The formation of solid-solutions of iodide, bromide, and chloride provides the means to control the structure, band gap, and stability of hybrid halide perovskite semiconductors for photovoltaic applications. We report a computational investigation of the CH3NH3PbI3/CH3NH3PbBr3 alloy from density functional theory with a thermodynamic analysis performed within the generalized quasi-chemical approximation. We construct the phase diagram and identify a large miscibility gap, with a critical temperature of 343 K. The observed photoinstability in some mixed-halide solar cells is explained by the thermodynamics of alloy formation, where an initially homogeneous solution is subject to spinodal decomposition with I and Br-rich phases, which is further complicated by a wide metastable region defined by the binodal line.

http://pubs.acs.org/doi/pdf/10.1021/acs.jpclett.6b00226

Thermodynamic Origin of Photoinstability in the CH3NH3Pb(I1-xBrx)3 Hybrid Halide Perovskite Alloy.

Ab initio phase stabilities and mechanical properties of multicomponent alloys: A comprehensive review for high entropy alloys and compositionally complex alloys

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 \ensuremath{\Delta}H, entropy \ensuremath{\Delta}S, and hence the phase diagram. The method is illustrated for two prototype semiconductor fcc alloys: one with a large size mismatch (${\mathrm{GaAs}}_{\mathrm{x}}$${\mathrm{Sb}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$) and one with a small size mismatch (${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Ga}}_{\mathrm{x}}$As), producing excellent agreement with the measured miscibility temperature and excess enthalpies. For lattice-mismatched systems, we find 0${H}^{O}$${H}^{D}$, where O denotes some ordered Landau-Lifshitz (LL) structures, and D denotes the disordered phase. We hence predict that such alloys will disproportionate at low-temperature equilibrium into the binary constituents, but if disproportionation is kinetically inhibited, some special ordered phases (i.e., chalcopyrite) will be thermodynamically stabler below a critical temperature than the disordered phase of the same composition. For the lattice-matched systems, we find 0${H}^{D}$${H}^{O}$ for all LL structures, so that only a phase-separating behavior is predicted. However, in these systems, longer-period ordered superlattices are found to be stabler, at low temperatures, than the disordered alloy.

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

A binary substitutional system can exist in 2N configurations that can be formed by occupying any of the N sites of a lattice by either an A or a B atom. Substitutional configurations include compounds, alloys, superlattices, and substitutional impurities. This article addresses the questions of (i) finding the lowest energy configuration of a given A/B substitutional system, (ii) calculating its composition-temperature phase diagram, and (iii) its finite-temperature thermodynamic properties, using the first-principles local density approximation (LDA). Mapping of the LDA energies of 10–20 ApBq compounds onto an Ising-like “cluster expansion” enables use of lattice statistical mechanics techniques that elegantly solve the above problems. This extends the utility of the LDA from simple, perfectly-ordered compounds to truly complex structures. We illustrate the method for semiconductor systems and transition-metal intermetallic systems, emphasizing the role of lattice relaxation.

First-Principles Statistical Mechanics of Semiconductor Alloys and Intermetallic Compounds

The search for high entropy alloys: A high-throughput ab-initio approach

In this theoretical study, the quasichemical approximation for an ${A}_{1\mathrm{\ensuremath{-}}x}$${B}_{x}$ alloy is formulated for an arbitrary lattice and choice of cluster. The statistical problem of the average number of each class of clusters is collapsed into a polynomial equation. An n-atom cluster of type j is characterized by an excess energy ${\ensuremath{\varepsilon}}_{j}$, the number of B atoms ${n}_{j}$(B) and a degeneracy ${g}_{j}$. If ${\ensuremath{\varepsilon}}_{j}$ is a linear function of ${n}_{j}$(B) and ${g}_{j}$ is a binomial coefficient of n and ${n}_{j}$(B), then the cluster populations are random. Strains due to lattice-size mismatches, chemical (electron-ion interaction) differences, and differences between the electron-electron Coulomb interactions of the alloy constituents drive nonlinear variations of ${\ensuremath{\varepsilon}}_{j}$ on ${n}_{j}$(B). The ${g}_{j}$ is modified by coherent, externally applied stresses and temperature gradients present during crystal growth. We derive the conditions under which compounds are formed or spinodal decomposition occurs. We also discuss the possibility of materials consisting of arrays of two kinds of domains: one a random alloy and the other an ordered compound. The theory is specialized to semiconductor alloys ${A}_{1\mathrm{\ensuremath{-}}x}$${B}_{x}$C in a distorted zinc-blende structure; numerical results are presented for ${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{In}}_{\mathrm{x}}$As and ${\mathrm{GaAs}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Sb}}_{\mathrm{x}}$ alloys. A major conclusion is that semiconductor alloys are almost never truly random.

An-Ban Chen

Papers

Quasichemical approximation in binary alloys.