Europhys. Lett., 57 (4), pp. 526–532 (2002) EUROPHYSICS LETTERS 15 February 2002 Prediction of the mixing enthalpy of alloys M. H. F. Sluiter and Y. Kawazoe Institute for Materials Research, Tohoku University 2-1-1 Katahira, Aoba-ku, 980-8577 Sendai, Japan (received 14 August 2001; accepted in final form 19 November 2001) PACS. 64.75.+g – Solubility, segregation, and mixing; phase separation. PACS. 65.20.+w – Thermal properties of liquids: heat capacity, thermal expansion, etc. PACS. 81.30.Bx – Phase diagrams of metals and alloys. Abstract. – A method for calculating the mixing enthalpy and the solution enthalpy is presented and applied to fcc Al-Li and Al-Mg alloys. Results are critically compared with those from other methods. In recent years much progress has been made in the ab initio theory of alloy phase sta- bility [1–3]. Of particular interest has been the prediction of composition temperature phase diagrams of alloys because the phase diagram has important practical applications. Moreover, it is a very sensitive test of predictive capabilities because it depends on small enthalpy dif- ferences. The order-disorder temperature of ordered superstructures, e.g., is proportional to the ordering enthalpy which is given by the difference of the formation enthalpy of an ordered structure and the mixing enthalpy at the same composition. The enthalpy of mixing refers to the configurationally random alloy where the atomic species randomly occupy lattice posi- tions [4]. The extent of solid solubility, too, is determined by a subtle balance of the mixing enthalpy and the formation enthalpy of ordered ground states. However, whereas the enthalpy of formation can be obtained ab initio from a few total-energy calculations without any ap- proximations beyond those pertaining to a density functional method, the calculation of the mixing enthalpy is more involved. The difficulty arises from the fact that the mixing enthalpy refers to a configurationally random alloy that is not well represented by a small supercell. In the past three decades, three methods have emerged for the study of configurationally random alloys. In the early seventies the coherent potential method (CPA) was developed and imple- mented within the multiple scattering formalism of Korringa, Kohn and Rostoker (KKR) [5]. The method approximates the configurationally random alloy with an effective medium that is determined self-consistently from the condition of stationarity of scattering. Despite recent improvements to the CPA concerning the treatment of charge correlations [6], other effects that go beyond the single-site approximation, such as relaxations of the atomic positions, cannot currently be treated. The Connolly-Williams (CW) method and its extensions appeared in the eighties [7]. Its essence is that a number of effective cluster interactions (ECIs) are extracted from the forma- tion enthalpies of a set of ordered structures with relatively small unit cells. These ECIs can be used to compute the formation enthalpies of any structure including the configurationally random alloy. Approximations of the CW method and its extensions are concerned with the arbitrariness of which ECIs and structures are selected. c  EDP Sciences