A Biperiodic Network of Misfit Dislocations in a Thin Bicrystalline Foil

Abstract

The elastic displacement field u associated with a planar, periodic, hexagonal-based network extended parallel to the two free surfaces of an ultrathin foil is investigated when the material is a bicrystal formed by two different isotropic crystals. The geometry of the network may include, in principle, different interfacial domains limited by straight or curved MD segments. An explicit formulation of each harmonic term is derived that depends explicitly on the isotropic elasticity coefficients and thickness of each phase. The key of the solution is the inversion of a system of 12 Â 12 linear equations with 12 complex unknowns that expresses the limiting boundary conditions. Applications are given for regular honeycomb networks of MDs in CoSi 2 /Si thin foils.

Anisotropic Elastic Field of a Thin Bicrystal Deformed by a Biperiodic Network of Misfit Dislocations

“…To have a better insight on the importance of the anisotropic effects in a thin foil, all the data considered in [32] for a (111)CoSi 2 /(111)Si heterotwin are used again, except for the elastic constants. Si is considered as crystal --while CoSi 2 is crystal +.…”

“…(a) 188, No. 3 (2001) CoSi 2 , they are C 11 = 228, C 12 = 140, C 44 = 83 (Zener coefficient 1.89) see [32]. These crystals are hence not considerably anisotropic.…”

“…For a single family of parallel, periodic, misfit dislocations (MD) lying in a thin bicrystalline sandwich, an exact analytical solution was found in [31] using isotropic crystals. For the more difficult problem of a biperiodic, hexagonal, MD network, an explicit Fourier series solution was proposed recently in this journal by one of the author [32]. The present paper is an extension of this solution to the case of anisotropic crystals.…”

“…[33]. To illustrate quantitatively some anisotropic effects in a thin foil near the internal interface, numerical applications will be presented for the (111)CoSi 2 /(111)Si heterotwin foil already considered in [32] using isotropic elasticities. The geometry is that of a honeycomb network with nodes denoted U, V, W, R, S and Z with dislocation segments oriented according to Fig.…”

Initial stages of misfit stress relaxation in composite nanostructures through generation of rectangular prismatic dislocation loops

“…[28,33,35,51,52], in bi-nanolayers in Refs. [22,[59][60][61][62][63][64][65][66][67][68][69] and in tri-nanolayers in Ref. [22].…”