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I.

INTRODUCTION

THEternary system Fe-Ni-Cr forms the basis of austenitic stainless steels, a material of utmost practical importance. Speich 1 assessed the literature data and presented several isothermal sections in addition to a liquidus and a solidus projection. Kaufman and Nesor, 2 Hillert and Waldenstrrm, 3 Hasebe and Nishizawa, 4 Counsell, Lees, and Spencer, 5 and Hertzman and Sundman 6 modeled the system thermodynamically and calculated the phase equilibria over a wide range of temperature. The study of Hertzman and Sundman6 is the most thorough among these investigations. Their study also includes the magnetic contributions to the thermodynamic properties of the fcc and bcc phases. However, we have recently completed thermodynamic modeling of phases and phase diagram calculation/prediction of Fe-Ni,7'8 Fe-Cr, 9'1~and Cr-Ni, u employing a different formalism to account for the magnetic contributions to the thermodynamic functions of metals and alloys. 12:3 The agreement between the model-calculated thermodynamic properties and phase boundaries with experimental data is better than those reported in the literature. The objective of the present study is to extend the binary studies to ternary Fe-Ni-Cr first by assessing the reliability of the thermodynamic models in terms of known thermodynamic and phase diagram data. And then We can calculate the phase equilibria over a wide range of temperatures and compositions, including the regions where experimental data are not available. In the present study, only phase equilibria from the liquid phase down to 500 K are reported.

G ~'

=

Zxi(~

[1] with ~ being the Gibbs energy of element i using the equilibrium magnetic state as the standard state, i.e., ~

= ~

z~SG 4>'m = A G 49,cpm''*eqm -

3 Zxim~ i=l

'cpm''~eqm

3 i=I ~- A G ep'cpm'')eqm

[4]

The last three terms of the RHS of Eq. [1] stand for the Gibbs energy of a mechanical mixture of elements exhibiting equilibrium magnetic state, while those of Eq. [4] for elements exhibiting completely paramagnetic state.

A. The Liquid Phase For the liquid phase, A G l'cpm-')eqm : 0. The AX~Gt''" term is given below. =

1 ~ ~ [wljxixj + (wlj

t i x j2] -- Wji)X

"= i=l

[5] No ternary interaction terms are introduced. The corresponding partial expressions are 3

In 7tp = ~ [(wlp + Wtpi)/2 + (w[p - wli)(Xp

-

-

Xi/2)]Xi

i-1 3

- ~ ~ [w~/2 + (wi~ - w~)xj]xixj

METALLURGICALTRANSACTIONS A

[3]

G e~ = ~ x i ( ~ 4''Cpm + RT In xi) + Agoge~'"m

3 YING-YU CHUANG, deceased, was with the Department of Metallurgical and Mineral Engineering, University of Wisconsin. Y. AUSTIN CHANG is Professor and Chairman, Department of Metallurgical and Mineral Engineering, University of Wisconsin, 1509 University Avenue, Madison, WI 53706. Manuscript submitted August 26, 1986.

[21

'cpm~eqm

Substituting Eqs. [2] and [3] into [1] yields

THERMODYNAMIC MODELS

To specify the thermodynamic expressions, the following subscripts and superscripts are used: subscripts 1, 2, and 3 denote Fe, Ni, and Cr, respectively, and superscripts I, y, an