Linking first-principles energetics to CALPHAD: An application to thermodynamic modeling of the Al-Ca binary system
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I. INTRODUCTION
THE Al-Ca binary is an important subsystem in the new family of creep-resistant Mg-Al-Ca-Sr alloys. Therefore, accurately assessing the thermodynamics and phase stability in AlCa is important toward developing a reliable, robust database of Mg alloy thermodynamics for use in CALPHAD (CALculation of PHAse Diagram) modeling. In the Al-Ca binary system,[1] there has been relatively little experimental data in the literature on the Ca-rich side of the phase diagram, compared with the Al-rich side. Even in such a seemingly simple binary system, new phases have recently been discovered: The existence of Al14Ca13 and Al3Ca8 compounds was recently reported by X-ray diffraction studies.[2,3] In earlier assessments,[4,5] the Al-Ca binary phase diagram had been given as a two-compound system (i.e., Al4Ca and Al2Ca compounds after References 6 and 7) with two eutectic and one peritectic invariant points. Recent CALPHAD modeling studies,[1,8] have been modified to include all the known existing compounds in the Al-Ca binary system. The Al-Ca is now considered a four-compound system having three eutectic and two peritectic invariant reaction points on its phase diagram. Although crystal structures and phase equilibria of the Al14Ca13 and Al3Ca8 compounds have recently been reported, very little is known regarding their thermodynamic properties. There is, for example, only one measured enthalpy of formation available for the Al3Ca8 compound in the literature.[8] For the Al14Ca13 compound, experimental reports are so sparse that only its peritectic reaction temperature is reported.[8] In KORAY OZTURK, YU ZHONG, LONG-QING CHEN, and ZI-KUI LIU, Department of Materials Science and Engineering, and JORGE O. SOFO, Materials Research Institute & Department of Physics, are with The Pennsylvania State University, University Park, PA 16802. Contact e-mail: [email protected] C. WOLVERTON is with Ford Research and Advanced Engineering, MD3083/SRL, Dearborn, MI 48121-2053. Manuscript submitted May 15, 2003. METALLURGICAL AND MATERIALS TRANSACTIONS A
addition, even for the relatively well-known C15 Al2Ca phase, modeling off-stoichiometry requires knowledge of energetics of antisite defects in the structure. These energetics are either difficult or impossible to obtain from experiment, but are nevertheless critical toward accurate CALPHAD modeling. This scarcity of information has led us to re-examine the energetics of this alloy system with a first-principles (FP) densityfunctional theory based approach to predict the T 0 K enthalpies of formation, and end-member energetics. Complexities that may arise from configurational or vibrational entropies at finite temperatures are not considered in the present FP calculations. These entropic effects are, of course, included in the CALPHAD modeling accordingly. Wolverton et al.[9] have recently shown how FP calculations may provide key unknown energetics, and hence be used as a useful complement to experimental information, in the CALPHAD approach. We follow the proposed hybrid FP CAL
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