Supercell Approximation Research Articles

Crystal structures of η''-Cu3+xSi and η'''-Cu3+xSi.

The binary phase diagram of Cu-Si is unexpectedly complex in the vicinity of Cu3+xSi. The low-temperature region contains three closely related incommensurately modulated phases denoted, in order of increasing temperature of stability, η''', η'' and η'. The structure analysis of η' has been reported previously [Palatinus et al. (2011). Inorg. Chem. 50, 3743]. Here the structure model for the phases η'' and η''' is reported. The structures could be solved in superspace, but no superspace structure model could be constructed due to the complexity of the modulation functions. Therefore, the structures were described in a supercell approximation, which involved a 4 × 4 × 3 supercell for the η'' phase and a 14 × 14 × 3 supercell for the η''' phase. Both structures are very similar and differ only by a subtle symmetry lowering from η'' to η'''. A comparison of the structure models of η'' and η''' with the reported structure of η' suggests that the reported structure model of η' contains an incorrect assignment of atomic types.

Energetics of intrinsic point defects in aluminium via orbital-free density functional theory

The formation and migration energies for various point defects, including vacancies and self-interstitials, in aluminium are systematically reinvestigated using the supercell approximation in the framework of orbital-free density functional theory. In particular, the finite-size effects and the accuracy of various kinetic energy density functionals are examined. It is demonstrated that as the supercell size increases, the finite-size errors asymptotically decrease as . Notably, the formation energies of self-interstitials converge much more slowly than that of vacancies. With carefully chosen kinetic energy density functionals, the calculated results agree quite well with the available experimental data and those obtained through Kohn–Sham density functional theory, which has an exact kinetic term.

Possible n/p-type conductivity of two-dimensional graphene oxide by boron and nitrogen doping: Evaluated via constrained excitation

As the first-principles calculations using the supercell approximation give widely scattered results in a two-dimensional charged system, making the evaluation of defect ionization energy difficult, here an alternative constrained excitation is applied to overcome this problem for defect analysis. As an example in graphene oxide with 50% oxygen coverage (according to the popular epoxy-chain-plus-hydroxyl-chain model), the structures, stabilities, and electronic properties of nitrogen and boron dopants are investigated. Generally, boron prefers to replace carbon in the sp3 region as an acceptor while nitrogen has a tendency to substitute the sp2 carbon close to the boundary between the sp2 region and the sp3 region as a donor. Their ionization energies are 0.24–0.42 eV for boron and 0.32–0.67 eV for nitrogen. However, a special case of nitrogen doped in the boundary-sp3 carbon can change to be an acceptor with the assistance of its neighboring (epoxy) oxygen “Lift-off,” leading to the shallowest ionization energy of 0.12 eV and the best candidate for p-type conductivity. The present study offers the detailed pictures of boron and nitrogen defects in graphene oxide for the potential n- and p-type conductivity.

Supercell program: a combinatorial structure-generation approach for the local-level modeling of atomic substitutions and partial occupancies in crystals

BackgroundDisordered compounds are crucially important for fundamental science and industrial applications. Yet most available methods to explore solid-state material properties require ideal periodicity, which, strictly speaking, does not exist in this type of materials. The supercell approximation is a way to imply periodicity to disordered systems while preserving “disordered” properties at the local level. Although this approach is very common, most of the reported research still uses supercells that are constructed “by hand” and ad-hoc.ResultsThis paper describes a software named supercell, which has been designed to facilitate the construction of structural models for the description of vacancy or substitution defects in otherwise periodically-ordered (crystalline) materials. The presented software allows to apply the supercell approximation systematically with an all-in-one implementation of algorithms for structure manipulation, supercell generation, permutations of atoms and vacancies, charge balancing, detecting symmetry-equivalent structures, Coulomb energy calculations and sampling output configurations. The mathematical and physical backgrounds of the program are presented, along with an explanation of the main algorithms and relevant technical details of their implementation. Practical applications of the program to different types of solid-state materials are given to illustrate some of its potential fields of application. Comparisons of the various algorithms implemented within supercell with similar solutions are presented where possible.ConclusionsThe all-in-one approach to process point disordered structures, powerful command line interface, excellent performance, flexibility and GNU GPL license make the supercell program a versatile set of tools for disordered structures manipulations.Electronic supplementary materialThe online version of this article (doi:10.1186/s13321-016-0129-3) contains supplementary material, which is available to authorized users.

