A simple theory of the Invar effect in iron-nickel alloys
  Certain alloys of iron and nickel (so-called 'Invar' alloys) exhibit almost no thermal expansion over a wide range of temperature. It is clear that this is the result of an anomalous contraction upon heating which counteracts the normal thermal expansion arising from the anharmonicity of lattice vibrations. This anomalous contraction seems to be related to the alloys' magnetic properties, since the effect vanishes at a temperature close to the Curie temperature. However, despite many years of intensive research, a widely accepted microscopic theory of the Invar effect in face-centered-cubic Fe-Ni alloys is still lacking. Here we present a simple theory of the Invar effect in these alloys based on Ising magnetism, ab initio total energy calculations, and the Debye-Gruneisen model. We show that this theory accurately reproduces several well known properties of these materials, including Guillaume's famous plot1 of the thermal expansion coefficient as a function of the concentration of nickel. Within the same framework, we are able to account in a straightforward way for experimentally observed deviations from Vegard's law. Our approach supports the idea that the lattice constant is governed by a few parameters, including the fraction of iron-iron nearest-neighbour pairs. 
Francois Liot and Christopher A. Hooley