Thermally Induced Strains in Cubic Metal Films

Abstract

Thin films bonded to substrates of different thermal expansion coefficients will experience ``thermal strains'' when their temperature is changed. Calculations of these thermal strains and the corresponding strain energies for crystals having various crystallographic orientations relative to the surface of the film were made for a number of fcc and bcc metals. Results are given for the (111), (200), (220), (311), (331), (420), (422), (511), (531), (442), (620), and (533) orientations of the fcc metals Cu, Au, Ag, Al, Ni, Pb, and Pd. They are basically similar for all fcc metals studied with the (100) orientation having the lowest strain energy and the (111) orientation the highest. For the bcc metals Cr, Fe, Nb, Mo, Ta, V, and W, calculations were made for the (110), (200), (211), (310), (222), (321), (411), (420), (332), (510), (431), (521), (530), (433), and (442) orientations. Neglecting W, which is isotropic, it was possible to classify the bcc metals into two groups depending upon whether the (100) orientation had a higher or lower strain energy than the (111) orientation. The strain energies for the other orientations lay between these extreme values in all cases.