High-temperature transition in SrFeO2.5: LSDA+U simulation

The effects of oxygen vacancy disordering in structural features and magnetic characteristics of SrFeO2.5 are studied by the LMTO method in frameworks of the LSDA+U formalism in supercell approximation. Results clearly show that the high-temperature pseudocubic phase of SrFeO2.5 may contain iron ions in five-fold oxygen coordination.

Effects of Ni and Ti on the phase stability, martensitic transformation and mechanical properties of B2 CuZr phase

We systematically investigate the phase stability, martensitic transformation (MT) behavior and mechanical properties of Ni or Ti doped B2 CuZr phase with the supercell and virtual crystal approximation (VCA) methods. Formation energies of different supercells are used to judge the preference site of the dopants and to study the alloying effects on the stability of CuZr phase. By analyzing the alloying effects on two cubic elastic moduli (C′ and C44), we make a prediction of the composition-dependent martensitic transformation start temperature (Ms), which may give a theoretical interpretation of the different experimental observations for the Ni doped CuZr alloys and may also explain the effects of Ti on the decreasement of Ms from Ti’s destabilizing-effect induced decomposition of CuZr alloys. In addition, with the calculated elastic constants, mechanical properties including ductility and negative Poisson’s ratio (PR) of the Ni or Ti doped CuZr alloys are also discussed.

Determination of formation and ionization energies of charged defects in two-dimensional materials.

We present a simple and efficient approach to evaluate the formation energy and, in particular, the ionization energy (IE) of charged defects in two-dimensional (2D) systems using the supercell approximation. So far, first-principles results for such systems can scatter widely due to the divergence of the Coulomb energy with vacuum dimension, denoted here as L_{z}. Numerous attempts have been made in the past to fix the problem under various approximations. Here, we show that the problem can be resolved without any such assumption, and a converged IE can be obtained by an extrapolation of the asymptotic IE expression at large L_{z} (with a fixed lateral area S) back to the value at L_{z}=0. Application to defects in monolayer boron nitride reveal that defects in 2D systems can be unexpectedly deep, much deeper than the bulk.

Variational solution of Poisson's equation using plane waves in adaptive coordinates.

A procedure for solving Poisson's equation using plane waves in adaptive coordinates (u) is described. The method, based on Gygi's work, writes a trial potential ξ as the product of a preselected Coulomb weight μ times a plane-wave expansion depending on u. Then, the Coulomb potential generated by a given density ρ is obtained by variationally optimizing ξ, so that the error in the Coulomb energy is second-order with respect to the error in ξ. The Coulomb weight μ is chosen to provide to each ξ the typical long-range tail of a Coulomb potential, so that calculations on atoms and molecules are made possible without having to resort to the supercell approximation. As a proof of concept, the method is tested on the helium atom and the H_{2} and H_{3}^{+} molecules, where Hartree-Fock energies with better than milli-Hartree accuracy require only a moderate number of plane waves.

Rigorous Analysis of Diffraction from Quasicrystalline Gratings via Floquet’s Theorem in Higher-Dimensional Space

A rigorous approach for the analysis of diffraction from quasicrystalline gratings is presented. Previous methods for determining the diffraction properties of quasicrystalline gratings have relied on periodic supercell approximations. Our method exploits the cut-and-project method, which constructs quasicrystals as irrational slices of higher-dimensional periodic structures onto the physical space. The periodicity in the higher-dimensional space allows for the application of Floquet’s theorem. The solutions can then be obtained by solving Maxwell’s equations in the higher-dimensional space and projecting the results to the lower dimensional physical space. As an example, the method is applied to a one-dimensional aperiodic grating based on a Fibonacci quasicrystal (QC) where the results that were generated are shown to be in near-perfect agreement with those obtained using the supercell approximations.

