Magnetic contributions to the thermodynamic functions of pure Ni, Co, and Fe
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I.
INTRODUCTION
THEimpact of magnetic effects on phase stability has been demonstrated in 1955 by Zener I and later by Meijering-' and Hillert, Wada, and Wada. 3 Recently, this field has attracted considerable interest. 4 u Rather unusual phase diagrams, e.g., with horns on binary miscibility gaps, are a consequence of magnetic alloying effects, which are not at all negligible. In order to perform quantitative calculations of phase stabilities in binary or multicomponent systems with magnetic elements, the most crucial input quantity for any thermodynamic model is the magnetic Gibbs energy of the pure elements as a function of temperature. In a major contribution, lnden 5'9 suggested to derive this quantity from an empirical equation for the magnetic specific heat. This equation implies a logarithmic singularity at the critical temperature, but no integration in closed form is available to derive the magnetic Gibbs energy or entropy. Hillert and Jarl 7 replaced lnden's equation by a truncated power series and obtained a bandy form for the magnetic Gibbs energy. In this study, we propose a different simple equation for the magnetic specific heat which leads immediately to an equation for the magnetic Gibbs energy in a short closed form. In addition, a new separation of magnetic and nonmagnetic contributions to the experimental specific heat has been performed in order to obtain the most reliable data for empirical factors in the equations proposed here. The objectives of this study are to propose analytical descriptions of the magnetic Gibbs energy, entropy, enthalpy, and specific heat in a closed form, to determine empirical factors in these equations for pure Ni, Co, and Fe. and to apply this concept to the fcc-bcc phase stability of iron. In particular, the YING-'tU CHUANG and Y. AUSTIN CHANG are, respectively, Research Associate and Professor and Chairman, Department of Metallurgical and Mineral Engineering, University of Wisconsin, Madison, WI 53706. RAINER SCHMID, Visiting Associate Professor, Department of Metallurgical and Mineral Engineering, University of Wisconsin, Madison, WI 53706, is with the Technical University Clausthal, West Germany. Manuscript submitted May 14, 1984.
METALLURGICALTRANSACTIONS A
stability of bcc-Fe at low temperatures is rationalized quantitatively in terms of the magnetic contributions.
II.
SEPARATION OF MAGNETIC AND NONMAGNETIC SPECIFIC HEAT
The empirical approach used by Weiss and Tauer ~3 and Hofmann et a1.14 to split up the experimental specific heat data in additive lattice, electronic, and magnetic contributions is followed here. But the presumably most crucial parameter, the Debye temperature 0, is determined here from the data over a wide temperature range, up to half of the Curie temperature, T,. The magnetic contribution over that temperature range is not negligible. In the present study, it has been approximated from spin wave theory merely for the determination of 0, This procedure to obtain values of 0 from specific heat data over a wide range of temperature is
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