Twin bands in martensites: Statics and dynamics

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{~} {}L₂ , with L₂ 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 T³ temperature dependence to T² 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.