Efficient cluster expansion for substitutional systems

Informatics-Based Learning of Oxygen Vacancy Ordering Principles in Oxygen-Deficient Perovskites

Ordered oxygen vacancies (OOVs) in perovskites can exhibit long-range order and may be used to direct materials properties through modifications in electronic structures and broken symmetries. Based on the various vacancy patterns observed in previously known compounds, we explore the ordering principles of oxygen-deficient perovskite oxides with ABO2.5 stoichiometry to identify other OOV variants. We performed first-principles calculations to assess the OOV stability on a data set of 50 OOV structures generated from our bespoke algorithm. The algorithm employs uniform planar vacancy patterns on (111) pseudocubic perovskite layers and the approach proves effective for generating stable OOV patterns with minimal computational loads. We find as expected that the major factors determining the stability of OOV structures include coordination preferences of transition metals and elastic penalties resulting from the assemblies of polyhedra. Cooperative rotational modes of polyhedra within the OOV structures reduce elastic instabilities by optimizing the bond valence of A- and B cations. This finding explains the observed formation of vacancy channels along low-index crystallographic directions in prototypical OOV phases. The identified ordering principles enable us to devise other stable vacancy patterns with longer periodicity for targeted property design in yet to be synthesized compounds.

Phase transition and electrochemical properties of S-functionalized MXene anodes for Li-ion batteries: a first-principles investigation

The advancement of anode materials for achieving high energy storage is a crucial topic for high-performance Li-ion batteries (LIBs). Here, first-principles calculations were used to conduct a thorough and systematic investigation into lithium storage properties of MXenes with new S functional groups as LIB anode materials. Density of states, diffusion energy barriers, open circuit voltages and storage capacities were calculated to comprehensively evaluate the lithium storage properties of S-functionalized MXenes. Based on the computational results, Ti2CS2 and V2CS2 were selected as excellent candidates from ten M2CS2 MXenes. The diffusion energy barriers of M2CS2 within the range of 0.26-0.32 eV are lower than those of M2CO2 and M2CF2, indicating that M2CS2 anodes exhibit faster charge/discharge rates. By examining the stable crystal structures and comparing atomic positions before and after Li adsorptions, structural phase transitions during Li-ion adsorptions could happen for nearly all M2CS2 MXenes. The phase transitions predicted were directly observed using ab initio molecular dynamic simulations. The cycle stability, storage capacity and other lithium storage properties were enhanced by the reversible structural phase transition.

Exploring the Phase Stability of Li2Mn1-x TM x O3 (TM = Ni, Co, Cr, Ru) Cathode Materials in Lithium-Ion Batteries via the Cluster Expansion Method

Li2MnO3 has garnered significant interest as a potential cathode material due to its high electrochemical capacity, cost-effectiveness, and eco-friendliness. Nonetheless, its practical utilization is hindered by structural deterioration, which results in rapid capacity and voltage decay during cycling. To mitigate these challenges, cationic dopants have been incorporated to minimize structural collapse and enhance cathode material performance. Consequently, there is a strong desire to identify novel doped configurations as a remedial strategy for optimizing Li2MnO3 properties. In this study, the stability of the Li2Mn1-x TM x O3 system (TM = Ni, Co, Cr, Ru) was explored using cluster expansion and Monte Carlo simulations. By employing cluster expansion, binary ground state diagrams were generated, revealing 73, 65, 90, and 83 newly stable phases in Li2Mn1-x Ni x O3, Li2Mn1-x Co x O3, Li2Mn1-x Cr x O3, and Li2Mn1-x Ru x O3, respectively. The outcomes indicated that Li2Mn0.83Ni0.17O3, Li2Mn0.5Co0.5O3, Li2Mn0.5Cr0.5O3, and Li2Mn0.5Ru0.5O3 represent the most stable doped phases within the Li2MnO3 system. The application of Monte Carlo simulations enabled the assessment of high-temperature characteristics across the entire range of TM concentrations (0 ≤ x ≤ 1), facilitating the construction of phase diagrams. The Li2Mn1-x Ni x O3, Li2Mn1-x Co x O3, Li2Mn1-x Cr x O3, and Li2Mn1-x Ru x O3 systems exhibited favorable mixing at temperatures of 850, 700, 1700, and 1300 K, respectively. These discoveries present a clear trajectory for optimizing the properties of Li2MnO3, offering valuable insights into conceptualizing innovative cathode materials characterized by enhanced stability and performance.

