Twin bands in martensites: Statics and dynamics

Abstract

The theory of forming a coherent twin band and its relation to the parent-product interface in a martensitic transition is studied. We find that the twin band is stabilized by a long-range elastic interaction between the twin boundaries, which is mediated via the parent phase. The mean distance l between twin boundaries is then l∼ √${\mathit{L}}_2$ , with ${\mathit{L}}_2$ the size of a twin boundary, i.e., the product ‘‘grain’’ size. The collective twin-boundary oscillations (‘‘dyadons’’) have unusually low frequencies and a limiting dispersion of frequency, which goes as the square root of the wave vector. Explicit results are given for a tetragonal-to-orthorhombic transition. We also show that dyadons cause the specific heat to change from a ${\mathit{T}}^3$ temperature dependence to ${\mathit{T}}^2$ at lower temperatures and to allow for a linear temperature dependence of the resistivity to extend to low temperatures. We compare our results with data on conventional martensites and on the more recent ceramic superconductors.