Structurally-induced elastic anomalies in a superlattice of (001) twist grain boundaries

It is suggested that the “supermodulus effect” observed for composition-modulated strained-layer superlattices may arise from the presence of the structurally disordered solid interfaces and not necessarily from electronic-structure effects. The latter are excluded by investigating the elastic properties of a so-called grain-boundary superlattice in which chemically identical materials are joined to form a three-dimensional superlattice. Both an embedded-atom-method and Lennard-Jones potential are employed in our zero-temperature atomistic calculations of the elastic constants and moduli of such a superlattice. They yield qualitatively similar results which, for large modulation wavelengths, can be represented by a mean-field model in which the interfacial regions are characterized by a set of effective elastic constants which are different from those of the bulk regions. The appearance of a maximum in the biaxial modulus and a minimum in the shear modulus is shown to arise from the interaction between interfaces. It is also shown that such extreme anomalies appear only in the moduli but not in the elastic constants of the grain-boundary superlattice.