Coexisting Ordering and Phase Separation in Binary FCC Alloys
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COEXISTING ORDERING AND PHASE SEPARATION IN BINARY FCC ALLOYS
P.L. ROSSITER AND P.J. LAWRENCE Department of Materials Engineering, Monash University, Clayton, Victoria, 3168, Australia
ABSTRACT Consideration of only nearest neighbour pairwise interactions Vij in a binary alloy leads to the classification of the system as ordering (unlike near neighbours) or clustering (like near neighbours), depending upon the sign of Vij. However, this simple classification loses meaning when multi-atom correlations, many-body interactions or a longer range interaction are considered. For example, the first nearest neighbour interaction may favour ordering while the second, which may be of comparable magnitude, may favour clustering. By extending the Bragg-Williams model to include second near-neighbour interactions in fcc alloys, it is shown that a miscibility gap may form in the region of the orderdisorder solvus, leading to a complicated sequence of atomic rearrangement upon slow cooling. Despite the well-known failings of the point approximation when applied to fcc alloys, the results are shown to be consistent with the unusual behaviour exhibited by some systems.
INTRODUCTION Early studies of phase transitions in binary alloys (e.g. regular solution, Bragg-Williams) used the Bethd assumption which restricted the range of atomic interactions to first near-neighbours [1-3]. Systems could then be classified simply as ordering (unlike near-neighbours) or phase separating (clustering, like near-neighbours) depending upon the sign of the nearest-neighbour pairwise interchange energy
(V1. + v..BB
V= ( v.. ij
13
13
-(1
B 13j
However, extending the range of interaction has shown that the simple classification of a system as either clustering or ordering is no longer adequate [4]. For example, while Vij may be positive for first nearneighbours favouring atomic ordering, the interaction for second nearneighbours may be negative and of similar magnitude (as a consequence of the oscillating form of the interaction potential) favouring phase separation. Ino [5] has extended the Bragg-Williams theory in bcc alloys by incorporating second near-neighbour interactions. He showed that a miscibility gap is expected to occur below the order-disorder solvus resulting in a separation of the ordered phase into a two phase ordered + disordered mixture. Similar extensions have been applied to the fcc system only in determination of the ground state [6] or consideration of special point instabilities [7-9]. We will return to consideration of these latter theories in the discussion. The subject of the present study is to extend the Bragg-Williams theory to consider second near-neighbour interactions in fcc alloys for arbitrary temperature and composition.
Mat.
Res. Soc. Symp. Proc. Vol. 21 (1984) Q Elsevier Science Publishing Co., Inc.
482
CALCULATIONS While the method of calculation to be presented here is quite general with respect to sign and magnitude of the first and second near-neighbour interactions V, and V2 respectively, results
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