Stiffness constants for anisotropic hexagonal ultra thin overlayers

The elastic properties of overlayers are of interest in epitaxy, interplay of surface misfit and steps on crystal surfaces. The overlayer is represented by a thin slice from a bulk crystal regarded as an elastic continuum. In anisotropic crystals, the stiffness constants C-ijlk, are usually specified in principle axes (x(0),y(0),z(0)) and must be transformed to the local (x,y,z) axes, which are chosen to be convenient for the analysis of overlayers. We have computed a set of useful stiffness constant transformation relations for hexagonal ultra-thin overlayers, together with error probes i.e. equations for checking the correctness of transformed quantities when reduced to isotropic media. The transformed stiffness constants are expressed in terms of bulk ones and matrix elements that transform the principle axes to the local overlayer system. For the overlayer (1122) the transformed stiffness constants are derived explicitly. The results can be applied directly to several phenomena that generate surface stresses such as: (i) surface misfit; (ii) dislocations; (iii) monatomic steps and others. (C) 2002 Elsevier Science B.V All rights reserved.