Neural network kinetics for exploring diffusion multiplicity and chemical ordering in compositionally complex materials

Diffusion involving atom transport from one location to another governs many important processes and behaviors such as precipitation and phase nucleation. The inherent chemical complexity in compositionally complex materials poses challenges for modeling atomic diffusion and the resulting formation of chemically ordered structures. Here, we introduce a neural network kinetics (NNK) scheme that predicts and simulates diffusion-induced chemical and structural evolution in complex concentrated chemical environments. The framework is grounded on efficient on-lattice structure and chemistry representation combined with artificial neural networks, enabling precise prediction of all path-dependent migration barriers and individual atom jumps. To demonstrate the method, we study the temperature-dependent local chemical ordering in a refractory NbMoTa alloy and reveal a critical temperature at which the B2 order reaches a maximum. The atomic jump randomness map exhibits the highest diffusion heterogeneity (multiplicity) in the vicinity of this characteristic temperature, which is closely related to chemical ordering and B2 structure formation. The scalable NNK framework provides a promising new avenue to exploring diffusion-related properties in the vast compositional space within which extraordinary properties are hidden.

Crystal Structures and Phase Stability of the Li2S-P2S5 System from First Principles

The Li2S-P2S5 pseudo-binary system has been a valuable source of promising superionic conductors, with α-Li3PS4, β-Li3PS4, HT-Li7PS6, and Li7P3S11 having excellent room-temperature Li-ion conductivity >0.1 mS/cm. The metastability of these phases at ambient temperature motivates a study to quantify their thermodynamic accessibility. Through calculating the electronic, configurational, and vibrational sources of free energy from first principles, a phase diagram of the crystalline Li2S-P2S5 space is constructed. New ground-state orderings are proposed for α-Li3PS4, HT-Li7PS6, LT-Li7PS6, and Li7P3S11. Well-established phase stability trends from experiments are recovered, such as polymorphic phase transitions in Li7PS6 and Li3PS4, and the instability of Li7P3S11 at high temperature. At ambient temperature, it is predicted that all superionic conductors in this space are indeed metastable but thermodynamically accessible. Vibrational and configurational sources of entropy are shown to be essential toward describing the stability of superionic conductors. New details of the Li sublattices are revealed and are found to be crucial toward accurately predicting configurational entropy. All superionic conductors contain significant configurational entropy, which suggests an inherent correlation between fast Li diffusion and thermodynamic stability arising from the configurational disorder.

Bandgaps of long-period polytypes of IV, IV-IV, and III-V semiconductors estimated with an Ising-type additivity model

We apply an Ising-type model to estimate the bandgaps of the polytypes of group IV elements (C, Si, and Ge) and binary compounds of groups: IV-IV (SiC, GeC, and GeSi), and III-V (nitride, phosphide, and arsenide of B, Al, and Ga). The models use reference bandgaps of the simplest polytypes comprising 2-6 bilayers calculated with the hybrid density functional approximation, HSE06. We report four models capable of estimating bandgaps of nine polytypes containing 7 and 8 bilayers with an average error of ≲0.05 eV. We apply the best model with an error of <0.04 eV to predict the bandgaps of 497 polytypes with up to 15 bilayers in the unit cell, providing a comprehensive view of the variation in the electronic structure with the degree of hexagonality of the crystal structure. Within our enumeration, we identify four rhombohedral polytypes of SiC-9R, 12R, 15R(1), and 15R(2)-and perform detailed stability and band structure analysis. Of these, 15R(1) that has not been experimentally characterized has the widest bandgap (>3.4 eV); phonon analysis and cohesive energy reveal 15R(1)-SiC to be metastable. Additionally, we model the energies of valence and conduction bands of the rhombohedral SiC phases at the high-symmetry points of the Brillouin zone and predict band structure characteristics around the Fermi level. The models presented in this study may aid in identifying polytypic phases suitable for various applications, such as the design of wide-gap materials, that are relevant to high-voltage applications. In particular, the method holds promise for forecasting electronic properties of long-period and ultra-long-period polytypes for which accurate first-principles modeling is computationally challenging.

