Electronic Structure and Phase Stability Properties in Ternary Substitutional Alloys
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ELECTRONIC STRUCTURE AND PHASE STABILITY PROPERTIES IN TERNARY SUBSTITUTIONAL ALLOYS Ariel J.S. Traiber" ** , Marcel Sluiter* , Patrice E.A. Turchi* and Samuel M. Allen** *Lawrence Livermore National Laboratory, Condensed Matter Division, L-268, Livermore, CA 94550 "*Massachusetts Institute of Technology, Department of Materials Science and Engineering, Cambridge, MA 02139 ABSTRACT Electronic structure and stability properties of ternary-metal alloys are examined using an extension of the Coherent Potential Approximation -Generalized Perturbation Method approach within the Tight-Binding description of the chemically random alloy. In particular, we report on calculations of density of states, mixing energies and effective cluster interactions which build up the ordering energy. The study focuses on the Ti-V-Fe system and its binary components. INTRODUCTION Solid solutions with ordered phases that exhibit interesting properties have attracted new interest for special applications (such as high-temperature intermetallic compounds). As materials with practical relevance rarely consist of binary systems, the study of multicomponent systems is highly desirable. In order to develop these materials, the type of ordering and the determination of phase equilibria are fundamental problems that need to be solved [1]. In the last decade, considerable improvement has been achieved in the calculation of both energies of formation of disordered and ordered alloys and of multisite effective interactions based on band structure calculations. Such parameters can be used to obtain fairly accurate predictions of phase stability at T=O K. These interactions can then be used in combination with statistical thermodynamic models to compute phase diagrams. Phenomenological theories for the study of ordering processes provide the link between electronic structure calculations and statisticals models. For instance, the generalperturbation method (GPM) [3) attempts a direct determination of concentration-dependent multisite interactions in real space. This method is a perturbation treatment performed from a reference medium, such as the complete disordered state described by the coherentpotential approximation (CPA) [4, 5], which is close to any alloy configuration. Our study of the electronic structure and the phase stability properties of ternary alloys is carried out within the CPA-GPM framework in the tight-binding (TB) approximation. Let p, be an occupation number; p, = 0 or 1 depending on wether or not the site n is occupied by an atom of type i. Any chemical configuration is completely specified by the set of {p,}. Then, in the GPM framework, the band energy of a given configuration is -written as E({p'}) = Edi.(c) + AEo.d({pi}), (1) where the energy of the disorder state Edi, is configuration-independent as calculated with the CPA method, and AEoŽEad is the ordering energy which can be expanded as follows
A Eord
Si +ijk(3)b 1n 2 i VnM2( )V6ct n + 3-N
i2 i3N n~m rnl~
i
cc'
""omq"tiAn
WMat. Res. Soc. Symp. Proc. Vol. 291. 01993 Ma
