method, Thin Solid Films, 214 (1992) 169-174.
[94] K.V. Acker, L. De Buyser, J.P. Celis, P.V. Houtte, Characterization of thin nickel electrocoatings by the low-incident-beam-angle diffraction method, J. Appl. Cryst., 27 (1994) 56-66.
[95] P. Predecki, B. Ballard, X. Zhu, Proposed methods for depth profiling of residual stresses using beam-limiting masks, Adv. X-Ray Anal., 36 (1993) 237-245.
[96] M.F. Toney, S. Brennan, Observation of the effect of refraction on X-rays diffracted in a grazing-incidence asymmetric bragg geometry, Phys. Rev. B, 39 (1989) 7963-7966.
[97] A. Benediktovitch, T. Ulyanenkova, J. Keckes, A. Ulyanenkov, Sample tilt-free characterization of residual stress gradients in thin coatings using an in-plane arm-equipped laboratory X-ray diffractometer, J. Appl. Cryst., 47 (2014) 1931-1938.
[98] C. Genzel, Formalism for the evaluation of strongly non-linear surface stress fields by X-ray diffraction performed in the scattering vector mode, Phys. Stat. Sol. A, 146 (1994) 629-637.
[99] A. Kumar, U. Welzel, M. Wohlschlögel, W. Baumann, E.J. Mittemeijer, An X-Ray diffraction method to determine stress at constant penetration/information depth, Mater. Sci. Forum, 524-525 (2006) 13-18.
[100] M.J. Marques, A.M. Dias, P. Gergaud, J.L. Lebrun, A methodology development for the study of near surface stress gradients, Mater. Sci. Eng., A, 287 (2000) 78-86.
[101] C.H. Ma, J.H. Huang, H. Chen, Residual stress measurement in textured thin film by grazing-incidence X-ray diffraction, Thin Solid Films, 418 (2002) 73-78.
[102] k. Nezu, H. Matsuzaka, R. Yokoyama, A current perspective of the state-of-the-art in stress analysis, Rigaku Journal 30 (2014) 4-12.
[103] M. Klaus, C. Genzel, H. Holzschuh, Residual stress depth profiling in complex hard coating systems by X-ray diffraction, Thin Solid Films, 517 (2008) 1172-1176.
[104] M. Klaus, C. Genzel, X-ray residual stress analysis on multilayer systems: an approach for depth-resolved data evaluation, J. Appl. Cryst., 46 (2013) 1266-1276.
[105] C. Genzel, C. Stock, W. Reimers, Application of energy-dispersive diffraction to the analysis of multiaxial residual stress fields in the intermediate zone between surface and volume, Mater. Sci. Eng., A, 372 (2004) 28-43.
[106] V. Hauk, B. Kruger, A new approach to evaluate steep stress gradients principally using layer removal, Mater. Sci. Forum, 347-349 (2000) 80-82.
[107] H.K. Tonshoff, J. Ploger, H. Seegers, Determination of residual stress gradients in brittle materials using an improved spline algorithm, Mater. Sci. Forum, 347-349 (2000) 83-88.
[108] I. Kraus, G. Gosmanova, On X-Ray measurements of residual-stresses in materials with lattice strain gradient, Czech. J. Phys., 39 (1989) 751-756.
[109] J. Koo, J. Valgur, Layer growing/removing method for the determination of residual stresses in thin inhomogeneous discs, Mater. Sci. Forum, 347-3 (2000) 89-94.
[110] C.L.A. Ricardo, M. D'Incau, P. Scardi, Revision and extension of the standard laboratory technique for X-ray diffraction measurement of residual stress gradients, J. Appl. Cryst., 40 (2007) 675-683.
[111] C. Genzel, Problems related to X-Ray stress analysis in thin films in the presence of gradients and texture, in: E.J. Mittemeijer, P. Scardi (Eds.) Diffraction Analysis of the Microstructure of Materials, Springer Berlin Heidelberg, Berlin, Heidelberg, 2004, pp. 473-503.
