Abstract
Variations of residual stresses in layers on substrates can occur in directions parallel and perpendicular to the surface as a result of compositional inhomogeneity and/or porosity or cracks. Diffraction methods to evaluate such stress variations are presented. Comparison of the experimental value for the stress with a calculated value of the “diffraction-averaged stress,” on the basis of a model for the local stresses, proved to be a useful method of stress analysis. It is shown that a direct evaluation of occurring stress-depth profiles is less practical. The method of stress analysis proposed, is applied to chemically vapor deposited TiN coatings on Mo substrates. In these coatings a large tensile stress parallel to the surface develops during cooling from the deposition temperature, due to difference in thermal shrink between coating and substrate. As a result of the cooling-induced stress, cracking of the coating occurs. The mesh width of the crack pattern allows determination of the fracture-surface energy and the fracture toughness of the coating material. Conceiving the cracked coatings as assemblies of freestanding columns, and assuming full elastic accommodation of the thermal mismatch at the column/substrate interface, the stress variations in the coating are calculated. On this basis the diffraction-averaged stress and the depth profile of the laterally averaged stress can be predicted accurately for the cracked TiN layers.
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References
W. D. Nix, Metall. Trans. A 20A, 2217 (1989).
R. W. Hoffman, Thin Solid Films 89, 155 (1982).
M. Murakami, T. Kuan, and I.A. Blech, in Treatise on Mater. Sci. and Technol., edited by K. N. Tu and R. Rosenberg (Academic Press, New York, 1982), Vol. 24, pp. 163, 210.
F. M. D’Heurle, Int. Mater. Rev. 34, 53 (1989).
A. G. Evans, M. D. Dory, and M. S. Hu, J. Mater. Res. 3, 1043 (1988).
W. G. Sloof, H. J. M. Rijpkema, R. Delhez, Th.H. de Keijser, and E. J. Mittemeijer, Surf. Eng. 3, 59 (1987).
W. G. Sloof, R. Delhez, Th.H. de Keijser, and E. J. Mittemeijer, J. Mater. Sci. 22, 1701 (1987).
W. G. Sloof, M. A. J. Somers, R. Delhez, Th.H. de Keijser, and E. J. Mittemeijer, in Residual Stresses in Science and Technology, edited by E. Macherauch and V. Hauk (Deutsche Gesellschaft für Metallkunde, Oberursel, 1987), Vol. 1, pp. 493, 500.
R. Delhez, Th.H. de Keijser, and E. J. Mittemeijer, Surf. Eng. 3, 331 (1987).
M. A. J. Somers and E. J. Mittemeijer, Metall. Trans. A 21A, 189 (1990).
S. Komiya, N. Umezu, and C. Hayashi, Thin Solid Films 63, 341 (1979).
T. A. Mäntylä, P. J. Helevirta, T. T. Lepistö, and P. T. Siitonen, Thin Solid Films 126, 275 (1985).
P. A. Dearnley, Surf. Eng. 1, 43 (1985).
E. Brozeit and H. M. Gabriel, Z. Werkstofftech. 11, 31 (1980).
I. Yoshizawa and K. Kamada, J. Nucl. Mater. 122&123, 1309 (1984).
I. C. Noyan and J.B. Cohen, in Residual Stress-Measurement by Diffraction and Interpretation (Springer-Verlag Inc., New York, 1987), p. 121.
V. Hauk and E. Macherauch, in Adv. X-Ray Anal., edited by J. B. Cohen et al. (Plenum Press, New York, 1984), Vol. 27, pp. 81, 99.
H. Behnken and V. Hauk, Z. Metallk. 77, 620 (1986).
B. Eigenmann, B. Scholtes, and E. Macherauch, Mater.-wiss. u. Werkstofftech. 21, 257 (1990).
M.G. Moore and W.P. Evans, Trans. Soc. Automotive Eng. (SAE) 66, 340 (1958).
G. F. Bastin, H. J.M. Heijligers, and F. J. J. van Loo, Scanning 8, 45 (1986).
C. R. Hubbard, J. Appl. Crystallogr. 16, 285 (1983).
C. S. Barrett and T. B. Massalski, in Structure of Metals (Perga-mon Press, Oxford, England, 1980), p. 204.
R. Kieffer and F. Beneskovsky, in Hartstoffe (Springer, Wien, Austria, 1963), p. 303.
A.J. Perry, Thin Solid Films 193/194, 463 (1990).
