Kinematic scaling and crossover to scale invariance in martensite growth

Abstract

Scale invariance in acicular martensites emerges as a consequence of a competition between the front velocity v and the rate of nucleation I of the martensite grains. A renormalization group for the stationary probability distribution of the martensite grain size, P(l), has two fixed points-an unstable fixed point at v/I = 0, associated with a γ distribution, and a stable (critical) fixed point at v/I= ∞ with a Lévy distribution, P(l)~∫ -^α . Crossover functions and exponents governed by the unstable fixed point describe P(l) at intermediate v/I. Acicular martensites thus represent a novel example of a flow towards self-organized criticality. Our results provide a method to compute dynamic quantities (v or I) from static optical micrographs of martensite grains.