Coalescence kinetics under the action of alternative grain growth mechanisms
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TAL GROWTH
Coalescence Kinetics under the Action of Alternative Grain Growth Mechanisms P. Yu. Gubanov and I. L. Maksimov Nizhni Novgorod State University, pr. Gagarina 23, Nizhni Novgorod, 603950 Russia e-mail: [email protected] Received July 17, 2006
Abstract—The coalescence process is considered for the case where the prevailing grain growth mechanism is block-to-block diffusion, during which the motion of atoms in a solution occurs in the form of diffusion flux along the block boundaries. Numerical and analytical investigation of the coalescence kinetics in a homogeneous supersaturated solution is performed with allowance for the finite maximum grain size, and the time evolution of the size distribution function of new-phase grains is theoretically described. Possible transition regimes arising during coalescence at a change in the dominant grain growth mechanism are considered. PACS numbers: 64.90.+b, 68.43.Mn DOI: 10.1134/S1063774508010173
INTRODUCTION The process of formation of grains of a new phase during decomposition of a supersaturated solid solution in the late (coalescence) stage of a phase transition has been actively investigated, beginning with the classical studies by Lifshitz, Slyozov [1], and Wagner [2], where the most important coalescence mechanisms were considered: bulk diffusion and the mechanisms of surface reactions of atoms on the grain surface. Later, Slyozov et al. [3, 4] studied alternative coalescence mechanisms, which are effective in the case of Ostwald ripening in actual crystal structures that are either small or have a well-developed structure of defects of dislocation type. The form of the asymptotic size distribution function (DF) for the new-phase grains was found in [1–4], to which (in each case studied) almost any initial distribution evolves in the limit t ∞. A simplifying assumption, according to which grains can be infinitely large, was used in the previous approaches. This model simplification, being not quite realistic, makes it possible to construct a clear self-similar description of the coalescence kinetics. Recently, a generalization of the approach of [1, 2] was proposed in [5] for the case where a DF reflects the presence of the maximum grain size in an ensemble. On the basis of this approach, the coalescence kinetics of actual systems was considered in [5], where it was shown that, in the presence of a another class of DFs, characterized by a power-law (with exponent m) tendency toward zero near the maximum size, the asymptotic DF behavior becomes radically different. In this study, we theoretically analyzed the alternative mechanisms of supply of atoms to grains, which are implemented in actual crystal structures. 3D and 2D models of arrival of atoms to a grain via diffusion along
block-to-block boundaries or dislocation lines are considered in detail (Section 1); on the basis of this consideration, a generalized dynamic equation for the grain growth rate controlled by an alternative growth mechanism is formulated. The basic equation of coalescence kinetics is
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