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Certain alloys of iron and nickel (so-called 'Invar' alloys) exhibit almostno thermal expansion over a wide range of temperature. It is clear that this isthe result of an anomalous contraction upon heating which counteracts thenormal thermal expansion arising from the anharmonicity of lattice vibrations.This anomalous contraction seems to be related to the alloys' magneticproperties, since the effect vanishes at a temperature close to the Curietemperature. However, despite many years of intensive research, a widelyaccepted microscopic theory of the Invar effect in face-centered-cubic Fe-Nialloys is still lacking. Here we present a simple theory of the Invar effect inthese alloys based on Ising magnetism, ab initio total energy calculations, andthe Debye-Gruneisen model. We show that this theory accurately reproducesseveral well known properties of these materials, including Guillaume's famousplot1 of the thermal expansion coefficient as a function of the concentrationof nickel. Within the same framework, we are able to account in astraightforward way for experimentally observed deviations from Vegard's law.Our approach supports the idea that the lattice constant is governed by a fewparameters, including the fraction of iron-iron nearest-neighbour pairs.

A simple theory of the Invar effect in iron-nickel alloys