Calculation and evaluation of the gibbs energies of formation of Cr 3 C 2 , Cr 7 C 3 , and Cr 23 C 6
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formation for the two chromium carbides. Use is made of reliable standard thermal data for the compounds involved. Also, comparisons are given of all information on the Gibbs energies of formation of the various chromium carbides, both from this and previous investigations.
THERMODYNAMIC TREATMENT OF Fe-Cr-C ALLOYS Kuo 1~and Jellinghaus and Keller ~2(JK) heat-treated iron alloys containing 0.20 to 2.0 pct carbon and up to 25 pct chromium for 260 to 1460 h at 700 ~ This temperature is sufficiently above the miscibility gap in the iron-chromium binary system to obviate any complex phase transitions in the carbon-bearing alloys. Chemical analyses for the important elements in the ferrite and solid solution carbide ( M 7 C 3 o r M23C6; M = substitutional metal atom) phases of selected alloys are listed in Table I and, along with results for ferrite-M3C alloys, are displayed in Fig. 1. For this figure, selection of composition data for the construction of the two-phase ferrite-carbide regions from the two sources was based on 1) the agreement of the given carbon contents of the carbides with those expected from the stoichiometry of the individual M 7 C 3 and M23C 6 alloys and 2) the convergence of the ferrite phase boundaries in the two regions containing three solid phases at one point (not shown). Darken 13confined his analysis of the iron-chromium-carbon system to the two-phase regions ferrite-M7C3 and ferrite-M23C 6. The following assumptions were made in his thermodynamic treatment: a) In ferrite, with carbon present at very dilute levels, the activity of chromium may be approximated by that in a regular solution of the two metals. The activity coefficient of chromium can thus be obtained from
ISSN 0360-2133/81/0811-1389500,75/0 9 1981 AMERICAN SOCIETY FOR METALS AND THE METALLURGICAL SOCIETY OF AIME
VOLUME 12A, AUGUST 1981--1389
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lnTcr = a 9 N~ Values of the c o n s t a n t a, which is i n d e p e n d e n t of c o n c e n t r a t i o n a n d inversely related to t e m p e r a t u r e , were c o m p u t e d b a s e d o n the f o r m a t i o n of a n im-
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miscibility gap in the i r o n - c h r o m i u m system at Nor = NFo = 0.5 with a = 2.0 at 560 ~ the critical solution t e m p e r a t u r e d e t e r m i n e d b y W i l l i a m s a n d Paxton. 14 Values of the activity coefficients calculated in this f a s h i o n are in good a g r e e m e n t with those o b t a i n e d for this alloy system b y K i r c h n e r et al ]5 a n d J e a n n i n et al. ]6 b) T h e c o m p o n e n t metallic carbides, represented in single m e t a l a t o m form as F e C x a n d C r C x (x = 1/3, 3/7, a n d 6 / 2 3 ) , m a k e u p a n ideal s o l u t i o n within a carbide phase, with their activities, aFoc a n d act c , given simply b y their respective a t o m fractions 0~%r a n d 0~{. This a s s u m p t i o n was p r o v e n to b e valid b y R i c h a r d son 17 for the c a r b i d e phase in the F e - M n - C system. T h e f o r m a t i o n
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