A new model for diffusional growth
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I.
INTRODUCTION
NUMEROUS articles have been published on the simulation of phase transformations. A large portion of these articles has treated diffusion-controlled phase transformations, and most treatments have relied on the assumption of local equilibrium at the interface, t~ 27] Comparisons with experiments have, with a few exceptions, shown satisfactory to good agreement for the local equilibrium treatments. Lately, models of diffusioncontrolled phase transformations with nonequilibrium interface conditions have been published.12~.29.3~ Despite the capability of the local equilibrium model to describe the major features of diffusion-controlled phase transformations in many alloy systems, its inability to treat, e.g., the massive transformation and the appearance of metastable phases during the evolution of a system is a severe limitation. Therefore, it is not suitable to model transformations far away from equilibrium, e.g., rapid quenching, welding, and low-temperature reactions. A model with the assumption about the interface compositions removed should make it possible to improve the descriptions of these cases. II.
THE MODEL
A. General The model is restricted to multicomponent systems with planar, cylindrical, or spherical symmetry, i.e., one space variable, here chosen as z, is sufficient to describe the space dependence of the molar fractions x of the elements in the phases. The main features of the phase transformation model are illustrated for a two-component model system A-B with phases a and /3, A being the solute and B the solvent, before it is applied to the Fe-C system. The treatment of phase transformations in this work is restricted to the growth of phases; i.e., the phases stable ANDERS SALWI~N, Doctor, of ASEA Brown Boveri Powdermet AB, S-73523 Surahammar, Sweden. Manuscript submitted September 23, 1992. METALLURGICAL TRANSACTIONS A
at the actual temperature are assumed to have already been nucleated. A system is considered to be composed of two types of regions, bulk regions and interphases, 119,2s,31-331 the latter always separating bulk regions. The separating surface between a bulk region and an interphase has to be planar, cylindrical, or spherical and is chosen so that the bulk region becomes as large as possible while still having a unique and well-defined lattice structure and therefore also a unique and welldefined Gibbs free energy. An interphase contains the part of the system where the growth of one phase at the expense of the other takes place by rearrangement of the lattice by some mechanism. The lattice structure of a real interphase may be disordered, partially coherent, or coherent. ~341In this work, no attempt is made to model or estimate the composition within the interphase, as the model does not require this as an input. The only properties needed for the interphases are the mobilities of atomic diffusion across the interphase from one bulk region to the other due to the chemical potential difference and the structure-sensitive velocity of the interphase itself. The t
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