Phenomenological interatomic potentials for silicon, germanium and their binary alloy

A phenomenological potential is constructed for silicon, germanium, and their binary alloy. As in the modified embedded atom model (MEAM), the interatomic interactions are assumed to arise from the overlap of the electron wave functions. However, the calculation of energy is quite different in the two models. The proposed potential has seven adjustable parameters in contrast to ten or more in MEAM but gives perfect fit with the measured values of seven most important quantities for characterizing strained silicon: cohesive energy, equilibrium lattice constant, vacancy formation energy, Raman frequency, and the three elastic constants. The potential should be suitable for lattice statics calculations on strained silicon.     

Angular forces in the lattice dynamics of diamond crystal lattices

The lattice dynamics of the diamond lattice has been investigated using a model in which the interatomic forces include, in addition to central forces, the angular forces of the type employed by de Launay and Clark, Gazis and Wallis. The 2 models have been applied to silicon and germanium to investigate the phonon dispersion curves in the three symmetry directions of the Brillioun zone. The results are found to be qualitatively in good agreement with experiments.     

Pressure-dependent EXAFS mean-square relative displacements of germanium and silicon crystals

In this paper, the statistical moment method (SMM) has been developed to study the pressure dependence of thermodynamic quantities of germanium and silicon crystals. We have derived the analytical expressions of the pressure-dependent parallel mean-square relative displacement (MSRD) or extended X-ray absorption fine structure (EXAFS) Debye–Waller factor, mean-square displacement (MSD) as well as lattice constant and volume change of diamond-type crystals. Numerical calculations performed for these semiconductors up to 11 GPa are found to be in good and reasonable agreement with available experimental data as well as with previous theoretical studies. Our results indicate that the SMM can be efficiently used for determining the relative change of the pressure-dependent MSRDs of germanium and silicon semiconductors. The research also shows the advantage of SMM on studying other thermodynamic properties of materials under high pressures.     

Effect of normal processes on thermal conductivity of germanium,silicon and diamond

The effect of normal scattering processes is considered to redistribute the phonon momentum in (a) the same phonon branch — KK-S model and (b) between different phonon branches — KK-H model. Simplified thermal conductivity relations are used to estimate the thermal conductivity of germanium, silicon and diamond with natural isotopes and highly enriched isotopes. It is observed that the consideration of the normal scattering processes involving different phonon branches gives better results for the temperature dependence of the thermal conductivity of germanium, silicon and diamond with natural and highly enriched isotopes. Also, the estimation of the lattice thermal conductivity of germanium and silicon for these models with the consideration of quadratic form of frequency dependences of phonon wave vector leads to the conclusion that the splitting of longitudinal and transverse phonon modes, as suggested by Holland, is not an essential requirement to explain the entire temperature dependence of lattice thermal conductivity whereas KK-H model gives a better estimation of the thermal conductivity without the splitting of the acoustic phonon modes due to the dispersive nature of the phonon dispersion curves.      

Simulation of α-Zr structural stability under pressure using the molecular dynamics method

The structural stability of α-Zr was studied using the molecular dynamics method in wide temperature and pressure ranges. The interatomic interaction was described by a pair potential calculated within the Animalu pseudopotential model. The potential parameters were selected using α-Zr phonon spectra. The features in the dynamics of the α-β and α-ω phase transitions at various temperatures and pressures were considered. The calculated hysteresis of forward and backward phase transitions and its pressure and temperature dependences are discussed. The data obtained were used to plot phase equilibrium lines in the P-T phase diagram.     

Density of phonon states in amorphous germanium and silicon

The density of phonon states in amorphous germanium and silicon is calculated by statistically averaging the crystalline phonon density of states according to the radial distribution function. A simple rigid ion model is used to calculate the density of phonon states at various lattice spacings. The appropriate model parameters are obtained from the pressure dependent elastic constants and the Raman frequency. The calculated results compare favorably to experimental data obtained by infrared and Raman scattering and the results of other theoretical calculations.     

Effect of pressure on the structure and the electronic properties of LiClO4, NaClO<Subscript>4</Subscript>, KClO<Subscript>4</Subscript>, and NH<Subscript>4</Subscript>ClO<Subscript>4</Subscript>

The effect of pressure on the structural and electronic properties of lithium, sodium, potassium, and ammonium perchlorates have been studied in terms of the density functional theory with allowance for the Van der Waals dispersion interaction. The pressure dependences of the geometric parameters, the band gaps, the densities of states, the charge distributions, and the atomic charges are calculated. The compressibilities of the perchlorates are found to be anisotropic, which is due to the differences of the lattice parameters and the nature of interatomic bonds. Ammonium cation is rotated under pressure around axis b at an angle of ~9°. The band gaps of the perchlorates are ~4.5–4.7 eV and increase with pressure.     

