Mathematical Proceedings of the Cambridge Philosophical Society · 1937 · 33 citations · 5 references
Natural SciencesMaterials SciencePhysicsCondensed Matter PhysicsSolid State PhysicsThermodynamicsAlloysCritical PhenomenaMetalsOrder-disorder TransformationsOrdering TransformationsPhase TransitionsBragg-williams ApproximationCritical TemperatureOrder-disorder Phase DiagramOrder-disorder Phase TransitionOrdered AlloysSuperlattice FormationSuperlatticesTemperature-dependent Ordering
The statistical treatment of order-disorder transformations, as developed by Bethe and Peierls, has been extended to alloys having superlattices of the AB and AB 3 types but compositions which differ slightly from the ideal compositions required for the formation of perfect superlattices. If the composition of the alloy is specified by the concentration c of one component, which we have chosen to be the A component, then the results show that for alloys of the AB type the critical temperature should have a maximum value when c = ½, that is, for the ideal composition. This is in agreement with experiment. For alloys of the AB 3 type it is found that the maximum value should occur for some value of c > ¼. This result disagrees with that obtained experimentally, but both results agree, at least qualitatively, with those obtained by the theory of Bragg and Williams.
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