Internal stresses and strains in coherent multilayers

Formulae are given for the strain and stress tensors in a periodic multilayer which may contain any number of layers, each with a different lattice parameter, different elastic constants and different thickness. The layers are assumed to be parallel sided, elastically isotropic and to have a thickness much smaller than the dimensions in the plane of the layers. The results are applied to metal and semiconductor heterostructures which contain equi-biaxial tensions and compressions and to lamellar Ti-Al in which there are additional in-plane shears. A preliminary discussion is given of the loss of coherency in a multilayer with layers of different thicknesses. (C) 1998 Acta Metallurgica Inc.