INVESTIGATION OF THE NON-EQUILIBRIUM CRYSTALLIZATION OF SOLID SOLUTION ALLOYS IN THE THREE-COMPONENT SYSTEM

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1 INVESTIGATION OF THE NON-EQUILIBRIUM CRYSTALLIZATION OF SOLID SOLUTION ALLOYS IN THE THREE-COMPONENT SYSTEM Sidorov Eugeny Vasilevich 1, Drápala Jaromír 2 1 Vladimir State University, Department of casting processes and constructional materials 87, Gorky St., Vladimir, Russian Federation, ferromag@vtsnet.ru 2 Vysoká škola báňská - Technical University of Ostrava, FMMI, Department of non-ferrous metals, refining and recycling, Ostrava - Poruba, Czech Republic Jaromír.Drapala@vsb.cz Abstract The model of the non-equilibrium crystallization of continuous solid solutions has been studied in case when the temperature gradient within the whole alloy volume is zero, undercooling before the beginning and in the course of crystallization is absent, diffusion in the liquid phase is realized completely (D L ) and in the solid one is suppressed entirely (D S 0), i.e. the diffusion mass transfer between the liquid and the solid phases is absent. A computer program developed at VŠB TU Ostrava was used to investigate the nonequilibrium crystallization in the three-component system according to the model being considered. Several alloy compositions from different areas of a conventional threecomponent system have been studied. The ways how the liquid phase compositions change in the non-equilibrium crystallization process have been revealed, the component distribution coefficients in the temperature interval from liquidus to the melting temperature of the lowmelting-point component have been determined, mass fractions and compositions of the crystallizing solid phase have been established, diagrams of the component distribution as a function of the crystallized alloy fraction have been plotted. 1. INTRODUCTION Quantitative description of the equilibrium crystallization of solid solution alloys, making it possible to determine the beginning and the end of the process, the masses of the solid and liquid phases and their compositions, is feasible in practice for binary and ternary alloys on condition of complete equilibrium by means of nodes (in literature terms tie-line and conode are also used) and the law of the component permanency in alloys. These conditions provide unimpeded diffusion mass transfer in each phase and between them which is not feasible in real circumstances. 2. THEORY If we assume that the diffusion mass transfer in the solid phase and between it and the liquid phase is completely suppressed (D S 0) and in the liquid phase it as usual proceeds freely (D L ), then the crystallization process proves to be non-equilibrium. Neglecting undercooling, it can be considered that it begins at the equilibrium liquidus temperature. As temperature decreases, crystals of the composition C S = K C L, where K is the distribution coefficient of the second component (in case of binary alloys), are continuously precipitating from the liquid. Owing to the accepted assumption that the diffusion mass transfer is absent in the solid phase and between it and the liquid phase the precipitating crystals prove to be inhomogeneous by composition, whereas the liquid is absolutely homogeneous in the 1

2 crystallization process. The liquid mass in the process of such non-equilibrium crystallization is described by the relationship 1. = / K L NE L o ( C C ) 1 m (1) where C L is the liquid composition at the given temperature (the content of the second component in it); C o is the initial alloy composition. Formula (1) was devised by E.Scheuer [1], it was extensively used by E.Sheil [2] and D.A. Petrov [3] to analyze the non-equilibrium crystallization. This formula analysis shows that at K > 1 the liquid mass reaches the null value at C L = 0. This means that irrespective of the initial alloy composition and the external cooling conditions crystallization always completes at the melting point of the low melting point component the alloy basis. At K < 1 the liquid always reaches the composition of the nearest low temperature non-variant transformation. The mass of such liquid will have the finite value. Despite the evident extremity of the accepted assumptions, formula (1) describes the alloy actual crystallization considerably more comprehensively and precisely [4, 5] than a number of others. In paper [6] D.A. Petrov analyzed theoretically the non-equilibrium crystallization of the three-component alloys with liquid and solid solutions and with the four-phase eutectic transformation. In this paper, probably for the first time, in was established that in the ternary system with a continuous number of solid solutions crystallization, when diffusion is absent in the solid phase (D S 0) and complete in the liquid one (D L ), completes at the melting temperature of the most low melting point component C (Fig. 1). Crystallization of any ternary system alloys with the four-phase eutectic transformation under similar terms (D S 0, D L ) can complete only with the ternary eutectic crystallization. In paper [6] it is shown qualitatively in what way the liquid and solid phase compositions change in the course of crystallization in three-component alloys. Theoretical conclusions of paper [6] were corroborated by experiments on Al Cu Si and Al Cu Mn system alloys. In paper [7] the equilibrium and non-equilibrium crystallization process of three alloy compositions in the A B C three-component system was examined, these alloy compositions form continuous liquid and solid solutions on condition that the component melting temperatures correlate as t B > t C > t A (Fig. 2). Since analytical relationships characterizing non-equilibrium crystallization are extremely complex, in paper [7] this process was investigated by means of graphic plots. In Fig. 3 the component distribution in the solid phase after the non-equilibrium crystallization of alloys 1, 2, 3 as per Fig. 2 is presented. It is obvious that the content of the most low melting point component A in all three alloys increases from the centre to the crystal boundary and reaches 100%. The content of the most high melting point component B in all three alloys decreases from the centre to the boundary and reaches the null value. The distribution of the component C having the medium melting temperature is more complicated. In this paper it was also corroborated that the crystallization processes under non-equilibrium conditions would complete at the melting temperature of the most low melting point component A. If there are three-phase and more complex transformations in the three-component system, the non-equilibrium conditions of the transfer from the liquid into the solid state cause more serious changes in the crystallization process and in the resulting alloy structure. In paper [8] the A B C three-component system was examined (Fig. 4) in which there is one four-phase eutectic transformation L α + β + γ, three three-phase eutectic transformations L α + β, L α + γ, L β + γ and three two-phase transformations L α, L β, L γ, where α, β, γ are solid solutions on the A, B, C component basis. The equilibrium crystallization process of any alloy in this system and the resulting structure (the mass and the phase composition) can be described precisely be means of the devised propositions [9, 10]. 2