[112] M. Birkholz, P.F. Fewster, C. Genzel, Thin film analysis by X-ray scattering, Wiley-VCH, Weinheim, 2006, pp. 155-157.
[113] H. Ruppersberg, I. Detemple, Evaluation of the stress field in a ground steel plate from energy-dispersive X-ray diffraction experiments, Mater. Sci. Eng., A, 161 (1993) 41-44.
[114] A.Y. Kuznetsov, R.S. Neves, L.P. Linares, T.L. Oliveira, E.G. Gravina, T.K. Hirsch, C.A. Achete, Simple approach to residual stress depth by X-ray diffraction using conventional Y or W Geometries, ICEM15: 15th International Conference on Experimental Mechanics, 2012.
[115] C. Genzel, X-ray stress analysis in presence presence of gradients and texture, Adv. X-Ray Anal., 44 (2001) 247-256.
[116] T. Hong, J.Y. Ooi, B. Shaw, A numerical simulation to relate the shot peening parameters to the induced residual stresses, Eng. Fail. Anal., 15 (2008) 1097-1110.
[117] P.J. Withers, P.J. Webster, Neutron and synchrotron X-ray strain scanning, Strain, 37 (2001) 19-33.
[118] I.A. Denks, M. Klaus, C. Genzel, Determination of real space residual stress distributions σij(z) of surface treated materials with diffraction methods part II: energy dispersive approach, Mater. Sci. Forum, 37–42 (2006) 524–525.
[119] R. Daniel, J. Keckes, I. Matko, M. Burghammer, C. Mitterer, Origins of microstructure and stress gradients in nanocrystalline thin films: The role of growth parameters and self-organization, Acta Mater., 61 (2013) 6255-6266.
[120] M. Stefenelli, J. Todt, A. Riedl, W. Ecker, T. Muller, R. Daniel, M. Burghammer, J. Keckes, X-ray analysis of residual stress gradients in TiN coatings by a Laplace space approach and cross-sectional nanodiffraction: a critical comparison, J. Appl. Crystallogr., 46 (2013) 1378-1385.
[121] A.S. Budiman, S.M. Han, J.R. Greer, N. Tamura, J.R. Patel, W.D. Nix, A search for evidence of strain gradient hardening in Au submicron pillars under uniaxial compression using synchrotron X-ray microdiffraction, Acta Mater., 56 (2008) 602-608.
[122] N. Schalk, J. Keckes, C. Czettl, M. Burghammer, M. Penoy, C. Michotte, C. Mitterer, Investigation of the origin of compressive residual stress in CVD TiB2 hard coatings using synchrotron X-ray nanodiffraction, Surf. Coat. Technol., 258 (2014) 121-126.
[123] M. Tkadletz, J. Keckes, N. Schalk, I. Krajinovic, M. Burghammer, C. Czettl, C. Mitterer, Residual stress gradients in α-Al2O3 hard coatings determined by pencil-beam X-ray nanodiffraction: The influence of blasting media, Surf. Coat. Technol., 262 (2015) 134-140.
[124] J. Keckes, M. Bartosik, R. Daniel, C. Mitterer, G. Maier, W. Ecker, J. Vila-Comamala, C. David, S. Schoeder, M. Burghammer, X-ray nanodiffraction reveals strain and microstructure evolution in nanocrystalline thin films, Scripta Mater., 67 (2012) 748-751.
[125] N. Vaxelaire, P. Gergaud, G.B.M. Vaughan, Sub-micrometre depth-gradient measurements of phase, strain and texture in polycrystalline thin films: a nano-pencil beam diffraction approach, J. Appl. Cryst., 47 (2014) 495-504.
[126] R. Daniel, E. Jager, J. Todt, B. Sartory, C. Mitterer, J. Keckes, Mono-textured nanocrystalline thin films with pronounced stress-gradients: On the role of grain boundaries in the stress evolution, J. Appl. Phys., 115 (2014).
[127] A. Riedl, R. Daniel, J. Todt, M. Stefenelli, D. Holec, B. Sartory, C. Krywka, M. Müller, C. Mitterer, J. Keckes, A combinatorial X-ray sub-micron diffraction study of microstructure, residual stress and phase stability in TiAlN coatings, Surf. Coat. Technol., 257 (2014) 108-113.
