Theory of Order-Disorder Transition in Binary Alloy with Arbitrary Mole Fraction. I. Case of b.c.c. Type Lattice

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By means of symmetry-breaking potential method originally due to Kramers and Opechowski, the free energy of binary alloy with the b.c.c. type lattice is obtained. The calculation is made up to the fifth order in an expansion into power series of a parameter ξ=tanh (βJ), where J denotes the pair interaction energy between the nearest neighbouring sites. The phase transitions are found to be always of second order through whole range of the mole fraction and in all stages of first to fifth order approximations. The transition temperature and temperature dependence of the order parameter and of the specific heat are obtained and shown diagrammatically. By neglecting terms higher than third or fourth order with βJ, the results reduce to those previously obtained by other authors.

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