K-space symmetry rules for order-disorder reactions

Abstract

Abstract A mean-field free energy is formulated in k-space and applied to order-disorder reactions in substitutional solid solutions whose average lattice is i'.c.c. or b.c.c. The different symmetry properties of the harmonic and anharmonic contributions are described. The dynamics of concentration fluctuations and the early-stage kinetics of decomposing solutions are governed mainly by the harmonic terms whose basic properties are related to the special points of the first Brillouin zone. Useful predictions can be made about short-range order intensity profiles in the vicinity of the special points with the help of tables of eigenvalues of standard k-space functions derived for pair interactions out to fifth coordination shell. These new concepts are applied to the case of order-disorder reactions in the Ni-Mo system. An explanation given for the appearance of 〈1 1 2 0〉 special point diffuse intensity peaks at all accessible concentrations, from Ni4Mo to Ni2Mo. It is suggested, in general, that the appearance in quenched samples of imperfectly ordered special-point structures is due to a spinodal ordering reaction. A classification of ordering mechanisms is then proposed based on the Landau and Lifshitz symmetry rules for second-kind transitions.