Basic and Applied Research: Section I Critical Evaluation and Optimization of the Thermodynamic Properties and Phase Diagrams of the AI-Mg, AI-Sr, Mg-Sr, and AI-Mg-Sr Systems P. Chartrand and A.D. Pelton Centre de Recherche en Calcul Thermochimique Ecole Polytechnique P.O. Box 6079, Station "Centre Ville" Montreal, Quebec, Canada, H3C 3A7 (Submitted May 3, 1994; in revised form October 4, 1994) All available thermodynamic and phase diagram data were critically assessed for all phases in the AI- Mg, AI-Sr, and Mg-Sr systems at 1 bar pressure from room temperature to above the liquidus tem- peratures. For these systems, all reliable data were simultaneously optimized to obtain a set of model equations for the Gibbs energy of the liquid alloy and all solid phases as functions of composition and temperature. The modified quasi-chemical model was used for the liquid. The AI-Mg-Sr ternary phase diagram was calculated from the optimized thermodynamic properties of the binary systems. Since no reliable ternary data were available, three assumptions were made: no ternary terms were added to the model parameters for the thermodynamic properties of the liquid, no ternary solid so- lutions are present in the system, and no ternary compound is present in the system. The calculated ternary phase diagram is thus a first approximation, which can be improved by the addition of new experimental data and can be used as a base for the calculation of phase diagrams of multicomponent systems. Introduction Strontium is used, like sodium, in aluminum cast alloys con- taining silicon to modify the acicular structure of the A1-Si eu- tectic. Timminco Ltd., which produces A1-Sr master alloys for the aluminum industry, has patented master A1-Sr-Mg compo- sitions with an increased Sr content. To control the production of ingots of these master alloys, the A1-Mg-Sr phase diagram is required, but no satisfactory experimental phase diagram is currently available. The prediction of the phase diagram is pos- sible from the thermodynamic optimizations of the three bi- nary systems using appropriate models. [82Mur] reviewed the literature and optimized the A1-Mg system. Other optimiza- tions of this system were performed by [77Sab], [86Lud], [90Saul, and [93Zuo]. [89Alc] studied and optimized the A1-Sr system. [91Sri] also made an optimization of this system. [86Nay] made the only optimization of the Mg-Sr system. Because more recent thermodynamic data are now available, and in order to obtain more complete and precise results, the present authors decided to reoptimize the three binary systems before calculating the ternary phase diagram. A ternary diagram calculation requires that the same model be used in all binary systems for each phase present in the ternary field. For the liquid phase, the present authors used the modi- fied quasi-chemical model [86Pel], which is well adapted to describe the ordered liquid in the A1-Sr system. The model considers the Gibbs energy for the formation of two A-B bonds from one A-A bond and one B-B bond (see Eq 1). [A-A] + [B-BI =2 [A -BI (Eq 1) Expressions for enthalpies and entropies of mixing are written in terms of the bond fractions XAA,Xse, and Xae, and in terms of (m-qT) which is the Gibbs energy change of the bond ex- change reaction (Eq 1). The equilibrium bond fractions are ob- tained by setting: | (Eq 2) 3XA8 ; while taking account of the mass balances. This results in an "equilibrium constant" for the bond exchange reaction (Eq 1). Details of the model were presented by [86Pel]. The fixed pa- rameters of the model in the present evaluation are "coordina- tion numbers" ZA1 = bAiX, ZMg = bMgZ, and Zsr = bsrZ where Z = 6, bAl --- 1.3774, bMg --- 0.9183, and bsr = 2.0661. These pa- rameters are those used in previous evaluations, which are forming a data base on metalhc liquid solutions. The thermodynamic properties of A1, Mg, and Sr used in this evaluation are given in Table 1 and apply to Eq 3: H = A + ; CvdT J/g-atom 298 15 S=B+;29815 (C[/T~tr J/K . g-atom Cp =a + b (10-3)T+ c (105)T -~- + d (10-6)T2 J/K. g-atom (Eq3) Journal of Phase Equilibria Vol. 15 No. 6 1994 591