The critical temperatures of binary alloys with one magnetic component

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Abstract
Binary alloys with N A atoms of component A and N B atoms of component B on N A + N B lattice sites are considered. Component A is ferromagnetic or anti-ferromagnetic with an arbitrary number of Bohr magnetons per atom while B is without magnetic properties. There is a Heisenberg exchange interaction between nearest-neighbour A-A pairs and interaction energies for nearest-neighbour A-B and B-B pairs are introduced. The effect of the local order in the lattice distribution of the A and B atoms on the Curie or Néel temperature is examined both for equilibrium (annealed) alloys where the local order is temperature dependent and for quenched alloys where the lattice distribution is fixed (though not necessarily random). A Bethe-pair (first-order quasi-chemical) statistical approximation is used. It is shown that even though magnetic moments are taken as constant on the A atoms and zero on the B atoms the curves of Curie or Néel temperature against composition vary widely according to the value of the A-B interaction energy and the heat treatment. For quenched alloys there is a critical mole-fraction of A below which there is no spontaneous magnetization; this critical mole-fraction depends on the temperature from which the alloy is quenched. For equilibrium alloys there is also a critical mole-fraction for some values of the A-B interaction parameter but for others a Curie temperature exists for all finite mole-fractions of A. Where A is anti-ferromagnetic there is always a critical mole-fraction below which no Néel temperature exists but its value varies widely. Some relevant experimental results are discussed.