Heterogeneous Design: Concentration Fields Determination with the Unique Crystallization Schemes and Microstructures
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Heterogeneous Design: Concentration Fields Determination with the Unique Crystallization Schemes and Microstructures Vasily I. Lutsyk, Vera P. Vorob'eva Buryat Scientific Center, Russian Academy of Sciences 8, Sakhyanova str., Ulan-Ude, 670047, RUSSIA ABSTRACT New approach to calculation of microstructure by means of the one-phase regions borders equations is proposed. Projections of all geometrical elements of phase diagram to the concentration simplex divide it to fields with unique crystallization schemes. All crystallization stages for the given concentration field are simulated and as a result the all elements of microstructure is designed and origin of every phase is shown. INTRODUCTION The state diagram is the concentrated store of information about a system. However it does not contain the only experimental data about properties of components and their interaction. It is an important source of additional secondary information. It is necessary to study to extract it from the diagram only. Usually one tries to represent on the two-component isobaric phase diagram (PD) in coordinates “concentration-temperature” the most complete data about liquidus, solidus, solvus [1]. Three-component diagram is usually showed by concentration projections of liquidus and sometimes with polythermal sections in addition. Curvature of liquidus surfaces is depicted with a help of isothermal lines. As for four-component systems but their diagrams are constructed experimentally very seldom. They are presented by means of two-dimensional polythermal sections (and more seldom by three-dimensional iso- and polythermal cross-sections [2]). There are many methods of mathematical description of PD lines and surfaces (approximations of experimental data [3], thermodynamical equations based on properties of components [4] and so on). However it is known that cross-sections of (hyper)surfaces of liquidus, solidus, solvus (one-phase regions borders in general) produce ruled (hyper)surfaces bordering heterogeneous regions [5, 6]. It had been shown that as the PD geometrical elements which have been got by one-phase regions borders intersection are the directing elements for the ruled surfaces then the last do not need in additional mathematical description [7]. Moreover it is possible to say that equations of (n-1)-dimensional unruled (hyper)surfaces of the ncomponent isobaric PD give its full mathematical description in a form FI(z1, z2, ..., zn)=T, (1) where the index I marks all unruled (n-1)-dimensional PD elements. Equations (1) in compact form contain experimental information about the system. And these data may be used for the description of crystallization processes and the microstructure design. EXPERIMENTAL DETAILS Some variants of interaction Cd with Pb (Figure 1,a), Cd with Pb in presence of Sn (Figure 1,b), Cd with Pb in presence of Bi (Figure 1,d) and Cd with Pb in presence of Sn and Bi (Figure 1,e) are used for illustrations of the proposed approach. Cd with Pb, Bi, Sn and Sn with Bi and
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Pb interact on the
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