[128] M. Stefenelli, R. Daniel, W. Ecker, D. Kiener, J. Todt, A. Zeilinger, C. Mitterer, M. Burghammer, J. Keckes, X-ray nanodiffraction reveals stress distribution across an indented multilayered CrN–Cr thin film, Acta Mater., 85 (2015) 24-31.
[129] C. Genzel, I.A. Denks, M. Klaus, Residual stress analysis by X-ray diffraction methods, Modern Diffraction Methods, Wiley-VCH Verlag GmbH & Co. KGaA2012, pp. 127-154.
[130] W.J. Chou, G.P. Yu, J.H. Huang, Corrosion behavior of TiN-coated 304 stainless steel, Corros. Sci., 43 (2001) 2023-2035.
[131] W.J. Chou, G.-P. Yu, J.-H. Huang, Effect of heat treatment on the structure and properties of ion-plated TiN films, Surf. Coat. Technol., 168 (2003) 43-50.
[132] L. Hultman, Thermal stability of nitride thin films, Vacuum, 57 (2000) 1-30.
[133] F.J. Espinoza-Beltran, O. Che-Soberanis, L. Garcia-Gonzalez, J. Morales-Hernandez, Effect of the substrate bias potential on crystalline grain size, intrinsic stress and hardness of vacuum arc evaporated TiN/c-Si coatings, Thin Solid Films, 437 (2003) 170-175.
[134] B.O. Johansson, Growth and properties of single crystal TiN films deposited by reactive magnetron sputtering, J. Vac. Sci. Technol., A, 3 (1985) 303-307.
[135] S. Jin, Y. Zhang, Q. Wang, D. Zhang, S. Zhang, Influence of TiN coating on the biocompatibility of medical NiTi alloy, Colloids Surf., B, 101 (2013) 343-349.
[136] H. Hämmerle, K. Kobuch, K. Kohler, W. Nisch, H. Sachs, M. Stelzle, Biostability of micro-photodiode arrays for subretinal implantation, Biomaterials, 23 (2002) 797-804.
[137] H.O. Pierson, Handbook of Refractory Carbides and Nitrides: Properties, Characteristics, Processing and Apps, William Andrew1996, pp. 193-194.
[138] A.J. Perry, On the existence of point defects in physical vapor deposited films of TiN, ZrN, and HfN, J. Vac. Sci. Technol., A, 6 (1988) 2140-2148.
[139] M.M. Lacerda, Y.H. Chen, B. Zhou, M.U. Guruz, Y.W. Chung, Synthesis of hard TiN coatings with suppressed columnar growth and reduced stress, J. Vac. Sci. Technol., A, 17 (1999) 2915-2919.
[140] S. Mahieu, P. Ghekiere, G. De Winter, R. De Gryse, D. Depla, G. Van Tendeloo, O.I. Lebedev, Biaxially aligned titanium nitride thin films deposited by reactive unbalanced magnetron sputtering, Surf. Coat. Technol., 200 (2006) 2764-2768.
[141] G. Abadias, Stress and preferred orientation in nitride-based PVD coatings, Surf. Coat. Technol., 202 (2008) 2223-2235.
[142] R. Machunze, G.C.A.M. Janssen, Stress gradients in titanium nitride thin films, Surf. Coat. Technol., 203 (2008) 550-553.
[143] R. Machunze, A.P. Ehiasarian, F.D. Tichelaar, G.C.A.M. Janssen, Stress and texture in HIPIMS TiN thin films, Thin Solid Films, 518 (2009) 1561-1565.
[144] S. Mahieu, D. Depla, Reactive sputter deposition of TiN layers: modelling the growth by characterization of particle fluxes towards the substrate, J. Phys. D: Appl. Phys., 42 (2009) 053002.
[145] A.G. Gómez, A.A.C. Recco, N.B. Lima, L.G. Martinez, A.P. Tschiptschin, R.M. Souza, Residual stresses in titanium nitride thin films obtained with step variation of substrate bias voltage during deposition, Surf. Coat. Technol., 204 (2010) 3228-3233.