Optical absorption and emission of α-Sn nanocrystals from first principles

We investigate the optical properties of hydrogenated α-Sn nanocrystals up to diameters of 3.6 nm in the framework of an ab initio pseudopotential method including spin–orbit interaction (SOI) and the repeated supercell approximation. The fundamental absorption and emission edges are determined including quasiparticle effects and electron–hole interaction. The atomic geometries in the ground and excited electronic states follow from total energy optimization. We discuss the oscillator strengths of the optical absorption near the fundamental gaps for the most important transitions. We demonstrate that the spectra can only be correctly described including SOI. The strongly size-dependent Stokes shifts between optical absorption and emission are shown to be mainly a consequence of the different atomic geometries.

Efficient stochastic generation of special quasirandom structures

We present a new algorithm to generate Special Quasirandom Structures (SQS), i.e., best periodic supercell approximations to the true disordered state for a given number of atoms per supercell. The method is based on a Monte Carlo simulated annealing loop with an objective function that seeks to perfectly match the maximum number of correlation functions (as opposed to merely minimizing the distance between the SQS correlation and the disordered state correlations for a pre-specified set of correlations). The proposed method optimizes the shape of the supercell jointly with the occupation of the atomic sites, thus ensuring that the configurational space searched is exhaustive and not biased by a pre-specified supercell shape. The method has been implemented in the “mcsqs” code of the Alloy Theoretic Automated Toolkit (ATAT) in the most general framework of multicomponent multisublattice systems and in a way that minimizes the amount of input information the user needs to specify and that allows for efficient parallelization.

Tunable acoustic waveguides in periodic arrays made of rigid square-rod scatterers: theory and experimental realization

The tunable and the engineering possibilities of waveguides in periodic arrays made of rigid square-rod scatterers are theoretically and experimentally reported in this work. Due to the square shape of the scatterers, the control of their orientation with respect to the direction of the incident wave can be used for moulding the propagating acoustic waves inside the periodic structure. On the one hand, the plane wave expansion with supercell approximation is used to obtain the band structure of the periodic system. On the other hand, the scattering of waves in finite periodic arrays is analysed using the finite elements method. Experimentally, a prototype made of rigid square-rod scatterers is used to validate the theoretical predictions. A spatial-frequency filter and some applications in waveguiding for audible sound are discussed in this work. Good agreement between theory and experiments and the high tunability of the system are demonstrated.

Experimental investigation of two-dimensional multi-point defect phononic crystals with square lattice

The characteristics of multi-point defect phononic crystal (PC) composed of square array of circular steel cylinders in water are investigated experimentally using the ultrasonic immersion transmission technique. The band structures of the PCs are obtained by the finite element method with 9×9 supercell approximation. A very good agreement with the experimental results, numerical transmission data and eigenmode frequencies of band structures is observe. Meanwhile the number of multi-point defects affects the localized modes of cavities and propagation characteristics, and the eigenmodes of defects show the symmetric or antisymmetric modes in designing the new type of acoustic wave devices.

Characteristics and applications of line defect modes in two-dimensional magnonic crystals

In this paper, band structures and defect modes of two-dimensional magnonic crystals with line defect are calculated by using the plane-wave expansion method under supercell approximation. The obtained results show that line defect modes can be produced in the band gap by introducing the line defect bodies into the two-dimensional magnonic crystal. The presence of the line defect modes leads to the spin waves propagating along the direction of the line defects in these structures. Utilizing the wave-guide characteristic of line defect modes, two-dimensional magnonic crystals can be used as the materials for fabricating spin-wave waveguides.

