Order-disorder transitions in binary alloys

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Abstract
A quantum theory of order-disorder transitions in binary alloys is developed by studying the behaviour of the Gibbs free energy as a function of the distribution of positive ions on lattice sites and the accompanying distribution of valence electrons around them. An expression is derived determining the transition point in terms of the alloying potential, the Coulomb and exchange interactions between the valence electrons, the ionic and core repulsions between neighbouring positive ions, the relative concentration and the generalized susceptibility function of the electrons of the solid solution. The physical interpretation of the result is that the feasibility of a transition depends on the balance of Gibbs free energy which is restricted by the electron distribution in reciprocal space because of the geometry of the Fermi surface and of the Pauli exclusion principle. The compact analytic result provides a very convenient tool for testing various possible modes of transformation. The transfer of electrons as a result of ordering and the concept of bonding are also discussed.

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