[146] X. Pang, L. Zhang, H. Yang, K. Gao, A.A. Volinsky, Residual stress and surface energy of sputtered TiN films, J. Mater. Eng. Perform., 24 (2015) 1185-1191.
[147] T. Hirsch, P. Mayr, Residual stresses and residual stress distributions in TiCN- and TiN-coated steels, Surf. Coat. Technol., 36 (1988) 729-741.
[148] R. Ali, M. Sebastiani, E. Bemporad, Influence of Ti–TiN multilayer PVD-coatings design on residual stresses and adhesion, Mater. Design, 75 (2015) 47-56.
[149] C. Sarioglu, The effect of anisotropy on residual stress values and modification of Serruys approach to residual stress calculations for coatings such as TiN, ZrN and HfN, Surf. Coat. Technol., 201 (2006) 707-717.
[150] L.E. Toth, Transition metal carbides and nitrides Academic Press, New York, 1971, pp. 118-119.
[151] S. Nagakura, T. Kusunoki, F. Kakimoto, Y. Hirotsu, Lattice-parameter of nonstoichiometric compound TiNx, J. Appl. Cryst., 8 (1975) 65-66.
[152] S.Y. Zhang, W.G. Zhu, TiN coating of tool steels - a review, J. Mater. Process. Technol., 39 (1993) 165-177.
[153] A.J. Perry, J.N. Matossian, S.J. Bull, D.I. Proskurovsky, P.C. Rice-Evans, T.F. Page, D.E. Geist, J. Taylor, J.J. Vajo, R.E. Doty, V. Rotshtein, A.B. Markov, The effect of rapid thermal processing (RTP) on TiN coatings deposited by PVD and the steel-turning performance of coated cemented carbide, Surf. Coat. Technol., 120 (1999) 337-342.
[154] J.Y. Chang, G.P. Yu, J.H. Huang, Determination of Young's modulus and Poisson's ratio of thin films by combining sin2y X-ray diffraction and laser curvature methods, Thin Solid Films, 517 (2009) 6759-6766.
[155] A.J. Perry, L. Chollet, States of residual-stress both in films and in their substrates, J. Vac. Sci. Technol., A, 4 (1986) 2801-2808.
[156] A.S. Maxwell, S. Owen-Jones, N.M. Jennett, Measurement of Young's modulus and Poisson's ratio of thin coatings using impact excitation and depth-sensing indentation, Rev. Sci. Instrum., 75 (2004) 970-975.
[157] C. Ernsberger, A.J. Perry, L.P. Lehman, A.E. Miller, A.R. Pelton, B.W. Dabrowski, Low-temperature tempering-induced changes in bulk resistivity, temperature-coefficient of resistivity and stress in physically vapor-deposited TiN, Surf. Coat. Technol., 36 (1988) 605-616.
[158] M.D. Tran, J. Poublan, J.H. Dautzenberg, A practical method for the determination of the Young's modulus and residual stresses of PVD thin films, Thin Solid Films, 308 (1997) 310-314.
[159] A.J. Perry, A contribution to the study of Poisson ratios and eElastic-constants of TiN, ZrN and HfN, Thin Solid Films, 193 (1990) 463-471.
[160] M. Zhang, J. He, Ab-initio calculation of elastic constants of TiN, Surf. Coat. Technol., 142 (2001) 125-131.
[161] D. Holec, M. Friák, J. Neugebauer, P.H. Mayrhofer, Trends in the elastic response of binary early transition metal nitrides, Phys. Rev. B, 85 (2012) 064101.
[162] M. Bielawski, K. Chen, Computational evaluation of adhesion and mechanical properties of nanolayered erosion-resistant coatings for gas turbines, J. Eng. Gas Turbines Power, 133 (2011) 042102.
[163] K. Tanaka, Y. Akiniwa, Diffraction measurements-of residual macrostress and microstress using X-rays, synchrotron and neutrons, JSME Int J., Ser. A, 47 (2004) 252-263.
