Calculation of the magnetic contribution for intermetallic compounds

Celphad, Vol. 24, No. 2, pp. 181-182,200O (D 2001 Published by Elsevier Science Ltd All rights reserved 0384-5916/00/$ - see front matter

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Calculation of the magnetic contribution for intermetallic compounds I. Ansara*, B. Sundman+

* Laboratoire de Thermodynamique et de Physico-Chimie M&allurgiques, ENSEEG, BP. 75,38402 Saint-Martin-d’Hi?res Cedex, France. + Department of Materials Science and Engineering, Royal Institute of Technology, Stockholm, Sweden. Many software systems for phase diagram calculations use the so called “localized” magnetic model to describe the entropy contribution due to magnetic spins. In this model the entropy contribution due to the magnetic moment, ,0, of the constituents in the disordered paramagnetic state is given by the equation

s, = -R aj(7-) . ln(/3 + 1)”

(1)

where r is T/Tc, Tc the temperature for magnetic ordering, f, a function proposed by Inden [76Ind], /I, the magnetic moment in Bohr magnetons and n, the number of sites for the magnetic constituents. For a compound A,Bb where the element A is magnetic only, the entropy contribution is equal to S m = -R . f(r) - ln(/3 + 1)” (2) If both A and B are magnetic, with the average magnetic moment equal to ,& the contribution to the entropy is S, = -R - f(7) - ln(/3 + l)a+b (3) In the Thermo-Calc software [85&n], which is frequently used for assessing thermodynamic parameters, attention must be paid to the stoichiometric factors in this equation. The Gibbs energy with magnetic properties is expressed, per mole of formula unit of a compound, as G, = Gkrn+ G”,“s (4) where G”, is the Gibbs enery of formation of the hypothetical non-magnetic compound and GFs is the magnetic contribution to the Gibbs energy. The magnetic contribution to the Gibbs energy for a phase with the magnetic moment /3, is calculated in Them-to-&k as GE% = R. T - f(~) - ln(/3 + 1) Received3 Cktober2000 181

(5)

I. ANSARA AND B. SUNDMAN

182

independent of the number of sites for the magnetic constituents. Thus the number of sites for the sublattice with the magnetic constituents must be unity, or the number of sites must be incorporated in the ,LIas was done for the spine1 phase in Fe-O [91Sun]: ln(p + 1)” = In@ + 1)

(6)

where p’ is evaluated to be the same as (p + 1)” - 1. In the present version of Thermo-Calc the only parameters that can be varied in the magnetic contribution are p and TC and not the number of sites for the magnetic element and thus some care must be taken to have the correct magnetic contribution. The simplest way is to have exactly one site of the sublattice for magnetic elements; hence a compound A,Bb, where only element A is magnetic, should be modelled as ArBb/(a+b). If both elements are magnetic it should be modelled as Aa/(a+b)Bb/(a+b). In a future release of Thermo-Calc it will be possible to specify the number of sites for the magnetic elements.

References [761nd]

G. Inden, Report of the Project Meeting Calphad V, (1976) III&l

[85Sun]

B. Sundman, B. Jansson, and J.-O. Andersson, Calphad, 2,9 (1985) 153-190.

[91Sun]

B. Sundman, J. Phase Equil., 12,2 (1991) 127-140.