The Heterogeneous Character of Phase Transformations Caused by Limited Vacancy Mobility
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The Heterogeneous Character of Phase Transformations Caused by Limited Vacancy Mobility Wolfgang Püschl,1 William A. Soffa,2 and Wolfgang Pfeiler1 1 Institut für Materialphysik, University of Vienna, Strudlhofgasse 4, A-1090 Vienna, Austria 2 Department of Materials Science and Engineering, University of Pittsburgh, 842 Benedum Hall, Pittsburgh, PA 15261, U.S.A.
ABSTRACT In homogeneous phase transformations the order parameter proceeds towards equilibrium uniformly in all microvolumes of the system. However, defect-mediated diffusion (vacancy mechanism) involving local atomic jump processes during the early stages of transformation kinetics can produce discrete regions within which the order parameter has changed significantly embedded in an unperturbed matrix. This effect is evident in order-order transformations in B2 FeAl as measured by residual resistivity. An estimate of the heterogeneity regime is calculated in terms of vacancy diffusion parameters.
INTRODUCTION Quenching an alloy from a homogeneous state into a region where a two-phase equilibrium is stable leads to a first-order phase transition. It can take place in two qualitatively different ways traditionally assumed to be clearly distinguishable: Either even very small composition fluctuations result in a reduction of free energy and grow therefore spontaneously or the fluctuations must overcome an energy barrier by creating a part of the new phase with a critical minimum size. In the first case - spinodal decomposition - the phase transformation takes place continuously starting from the homogeneous state, in the second case - nucleation - the transformation begins with a heterogeneous state. Which of the two different mechanisms will be operative is thought to depend on the properties of the Gibbs free energy per volume g(c) as a function of composition: If the second derivative at the given composition is negative, then phase separation should happen spontaneously by spinodal decomposition. This clear distinction cannot be upheld, however, in a realistic system, as discussed by Binder and Fratzl [1]. In the first place, in order to define a smooth local composition an average has to be taken over a finite volume (coarse graining). The shape of g(c) can be shown to depend sensitively on the ratio of coarse-graining length to characteristic length of concentration change [1]. It follows that a spinodal curve cannot be defined in an unambiguous way, therefore in real systems the boundary between the two scenarios of phase separation is uncertain and in addition shifted owing to kinetic effects and elastic interaction of coherent precipitates. In fact there is rather a gradual than a sharp transition from one mode of phase separation to the other. The classical spinodal decomposition theory by Cahn and Hilliard [2-5, see also 6,7] takes the free energy to be a functional of local composition with gradient-dependent terms. Diffusion fluxes are set proportional to the gradient of chemical potential difference. This implies that a diffusion mech
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