Transition Temperature for Spin-Crossover Materials with the Mean Value Ensemble Hubbard-U Correction

Calculation of transition temperatures T1/2 for thermally driven spin-crossover in condensed phases is challenging, even with sophisticated state-of-the-art density functional approximations. The first issue is the accuracy of the adiabatic crossover energy difference ΔEHL between the low- and high-spin states of the bistable metal-organic complexes. The other is the proper inclusion of entropic contributions to the Gibbs free energy from the electronic and vibrational degrees of freedom. We discuss the effects of treatments of both contributions upon the calculation of thermochemical properties for a set of 20 spin-crossover materials using a Hubbard-U correction obtained from a reference ensemble spin-state. The U values obtained from a simplest bimolecular representation may overcorrect, somewhat, the ΔEHL values, hence giving somewhat excessive reduction of the T1/2 results with respect to their U = 0 values in the crystalline phase. We discuss the origins of the discrepancies by analyzing different sources of uncertainties. By use of a first-coordination-sphere approximation and the assumption that vibrational contributions from the outermost atoms in a metal-organic complex are similar in both low- and high-spin states, we achieve T1/2 results with the low-cost, widely used PBE generalized gradient density functional approximation comparable to those from the more costly, more sophisticated r2SCAN meta-generalized gradient approximation. The procedure is promising for use in high-throughput materials screening, because it combines rather low computational effort requirements with freedom from user manipulation of parameters.

A method to computationally screen for tunable properties of crystalline alloys

Conventionally, high-throughput computational materials searches start from an input set of bulk compounds extracted from material databases, but, in contrast, many real functional materials are heavily engineered mixtures of compounds rather than single bulk compounds. We present a framework and open-source code to automatically construct and analyze possible alloys and solid solutions from a set of existing experimental or calculated ordered compounds, without requiring additional metadata except crystal structure. As a demonstration, we apply this framework to all compounds in the Materials Project to create a new, publicly available database of > 600,000 unique "alloy pair" entries that can be used to search for materials with tunable properties. We exemplify this approach by searching for transparent conductors and reveal candidates that might have been excluded in a traditional screening. This work lays a foundation from which materials databases can go beyond stoichiometric compounds and approach a more realistic description of compositionally tunable materials.

Computational design of novel MAX phase alloys as potential hydrogen storage media combining first principles and cluster expansion methods

Finding a suitable material for hydrogen storage under ambient atmospheric conditions is challenging for material scientists and chemists. In this work, using a first principles based cluster expansion approach, the hydrogen storage capacity of the Ti₂AC (A = Al, Ti, Cr, Mn, Fe, Co, Ni, Cu, and Zn) MAX phase and its alloys was studied. We found that hydrogen is energetically stable in Ti-A layers in which the tetrahedral site consisting of one A atom and three Ti atoms is energetically more favorable for hydrogen adsorption than other sites in the Ti-A layer. Ti₂CuC has the highest hydrogen adsorption energy than other Ti₂AC phases. We find that the 83.33% Cu doped Ti₂Al_xCu_1-xC alloy structure is both energetically and dynamically stable and can store 3.66 wt% hydrogen under ambient atmospheric conditions, which is higher than that stored by both Ti₂AlC and Ti₂CuC phases. These findings indicate that the hydrogen capacity of the MAX phase can be significantly improved by doping an appropriate atom species.

High-throughput inverse design and Bayesian optimization of functionalities: spin splitting in two-dimensional compounds

The development of spintronic devices demands the existence of materials with some kind of spin splitting (SS). In this Data Descriptor, we build a database of ab initio calculated SS in 2D materials. More than that, we propose a workflow for materials design integrating an inverse design approach and a Bayesian inference optimization. We use the prediction of SS prototypes for spintronic applications as an illustrative example of the proposed workflow. The prediction process starts with the establishment of the design principles (the physical mechanism behind the target properties), that are used as filters for materials screening, and followed by density functional theory (DFT) calculations. Applying this process to the C2DB database, we identify and classify 358 2D materials according to SS type at the valence and/or conduction bands. The Bayesian optimization captures trends that are used for the rationalized design of 2D materials with the ideal conditions of band gap and SS for potential spintronics applications. Our workflow can be applied to any other material property.

