Cluster expansion Monte Carlo study of indium-aluminum segregation and homogenization in CuInSe2-CuAlSe2 pseudobinary alloys.

The influence of temperature and Al content on the segregation and homogenization behaviour of In-Al atoms in CuIn1-xAlxSe2 (CIAS) pseudobinary alloys is studied using a combination of cluster expansion Monte Carlo simulations and first-principles calculations. Such alloys are promising materials for a number of solar-energy-related applications. We found that the segregation of In-Al atoms in CIAS alloys with different Al contents occurs at relatively low temperatures. The cluster morphology of Al(In) atoms in CIAS alloys at 73 K appears in an ellipsoidal, rod-like or lamellar form, depending on the Al(In) content. The spatial distribution of In-Al atoms becomes homogeneous as the temperature increases. By determining the inhomogeneity degree σ of In-Al distributions in CIAS alloys at a series of temperatures, we found that the variation of σ with temperature (T) for all the considered CIAS alloys are sigmoidal in general and the sharp decrease in σ within a certain temperature range implies the occurrence of inhomogeneous-to-homogeneous phase transition. The inhomogeneity degree σ of CIAS alloys before or after the phase transition (phase segregation) increases as the content of Al(x) and In(1 - x) atoms gets closer. The σ(T) data points obtained by us can be well fitted with the Boltzmann function, which can give several physically meaningful parameters such as the phase transition temperature T0, temperature range of phase transition ΔT and so on. The fitted T0 and ΔT values for CIAS alloys with different Al content were proved to be reliable. The novel method for predicting the T0 and ΔT may be applied to many other binary or pseudobinary material systems with positive formation energy.

The ONETEP linear-scaling density functional theory program.

We present an overview of the onetep program for linear-scaling density functional theory (DFT) calculations with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, onetep is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchange-correlation functionals (with and without exact exchange), finite electronic temperature methods for metallic systems, methods for strongly correlated systems, molecular dynamics, vibrational calculations, time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mechanical (QM)/molecular mechanical and QM-in-QM embedding, density of states calculations, distributed multipole analysis, and methods for partitioning charges and interactions between fragments. Calculations with onetep provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples. onetep has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications.

Electronic annealing Fermi operator expansion for DFT calculations on metallic systems.

Density Functional Theory (DFT) calculations with computational effort which increases linearly with the number of atoms (linear-scaling DFT) have been successfully developed for insulators, taking advantage of the exponential decay of the one-particle density matrix. For metallic systems, the density matrix is also expected to decay exponentially at finite electronic temperature and linear-scaling DFT methods should be possible by taking advantage of this decay. Here we present a method for DFT calculations at finite electronic temperature for metallic systems which is effectively linear-scaling (O(N)). Our method generates the elements of the one-particle density matrix and also finds the required chemical potential and electronic entropy using polynomial expansions. A fixed expansion length is always employed to generate the density matrix, without any loss in accuracy by the application of a high electronic temperature followed by successive steps of temperature reduction until the desired (low) temperature density matrix is obtained. We have implemented this method in the ONETEP linear-scaling (for insulators) DFT code which employs local orbitals that are optimised in situ. By making use of the sparse matrix machinery of ONETEP, our method exploits the sparsity of Hamiltonian and density matrices to perform calculations on metallic systems with computational cost that increases asymptotically linearly with the number of atoms. We demonstrate the linear-scaling computational cost of our method with calculation times on palladium nanoparticles with up to ∼13 000 atoms.

Ideal versus real: simulated annealing of experimentally derived and geometric platinum nanoparticles.

Platinum nanoparticles find significant use as catalysts in industrial applications such as fuel cells. Research into their design has focussed heavily on nanoparticle size and shape as they greatly influence activity. Using high throughput, high precision electron microscopy, the structures of commercially available Pt catalysts have been determined, and we have used classical and quantum atomistic simulations to examine and compare them with geometric cuboctahedral and truncated octahedral structures. A simulated annealing procedure was used both to explore the potential energy surface at different temperatures, and also to assess the effect on catalytic activity that annealing would have on nanoparticles with different geometries and sizes. The differences in response to annealing between the real and geometric nanoparticles are discussed in terms of thermal stability, coordination number and the proportion of optimal binding sites on the surface of the nanoparticles. We find that annealing both experimental and geometric nanoparticles results in structures that appear similar in shape and predicted activity, using oxygen adsorption as a measure. Annealing is predicted to increase the catalytic activity in all cases except the truncated octahedra, where it has the opposite effect. As our simulations have been performed with a classical force field, we also assess its suitability to describe the potential energy of such nanoparticles by comparing with large scale density functional theory calculations.

Predicting the Oxygen-Binding Properties of Platinum Nanoparticle Ensembles by Combining High-Precision Electron Microscopy and Density Functional Theory.

Many studies of heterogeneous catalysis, both experimental and computational, make use of idealized structures such as extended surfaces or regular polyhedral nanoparticles. This simplification neglects the morphological diversity in real commercial oxygen reduction reaction (ORR) catalysts used in fuel-cell cathodes. Here we introduce an approach that combines 3D nanoparticle structures obtained from high-throughput high-precision electron microscopy with density functional theory. Discrepancies between experimental observations and cuboctahedral/truncated-octahedral particles are revealed and discussed using a range of widely used descriptors, such as electron-density, d-band centers, and generalized coordination numbers. We use this new approach to determine the optimum particle size for which both detrimental surface roughness and particle shape effects are minimized.

Perspective: Methods for large-scale density functional calculations on metallic systems.

Current research challenges in areas such as energy and bioscience have created a strong need for Density Functional Theory (DFT) calculations on metallic nanostructures of hundreds to thousands of atoms to provide understanding at the atomic level in technologically important processes such as catalysis and magnetic materials. Linear-scaling DFT methods for calculations with thousands of atoms on insulators are now reaching a level of maturity. However such methods are not applicable to metals, where the continuum of states through the chemical potential and their partial occupancies provide significant hurdles which have yet to be fully overcome. Within this perspective we outline the theory of DFT calculations on metallic systems with a focus on methods for large-scale calculations, as required for the study of metallic nanoparticles. We present early approaches for electronic energy minimization in metallic systems as well as approaches which can impose partial state occupancies from a thermal distribution without access to the electronic Hamiltonian eigenvalues, such as the classes of Fermi operator expansions and integral expansions. We then focus on the significant progress which has been made in the last decade with developments which promise to better tackle the length-scale problem in metals. We discuss the challenges presented by each method, the likely future directions that could be followed and whether an accurate linear-scaling DFT method for metals is in sight.