Distributed-activation kinetics of
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I.
INTRODUCTION
K I N E T I C phenomena in crystalline solids of relatively high perfection can often be adequately described with the approximation of a single activation energy. In contrast, it is well established that in highly imperfect solids, such as glasses, t1'21 a potency distribution of structural defects gives rise to a distribution of activation energies which is essential to quantitative description of kinetic behavior. When behavior of a crystalline solid is dominated by strong defect interactions, as in the case of heterogeneous nucleation of a phase transformation, it can similarly be anticipated that distributed-activation kinetics will prevail. The relative ease of direct nucleationrate measurements allowed by rapid growth to macroscopic dimensions makes martensitic transformations an ideal case for quantitative study of heterogeneous nucleation kinetics. While it has long been recognized that a defect potency distribution likely exerts a strong influence on both the athermal (temperature-dependent) E3j and isothermal (time-dependent) t41 aspects of heterogeneous martensitic nucleation kinetics, the most highly developed theory of martensitic kinetics has thus far employed the approximation of a single activation energy, t51 A recent comprehensive review of martensitic kinetics t6] has emphasized common features of athermal and isothermal modes of transformation, offering hope of a universal kinetic model. MINFA LIN, formerly Graduate Student, Massachusetts Institute of Technology, is Research Engineer, Bethlehem Steel Corporation, Bethlehem, PA 18016. GREGORY B. OLSON, formerly Senior Research Associate, Massachusetts Institute of Technology, is Professor, Department of Materials Science and Engineering, Northwestern University, Evanston, IL 60208. MORRIS COHEN, Institute Professor Emeritus, is with the Massachusetts Institute of Technology, Cambridge, MA 02139. Manuscript submitted March 4, 1992. METALLURGICAL TRANSACTIONS A
We here explore such a unified framework for martensitic nucleation kinetics, employing a distributed-activation model to incorporate variations in defect potencies and their associated nucleation activation energies. Previous work upon which the model is based will be briefly reviewed first.
A.
Preexisting Defect Size Distribution
The heterogeneity of martensitic nucleation is well demonstrated by the small-particle experiments of Cech and Turnbull on an Fe-30.2Ni (weight percent) alloy, which showed that the martensite start temperature on cooling is particle size dependent, t7] In these studies, the particles were found to transform over a wide range of temperatures and particle sizes; in fact, some of the smallest particles did not transform at all on cooling to the lowest temperature. These findings suggest two features of the transformation: (1) larger particles are more probable to contain nucleation sites or defects and (2) these defects have different potencies. The implication of a potency distribution for nucleation defects arising from these results was ana
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