Three-body interaction and phonon dispersion relations in aluminium

Based on an ab initio cohesive energy calculation and a model of three-body interaction, the pair potential can be calculated using the Möbius inversion theorem in the theory of numbers. Then the atomic force constants and the phonon dispersion for A1 are evaluated both with and without three-body interaction. Compared with experiments, the results show that taking the three-body interaction into account considerably improves the dispersions. Contrary to previous work, the method for calculating the atomic force constants and phonon dispersions presented here is simple, with only two adjustable parameters.     

A general Mobius inversion transform formula for hcp lattices and its application

In this paper,we present a general Mobius inversion transform formula for hcp lattices.This formula can be applied to hcp lattices with a non-ideal c/a value and to obtain the pair potential between atoms in these lattices from the cohesive energy.Also,the three-body interaction among atoms in the lattices can be taken into account in the method.This method gives a useful means to obtain interatomic interactions in the interatomic force model.The method has been applied to zinc,and the pair potential obtained is used to calculate the phonon dispersion relations for some high-symmetry directions.It is found that,by properly considering a three-body interaction,one can acquire satisfactory results.     

Structure factors and phonon dispersion in liquid Li<Subscript>0.61</Subscript>Na<Subscript>0.39</Subscript> alloy

The phonon spectra for liquid Li and Na have been computed through the phenomenological model of Bhatia and Singh for disordered systems like liquids and glasses and the obtained results have been compared with the available data obtained by inelastic neutron scattering (INS) and inelastic X-ray scattering (IXS) experiments. The effective pair potentials and their space derivatives are important ingredients in the computation of the dispersion curves. The pair potentials are obtained using the pseudo-potential theory. The empty core model proposed by Ashcroft is widely used for pseudo-potential calculations for alkali metals. But, it is thought to be unsuitable for Li because of its simple 1s electronic structure. However, it can be used with an additional term known as Born-Mayer (BM) core term. The influence of the BM core term on the phonon dispersion is discussed. The same pseudo-potential formalism has been employed to obtain the dispersion relation in liquid Li_0.61Na_0.39 alloy. Apart from the phonon spectra, the Ashcroft-Langreth structure factors in the alloy are derived in the Percus-Yevick approximation.     

Lattice dynamics and ionic charge of VI2

We present an Extended Shell Model calculation of the phonon dispersion curves in VI₂. The dynamical matrix is derived from interionic potentials including Coulomb monopole and dipole, van der Waals, nearest-neighbor and next-nearest-neighbor Born-Mayer repulsive interactions. The potential parameters are either known in literature or derived from lattice constants and cohesive energy. A suitable choice of only three adjustable parameters (net charge Z, shell charge and shell-core displacement) yields an excellent fit of the five optical frequencies and of the anion static dipole. The resulting ionic charge Z = 0.75 is very well consistent with the recent neutron data on transferred hyperfine interaction.     

Hole-interface optical phonon relaxation rates with valence band-mixing effects

We theoretically investigate the hole-interface optical phonon scattering rates for a InGaAs-AlGaAs quantum well structure, taking into account the valence-band mixing. The dispersion relation and the electrostatic potentials for interface optical phonon modes are obtained based on the macroscopic dielectric continuum model. For the hole dispersion relation, the Luttinger-Kohn Hamiltonian is used. The hole-interface optical phonon interaction is evaluated by the Fermi's golden rule taking into account the Bloch overlap factor.Our results show that the hole-interface phonon scattering rates within the parabolic band approximation are different from those including valence band mixing effects. Especially, in the low energy region, the hole-interface phonon scattering rates within the parabolic band approximation are overestimated very significantly.     

Phonon dispersion relations of crystalline solids based on LAMMPS package

The phonon dispersion relations of crystalline solids play an important role in determining the mechanical and thermal properties of materials. The phonon dispersion relation, as well as the vibrational density of states, is also often used as an indicator of variation of lattice thermal conductivity with the external stress, defects, etc. In this study, a simple and fast tool is proposed to acquire the phonon dispersion relation of crystalline solids based on the LAMMPS package. The theoretical details for the calculation of the phonon dispersion relation are derived mathematically and the computational flow chart is present. The tool is first used to calculate the phonon dispersion relation of graphene with two atoms in the unit cell. Then, the phonon dispersions corresponding to several potentials or force fields, which are commonly used in the LAMMPS package to modeling the graphene, are obtained to compare with that from the DFT calculation. They are further extended to evaluate the accuracy of the used potentials before the molecular dynamics simulation. The tool is also used to calculate the phonon dispersion relation of superlattice structures that contains more than one hundred of atoms in the unit cell, which predicts the phonon band gaps along the cross-plane direction. Since the phonon dispersion relation plays an important role in the physical properties of condensed matter, the proposed tool for the calculation of the phonon dispersion relation is of great significance for predicting and explaining the mechanical and thermal properties of crystalline solids.     