3 At the non-equilibrium crystallization on condition that D S 0, D L in paper [8] by means of the graphic plots it was established that in alloy n (Fig. 5) the finite amount of the non-equilibrium ternary eutectic is formed, as follows from the general regularities of the non-equilibrium crystallization. With this, in was found for the first time that as a result of the non-equilibrium crystallization another binary eutectic (β + γ) is formed in the alloy structure instead of the one that must be at the equilibrium process (β + α). Such phenomena are the more probable, the closer is the point e 2 to the component B and the further from this component is the point e 1. The obligatory condition is the higher e 1 binary eutectic temperature in comparison with the e 2 eutectic. 3. RESULTS To obtain more precise data on the changes in compositions and masses of the liquid and solid phases at the non-equilibrium crystallization in the three-component system with continuous liquid and solid solutions calculations were done by means of the computer program developed in Technical University of Ostrava [11]. With this purpose the A B C threecomponent system was chosen in which component melting temperatures were the following: t A = 1200 C, t B = 1000 C, t C = 800 C. The non-equilibrium crystallization of two compositions was studied: alloy 1 (80% A, 10% B, 10% C) and alloy 2 (80% B, 10% A, 10% C). The first alloy is in the region of the most high melting point component A and the second is in the region of the medium melting point component B. Calculation of the crystallization process was done with the 5 C interval beginning from the alloy liquidus temperature to the temperature at which the liquid phase vanished completely. For each temperature compositions of the non-equilibrium liquid and solid phases, masses of the liquid and the precipitated solid phases and also the sum of all non-equilibrium precipitated previously solid phases and the equilibrium distribution coefficients were determined. In Fig. 6 changes of the liquid and solid phase compositions for alloy 1 and in Fig. 7 for alloy 2 are shown. From the figures it is evident that the crystallization process in any alloy also finishes at the melting temperature of the most low melting point component C. In Fig. 8a the component distribution of alloy 1 and in Fig. 8b of alloy 2 is shown, in the dendrite cell or in the directionally solidified sample with the plane front on condition that D S 0, D L. In Fig. 8a it can be seen that the content of the most high melting point component A in alloy 1 (80% A, 10% B, 10% C) constantly decreases from 90% A in the centre of the dendrite cell to 0% on the boundary. The content of the most low melting point component C constantly increases from 4.5% C in the centre to 100% C on the boundary. The content of the medium melting point component B at first gradually increases from 5% B in the centre to 31% B in the periphery, i.e. when the solid phase fraction reaches Further the content of the medium melting point component B in the dendrite cell decreases and reaches 0% on the boundary. From Fig. 8b one can see that the content of the most high melting point component A in alloy 2 (80% B, 10% A, 10% C) gradually decreases by the linear law from 22% A in the centre of the dendrite cell to 0% on the boundary. The content of the most low melting point component C constantly increases from 4.5% C in the centre of the dendrite cell to 100% C on the boundary. The content of the medium melting point component B gradually increases from 74% B in the centre of the dendrite cell to 85% B when the solid phase fraction is Further the component B content starts to decrease and comes up to 0% on the boundary. It should be noted that in actual conditions diffusion processes in the solid phase and between it and the liquid phase to a certain extent take place (i.e. D S > 0). It is obvious that owing to this by analogy with binary alloys crystallization will be completed at a much higher temperature than the melting temperature of the most low melting point component [12]. 3

