  The Invar effect in ferromagnetic Fe-Ni, Fe-Pt, and Fe-Pd alloys is
investigated theoretically by means of a computationally efficient scheme. The
procedure can be divided into two stages: study of magnetism and calculations
of structural properties. In the first stage, an Ising model is considered and
fractions of Fe moments which point up as a function of temperature are
determined. In the second stage, density-functional theory calculations are
performed to evaluate free energies of alloys in partially disordered local
moment states as a function of lattice constant for various temperatures.
Extensive tests of the scheme are carried out by comparing simulation results
for thermal expansion coefficients of Fe1-xNix with x = 0.35, 0.4, ..., 0.8,
Fe0.72Pt0.28, and Fe0.68Pd0.32 with measurements. The scheme is found to
perform well, at least qualitatively, throughout the whole spectrum of test
compounds. For example, the significant reduction of the thermal expansion
coefficient of Fe1-xNix as x decreases from 0.55 to 0.35 near room temperature,
which was discovered by Guillaume, is reliably reproduced. As a result of the
overall qualitative agreement between theory and experiment, it appears that
the Invar effect in Fe-Ni alloys can be investigated within the same
computational framework as Fe-Pt and Fe-Pd.
