Kinematic scaling and crossover to scale invariance in martensite growth

Rao, Madan ; Sengupta, Surajit ; Sahu, H. K. (1995) Kinematic scaling and crossover to scale invariance in martensite growth Physical Review Letters, 75 (11). pp. 2164-2167. ISSN 0031-9007

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Official URL: http://prl.aps.org/abstract/PRL/v75/i11/p2164_1

Related URL: http://dx.doi.org/10.1103/PhysRevLett.75.2164

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.

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