BUCKLING OF COMPRESSIVELY STRAINED EPITAXIAL CRYSTAL-STRUCTURES

The buckling of a compression member of finite and of infinite length is analysed in the case of continuous elastic support. The effective spring constant of the support can vary with the buckling wavelength, and we find the conditions under which the infinite elastically supported structure buckles at a finite load and a finite buckling wavelength. The results are applied to two cases of interest in solid-state physics and the following conclusions reached: a biaxially compressed layer on a semi-infinite substrate with the same elastic constants, such as a pseudomorphic epitaxial strained layer, will not buckle. An idealized cross-sectional transmission electron microscopy sample made from such a layer is stable up to a finite critical strain, which is proportional to the wedge angle of the thinned edge.