Thermodynamic and transport properties of simple fluids using lattice sums: bulk phases and liquid-vapour interface

Molecular dynamics simulations in the canonical ensemble have been performed to obtain the thermodynamic and transport properties of the Lennard-Jones fluid. The dispersion interactions were calculated using lattice sums. This method makes it possible to simulate the full potential avoiding the inclusion of the long range corrections (LRC) during or at the end of simulations. In the calculation of dynamic properties in bulk phases and thermodynamic quantities of inhomogeneous systems where the interface is physically present, in general the LRC cannot easily be included. By using the lattice sums method, the results are independent of the truncation of the potential. In the liquid-vapour interface simulations it is not necessary to make any pre-judgments about the form of the LRC formula to calculate coexisting properties such as the surface tension. The lattice sums method has been applied to evaluate how well the full interaction can be calculated in the liquid phase and in the liquid-vapour interface. In the liquid phase the pressure, configurational energy, diffusion coefficient and shear viscosity were obtained. The results of the thermodynamic properties are compared with those obtained using the spherically truncated and shifted (STS) potential with the LRC added at the end of simulations, and excellent agreement is found. The transport properties are calculated on different system sizes for a state near the triple point. The diffusion coefficient using the lattice sums method increases with the number of molecules, and the results are higher than those of the STS model truncated at 2.5σ (STS2.5). The shear viscosity does not show any system size dependence for systems with more than 256 molecules, and the lattice sums results are essentially the same as those for the STS2.5. In the liquid-vapour equilibria the coexisting densities and vapour pressures for the full potential agree well with those obtained using the Gibbs ensemble and the NPT + test particle methods. The surface tension using lattice sums and truncation of forces at 2.5σ agrees well with STS results using large system sizes and cutoff distances.     

Statistical mechanical models for liquid and amorphous structure in covalently bonded systems

Summary Considerable effort has been given for some years to developing models of interatomic forces aimed at accounting for bond directionality in liquid and amorphous state calculations. Models involving three-body potentials have been especially useful for computer simulation studies of liquid and amorphous states in elemental semiconductors and binary chalcogenides of group-IV elements, starting with the work of Stillinger and Weber on silicon. However, pair potential models that may still account for the main effects of angular dependences of the effective interatomic forces, though at a primitive level, are desirable from the viewpoint of liquid structure theory. Developments in this direction are briefly reviewed, with particular emphasis on bond particle models for the structure of liquid and amorphous germanium. We also discuss the relation between liquid structure in a bond-particle model and crystallization accompanied by electron localization and volume expansion, as observed in elemental and III-V polar semiconductors. Paper presented at the workshop ?Highlights on Simple Liquids?, held in Turin at ISI on 1–3 May, 1989.     

Thermoelectric properties of high-pressure silicon phases

The thermo emf in Czochralski-grown silicon single crystals (Cz-Si) was experimentally studied in a range of pressures up to 20 GPa. The pressure dependences revealed phase transitions in the metallic phase of silicon, which passed from tetragonal to orthorhombic and then to hexagonal lattice. The high-pressure silicon phases, as well as the metallic high-pressure phases in A_NB_8?N semiconductors, possess conductivity of the hole type. As the pressure decreases, the emf behavior reveals transitions to the metastable phases Si-XII and Si-III. Preliminary thermobaric treatment of the samples at a pressure of up to 1.5 GPa and a temperature of T=50–650°C influences the thermoelectric properties of Cz-Si at high pressures.     

Pressure dependence of the Raman scattering in the ordered phase of NH4Cℓ

We have observed Raman scattering in NH₄C? from 105K to 295K and up to 7kbar hydrostatic pressure, including the disordered phase II and the ordered phase IV. The pressure dependences of internal and lattice modes are reported, as well as that of the libration mode. The results are applied to several theories of the potential barrier to rotation.     

An approximate multi-property empirical isotropic interatomic pair potential for the krypton dimer

An approximate empirical isotropic interatomic potential for krypton interaction is developed by simultaneously fitting the Morse-Morse-Morse-Spline-van der Waals potential form to the pressure second virial coefficient, viscosity, thermal conductivity and depolarized interaction-induced light scattering data. Absolute zeroth and second moments of the two-and three-body spectra, the pressure third virial coefficient and isotopic thermal diffusion factor have been measured and compared with theoretical calculations using various models for the interatomic potential. The results show that it is the most accurate potential yet reported for this system. The use of the new potential in lattice sum calculations yields good results for several properties of solid krypton.     