A casting combined quenching strategy to prepare PdAg single atom alloys designed using the cluster expansion combined Monte Carlo method

In this work, the surface structure of a PdAg alloy is investigated by cluster expansion (CE) combined Monte Carlo (MC) simulations. All systems with different component proportions show an obvious component segregation corresponding to the depth from the surface. A significant amount of Ag is observed on the first layer, and Pd is concentrated significantly on the second layer. The Pd distribution on the PdAg surfaces is closely related to the temperature and composition ascribed to the concentration and configurational entropy effects, which are explicitly treated in MC simulations. The vacancies mainly distribute separately. The simulation results show good agreement with the experimental evidence. Moreover, we demonstrated a general and highly effective casting combined quenching strategy for controlling the ensemble size and chemical composition of alloy surfaces which could successfully be applied to the large-scale production of SAA.

Development of a prototype thermodynamic database for Nd-Fe-B permanent magnets

For the Nd-Fe-B permanent magnets, a prototype thermodynamic database of the 8-element system (Nd, Fe, B, Al, Co, Cu, Dy, Ga) was constructed based on literature data and assessed parameters in the present work. The magnetic excess Gibbs energy of the Nd₂Fe₁₄B compound was reassessed using thoroughly measured heat capacity data. The Dy-Nd binary system was reassessed based on formation energies estimated from ab initio calculations. The constructed database was applied successfully for estimations of phase equilibria during the grain boundary diffusion processes (GBDP) and the reactions in the hydrogenation decomposition desorption recombination (HDDR) processes.

Rapid Prediction of Bimetallic Mixing Behavior at the Nanoscale

The nanoparticle (NP) design space allows for variations in size, shape, composition, and chemical ordering. In the search for low-energy structures, this results in an extremely large search space which cannot be screened by brute force methods. In this work, we develop a genetic algorithm to predict stable bimetallic NPs of any size, shape, and metal composition. Our method predicts nanostructures in agreement with experimental trends and it captures the detailed chemical ordering of an experimental 23,196-atom FePt NP with nearly atom-by-atom accuracy. Our developed screening process is extremely fast, allowing us to generate and analyze a database of 5454 low-energy bimetallic NPs. By identifying thermodynamically stable NPs, we rationalize bimetallic mixing at the nanoscale and reveal metal-, size-, and temperature-dependent mixing behavior. Importantly, our method is applicable to any bimetallic NP size, bridging the materials gap in nanoscale simulations, and guides experimentation in the lab by elucidating stability, mixing, and detailed chemical ordering behavior of bimetallic NPs.

Phase stability of three-dimensional bulk and two-dimensional monolayer As1-x Sb x solid solutions from first principles

The mixing thermodynamics of both three-dimensional bulk and two-dimensional mono-layered alloys of As_1-x Sb _x as a function of alloy composition and temperature are explored using a first-principles cluster-expansion method, combined with canonical Monte-Carlo simulations. We observe that, for the bulk phase, As_1-x Sb _x alloy can exhibit not only chemical ordering of As and Sb atoms at x  =  0.5 to form an ordered compound of AsSb stable upon annealing up to [Formula: see text] K, but also a miscibility gap at 475 K [Formula: see text] T [Formula: see text] 550 K in which two disordered solid solutions of As_1-x Sb _x of different alloy compositions thermodynamically coexist. At T  >  550 K, a single-phase solid solution of bulk As_1-x Sb _x is predicted to be stable across the entire composition range. These results clearly explain the existing uncertainties in the alloying behavior of bulk As_1-x Sb _x alloy, as previously reported in the literature, and also found to be in qualitative and quantitative agreement with the experimental observations. Interestingly, the alloying behavior of As_1-x Sb _x is considerably altered, as the dimensionality of the material reduces from the three-dimensional bulk state to the two-dimensional mono-layered state-for example, a single-phase solid solution of monolayer As_1-x Sb _x is predicted to be stable over the whole composition range at T  >  250 K. This distinctly highlights an influence of the reduced dimensionality on the alloying behavior of As_1-x Sb _x .

