Empirical Expression of Phosphorus Solubility in Molten Fe1-yCry Given as Functions of Temperature and Phosphorus Activity

Abstract

Chemical activity-temperature-composition (a -T-x-y) relationships determined by Knudsen effusion technique were made available for molten Fe-Cr-P system by a group of Russian researchers. Nevertheless, they were not presented in form of solubility x in Fe 1Ϫy Cr y P x as explicit functions of phosphorus activity a P and temperature T for given y and thence they are not readily usable for evaluating P solubility in molten Fe 1Ϫy Cr y at arbitrary T under certain a P . In the present work, effort was invested to derive empirical expression for the solubility x in Fe 1Ϫy Cr y P x as functions of T and a P at given y from the reported a P -T-x-y relationships in discrete tabulated format. Such analytical expression of solubility x might allow us to proceed with more profound consideration for atomic interaction and atomic configuration in the molten Fe 1Ϫy Cr y P x on the basis of statistical thermodynamics.KEY WORDS: molten Fe-Cr-P; non-stoichiometry; interstitial compound; phosphorus activity; Knudsen effusion technique. Analysis Available Equilibrium Phase Relationships forMolten Fe 1؊y Cr y P x Zaitsev et al.1) measured a Fe , a Cr and a P using Knudsen effusion technique over Fe-Cr-P ternary melt of specified compositions. As our interest was to derive expressions for x as functions of a P and T for given y in molten Fe 1Ϫy Cr y P x , we reproduce partially the presented data in Table I Form of Expression for xIn the earlier work 3) on comparative analysis of solubility of H, N and C in Fe, solubilities of H and N (diatomic ideal gas) were demonstrated to be most conveniently represented by expressionwhere A, B and C are constants to be determined to yield the best-fit experimental relationships (XϭH, N) whereas solubility x of C (solid element) in Fe was simulated by simpler expression (2) where A and C are constants determined with reference to available experimental solubility data.We decided to use the format of Eq. (1) for the expression of x for Fe 1Ϫy Cr y P x at any given y. For this purpose, we re-organised the equilibrium data presented by Zaitsev et al. 1) according to ascending order of y discarding the groups which possess the number of data sets no more than 5 (see Table 2) to ensure minimised margin of error in stochastic data processing. Determining Values of Parameters, A, B and C, in the x Estimation FormulaThe values of A, B and C for given values of y were determined as follows from the reported sets of experimental data. Among selected six groups of (x, y) data combinations, number of (a P , T) data combination was the highest in the group V (there are ten sets of (a P , T) available in the group V while there were eight sets in the other chosen groups). Thus, preliminary determination of values for constants, A, B and C, was made for the group V. As listed in Table 2, A for the group V (Fe 0.726 Cr 0.274 P 0.212 ) was determined to be 1.002ϫ10 4 , B Ϫ1.41 and C 1.594ϫ10 4 by repeated numerical iteration to make the minimum for the sum of squares of the difference between xϭ0.212 and t...