4 However in contrast to two-component alloys changes of the liquid phase compositions and accordingly the forming solid phase layers will be different than at D S = 0. In Fig. 9 probable changes of the phase composition at various crystallization conditions of alloy C o are presented. 4. CONCLUSION 1. A literary survey of the non-equilibrium crystallization processes of the three-component alloys of continuous liquid and solid solutions is made. 2. By means of the computer program developed in Technical University of Ostrava calculations of the non-equilibrium crystallization of some alloy compositions in the threecomponent system A B C with continuous liquid and solid solutions have been done. 3. More precise data on the liquid and solid phase compositions in the non-equilibrium crystallization process and on the alloy component distribution in the dendrite cell have been obtained. 4. At present work is being done to calculate the non-equilibrium crystallization with partial diffusion interaction in the solid phase and between the liquid and solid phases. ACKNOWLEDGEMENTS The present work was solved in the frame of the research project of Grant Agency of the Czech Republic No. 106/06/1190 Study of crystallization processes in multi-component alloys with the aim to determine regularities of interaction of elements and structure formation" and research project MSM Processes of preparation and properties of highly pure and structural defined materials. LITERATURE [1] SCHEUER, E. Zum Kornseigerungsproblem. Zeitschrift für Metallkunde, 1931, B.23, H.8, S [2] SCHEIL, E. Bemerkungen zur Schichtkristallbildung. Zeitschrift für Metallkunde, 1942, B.34, H.3, S [3] PETROV, D.A. Disturbance of equilibrium at the solid solution crystallization. Journal of Physical Chemistry, 1947, XXI, issue 12, p [4] NOVIKOV, I.I., ZOLOTOREVSKY, V.S. Dendrite liquation in alloys. Moscow, Nauka, 1966, 156 p. [5] GOLIKOV, I.N., MASLENKOV, S.B. Dendrite liquation in steels and alloys. Moscow, Metallurgiya, 1977, 224 p. [6] PETROV, D.A., KOLACHEV, B.A. Non-equilibrium crystallization of ternary alloys. Thermal treatment and properties of steel and light alloys. Proceedings of MATI. Moscow, 1960, issue 43, p [7] СИДОРОВ, Е.В., ПИКУНОВ, М.В. Особенности неравновесной кристаллизации трёхкомпонентных сплавов твёрдых растворов и возникающей дендритной ликвации. Металлы. 1994, 6, с [8] ПИКУНОВ, М.В., СИДОРОВ, Е.В. Некоторые особенности неравновесной кристаллизации сплавов в трёхкомпонентной системе с эвтектическими превращениями. Металлы. 1996, 1, с [9] ПЕТРОВ, Д.А. Двойные и тройные системы. М.: Металлургия. 1986, 256 с. [10] ЗАХАРОВ, А.М. Диаграммы состояния двойных и тройных систем. Мocквa, Металлургия. 1990, 240 с. [11] DRÁPALA, J., MORÁVKOVÁ, Z., SIDOROV, E.V. Computer simulation of crystallization in ternary systems. Transactions of the VŠB Technical University Of Ostrava, Metallurgical Series. 1, 2005, XLVIII, p [12] ПИКУНОВ, М.В., СИДОРОВ, Е.В. О неравновесной кристаллизации однофазных сплавов. Металлы. 1994, 2, с

5 A S B L L K C Fig. 1. Change of the liquid and solid phase compositions at the equilibrium (solid line) and non-equilibrium (dotted line) crystallization of ternary alloys of the system with continuous liquid and solid solutions (according to D.A. Petrov) B A C Fig. 2. Compositions of the liquid (C L ) and solid (C S ) phases at the equilibrium crystallization (t B > t C > t A ). 5

6 a. m S b. c. m S Fig. 3. Component distribution in ternary alloy crystals of the A B C system (see Fig. 2) 1(a), 2(b), 3(c) after the nonequilibrium crystallization (D S 0, D L A B C ). C o, Co, Co are the mean component contents in alloys. The crystal centre m = 0, the crystal boundary m = 1. m S Fig. 4. Equilibrium crystallization of alloy n in the A B C ternary system. 6

7 Fig. 5. Non-equilibrium crystallization (D S 0, D L ) of alloy n in the A B C ternary system. Fig. 6. Change of the liquid and solid phase Fig. 7. Change of the liquid and solid phase compositions at the non-equilibrium compositions at the non-equilibrium crystallization (D S 0, D L ) crystallization (D S 0, D L ) of alloy 1 (80% A, 10% B, 10% C) of alloy 2 (10 % A, 80 % B, 10 % C (t A > t B > t C ). (t A > t B > t C ). 7

8 Fig. 8. Component distribution in ternary alloy crystals of the A B C system (80% A, 10% B, 10% C) а), (80% B, 10% A, 10% C) b) after the non-equilibrium crystallization at D S 0, D L. C C L II C L I C L III C L C S III C S C o C S I C S II A B Fig. 9. The estimated change of the liquid and solid phase compositions of the C o alloy in the A B C ternary system (t A > t B > t C ) at the equilibrium crystallization (C L, C S ), at the completely non-equilibrium crystallization (D S 0, D L ) (C III L, C III S ), at the partial diffusion interaction (D S > 0, D L ) (C I L, C I S and C II L, C II S ) I II ( v > v ). cooling cooling 8