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.