A. van de Walle

The Alloy Theoretic Automated Toolkit: A User Guide

Although the formalism that allows the calculation of alloy thermodynamic properties from first-principles has been known for decades, its practical implementation has so far remained a tedious process. The Alloy Theoretic Automated Toolkit (ATAT) drastically simplifies this procedure by implementing decision rules based on formal statistical analysis that frees the researchers from a constant monitoring during the calculation process and automatically “glues” together the input and the output of various codes, in order to provide a high-level interface to the calculation of alloy thermodynamic properties from first-principles. ATAT implements the Structure Inversion Method (SIM), also known as the Connolly-Williams method, in combination with semi-grand-canonical Monte Carlo simulations. In order to make this powerful toolkit available to the wide community of researchers who could benefit from it, this article present a concise user guide outlining the steps required to obtain thermodynamic information from ab initio calculations.

Automating first-principles phase diagram calculations

Devising a computational tool that assesses the thermodynamic stability of materials is among the most important steps required to build a “virtual laboratory,” where materials could be designed from first principles without relying on experimental input. Although the formalism that allows the calculation of solid-state phase diagrams from first principles is well established, its practical implementation remains a tedious process. The development of a fully automated algorithm to perform such calculations serves two purposes. First, it will make this powerful tool available to a large number of researchers. Second, it frees the calculation process from arbitrary parameters, guaranteeing that the results obtained are truly derived from the underlying first-principles calculations. The proposed algorithm formalizes the most difficult step of phase diagram calculations, namely the determination of the “cluster expanison,” which is a compact representation of the configurational dependence of the alloy’s energy. This is traditionally achieved by a fit of the unknown interaction parameters of the cluster expansion to a set of structural energies calculated from first principles. We present a formal statistical basis for the selection of both the interaction parameters to include in the cluster expansion and the structures to use to determine them. The proposed method relies on the concepts of cross-validation and variance minimization. An application to the calculation of the phase diagram of the Si-Ge, CaO-MgO, Ti-Al, and Cu-Au systems is presented.

The effect of lattice vibrations on substitutional alloy thermodynamics

A long-standing limitation of first-principles calculations of substitutional alloy phase diagrams is the difficulty in accounting for lattice vibrations. A survey of the theoretical and experimental literature seeking to quantify the effect of lattice vibrations on phase stability indicates that they can be significant. Typical vibrational entropy differences between phases are of the order of 0.1 to 0.2kB/atom, which is comparable to the typical values of configurational entropy differences in binary alloys (at most 0.693kB/atom). This article presents the basic formalism underlying ab initio phase diagram calculations, along with the generalization required to account for lattice vibrations. The authors review the various techniques allowing the theoretical calculation and the experimental determination of phonon dispersion curves and related thermodynamic quantities, such as vibrational entropy or free energy. A clear picture of the origin of vibrational entropy differences between phases in an alloy system is presented that goes beyond the traditional bond counting and volume change arguments. Vibrational entropy change can be attributed to the changes in chemical bond stiffness associated with the changes in bond length that take place during a phase transformation. This so-called “bond stiffness vs bond length” interpretation both summarizes the key phenomenon driving vibrational entropy changes and provides a practical tool to model them.

Self-driven lattice-model Monte Carlo simulations of alloy thermodynamic properties and phase diagrams

Monte Carlo (MC) simulations of lattice models are a widely used way to compute thermodynamic properties of substitutional alloys. A limitation to their more widespread use is the difficulty of driving a MC simulation in order to obtain the desired quantities. To address this problem, we have devised a variety of high-level algorithms that serve as an interface between the user and a traditional MC code. The user specifies the goals sought in a high-level form that our algorithms convert into elementary tasks to be performed by a standard MC code. For instance, our algorithms permit the determination of the free energy of an alloy phase over its entire region of stability within a specified accuracy, without requiring any user intervention during the calculations. Our algorithms also enable the direct determination of composition-temperature phase boundaries without requiring the calculation of the whole free energy surface of the alloy system.

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.

First-principles study of the structure of stoichiometric and Mn-deficient MnO2

Abstract We present an extensive Density Functional Theory study on the phases and magnetic states of MnO2, with over 300 calculations of various Mn–vacancy configurations and magnetic spin states. It is shown that the paramagnetic extrapolations of spin-polarized results are essential to correctly reproduce pyrolusite as the ground state of MnO2. Paramagnetic energies are obtained by fitting a Heisenberg Hamiltonian to the energy of 10–20 magnetic configurations for each of 16 possible MnO2 polymorphs. Near groundstate degeneracy is shown to occur due to the frustration of otherwise large interactions. While many other structures are found to be near degenerate in energy with pyrolusite, no thermal disorder exists in the system up to several thousand degrees. The thermal disorder is suppressed because the strong correlation of the Mn–vacancy order along the lines of face-sharing octahedra removes any low-energy excitations from the system. Mn vacancies compensated by protons (Ruetschi defects), ubiquitously present in commercial MnO2, are shown to have a dramatic effect on phase stability. The stabilizing effects of Ruetschi defects may explain the presence in MnO2 of ramsdellite and twinning, both of which are unstable in the pure material. We believe Ruetschi defects to be an important source of the structural complexity of synthetic MnO2 produced either electrochemically or chemically.

First principles phase diagram calculations for the wurtzite-structure systems AlN–GaN, GaN–InN, and AlN–InN

First principles phase diagram calculations were performed for the wurtzite-structure quasibinary systems AlN–GaN, GaN–InN, and AlN–InN. Cluster expansion Hamiltonians that excluded, and included, excess vibrational contributions to the free energy, Fvib, were evaluated. Miscibility gaps are predicted for all three quasibinaries, with consolute points, (XC,TC), for AlN–GaN, GaN–InN, and AlN–InN equal to (0.50, 305 K), (0.50, 1850 K), and (0.50, 2830 K) without Fvib, and (0.40, 247 K), (0.50, 1620 K), and (0.50, 2600 K) with Fvib, respectively. In spite of the very different ionic radii of Al, Ga, and In, the GaN–InN and AlN–GaN diagrams are predicted to be approximately symmetric.

Atomic-scale structure of the SrTiO3(001)-c(6×2) reconstruction : Experiments and first-principles calculations

The c(6×2) is a reconstruction of the SrTiO3(001) surface that is formed between 1050 and 1100 °C in oxidizing annealing conditions. This work proposes a model for the atomic structure for the c(6×2) obtained through a combination of results from transmission electron diffraction, surface x-ray diffraction, direct methods analysis, computational combinational screening, and density functional theory. As it is formed at high temperatures, the surface is complex and can be described as a short-range-ordered phase featuring microscopic domains composed of four main structural motifs. Additionally, nonperiodic TiO2 units are present on the surface. Simulated scanning tunneling microscopy images based on the electronic structure calculations are consistent with experimental images.

Atomic-Scale Simulation Study of Equilibrium Solute Adsorption at Alloy Solid-Liquid Interfaces

AbstractEquilibrium structural properties of solid-liquid interfaces in Cu-Ni alloys are studied by Monte-Carlo simulations employing interatomic potentials based on the embedded-atom method. We describe a thermodynamic-integration approach used to derive bulk concentrations and densities for solid and liquid phases in two-phase thermodynamic equilibrium. These results are used as a basis for constructing three-dimensional supercell geometries employed in Monte-Carlo-simulation studies of solid-liquid interface properties for {100} and {111} crystallographic orientations. At a temperature of 1750 K (four percent below the calculated melting point of pure Ni) equilibrium density and concentration profiles have been derived, allowing a calculation of the relative Gibbsian adsorption,