Cluster expansion based configurational averaging approach to bandgaps of semiconductor alloys

Configurationally disordered semiconducting materials including semiconductor alloys [e.g., (GaN)_1-x(ZnO)_x] and stoichiometric materials with fractional occupation (e.g., LaTiO₂N) have attracted a lot of interest recently in search for efficient visible light photo-catalysts. First-principles modeling of such materials poses great challenges due to the difficulty in treating the configurational disorder efficiently. In this work, a configurational averaging approach based on the cluster expansion technique has been exploited to describe bandgaps of ordered, partially disordered (with short-range order), and fully disordered phases of semiconductor alloys on the same footing. We take three semiconductor alloys [Cd_1-xZn_xS, ZnO_1-xS_x, and (GaN)_1-x(ZnO)_x] as model systems and clearly demonstrate that semiconductor alloys can have a system-dependent short-range order that has significant effects on their electronic properties.

Ordered and Disordered Phases in Mo1-xWxS2 Monolayer

With special quasirandom structure approach and cluster expansion method combined with first-principle calculations, we explore the structure and electronic properties of monolayer Mo_1−xW_xS₂ alloy with disordered phase and ordered phase. The phase transition from ordered phase to disordered phase is found to happen at 41 K and 43 K for x = 1/3 and x = 2/3, respectively. The band edge of VBM is just related with the composition x, while the band edge of CBM is sensitive to the degree of order, besides the concentration of W. Near the CBM band edge, there are two bands with the Mo-character and W-character, respectively. It is found that in disordered phase the Mo-character band is mixed with the W-character band, while the opposite happens in ordered phase. This result leads to that the splitting of two bands near CBM in ordered phase is larger than in disordered phase and gives rise to the smaller band gap in ordered phase compared to the disordered phase. The electron effective mass in ordered phase is smaller than in disordered phase, while the heavy hole effective mass in ordered phase is larger than that in disordered phase.

First-principles phase diagram calculations for the rocksalt-structure quasibinary systems TiN-ZrN, TiN-HfN and ZrN-HfN

We have studied the phase equilibria of three ceramic quasibinary systems Ti1-x Zr x N, Ti1-x Hf x N and Zr1-x Hf x N (0  ⩽  x  ⩽  1) with density functional theory, cluster expansion and Monte Carlo simulations. We predict consolute temperatures (T C), at which miscibility gaps close, for Ti1-x Zr x N to be 1400 K, for Ti1-x Hf x N to be 700 K, and below 200 K for Zr1-x Hf x N. The asymmetry of the formation energy ΔE f(x) is greater for Ti1-x Hf x N than Ti1-x Zr x N, with less solubility on the smaller cation TiN-side, and similar asymmetries were predicted for the corresponding phase diagrams. We also analyzed different energetic contributions: ΔE f of the random solid solutions were decomposed into a volume change term, [Formula: see text], and a chemical exchange and relaxation term, [Formula: see text]. These two energies partially cancel one another. We conclude that [Formula: see text] influences the magnitude of T C and [Formula: see text] influences the asymmetry of ΔE f(x) and phase boundaries. We also conclude that the absence of experimentally observed phase separation in Ti1-x Zr x N and Ti1-x Hf x N is due to slow kinetics at low temperatures. In addition, elastic constants and mechanical properties of the random solid solutions were studied with the special quasirandom solution approach. Monotonic trends, in the composition dependence, of shear-related mechanical properties, such as Vickers hardness between 18 to 23 GPa, were predicted. Trends for Ti1-x Zr x N and Ti1-x Hf x N exhibit down-bowing (convexity). It shows that mixing nitrides of same group transition metals does not lead to hardness increase from an electronic origin, but through solution hardening mechanism. The mixed thin films show consistency and stability with little phase separation, making them desirable coating choices.

A generalized Ising model for studying alloy evolution under irradiation and its use in kinetic Monte Carlo simulations

We derive an Ising Hamiltonian for kinetic simulations involving interstitial and vacancy defects in binary alloys. Our model, which we term 'ABVI', incorporates solute transport by both interstitial defects and vacancies into a mathematically-consistent framework, and thus represents a generalization to the widely-used ABV model for alloy evolution simulations. The Hamiltonian captures the three possible interstitial configurations in a binary alloy: A-A, A-B, and B-B, which makes it particularly useful for irradiation damage simulations. All the constants of the Hamiltonian are expressed in terms of bond energies that can be computed using first-principles calculations. We implement our ABVI model in kinetic Monte Carlo simulations and perform a verification exercise by comparing our results to published irradiation damage simulations in simple binary systems with Frenkel pair defect production and several microstructural scenarios, with matching agreement found.