[164] T. Schuster, J. Ploger, A.K. Louis, Depth-resolved residual stress evaluation from X-ray diffraction measurement data using the approximate inverse method, Z. Metallkd., 94 (2003) 934-937.
[165] A.N. Wang, C.P. Chuang, G.P. Yu, J.H. Huang, Determination of average X-ray strain (AXS) on TiN hard coatings using cos2αsin2ψ X-ray diffraction method, Surf. Coat. Technol., 262 (2015) 40-47.
[166] P.S. Prevey, A method of determining the elastic properties of alloys in selected crystallographic directions for X-ray diffraction residual stress measurement, Adv. X-Ray Anal., 20 (1977) 345-354.
[167] W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments, J. Mater. Res., 7 (1992) 1564-1583.
[168] B.B. He, Two-dimensional X-ray diffraction, John Wiley & Sons 2011, pp. 312-313.
[169] K. Holmberg, H. Ronkainen, A. Laukkanen, K. Wallin, S. Hogmark, S. Jacobson, U. Wiklund, R.M. Souza, P. Ståhle, Residual stresses in TiN, DLC and MoS2 coated surfaces with regard to their tribological fracture behaviour, Wear, 267 (2009) 2142-2156.
[170] M. Wohlschlögel, U. Welzel, E.J. Mittemeijer, Tailoring the stress-depth profile in thin films; the case of γ’-Fe4N1-x, Thin Solid Films 520 (2011) 287-293.
[171] V. Savaria, H. Monajati, F. Bridier, P. Bocher, Measurement and correction of residual stress gradients in aeronautical gears after various induction surface hardening treatments, J. Mater. Process. Technol., 220 (2015) 113-123.
[172] F. Witt, R.W. Vook, Thermally induced strains in cubic metal films, J. Appl. Phys., 39 (1968) 2773-2776.
[173] T. Wieder, Calculation of thermally induced strains in thin films of any crystal class, J. Appl. Phys., 78 (1995) 838-841.
[174] R.W. Vook, F. Witt, Thermally induced strains in evaporated films, J. Appl. Phys., 36 (1965) 2169-2171.
[175] N. Wan, J. Xu, T. Lin, L. Xu, K. Chen, Observation and model of highly ordered wavy cracks due to coupling of in-plane stress and interface debonding in silica thin films, Phys. Rev. B, 80 (2009).
[176] H. Chai, J. Fox, On delamination growth from channel cracks in thin-film coatings, Int. J. Solids Struct., 49 (2012) 3142-3147.
[177] S. Chang, Collaboration unlocks self-replicating crack patterns, Physics Today 67 (2014) 18-19.
[178] J. Marthelot, B. Roman, J. Bico, J. Teisseire, D. Dalmas, F. Melo, Self-replicating cracks: a collaborative fracture mode in thin films, Phys. Rev. Lett., 113 (2014) 085502.
[179] U. Wiklund, J. Gunnars, S. Hogmark, Influence of residual stresses on fracture and delamination of thin hard coating, Wear, 232 (1999) 262-269.
[180] H. Jiang, D.Y. Khang, J. Song, Y. Sun, Y. Huang, J.A. Rogers, Finite deformation mechanics in buckled thin films on compliant supports, PNAS, 104 (2007) 15607-15612.
[181] N. Wan, J. Xu, T. Lin, L. Xu, K. Chen, Observation and model of highly ordered wavy cracks due to coupling of in-plane stress and interface debonding in silica thin films, Phys. Rev. B, 80 (2009) 014121.
[182] A.A. Volinsky, J.B. Vella, W.W. Gerberich, Fracture toughness, adhesion and mechanical properties of low-K dielectric thin films measured by nanoindentation, Thin Solid Films, 429 (2003) 201-210.
[183] A.-N. Wang, G.-P. Yu, J.-H. Huang, Fracture toughness measurement on TiN hard coatings using internal energy induced cracking, Surf. Coat. Technol., 239 (2014) 20-27.