Coupling characteristics of point defects modes in two-dimensional magnonic crystals

The coupling characteristics of two-point defects modes and multi-point defects modes in two-dimensional magnonic crystals composed of Fe square rods/EuO square lattices are studied based on the plane-wave expansion method under supercell approximation. The results show that the coupling degree of these defect modes depends not only on the distance between defect bodies, but also on the arrangement direction of point defects. The phase of precession of defect modes' magnetization distributions varies as the distance between the defects changes. These magnonic crystals with multi-point defects can be used as the fabricating materials of the directional spin-wave filters or the narrow band spin-wave waveguides.

Improved fake mode free plane-wave expansion and three planar-slab waveguides method

We compare the extra modes introduced by plane-wave expansion with the two-dimensional (2D) and the three-dimensional (3D) supercell approximation method, and analyze the differences between those two kinds of extra modes. In the band structure of 2D photonic crystal (PhC) using the 2D supercell approximation, the extra modes are created through band folding, and those extra modes can really exist in the 2D PhC. However, in the band structure of a 2D PhC slab using the 3D supercell approximation, the extra modes are mainly generated by the coupling between supercells, and cannot exist in the real 2D PhC slab, thus these extra modes are defined as fake modes in our paper. Through a detailed analysis of the origin of the fake modes and of the energy distribution of the fake modes and of the real modes, we propose an improved fake mode free plane-wave expansion and three planar slab waveguides method which removes the fake modes. This is the first time such a fake mode free band structure is presented. This result can be definitely helpful in designing 3D devices.

Radiation resistance of the xenotime YPO4 from the computer simulation data

The radiation resistance of the mineral xenotime YPO4 has been investigated using computer simulation methods. The optimal criteria for the appropriate choice of the parameters of the interatomic potentials used for the simulation of α-decay in minerals have been proposed. The formation of a cascade of displaced atoms in the structure of xenotime after the passage of a primarily knocked thorium atom with an energy of 20 keV has been studied using the molecular dynamics method. The specific features of the formation and annealing of individual defects in the structure of xenotime have been considered using the Mott-Littleton method. The dependences of the energy of formation of Frenkel pairs and the probability of their annihilation during the annealing of a cascade of atomic displacements on the distance between the vacancy and the interstitial site have been analyzed within the framework of the supercell approximation.

Point defect states of exchange spin waves in all-ferromagnetic two-dimensional magnonic crystals

Using the plane-wave expansion method under supercell approximation, band structures of exchange spin waves propagating in all-ferromagnetic two-dimensional magnonic crystals with point defects are calculated. The results indicate that the point defects in these structures can create localized states inside the bandgap. The characteristics and the magnetization distributions of these localized states are studied. The results show that the group velocities of the localized states almostequal zero in the whole first Brillouin zone, and numbers of localized states and their frequency-positions in the bandgap are related to the size of the point defect. Magnonic crystalswith such defect states can be used as fabricating materials of narrow bandpass spin-wave filters.

Coupling characteristics of point defect modes in two-dimensional magnonic crystals

Using the plane-wave expansion method under supercell approximation, band structures of spin waves propagating in two-dimensional magnonic crystals with coupling multi-point defects and magnetization field distributions of some defect modes are calculated. The results indicate that the energies of point defect modes can couple each other, and propagate along the direction of the multi-point defects in these structures. Utilizing the coupling characteristics of defect modes, two-dimensional magnonic crystals can be used as the fabricating materials of spin-wave waveguides.

Evanescent waves and deaf bands in sonic crystals

The properties of sonic crystals (SC) are theoretically investigated in this work by solving the inverse problem k(ω) using the extended plane wave expansion (EPWE). The solution of the resulting eigenvalue problem gives the complex band structure which takes into account both the propagating and the evanescent modes. In this work we show the complete mathematical formulation of the EPWE for SC and the supercell approximation for its use in both a complete SC and a SC with defects. As an example we show a novel interpretation of the deaf bands in a complete SC in good agreement with multiple scattering simulations.