Estimation of Lattice Enthalpies of Ionic Liquids Supported by Hirshfeld Analysis

New measurements of vaporization enthalpies for 15 1:1 ionic liquids are performed by using a quartz-crystal microbalance. Collection and analysis of 33 available crystal structures of organic salts, which comprise 13 different cations and 12 anions, is performed. Their dissociation lattice enthalpies are calculated by a combination of experimental and quantum chemical quantities and are divided into the relaxation and Coulomb components to give an insight into elusive short-range interaction enthalpies. An empirical equation is developed, based on interaction-specific Hirshfeld surfaces and solvation enthalpies, which enables the estimation of the lattice enthalpy by using only the crystal-structure data.

Divide-and-conquer quantum mechanical material simulations with exascale supercomputers

Recent developments in large-scale materials science simulations, especially under the divide-and-conquer method, are reviewed. The pros and cons of the divide-and-conquer method are discussed. It is argued that the divide-and-conquer method, such as the linear-scaling 3D fragment method, is an ideal approach to take advantage of the heterogeneous architectures of modern-day supercomputers despite their relatively large prefactors among linear-scaling methods. Some developments in graphics processing unit (GPU) electronic structure calculations are also reviewed. The accelerators like GPU could be an essential part for the future exascale supercomputing.

First-principles Thermodynamic Models in Heterogeneous Catalysis

In this chapter we describe and demonstrate computational approaches to modeling surface adsorption, a process fundamental to all heterogeneous catalysts that takes into account surface structure, adsorbate–adsorbate interactions, and reaction conditions. We begin by describing the development of supercell density functional theory (DFT) models of adsorption at a surface, taking as an example O adsorption at the stepped and kinked Pt(321) surface. We then discuss how these DFT simulations can be used as a basis to parameterize a cluster expansion (CE) model, an Ising-type Hamiltonian that accounts for structural heterogeneity and for adsorbate–adsorbate interactions on a lattice. When converged, the DFT and CE models provide a self-consistent description of the ground states of the surface–adsorbate system. We present a detailed thermodynamic analysis of the system and describe how this can be used to extract equilibrium surface properties from the converged database and provide access to coverage-dependent adsorption energies and surface phase diagrams. Further, the CE enables Monte Carlo simulations of more extended surfaces under fixed temperature and chemical potential conditions, and the average properties from these simulations provide access to average coverages, heat capacities, and phase behavior. Finally, we describe how these same tools can be applied further to relate surface properties with reaction conditions and to describe surface kinetic processes such as diffusion or adsorption.

Symmetry and random sampling of symmetry independent configurations for the simulation of disordered solids

A symmetry-adapted algorithm producing uniformly at random the set of symmetry independent configurations (SICs) in disordered crystalline systems or solid solutions is presented here. Starting from Pólya's formula, the role of the conjugacy classes of the symmetry group in uniform random sampling is shown. SICs can be obtained for all the possible compositions or for a chosen one, and symmetry constraints can be applied. The approach yields the multiplicity of the SICs and allows us to operate configurational statistics in the reduced space of the SICs. The present low-memory demanding implementation is briefly sketched. The probability of finding a given SIC or a subset of SICs is discussed as a function of the number of draws and their precise estimate is given. The method is illustrated by application to a binary series of carbonates and to the binary spinel solid solution Mg(Al,Fe)2O4.

On the use of symmetry in configurational analysis for the simulation of disordered solids

The starting point for a quantum mechanical investigation of disordered systems usually implies calculations on a limited subset of configurations, generated by defining either the composition of interest or a set of compositions ranging from one end member to another, within an appropriate supercell of the primitive cell of the pure compound. The way in which symmetry can be used in the identification of symmetry independent configurations (SICs) is discussed here. First, Pólya's enumeration theory is adopted to determine the number of SICs, in the case of both varying and fixed composition, for colors numbering two or higher. Then, De Bruijn's generalization is presented, which allows analysis of the case where the colors are symmetry related, e.g. spin up and down in magnetic systems. In spite of their efficiency in counting SICs, neither Pólya's nor De Bruijn's theory helps in solving the difficult problem of identifying the complete list of SICs. Representative SICs are obtained by adopting an orderly generation approach, based on lexicographic ordering, which offers the advantage of avoiding the (computationally expensive) analysis and storage of all the possible configurations. When the number of colors increases, this strategy can be combined with the surjective resolution principle, which permits the efficient generation of SICs of a problem in |R| colors starting from the ones obtained for the (|R| - 1)-colors case. The whole scheme is documented by means of three examples: the abstract case of a square with C(4v) symmetry and the real cases of the garnet and olivine mineral families.