Internal equilibrium and crystal dynamics of tantalum

A lattice dynamical model for bcc metals, which satisfies the internal force equilibrium condition of the lattice is proposed. The present model combines a linearized Thomas-Fermi Theory for the electron-ion interaction and the central pair potential for ion-ion interaction. as an application, the computed phonon dispersion, vibrational spectrum, and lattice specific heat of tantalum show fairly good agreement with experiments.     

Vibrational properties of vacancy in bcc transition metals using embedded atom method potentials

The embedded atom method (EAM) potentials, with the universal form of the embedding function along with the Morse form of pair potential, have been employed to determine the potential parameters for three bcc transition metals: Fe, Mo, and W, by fitting to Cauchy pressure (C ₁₂???C ₄₄)/2, shear constants $G_\textrm{v} =({C_{11} -C_{12} +3C_{44}})/5$ and C ₄₄, cohesive energy and the vacancy formation energy. The obtained potential parameters are used to calculate the phonon dispersion spectra of these metals. Large discrepancies are found between the calculated results of phonon dispersion using the EAM and the experimental phonon dispersion results. Therefore, to overcome this inadequacy of the EAM model, we employ the modified embedded atom method (MEAM) in which a modified term along with the pair potential and embedding function is added in the total energy. The phonon dispersions calculated using potential parameters obtained from the MEAM show good agreement with experimental results compared to those obtained from the EAM. Using the calculated phonons, we evaluate the local density of states of the neighbours of vacancy using the Green’s function method. The local frequency spectrum of first neighbours of vacancy in Mo shows an increase at higher frequencies and a shift towards the lower frequencies whereas in Fe and W, the frequency spectrum shows a small decrease towards higher frequency and small shift towards lower frequency. For the second neighbours of vacancy in all the three metals, the local frequency spectrum is not much different from that of the host atom. The local density of states of the neighbours of the vacancy has been used to calculate the mean square displacements and the formation entropy of vacancy. The calculated mean square displacements of the first neighbours of vacancy are found to be higher than that of the host atom, whereas it is lower for the second neighbours. The calculated results of the formation entropy of the vacancy compared well with other available results.     

Phonon dispersion curves for niobium

Conclusion The experimentally measured phonon dispersion relation for niobium is very complex. This complexity may be due to the incomplete electronicd shells which make an important contribution to very large cohesive energy, and its likely effect on the phonon frequencies. Also the anomalies in the dispersion curves may be due to the departure of the Fermi surface from sphericity. In the present study none of the above effects is included explicitly and so theory fails to achieve exact agreement with the experimental data. Finally, we would like to put a concluding remark that an appropriate microscopic treatment given tod electron could explain the phonon dispersion curves of transition metal like niobium.One of the authors (ARJ) would like to express his appreciation to Professor M. K. Agarwal (Head of the Department) for his support and encouragement to carry out this work. Thanks are also due to Sardar Patel University for providing computer facilities.     

Phonon dispersion of d and f shell metals: A dynamical treatment

The effective pair potential is written as the sum of s-s, d-d, s-d, f-f and s-f contributions. The free electron part of the pair potential is obtained in second-order perturbation theory using rational dielectric function (RDF) in conjunction with Heine-Abarenkov model pseudopotential (HAMP). The exchange-correlation corrections due to Taylor are inherent to RDF. The overlap between d states and f states on different ions and the effect of sd and hybridization are included in an approximate manner, as has been suggested by Wills and Harrison [Phys. Rev. B 28 (1983) 4363], and Harrison [ibid., 550]. An approximate temperature dependence has been included in the effective potential through an asymptotic factor. The ion-ion interaction so defined is used to calculate the phonon dispersion curves for hcp metals Tb and Ho. The calculated phonon frequencies are found to be real and in reasonably good agreement with the neutron inelastic scattering measurements which establishes the validity of the effective pair potential for rare earths.     

A novel potential: the interlayer potential for the fcc (111) plane family

We propose a novel interlayer potential, which is different from usual interatomic potentials. The interlayer potential represents the interaction between atomic layers in a layered material. Based on the Chen-M?bius inversion method in combination with ab initio calculations, the interlayer interactions are obtained for the face centered cubic (fcc) (111) planes. In order to check the validity of our interlayer potential, we calculate the intrinsic stacking fault energy (γ(sf)) and the surface energy (γ(s)) of five metals: Al, Ni, Cu, Ag and Au. The predicted γ(sf) and γ(s) values are compared with the theoretical results obtained from direct calculations and also with the available experimental data. Using the interlayer potentials, we also investigate the phonon dispersion and phonon density of state in the fcc (111) plane family of the considered metals.     

