Ab initio ternary σ-phase diagram: The CrMoRe system

For the first time, the formation enthalpies at 0 K of every ordered configuration of a ternary σ-phase, i.e. 53=243 configurations, have been calculated using the electronic density functional theory. The CrMoRe system has been chosen for the present investigation since the two binary CrRe and MoRe σ-phase are known to show opposite Re site preference: high coordination number sites in CrRe and low coordination number sites in MoRe. The ternary CrMoRe σ-phase diagram has been computed at 0 K. It presents at this temperature several distinct single-phase regions separated by a large number of miscibility gaps. Finite temperature properties have been calculated using only the configurational entropy, in the BraggWilliams approximation. Only above 800 K, the Gibbs energy surface becomes convex. The occupancies of the inequivalent sites have been computed as a function of composition at several temperatures. Re site preference is shown to change progressively in the ternary field when passing from CrRe to MoRe binary borders. © 2010 Elsevier Ltd. All rights reserved.