B2 and B32 ordering transformations of equiatomic bcc alloys with ballistic and thermal atom movements
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We used Monte Carlo simulations to study the kinetics and steady states of B2 and B32 ordering in an equiatomic binary bcc alloy having both thermal and ballistic atom movements. Atom movements occurred by a vacancy mechanism, where first-neighbor atoms exchanged sites with the vacancy. In the thermodynamic case, where this jump probability was set by a Boltzmann factor alone, we found the formation of large amounts of transient B2 (B32) during disorder —• B32 (B2) order transformations. The transient order developed in distinct regions, but vanished completely when equilibrium was attained. Ballistic jumps were included as random interchanges of the vacancy with one of its neighboring atoms. Even with small fractions of ballistic jumps, there were large changes in the transient states and steady states of order in the alloy. A kinetic explanation is proposed, in which the presence of ballistic jumps contributed a greater amount of internal energy to the B2 phase than to the B32 phase when there was a strong asymmetry in the second-nearest neighbor pair potentials (VAA2 ^ ^BB2)- A two-phase coexistence in the steady state was explained by fluctuations in the local density of ballistic jumps.
I. INTRODUCTION Thermodynamics and statistical mechanics are the standard tools for understanding phase equilibria in materials. States of thermodynamic equilibrium are expected when atom movements are consistent with activated state rate theory, such as employed in studies with the path probability method 1 ^ or the kinetic master equation method.5"8 There are, however, a number of experimental techniques for the processing of materials where some atom movements are not expected to be understood by activated state rate theory alone. In these "driven systems", such as alloys subjected to highenergy ball milling or high-energy ion bombardment, some atom movements occur with a greater element of randomness than expected from the Boltzmann factors of activated state rate theory. It may be possible to consider these atom movements as occurring at a different temperature than the thermodynamic temperature of the alloy. Martin and co-workers9"18 have studied a canonical model of driven systems in which the normal thermal atom movements are accompanied by atom movements at an infinite temperature. These additional "ballistic jumps" are insensitive to the local chemical preferences of an atom, and these kinetic events sample all outcomes with equal probability. While this model is an oversimplification of the processes that occur in highenergy ball milling and ion beam bombardment, it does include an essential difference between driven systems and thermodynamic systems. Martin et al. showed that 126
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J. Mater. Res., Vol. 10, No. 1, Jan 1995
Downloaded: 24 Mar 2015
in comparison to alloy kinetics based on activated state rate theory, with ballistic jumps the kinetics and the final steady states of driven systems can be altered substantially.9"18 Ground state (T = 0) structures of bcc binary alloys have
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