X. Jiang, M. Wang, K. Schmidt, E. Dunlop, J. Haupt, and W. Gissler, J. Appl. Phys. 69, 3053 (1991).
D. S. Stone, K. B. Yoder, and W. D. Sproul, J. Vac. Sci Technol. A 9, 2543 (1991).
J. A. Sue, Surf. Coating Technol. 54/55, 154 (1992).
J. Birkholzer and V. Hauk, Harterei-Tech. Mitt. 48, 25 (1993).
J-E. Sundgren, Thin Solid Films 128, 21 (1985).
A.J. Perry, Thin Solid Films 170, 63 (1989).
W. Kress, P. Roedhammer, H. Bilz, W. D. Teuchert, and A.N. Christensen, Phys. Rev. B 17, 111 (1978).
F. Bollenrath, V. Hauk, and E. H. Muller, Z. Metallk. 58, 76 (1967).
S. Nagakura, T. Kusunoki, F. Kakimoto, and Y. Hirosutu, J. Appl. Crystallogr. 8, 65 (1975).
L. Wolff, G. F. Bastin, and H. Y. M. Heijligers, Solid State Ionics 16, 105 (1977).
C. J. Smithells and E. A. Brandes, in Metals Reference Book, 5th ed. (Butterworths & Co. Ltd., London, England, 1976), p. 100.
Y. S. Touloukian, R. K. Kirby, R. E. Taylor, and T. Y. R. Lee, in Thermophysical Properties of Matter, Thermal Expansion—Nonmetallic Solids (IFI/Plenum, New York, Washington, DC, 1977), Vol. 13, pp. 1147, 1151.
Y. S. Touloukian, R. K. Kirby, R. E. Taylor, and P. D. Desai, in Thermophysical Properties of Matter, Thermal Expansion-Metallic Elements and Alloys (IFI/Plenum, New York, Washington, DC, 1976), Vol. 12, pp. 208, 216.
L. E. Toth, in Transition Metal Carbides and Nitrides (Academic Press, New York, 1971), pp. 169, 174.
B. R. Lawn, in Fracture of Brittle Solids, 2nd ed. (Cambridge University Press, Cambridge, England, 1993), pp. 1, 15, and 55.
H.J. Frost and M. F. Ashby, in Deformation-Mechanism Maps, The Plasticity and Creep of Metals and Ceramics (Pergamon Press, Oxford, England, 1982), pp. 80, 83.
W. G. Sloof, Ph.D. Thesis (Delft University Press, The Netherlands, 1996).
B.J. Aleck, J. Appl. Mech. 16, 118 (1949).
I.A. Blech and A.A. Levi, J. Appl. Mech. 48, 442 (1981).
J.J. Blech and Y. Kantor, Computers and Structures 18, 609 (1984).
Z. Suo, J. Vac. Sci. Technol. A 11, 1367 (1993).
M. S. Hu, M. D. Thouless, and A. G. Evans, Acta Metall. 36, 1301 (1988).
M. D. Drory, M. D. Thouless, and A. G. Evans, Acta Metall. 36, 2019 (1988).
M.S. Hu and A.G. Evans, Acta Metall. 37, 917 (1989).
J.W. Hutchinson and Z. Suo, Adv. Appl. Mech. 29, 63 (1992).
M.T. Laugier, J. Mater. Sci. Lett. 2, 419 (1983).
A. E.H. Love, in A Treatise on the Mathematical Theory of Elasticity, 4th ed. (University Press, Cambridge, England, 1952), pp. 74, 91.
S. P. Timoshenko and J.N. Goodier, in Theory of Elasticity, 3rd ed. (McGraw-Hill, Tokyo, Japan, 1982), pp. 1, 14, and 246.
CM. van Baal, Phys. Status Solidi A 77, 521 (1983).
I.C. Noyan, Metall. Trans. A 14A, 1907 (1983).
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Sloof, W.G., Kooi, B.J., Delhez, R. et al. Diffraction analysis of nonuniform stresses in surface layers: Application to cracked TiN coatings chemically vapor deposited on Mo. Journal of Materials Research 11, 1440–1457 (1996). https://doi.org/10.1557/JMR.1996.0181
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DOI: https://doi.org/10.1557/JMR.1996.0181