An efficient computational method for use in structural studies of crystals with substitutional disorder

We present a computationally efficient semi-empirical method, based on standard first-principles techniques and the so-called virtual crystal approximation, for determining the average atomic structure of crystals with substitutional disorder. We show that, making use of a minimal amount of experimental information, it is possible to define convenient figures of merit that allow us to recast the determination of the average atomic ordering within the unit cell as a minimization problem. We have tested our approach by applying it to a wide variety of materials, ranging from oxynitrides to borocarbides and transition-metal perovskite oxides. In all the cases we were able to reproduce the experimental solution, when it exists, or the first-principles result obtained by means of much more computationally intensive approaches.

Indium-gallium segregation in CuIn(x)Ga(1-x)Se2: an ab initio-based Monte Carlo study

Thin-film solar cells with CuIn(x)Ga(1-x)Se2 (CIGS) absorber are still far below their efficiency limit, although lab cells already reach 20.1%. One important aspect is the homogeneity of the alloy. Large-scale simulations combining Monte Carlo and density functional calculations show that two phases coexist in thermal equilibrium below room temperature. Only at higher temperatures, CIGS becomes more and more a homogeneous alloy. A larger degree of inhomogeneity for Ga-rich CIGS persists over a wide temperature range, which contributes to the observed low efficiency of Ga-rich CIGS solar cells.

Cluster expansion approach for transmutative lattice systems

We propose a cluster expansion (CE) technique that can express any function of atomic arrangement on any given lattice with the same number of lattice points in a single formalism. In the proposed CE, two types of spin variable, σ and τ, on the base lattice and virtual lattice, respectively, are introduced. The former spin variable specifies the occupation of the constituent elements for each lattice point. The latter specifies the positions of each lattice point. Basis functions constructed from the two types of spin variable satisfy completeness and orthonormality for any atomic arrangement on given lattices. As examples, the proposed CE is applied to one- and three-dimensional lattices in a binary system, which clarifies the concept of base and virtual lattices, how the functions of atomic arrangements are expressed in terms of the two types of spin variable, and the efficiency and convergence of the proposed CE with a finite number of clusters and input structures.

Atomic and electronic structures of GaN/ZnO alloys

A new model Hamiltonian is developed to describe the ab initio energy differences of the nonisovalent alloy configurations based on the semiconductor electron counting rule. Monte Carlo simulations using this Hamiltonian show strong short range order of the GaN/ZnO alloy, which has significant effects on its electronic structure. We also predict further reduction of the band gap by increasing the synthesis temperature.

Thermodynamic theory of epitaxial alloys: first-principles mixed-basis cluster expansion of (In, Ga)N alloy film

Epitaxial growth of semiconductor alloys onto a fixed substrate has become the method of choice to make high quality crystals. In the coherent epitaxial growth, the lattice mismatch between the alloy film and the substrate induces a particular form of strain, adding a strain energy term into the free energy of the alloy system. Such epitaxial strain energy can alter the thermodynamics of the alloy, leading to a different phase diagram and different atomic microstructures. In this paper, we present a general-purpose mixed-basis cluster expansion method to describe the thermodynamics of an epitaxial alloy, where the formation energy of a structure is expressed in terms of pair and many-body interactions. With a finite number of first-principles calculation inputs, our method can predict the energies of various atomic structures with an accuracy comparable to that of first-principles calculations themselves. Epitaxial (In, Ga)N zinc-blende alloy grown on GaN(001) substrate is taken as an example to demonstrate the details of the method. Two (210) superlattice structures, (InN)(2)/(GaN)(2) (at x = 0.50) and (InN)(4)/(GaN)(1) (at x = 0.80), are identified as the ground state structures, in contrast to the phase-separation behavior of the bulk alloy.

