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Additional info for A system of physical chemistry. Kinetics
20, 349 (1982). Adhesion Aspects of Thin Films, Vol. 1, pp. 5 1 -65 Ed. K. L. *, STURE HOGMARK' and JENS GUNNARS ' Department of Materials Science, Uppsala Universiy, SE-751 21 Uppsala, Sweden * Det Norske Veritas, PO. Box 49306, SE-100 29 Stockholm, Sweden Abstract-Most of today's thin ceramic coatings generated by PVD or CVD techniques are in a residual stress state. This state has a number of origins and will be of either tensile or compressive nature. On topographic substrates which are not perfectly smooth, flat and infinitely large, tensile stresses are always induced across the coating-substrate interface.
5. Recently, Nix and Clemens [lo] have shown that the maximum tensile stress in PVD films may be estimated by balancing the sum of the elastic strain energy and the grain boundary energy with the energy of the two free surfaces that get eliminated in the island coalescence. This upper bound estimate may be as much as an order of magnitude higher than the experimentally measured peak stresses [ 111. Here we attempt to estimate the maximum tensile residual stress using the following expression from the grain boundary relaxation model originally proposed by Hoffman : tensile Omax E (1 - u ) Amax d ’ where c r ~ ~ ~isl lthe e maximum tensile stress, E is Young’s modulus, u is Poisson’s ratio, A is the relaxation distance and d is the grain size.
39, 545 (1998). C. V. Thompson, J. Muter. Res. 8, 237 (1993). X. W. Zhou, R. A. Johnson and H. N. G. Wadley, Acta Mater. 45,4441 (1997). C. M. Gilmore and J. A. Sprague, NanoStructured Mater. 9, 643 (1997). M. Nastasi, J. W. Mayer and J. K. Hirvonen, Ion-Solid Interucrions - Fundamentals and Applications, Cambridge Solid State Science Series, p. 343. Cambridge University Press, Cambridge (1996). P. Ehrhart, Atomic Defects in Metals, Landolt-Bornstein, New Series, Group 111, Vol. 25. Springer, New York (1991).
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