First-principles calculation of temperature-composition phase diagrams of semiconductor alloys (original) (raw)
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First-principles calculation of alloy phase diagrams: The renormalized-interaction approach
Physical Review B, 1989
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 compositionand 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. 4 (18 sets) CA,
Electronic structure, alloy phase stability and phase diagrams
Journal of the Less Common Metals, 1991
We review the relevance of electronic structure calculations to the determination of alloy phase stability and alloy phase diagrams. The Co~olly-W~li~s method, the generalized perturbation method, the embedded cluster method and the method of concentration waves are presented and their main features are discussed and compared. The results of calculations of effective cluster interactions in substitutionally disordered alloys and of phase diagrams for specific alloy systems, e.g. PdRh, PdV and AlLi, are shown and work currently in progress is briefly described.
Journal of Phase Equilibria, 1994
The possibility now exists of deriving phase diagrams at a high level of accuracy by combining both quantum mechanical and statistical thermodynamical contributions. These calculations have to take into account the local chemical environment, which is important in determining both the internal energy and the entropy of configuration. One of the most efficient methods for including short-and long-range order is the cluster variation method. This method needs as input the effective cluster interactions, which determine ordering or clustering reactions occurring in a given lattice. Phase stability in Ni-Ti and AI-Ni systems has been investigated using tight-binding energy calculations and linear muffin tin orbitals total energies calculations. The results are compared with literature data; i.e., experimental determinations, phase diagram optimization, and ab initio calculations.
Phase stability properties in complex substitutional alloys
Journal of the Less Common Metals, 1991
Order-disorder phenomena and structural transformations in substitutional alloys are of great interest in both the theoretical and technological fields of phase stability in general. In this paper, we first briefly review the advanced methodology which has been developed recently to study phase formation. Then we present our results on the effect of a tetragonal distortion of the b.c.c. crystalline structure onto the thermodynamic properties of transition metal alloys. Finally, we discuss our recent predictions pertaining to the possible existence of new ordered states based upon the Al 5 crystalline structure.
First-Principles Calculation of Semiconductor-Alloy Phase Diagrams
Combining first-principles self-consistent local-density total-energy calculations with the cluster variation method, we calculate the phase diagram of a semiconductor alloy. It is demonstrated that inclusion of both elastic and chemical interactions in the total-energy functional leads to new features, including the appearance in the same phase diagram of ordering and phase separation, and strain stabilization of both stable and metastable ordered phases.
Physical Review B, 2006
Some alloys show interstitial-induced phase transitions and order-disorder transitions due to the mutual interactions between the interstitial ͑I͒ species and the substitutional ͑S͒ host lattice. An innovative approach, based on the cluster variation method ͑CVM͒, that takes this coupling into account is proposed here for the calculation of thermodynamic data and phase boundaries. In the case of fcc substitutional alloys with interstitial species a simple cube is chosen as the basic cluster. The cube is defined such that it explicitly accounts for the mutual interaction between the S and the I sublattices comprising the system. Expressions for the configurational entropy in the cube approximation and the internal energy are derived. Phase diagrams for several hypothetical binary host alloys with interstitials are calculated. The results obtained using the proposed simplecube approximation demonstrate the effect of mutual interactions on the phase boundaries.
Use of the Ising model in the study of substitutional alloys
Physical Review B, 1995
We examine the mathematical and physical basis for choosing the coefFicients of an Ising model Hamiltonian, variably known as multisite interactions or effective cluster interactions, used in the study of phase stability of substitutionally disordered alloys. We show that concentrationindependent interactions can be defined if and only if the system is assumed to be strictly finite, i.e. , to contain a finite number of sites. If the system is infinite, only concentration-dependent interactions can be defined. This strict dichotomy has apparently been missed in previous discussions, and this oversight has led both to erroneous conclusions regarding the relationships between the two types of interactions, and to confusion about methods for determining them. Explicitly, no relationship between the two sets of interactions can exist since these two di8'erent types of interactions cannot be defined simultaneously. We also discuss the physical basis for the mapping of alloy configurational energies onto the Hamiltonian of an Ising model, and point out that the use of the model involves the generally unjustified assumption that the kinetics properties of an alloy will allow configurational transformations to occur according to the dictates of the equilibrium thermodynamics of a spin system. In a final section, we present the implications of our results to the study of alloy phase stability and transformations by means of the Ising model.
Free energy analysis of binary alloys at phase transition
2018
Order-disorder transformation in alloys is a fascinating and extensively studied problem for many years. This transformation has been studied widely using the two state Ising model. But vacancies are not considered in two state Ising model, which may play an important rule in determining the composition of stable configuration. So we used three state Ising model which takes vacancies also at lattice sites. To make a realistic study we have included kinetic energy of the particles in the total Hamiltonian.
Coarse-grained density functional theory of order-disorder phase transitions in metallic alloys
Physical Review B, 2009
The technological performances of metallic compounds are largely influenced by atomic ordering. Although there is a general consensus that successful theories of metallic systems should account for the quantum nature of the electronic glue, existing non-perturbative high-temperature treatments are based on effective classical atomic Hamiltonians. We propose a solution for the above paradox and offer a fully quantum mechanical, though approximate, theory that on equal footing deals with both electrons and ions. By taking advantage of a coarse grained formulation of the density functional theory [Bruno et al., Phys. Rev. B 77, 155108 (2008)] we develop a MonteCarlo technique, based on an ab initio Hamiltonian, that allows for the efficient evaluation of finite temperature statistical averages. Calculations of the relevant thermodynamic quantities and of the electronic structures for CuZn and Ni3V support that our theory provides an appropriate description of orderdisorder phase transitions.
Calphad, 2020
Over the last four years there has been a renewed interest in the development of new critically assessed data using physically based models. Nearly all work so far has been concerned with the critical assessment of data for the elements. This has involved the selection of Einstein or Debye temperatures for the stable crystalline phases and the liquid phase and associated parameters. However, until now, these data have not been extended in a comprehensive way to model the thermodynamic properties of binary, ternary and multicomponent systems. In this paper the way in which the parameters underlying these physical models vary with composition is explored. This includes a method to define the Einstein temperature for metastable phases of the elements and its relation to the so-called lattice stabilities used in the past, and the variation of the Einstein temperature with composition to account for the composition dependence of the excess entropy. This approach is demonstrated for the Al-Zn system which shows extensive regions of solid solution and complete miscibility in the liquid phase. Here Einstein temperatures are derived for Al in the HCP_ZN phase and Zn in the FCC_A1 phase together with parameters describing the variation of the Einstein temperature with composition for the HCP_ZN, FCC_A1 and liquid phases.