First-principles calculation of alloy phase diagrams: The renormalized-interaction approach

Abstract

We present a formalism for calculating the temperature-composition phase diagrams of isostructural solid alloys from a microscopic theory of electronic interactions. First, the internal energy of the alloy is expanded in a series of volume-dependent multiatom interaction energies. These are determined from self-consistent total-energy calculations on periodic compounds described within the local-density formalism. Second, distant-neighbor interactions are renormalized into composition-and volume-dependent effective near-neighbor multisite interactions. Finally, approximate solutions to the general Ising model (using the tetrahedron cluster variation method) underlying these effective interactions provide the excess enthalpy AH, entropy hS, and hence the phase diagram. The method is illustrated for two prototype semiconductor fcc alloys: one with a large size mismatch (CxaAs"Sb& ) and one with a small size mismatch (Al& Ga As), producing excellent agreement with the measured miscibility temperature and excess enthalpies. For latticernismatched systems, we find 0 & hH & AH, where 0 denotes some ordered Landau-Lifshitz (LL)structures, and D denotes the disordered phase. We hence predict that such alloys will disproportionate at low-temperature equilibrium into the binary constituents, but if disproportionation is kinetically inhibited, some special ordered phases (i.e., chalcopyrite) will be thermodynamically stabler below a critical temperature than the disordered phase of the same composition. For the lattice-matched systems, we find 0&EH &AH for all LL structures, so that only a phaseseparating behavior is predicted. However, in these systems, longer-period ordered superlattices are found to be stabler, at low temperatures, than the disordered alloy.

Possible complete miscibility of(BN)x(C2)Zheng1, Wang2, Wee3 et al. 2002Phys. Rev. B210131View full textAdd to dashboardCite

“…This theoretical prediction of very high critical temperature indicated very limited solid solution in (BN) x (C 2 ) 1-x alloys, which can't well interpret Badzian's report 1 of the synthesis of solid solutions within the compositional range 0.15<x BN <0.6. Two possible explanations could account for this discrepancy: (i) Mixing in the experiments took place in the liquid state and the solid solutions are metastable systems, as pointed out by Lambrecht et al 4 ; (ii) additional short-range ordered structures should be included to form a representative basis for all zinc blende structures to account for possible short-range interactions, as shown by Ferreira et al 20 . Specifically, the (111) orientation should be included, which we have shown to be the lowest-energy possible structure (Fig.…”

Ground State Searches in Fcc Intermetallics

“…Previous studies on several alloy systems [3,4,12] have shown that, for the fcc lattice, incorporation of pair interactions up to the 4NN is sometimes essential to obtain the correct ground states. To include interactions with this spatial extent, we have formulated the fcc ground state problem with the 13 and 14 point cluster as maximal clusters.…”

“…The first principles approaches for calculating ECl's fall into three main classes: 1) Methods based on a perturbative treatment of the coherent potential approximation (CPA), most notably, the generalized perturbation method (GPM) [11], 2) Methods involving the calculation of energies of ordered superstructures, and, in conjunction with expansion (1), extraction of the ECl's from these computations [4,5], and 3) The method of direct configurational averaging (DCA) [6]. DCAis a method of perturbing not the averaged, CPAmedium, but rather a truly randomly generated configuration.…”

“…Previously, phenomenological models were proposed to calculate the ECl's. However, there presently exist several methods of obtaining these composition-independent interactions from afrrst-principles approach [4][5][6]. In this paper, we use the method of direct configurational averaging (DCA) in conjunction with a linearized muffin-tin orbital Hamiltonian transformed into the tight-binding representation (TB-LMTO).…”

Subsolidus phase relations in theCaCO3–MgCO3system predicted from the excess enthalpies of supercell structures with single and double defects

“…In contrast to alloys, where the unit cell is composed of the exchangeable atoms solely, minerals often contain extra "inactive" elements, e.g., O, Si, Al, and C, which increase the system size. Typically one is concerned with ordering and mixing of cations of different metals which rest within an "inert" matrix built by anion complexes such as SiO 4 4− , AlO 6 9− , or CO 3 2− . The low symmetry and the chemical complexity typically imply a large unit cell, where the mixing occurs within a specific sublattice ͑Wyckoff position͒.…”