A First-Principles Study of the Phase Stability of FCC-and HCP-Based Ti-Al Alloys
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A FIRST-PRINCIPLES STUDY OF THE PHASE STABILITY OF FCC-AND HCP-BASED Ti-Al ALLOYS Mark Asta1, Mark van Schilfgaarde 2 and Didier de Fontaine 1 t Department of Materials Science and Mineral Engineering, University of California at Berkeley, Berkeley, CA 94720, and Materials Sciences Division, Lawrence Berkeley Laboratory, Berkeley CA 94720 2 SRI International, Menlo Park, CA 94025
ABSTRACT In this paper we present results of a first-principles study of phase stability and structural and thermodynamic properties of fcc- and hcp-based Ti-Al alloys. In particular, the full-potential linear muffin tin orbital method has been used to determine heats of formation and other zerotemperature properties of 9 fcc and 7 hcp ordered superstructures as well as fcc and hcp Ti and Al. From these results a set of effective cluster interactions are determined which are used in a cluster variation method calculation of the solid-state portion of the composition-temperature phase diagram for fcc- and hcp-based alloys. INTRODUCTION Despite the many attractive properties of Ti-Al compounds, such as low density and high elevated-temperature strength, these alloys have found only limited use as high-temperature structural materials due primarily to their brittleness at room temperature [1]. Substantial research has been devoted to improving the ductility of Ti-Al alloys without appreciably altering other desirable properties. In particular, through ternary additions, and by using novel processing techniques, alloy designers have worked to stabilize compounds with high (cubic) symmetry and to develop materials with multiphase microstructures [1]; somewhat improved ductilities have been achieved. Clearly an understanding of the relative stability and the properties of equilibrium and metastable phases is needed to guide research in the Ti-Al system. In the present paper we summarize the results of a first-principles study of structural and thermodynamic properties and the composition-temperature (c-T) phase diagram of fcc- and hcpbased Ti-Al alloys. In this type of study where the atomic numbers of the elements are the only information input, calculated phase diagrams cannot be expected to agree completely with experiment regarding absolute values of the temperatures of equilibrium reactions. However, abinitio calculations are valuable since alloy properties for stable and metastable phases can be calculated as a function of composition and temperature, the relative stability of competing structures can be reliably predicted, and a fundamental understanding of these results can be obtained in terms of the electronic structure and bonding mechanisms. COMPUTATIONAL APPROACH The computational approach taken in this study is described in detail in reference 2 and will only be briefly summarized here. The total energy of elemental Ti and Al and of 9 fcc and 7 hcp ordered alloy compounds were calculated as a function of the atomic volume using the fullpotential [3] linear muffin tin orbitals [4] method (FLMTO). It has been shown previously [2] th
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