[184] K. Jonnalagadda, S. Cho, I. Chasiotis, T. Friedmann, J. Sullivan, Effect of intrinsic stress gradient on the effective mode-I fracture toughness of amorphous diamond-like carbon films for MEMS, J. Mech. Phys. Solids, 56 (2008) 388-401.
[185] J.H. Huang, Y.H. Chen, A.N. Wang, G.P. Yu, H. Chen, Evaluation of fracture toughness of ZrN hard coatings by internal energy induced cracking method, Surf. Coat. Technol., 258 (2014) 211-218.
[186] C. Si, Z. Sun, F. Liu, Strain engineering of graphene- a review, Nanoscale, 8 (2016) 3207-3217.
[187] H.-W. Hsiao, J.-H. Huang, G.-P. Yu, Effect of oxygen on fracture toughness of Zr(N,O) hard coatings, Surf. Coat. Technol., 304 (2016) 330-339.
[188] W.H. Yang, D.J. Srolovitz, Surface morphology evolution in stressed solid: surface diffusion controlled crack initiation, J. Mech. Phys. Solids, 42 (1997) 1551-1574.
[189] B. Paliwal, K.T. Ramesh, An interacting micro-crack damage model for failure of brittle materials under compression, J. Mech. Phys. Solids, 56 (2008) 896-923.
[190] S. Lee, G. Ravichandran, Crack initiation in brittle solids under multiaxial compression, Eng. Fract. Mech., 70 (2003) 1645-1658.
[191] A.A. Griffith, The phenomena of rupture and flow in solids, Philos. Trans. R. Soc. Lond., 221 (1921) 163-198.
[192] P. Scherrer, The space grid of aluminium, Phys. Z., 19 (1918) 23-27.
[193] L.V. Azároff, M.J. Buerger, The powder method in X-ray crystallography, McGraw-Hill, New York, 1958, pp. 342-343.
[194] D.A. Shirley, High-resolution X-ray photoemission spectrum of valence bands of gold, Phys. Rev. B, 5 (1972) 4709-4714.
[195] M.A. Hopcroft, W.D. Nix, T.W. Kenny, What is the Young's modulus of silicon?, J. Microelectromech. Syst., 19 (2010) 229-238.
[196] P.A. Flinn, D.S. Gardner, W.D. Nix, Measurement and interpretation of stress in aluminum-based metallization as a function of thermal history, IEEE Trans. Electron Devices, 34 (1987) 689-699.
[197] W.D. Nix, Mechanical properties of thin films, Metall. Trans. A, 20 (1986) 2217-2245.
[198] X.S. Wang, T.Y. Zhang, Microbridge tests on bilayer thin films, Metall. Mater. Trans. A, 38 (2007) 2273-2282.
[199] P.H. Mott, C.M. Roland, Limits to Poisson’s ratio in isotropic materials, Phys. Rev. B, 80 (2009) 132104.
[200] A.P. Hammersley, S.O. Svensson, M. Hanfland, A.N. Fitch, D. Hausermann, Two-dimensional detector software: from real detector to idealised image or two-theta scan, High Pressure Res., 14 (1996) 235-248.
[201] W. Voigt, Über das Gesetz der Intensitätsverteilung innerhalb der Linien eines Gasspektrums, Sitzungsberichte Königliche Bayerische Akademie der Wissenschaften, 42 (1912) 603-620.
[202] J.O. Kim, J.D. Achenbach, P.B. Mirkarimi, M. Shinn, S.A. Barnett, Elastic-constants of single-crystal transition-metal nitride films measured by line-focus acoustic microscopy, J. Appl. Phys., 72 (1992) 1805-1811.
[203] Y. Huang, F. Zhang, K.C. Hwang, W.D. Nix, G.M. Pharr, G. Feng, A model of size effects in nano-indentation, J. Mech. Phys. Solids, 54 (2006) 1668-1686.
[204] R. Saha, W.D. Nix, Effects of the substrate on the determination of thin film mechanical properties by nanoindentation, Acta Mater., 50 (2002) 23-38.