First-principles theory of competing order types, phase separation, and phonon spectra in thermoelectric AgPbmSbTe(m+2) alloys

Using a first-principles cluster expansion, we shed light on the solid-state phase diagram and structure of the recently discovered high-performance Pb-Ag-Sb-Te thermoelectrics. The calculated bulk thermodynamics favors the formation of coherent precipitates of ordered Ag(m)Sb(n)Te(m+n) phases immiscible with rocksalt PbTe, such as AgSbTe2. The solubility is high for Pb in AgSbTe2 and low for (Ag,Sb) in PbTe (8% vs 0.6% at 850 K). The differences in the phonon spectra of PbTe and AgSbTe2 suggest that these precipitates enhance the thermoelectric performance by lowering thermal conductivity.

A complete representation of structure-property relationships in crystals

Whereas structure-property relationships have long guided the discovery and optimization of novel materials, formal quantitative methods to identify such relationships in crystalline systems are beginning to emerge. Among them is cluster expansion, which has been successfully used to parametrize the configurational dependence of important scalar physical properties such as bandgaps, Curie temperatures, equation-of-state parameters and densities of states. However, cluster expansion is currently unable to handle anisotropic properties, a key distinguishing feature of crystalline systems central to the design of modern epitaxial structures and devices. Here, I introduce a tensorial cluster expansion enabling the prediction of fundamental tensor-valued material properties such as elasticity, piezoelectricity, dielectric constants, optoelectric coupling, anisotropic diffusion coefficients, surface energy and stress. As an application, I develop predictive ab initio models of anisotropic properties relevant to the design and optimization of III-V semiconductor epitaxial optoelectronic devices.

Cluster expansions in multicomponent systems: precise expansions from noisy databases

We have performed a systematic analysis of the numerical errors contained in the databases used in cluster expansions of multicomponent alloys. Our results underscore the importance of numerical noise in the determination of the effective cluster interactions and in the expansion determination. The relevance of the size of and information contained in the input database is highlighted. It is shown that cross-validatory approaches by themselves can produce unphysical expansions characterized by non-negligible, long-ranged coefficients. A selection criterion that combines both forecasting ability and a physical limiting behavior for the expansion is proposed. Expansions performed under this criterion exhibit the remarkable property of noise filtering. A discussion of the impact of this unforeseen characteristic of the cluster expansion method on the modeling of multicomponent alloy systems is presented.

Strain-minimizing tetrahedral networks of semiconductor alloys

The atomic size mismatch between different binary semiconductors has been long known to limit their mutual solubility, leading instead to phase separation into incoherent phases, forming inhomogeneous mixtures that severely limit technological applications that rely on carrier transport. We show here that this atomic size mismatch can lead, under coherent conditions, to the formation of a homogeneous alloy with characteristic (201) two-monolayer ordering. This occurs because such specific layer arrangement corresponds to a unique strain-minimizing network in tetrahedral systems.

First-principles thermodynamics of coherent interfaces in samarium-doped ceria nanoscale superlattices

Nanoscale superlattices of samarium-doped ceria layers with varying doping levels have been recently proposed as a novel fuel cell electrolyte. We calculate the equilibrium composition profile across the coherent {100} interfaces present in this system using lattice-gas Monte Carlo simulations with long-range interactions determined from electrostatics and short-range interactions obtained from ab initio calculations. These simulations reveal the formation of a diffuse, nonmonotonic, and surprisingly wide (11 nm at 400 K) interface composition profile, despite the absence of space charge regions.

Density of Configurational States from First-Principles Calculations: The Phase Diagram of Al-Na Surface Alloys

The structural phases of Al(x)Na(1-x) surface alloys have been investigated theoretically and experimentally. We describe the system using a lattice-gas Hamiltonian, determined from density functional theory, together with Monte Carlo (MC) calculations. The obtained phase diagram reproduces the experiment on a quantitative level. From calculation of the (configurational) density of states by the recently introduced Wang-Landau MC algorithm, we derive thermodynamic quantities, such as the free energy and entropy, which are not directly accessible from conventional MC simulations. We accurately reproduce the stoichiometry, as well as the temperature at which an order-disorder phase transition occurs, and demonstrate the crucial role, and magnitude, of the configurational entropy.