Machine Learning Force Field-Aided Cluster Expansion Approach to Phase Diagram of Alloyed Materials

First-principles approaches based on density functional theory (DFT) have played important roles in the theoretical study of multicomponent alloyed materials. Considering the highly demanding computational cost of direct DFT-based sampling of the configurational space, it is crucial to build efficient and low-cost surrogate Hamiltonian models with DFT accuracy for efficient simulation of alloyed systems with configurational disorder. Recently, the machine learning force field (MLFF) method has been proposed to tackle complicated multicomponent disordered systems. However, the importance of integrating significant physical considerations, including, in particular, convex hull preservation, which is the prerequisite for the accurate prediction of phase diagrams, into the training process of the MLFF remains rarely addressed. In this work, a workflow is proposed to train a convex-hull-preserved (CHP) MLFF for binary alloy systems, based on which the order-disorder phase boundary is predicted by using the Wang-Landau Monte Carlo (WLMC) technique. The predicted values for order-disorder phase transition temperatures agree well with the experiment. The CHP-MLFF is further used to build CE models with the same accuracy as the MLFF and higher efficiency in sampling configurational space. Using the results obtained from the MLFF-based WLMC simulation as a reference, the performances of different schemes for constructing CE models were evaluated in a transparent manner, which revealed the close correlation between the prediction accuracy of ground-state configurations and that of the order-disorder phase transition temperature. This work clearly indicates the great importance of reproducing the convex hull and energetics of ground-state configurations when constructing surrogate Hamiltonians for the statistical modeling of alloyed systems.

Heteroanionic Materials by Design: Progress Toward Targeted Properties

The burgeoning field of anion engineering in oxide-based compounds aims to tune physical properties by incorporating additional anions of different size, electronegativity, and charge. For example, oxychalcogenides, oxynitrides, oxypnictides, and oxyhalides may display new or enhanced responses not readily predicted from or even absent in the simpler homoanionic (oxide) compounds because of their proximity to the ionocovalent-bonding boundary provided by contrasting polarizabilities of the anions. In addition, multiple anions allow heteroanionic materials to span a more complex atomic structure design palette and interaction space than the homoanionic oxide-only analogs. Here, established atomic and electronic principles for the rational design of properties in heteroanionic materials are contextualized. Also described are synergistic quantum mechanical methods and laboratory experiments guided by these principles to achieve superior properties. Lastly, open challenges in both the synthesis and the understanding and prediction of the electronic, optical, and magnetic properties afforded by anion-engineering principles in heteroanionic materials are reviewed.

Optimizing special quasirandom structure (SQS) models for accurate functional property prediction in disordered 2D alloys

2D materials such as MXenes have garnered attention in a wide field of applications ranging from energy to environment to medical. Properties of 2D materials can be tailored via alloying and in some cases, solid-solutions (disordered alloys) are formed. To predict the disordered alloy properties via first-principles, the model structure needs to imitate the random arrangements of alloyants and yet remains computationally tractable. Using density functional theory and the cluster expansion method, we investigate the accuracy of using of special quasirandom structures (SQSs) for predicting disordered 2D alloy properties, evaluating the effect of SQS supercell size on the prediction quality of formation energies, elastic properties, and structural parameters. We illustrate the findings with 5 different disordered binary [Formula: see text] MXene alloy systems (where M  =  Ti and M'  =  Zr, Hf, V, Nb, or Ta), demonstrating that SQSs around 6-8 times the primitive cell (N  =  6-8) are sufficient to attain convergence in the property predictions versus supercell size. For formation energies, SQSs with N  >  4 are found to reproduce the formation energies of the fully disordered phase within ~2.5 meV. For the simulation of the experimentally-synthesized TiNbCO₂, we find convergence in structural parameters and elastic tensors at N ~ 6. We traced the convergence of the predictions to the convergence in the band structure-related properties via analysis of the electronic densities-of-states and the projected crystal overlap Hamilton population. Our findings suggest that modest sized SQSs would reproduce the properties of disordered MXene alloys. The results should help guide the investigations of structure-property relationships in other disordered 2D materials as well.

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.

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.

Finding the atomic configuration with a required physical property in multi-atom structures

In many problems in molecular and solid state structures one seeks to determine the energy-minimizing decoration of sites with different atom types. In other problems, one is interested in finding a decoration with a target physical property (e.g. alloy band gap) within a certain range. In both cases, the sheer size of the configurational space can be horrendous. We present two approaches which identify either the minimum-energy configuration or configurations with a target property for a fixed underlying Bravais lattice. We compare their efficiency at locating the deepest minimum energy configuration of face centered cubic Au-Pd alloy. We show that a global-search genetic-algorithm approach with diversity-enhancing constraints and reciprocal-space mating can efficiently find the global optimum, whereas the local-search virtual-atom approach presented here is more efficient at finding structures with a target property.

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.

Superhard Pseudocubic BC2N superlattices

It is currently under debate whether diamondlike BC2N may be harder than cubic BN (c-BN). Using the bond counting rule, we have performed an unconstrained search and identified a series of short period (111) superlattices that have much lower total energy than previously proposed structures. By examining the ideal strength of these pseudocubic boron-carbonitrides, we show that they are harder than c-BN. Our results are consistent with experimental findings, but in contrast with a recent theoretical study, which claimed that the BC2N is less hard than c-BN.

Adaptive crystal structures: CuAu and NiPt

We discover that Au-rich Cu1-xAux and Pt-rich Ni1-xPtx contain a composition range in which there is a quasicontinuum of stable, ordered "adaptive structures" made of (001) repeat units of simple structural motifs. This is found by searching approximately 3x10(6) different fcc configurations whose energies are parametrized via a "cluster expansion" of first-principles-calculated total energies of just a few structures. This structural adaptivity is explained in terms of an anisotropic, long-range strain energy.

Origins of nonstoichiometry and vacancy ordering in Sc1-x squarexS

Whereas nearly all compounds A(n)B(m) obey Dalton's rule of integer stoichiometry (n: m, both integer), there is a class of systems, exemplified by the rocksalt structure Sc1-x squarexS, that exhibits large deviations from stoichiometry via vacancies, even at low temperatures. By combining first-principles total energy calculations with lattice statistical mechanics, we scan an astronomical number of possible structures, identifying the stable ground states. Surprisingly, all have the same motifs: (111) planes with (112) vacancy rows arranged in (110) columns. Electronic structure calculations of the ground states (identified out of approximately 3x10(6) structures) reveal the remarkable origins of nonstoichiometry.