[205] Y. Yang, H. Lu, C. Yu, J.M. Chen, First-principles calculations of mechanical properties of TiC and TiN, J. Alloys Compd., 485 (2009) 542-547.
[206] W.R. Chen, G.P. Yu, J.H. Huang, The mechanical properties of Ti-Si-N nanocomposite films deposited by magnetron sputtering, National Tsing Hua University Hsinchu, Taiwan, 2009.
[207] D.F. Bahr, D.E. Kramer, W.W. Gerberich, Non-linear deformation mechanisms during nanoindentation, Acta Mater., 46 (1998) 3605-3617.
[208] W.W. Gerberich, D.E. Kramer, N.I. Tymiak, A.A. Volinsky, D.F. Bahr, M.D. Kriese, Nanoindentation-induced defect-interface interactions: phenomena, methods and limitations, Acta Mater., 47 (1999) 4115-4123.
[209] M. Qin, D. Ju, Y. Wu, C. Sun, J. Li, Determination of the fracture strength for ceramic film on substrate by X-ray stress analysis method, Mater. Charact., 56 (2006) 208-213.
[210] C.H. Ma, J.H. Huang, H. Chen, Nanohardness of nanocrystalline TiN thin films, Surf. Coat. Technol., 200 (2006) 3868-3875.
[211] “On the determination of film stress from substrate bending: STONEY´s formula and its limits”, from http://nbn-resolving.de/urn:nbn:de:swb:ch1-200600111.
[212] J. Peng, V. Ji, J.M. Zhang, W. Seiler, Residual stresses gradient determination in Cu thin films, Mater. Sci. Forum, 524-525 (2006) 595-600.
[213] G.C.A.M. Janssen, F.D. Tichelaar, C.C.G. Visser, Stress gradients in CrN coatings, J. Appl. Phys., 100 (2006) 093512.
[214] G.A. Cheng, D.Y. Han, C.L. Liang, X.L. Wu, R.T. Zheng, Influence of residual stress on mechanical properties of TiAlN thin films, Surf. Coat. Technol., 228 (2013) 328-330.
[215] W. Ensinger, On the mechanism of crystal growth orientation of ion beam assisted deposited thin films, Nucl. Instrum. Meth. B, 106 (1995) 142-146.
[216] L.B. Freund, S. Suresh, Thin film materials : stress, defect formation, and surface evolution, Cambridge University Press, Cambridge, England ; New York, 2003, pp. 328-333.
[217] L.B. Freund, S. Suresh, Thin film materials : stress, defect formation, and surface evolution, Cambridge University Press, Cambridge, England ; New York, 2003, pp. 292-296.
[218] J. Frenkel, The Theory of the Elastic Limit and the Solidity of Crystal Bodies, Z. Angew. Phys., 37 (1926) 572-609.
[219] G.E. Dieter, Mechanical metallurgy, 3rd ed., McGraw-Hill, New York, 1986.
[220] T. Kundu, Fundamentals of fracture mechanics, CRC Press, Boca Raton, FL, 2008, pp. 286-287.
[221] D. Broek, Elementary engineering fracture mechanics, 3rd rev. ed., Martinus Nijhoff; Distributed by Kluwer Boston, The Hague ; Boston Hingham, Mass., 1982.
[222] S. Zhang, D. Sun, Y. Fu, H. Du, Toughness measurement of ceramic thin films by two-step uniaxial tensile method, Thin Solid Films, 469 (2004) 233-238.
[223] S. Massl, W. Thomma, J. Keckes, R. Pippan, Investigation of fracture properties of magnetron-sputtered TiN films by means of a FIB-based cantilever bending technique, Acta Mater., 57 (2009) 1768-1776.
[224] M.E. Kipp, G.C. Sih, The strain energy density failure criterion applied to notched elastic solids, Int. J. Solids Struct., 11 (1975) 153-173.
[225] M. Ohring, Materials science of thin films : deposition and structure, Academic Press 2002, pp. 568-570.
[226] R.W. Hertzberg, Deformation and fracture mechanics of engineering materials, J. Wiley & Sons, New York, 1996, pp. 335-336.