Phase Stability and Diagrams from First Principles
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PHASE STABILITY AND DIAGRAMS FROM FIRST PRINCIPLES
J.M. SANCHEZ AND J.D. BECKER Center for Materials Science and Engineering, The University of Texas at Austin, Austin, Texas 78712
ABSTRACT First principles theories of alloy phase equilibrium have been successfully used in recent years to compute temperature-composition phase diagrams for solid state phases. One particular approach, originating with the successful phenomenological Ising models to describe the alloy Hamiltonian, uses a cluster expansion of the configurational energy in terms of short-ranged pair and many-body interactions. The approach is deeply rooted in our ability to compute accurate total energies of relatively complex compounds, using density functional theory in the local approximation, from which effective interactions may be obtained. Fundamental aspects of the method which include convergence of the cluster expansion, treatment of the configurational entropy and description of vibrational modes are reviewed. Applications of the theory are given for binary alloys in the Ru-Zr-Nb system using the Linear Muffin Tin Orbital method for the total energy calculations, the Cluster Variation method for the description of the configurational entropy, and the Debye-Griineisen approximation for the vibrational modes. The results are used to compute the equilibrium phase diagram for the Zr-Nb system and to assess current experimental data on phase stability in the Ru-Nb system. In the latter case, the calculations indicate that the D019 structure is a likely candidate structure for the experimentally observed hexagonal-based compound Ru 3 Nb. Investigation of the energies and interactions of tetragonal structures as a function of the c/a ratio suggest the LI 0 structure as a likely candidate for the observed tetragonal phase near 1: 1 stoichiometry.
INTRODUCTION A number of physical properties, such as cohesive energies, elastic moduli and expansion coefficients of elemental solids and intermetallic compounds, are now routinely calculated from first principles using, as input, only the atomic numbers of the constituent elements and the crystal structure of the solid. These achievements are a direct consequence of a mature theoretical and computational framework in solid state physics which has been in place for some time. Here we will focus on recent theoretical and computational developments in alloy theory which make possible the non-empirical calculation of phase diagrams and, in general, the study of phase stability strictly from first principles. Early studies of alloy phase equilibrium have shown that simple models are capable of reproducing quite well the most important features of alloy phase diagrams [1-5]. The essence of these models is the description of the energy in terms of pair and many-body interactions. In these developments, the Cluster Variation Method (CVM) of Statistical Mechanics [6] played a key role since it provided an efficient and computationally economical way of describing the configurational thermodynamic of alloys. One
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