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Kinetics of short- and long-range B2 ordering in the pair approximation

  • B. Fultz (a1)

Abstract

The kinetic master equation is developed in the pair approximation to study disorder ⇉ B2 order transformations in bee binary alloys. Coupled sets of rate equations for the pair variables are obtained for atom movements by either the direct interchange mechanism or the vacancy mechanism. Numerical integrations provide the nonequilibrium relaxations of short- and long-range order (SRO and LRO) and the vacancy balances between the two sublattices. For binary alloys, disorder ⇉ order transformations were studied for all combinations of interatomic interaction strengths, activation barrier heights, and alloy stoichiometry variations. After a transient vacancy relaxation, all cases began with a quick relaxation of SRO, followed later and independently by the growth of LRO and additional SRO. There were some variations in kinetic path through SRO and LRO, moderate variations in overall kinetics, and large variations in vacancy balance. Some nonphysical aspects of kinetics in the pair approximation are discussed.

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1Fultz, B., Acta Metall. 37, 823 (1989).
2Fultz, B., Hamdeh, H., and Pearson, D. H., Acta Metall. (in press).
3Anthony, L. and Fultz, B., J. Mater. Res. 4 (5), 1132 (1989); ibid. 4 (5), 1140 (1989).
4Kikuchi, R. and Sato, H., J. Chem. Phys. 51, 161 (1969); ibid. 57, 4962 (1972).
5Bakker, H., Phil. Mag. A 40, 525 (1979).
6Sato, H. and Kikuchi, R., Acta Metall. 24, 797 (1976).
7Sato, H., Gschwend, K., and Kikuchi, R., J. de Physique C7, 357 (1977).
8Gschwend, K., Sato, H., and Kikuchi, R., Chem, J.. Phys. 69, 5006 (1978).
9 The vector A is of rank 4 if all pair variables {N AA, N AB, N BA, N BB} are considered.
10 An A ↔ B interchange refers to an initial state with A on α and B on β.
11 Equation (34) is the same as the first expression for Process 1 in Appendix The, A. other 31 equations can be derived in a similar manner.
12Fultz, B., Chem, J.. Phys. 87, 1604 (1987).
13 It was possible to suppress this quiescent period by starting with an initial imbalance of species on the two sublattices on the order of 10% or greater, but such an initial state is hardly one of a dis-ordered alloy.
14 Because of APDBs, the concept of LRO in the pair approximation is not consistent with the LRO determined experimentally by diffraction techniques. The intensity of superlattice diffractions is unaffected by the presence of APDBs, whereas the theoretical LRO is destroyed by the presence of APDBs.

Kinetics of short- and long-range B2 ordering in the pair approximation

  • B. Fultz (a1)

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