Specific features of the crystallization of melts in systems with a transition from syntectic equilibrium to monotectic
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OMPUTATIONAL HARDWARE AND SOFTWARE
Specific Features of the Crystallization of Melts in Systems with a Transition from Syntectic Equilibrium to Monotectic Equilibrium V. I. Lutsyka ,*, A. É. Zelenayaa, and A. M. Zyryanovb a
Physical Problems Department, Buryatia Scientific Center, Siberian Branch, Russian Academy of Sciences, ul. Sakhyanovoy 8, UlanUde, 670047 Buryat Republic, Russia * email: [email protected] b Buryat State University, ul. Smolina 24a, UlanUde, 670000 Buryat Republic, Russia Received January 26, 2009
Abstract—A technology has been proposed for implementing the computer design of phase diagrams and their investigation with the kinematic specification of surfaces by using the T–x–y diagram with a monova riant syntectic equilibrium and a solidphase solubility as an example. The specific features of the crystalliza tion upon transition from syntectic equilibrium to monotectic equilibrium have been considered, and sur faces with a sign reversal of the mass increment and material balance for a threephase region have been con structed. PACS numbers: 61.43.Bn DOI: 10.1134/S1063774509070281
1. INTRODUCTION
2. GEOMETRIC STRUCTURING AND SELECTION OF THE MODEL
A complex study of the phase diagrams of different systems [1, 2] with the use of computer simulation methods implies not only the reconstruction of the threedimensional geometric pattern of a particular phase diagram as a whole but also its comprehensive investigation. The development of special algorithms for solving these problems makes it possible to exam ine all stages of crystallization, to calculate material balances, and to construct surfaces of transformations of the threephase reaction type [3–6], tielines on isothermal sections of twophase regions, and trajec tories of variations in phase compositions [7]. The boundaries of phase regions have been described by a specially developed method accounting for the com plex structure of the surface contour and its geometric singularities (extrema, saddle points, discontinuities in the smoothness, and strains at boundaries with a liquid–liquid immiscibility cupola) [4, 8]. In the case of the kinematic specification, any surface of the dia gram is represented in the form of a pseudoruled sur face, i.e., the surface formed by the sliding of the gen erating curve specified by the interpolation polyno mial along the similarly specified directrices. In this paper, we consider a technology for constructing a computer model of the phase diagram and its investi gation by using a ternary system with monovariant syntectic equilibrium and solidphase solubility as an example [9].
Let us consider the T–x–y diagram with an inter mediate compound δ in the AB binary system (Fig. 1), which is formed by 19 nonruled surfaces (four liquidus surfaces (Q), four solidus surfaces (S), ten solvus sur faces (V), and one liquid–liquid immiscibility surface (i)), 24 ruled surfaces (10(Qr) + 3(ir) + 5(Sr) + 6(Vr)), and two horizontal planes at temperatures of the ter nary eutectics (E1 and E2). In
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