Interatomic potential for uranium in a wide range of pressures and temperatures

Using the force-matching method we develop an interatomic potential that allows us to study the structure and properties of α-U, γ-U and liquid uranium. The potential is fitted to the forces, energies and stresses obtained from ab initio calculations. The model gives a good comparison with the experimental and ab initio data for the lattice constants of α-U and γ-U, the elastic constants, the room-temperature isotherm, the normal density isochore, the bond-angle distribution functions and the vacancy formation energies. The calculated melting line of uranium at pressures up to 80 GPa and the temperature of the α-γ transition at 3 GPa agree well with the experimental phase diagram of uranium.     

First-principles calculations of structural and thermodynamic properties of BeB2 compound

The lattice parameter bulk modulus and pressure derivative of BeB2 are calculated by using the Cambridge Serial Total Energy Package （CASTEP） program in the frame of density function theory. The calculated results agree well with the average experimental data and other theoretical results. Through the quasi-harmonic Debye model, the dependences of the normalized lattice parameters a/ao, c/c0 and the normalized primitive cell volume V/Vo on pressure P, the variation of the thermal expansion coefficient ~ with pressure P and temperature T, as well as the dependences of the heat capacity Cv on pressure P and temperature T are obtained systematically.     

Atomistic properties of γ uranium

The properties of the body-centered cubic γ phase of uranium (U) are calculated using atomistic simulations. First, a modified embedded-atom method interatomic potential is developed for the high temperature body-centered cubic (γ) phase of U. This phase is stable only at high temperatures and is thus relatively inaccessible to first principles calculations and room temperature experiments. Using this potential, equilibrium volume and elastic constants are calculated at 0 K and found to be in close agreement with previous first principles calculations. Further, the melting point, heat capacity, enthalpy of fusion, thermal expansion and volume change upon melting are calculated and found to be in reasonable agreement with experiment. The low temperature mechanical instability of γ U is correctly predicted and investigated as a function of pressure. The mechanical instability is suppressed at pressures greater than 17.2 GPa. The vacancy formation energy is analyzed as a function of pressure and shows a linear trend, allowing for the calculation of the extrapolated zero pressure vacancy formation energy. Finally, the self-defect formation energy is analyzed as a function of temperature. This is the first atomistic calculation of γ U properties above 0 K with interatomic potentials.     

Changes of the Thermodynamic Properties at Isochoric and Isobaric Decrease of the Silicon Nanocrystal Size

Physics of the Solid State - Equation of state P(ν/νo) and the baric dependences of the lattice and surface properties of silicon macro- and nanocrystals have been calculated using the...     

Inelastic neutron scattering and lattice dynamics of GaPO<Subscript>4</Subscript>

We report here measurements of phonon spectrum and lattice dynamical calculations for GaPO₄. The measurements in low-cristobalite phase of GaPO₄ are carried out using high-resolution medium-energy chopper spectrometer at ANL, USA in the energy transfer range 0–160 meV. Semiempirical interatomic potential in GaPO₄, previously determined using ab-initio calculations have been widely used in studying the phase transitions among various polymorphs. The calculated phonon spectrum using the available potential show fair agreement with the experimental data. However, the agreement between the two is improved by including the polarisability of the oxygen atoms in the framework of the shell model. The lattice dynamical models are also exploited for calculations of various thermodynamic properties of GaPO₄.     

Effect of pressure on phonon spectra and elastic properties of orthorhombic GeSe

The pressure dependences of the phonon frequencies of the Brillouin zone center and also the elastic constants of the GeSe compound have been calculated by the density functional theory method using the ABINIT program package. The results have been compared with the available data of theoretical calculations and measurements of the pressure dependences of the Raman frequency. The calculations have demonstrated that the compound undergoes a continuous phase transition from the simple orthorhombic to body-centered orthorhombic lattice at a pressure about 29 GPa.     

On the thermodynamic properties of higher and smaller fullerites

The temperature dependences of the saturation vapor pressure of C₉₆ and C₃₆ fullerites and their properties along the sublimation curves are calculated using a correlation method of unsymmetrized self-consistent field that allows for strong anharmonicity of the lattice vibrations. The calculation is performed in terms of the Girifalco intermolecular potential with parameters recently determined for these fullerenes. Since experimental data on C₉₆ and C₃₆ fullerites are unavailable, the results of our calculations are compared with our results obtained earlier for the most commonly encountered fullerite C₆₀. The specific features in the dependences of the properties of C₉₆ and C₃₆ fullerites on the number of atoms per molecule are revealed.