Equilibrium partition coefficients in iron-based alloys
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I. I N T R O D U C T I O N
THE equilibrium
partition coefficient is a critical physical parameter in studies of solute redistribution during solidification in such processes as metal casting, zone refining, and crystal growth. By defining the thermodynamic limit for solute partitioning, partition coefficients play an important role in all theories of microsegregation. Therefore, it is necessary to have accurate values of this parameter for use in process modeling. Examination of the current literature indicates that accurate values for the equilibrium partition coefficient are lacking for iron-based alloys, particularly for higher-order systems. Data available for binary systems are generally tabulated with the assumption that the partition coefficients are constant--functions neither of concentration nor of temperature. This is rarely true, particularly in concentrated solutions. Investigators often assume that binary-alloy partition coefficient values change little in the presence of additional alloy components. This is done for simplicity, or because data for complex systems are not readily available. In addition, many partition coefficient values are based solely on old experimental studies. There have been few attempts to evaluate partition coefficients using more recent data. In this study, a comprehensive survey of equilibrium partition coefficients in several iron-based systems is reported. Partition coefficients are calculated from fundamental thermodynamic data and compared to literature values. The tabulated partition coefficient equations will be useful to those interested in investigating solute segregation during solidification. II. T H E O R E T I C A L B A C K G R O U N D
The equilibrium partition coefficient (abbreviated in this paper as partition coefficient) can be defined in sevTHOMAS P. BATTLE, formerly Graduate Research Assistant, The University of Michigan, is Postdoctoral Research Fellow, Centre for Numerical Modelling and Process Analysis, Thames Polytechnic, Woolwich, London SE18 6PF, United Kingdom. ROBERT D. PEHLKE, Professor, is with the Department of Materials Science and Engineering, The University of Michigan, Ann Arbor, MI 48109-2136. This paper is based on a presentation made in the T.B. King Memorial Symposium on "Physical Chemistry in Metals Processing" presented at the Annual Meeting of The Metallurgical Society, Denver, CO, February, 1987, under the auspices of the Physical Chemistry Committee and the PTD/ISS. METALLURGICAL TRANSACTIONS B
eral similar ways; the one used here is, perhaps, the most common. For two phases, a solid (S) and a liquid (L), for example, the partition coefficient (k) for species i is defined as follows: k = xS/x~
[1]
where X s and X~ are the solute mole fractions when the two phases are in equilibrium at a given temperature. The closer the value of k to one, the less the partitioning effect. It should be noted that the value of k in any given system is a function of the chosen concentration units. Weight percent partition coefficients are generall
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