Phonon dispersion in Xe

The predictions of the Mie-Lennard-Jones potentials for phonon dispersion in solid Xe at 10°K and at 77°K are compared with the results of recent measurements. The dynamics of the crystal are described by the first order self-consistent phonon theory for the imaginary part of the one phonon Green's function. The fit obtained is quite poor though we point out that no conclusion can be drawn about the size of three-body forces. We conclude that improved potentials are needed to account for the experimental data.     

电—声超导电性的对称理论

利用新的库珀对平均汤近似，导出了电－声系统中声子－库珀对有效作用，证明了声子通过交换虚的库珀对能够产生一个有效的吸引力，导致两动量相反的声子配对并构成稳定的声超导态。发现电子超导态与声子超导态的直积能构成稳定的电－声对称的高温超导基态。在声子－库珀对弱耦合极限下，基态对称破缺成为传统的ＢＣＳ基态。     

Empirical construction of interatomic potentials for studies of grain boundaries and other crystal defects: Pure metals and binary alloys

It is first argued that pair potentials are physically meaningful if they are regarded as describing interaction between atoms embedded in an environment of similar density as that for which their derivation was made. These potentials are capable of describing structural aspects of lattice defects but not the cohesive properties. Guidelines for determination of the shape of potentials and an empirical scheme for their construction in pure metals is then outlined. It is shown that this method when applied to simple metals leads to potentials similar to those obtained on the basis of a pseudopotential theory and extension of this scheme to other metals is discussed. An empirical scheme of construction of potentials for binary alloys is then briefly described. It is shown that concentration dependences of elastic constants and lattice stability evaluated using these potentials agree with experimental data and thus these potentials are suitable for studies of defects in binary alloys.     

电-声超导电性的对称理论

利用新的库珀对平均汤近似，导出了电－声系统中声子－库珀对有效作用，证明了声子通过交换虚的库珀对能够产生一个有效的吸引力，导致两动量相反的声子配对并构成稳定的声超导态。发现电子超导态与声子超导态的直积能构成稳定的电－声对称的高温超导基态。在声子－库珀对弱耦合极限下，基态对称破缺成为传统的ＢＣＳ基态。     

Lattice dynamics of alkali cyanide crystals

The recent microscopic model of Michel and Naudts for the interaction of ionic vibrational displacements and molecular rotational displacements is combined with the lattice dynamical shell model to calculate phonon dispersion curves of KCN and NaCN. Very good agreement with the existing experimental data is obtained. In particular, the upward dispersion of the TA phonon branches, characteristic of the alkali cyanide crystals, is well reproduced.     

Infrared-phonon-polariton resonance of the nonlinear susceptibility in GaAs

Nonlinear probing of the fundamental lattice vibration of polar crystals is shown to reveal insight into higher-order cohesive lattice forces. With a free-electron laser tunable in the far infrared we experimentally investigate the dispersion of the second-order susceptibility due to the phonon resonance in GaAs. We observe a strong resonance enhancement of second harmonic light generation at half the optical phonon frequency, and in addition a minimum at a higher frequency below the phonon frequency. Measuring this frequency and comparison to a theoretical model allows the determination of competing higher-order lattice forces.     

Speed of sound in an optical lattice

A system of equal mixture of ⁶Li atomic Fermi gas of two hyperfine states loaded into a cubic three‐dimensional optical lattice is studied assuming a negative scattering length (BCS side of the Feshbach resonance). When the interaction is attractive, fermionic atoms can pair and form a superfluid. The dispersion of the phonon‐like mode and the speed of sound in the long‐wavelength limit are obtained by solving the Bethe‐Salpeter equations for the collective modes of the attractive Hubbard Hamiltonian.     

Ripples on the surface of a two-component fluid

The dispersion relation of ripplons on the surface of a two-component liquid has been derived using the hydrodynamic mean-field model, in terms of the interaction pair potentials of the constituent particles. The modes for planar and spherical geometries have been derived explicitly. The formalism is applied to ripples on the surfaces of liquids in which the interparticle interaction is not Coulombic, as also on the surfaces of jellium and on electron-hole droplets.     

A method to calculate the thermal conductivity of HMX under high pressure

A method based on Debye theory is developed to calculate the thermal conductivity of octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX). The phonon–phonon interaction model is built up for solid HMX. The phonon lifetime formula is derived by the phonon–phonon scattering mechanism, and the thermal conductivity tensor is derived by the phonon dispersion model. The thermal conductivities of α/β/δ-HMX are calculated in the temperature range 0–700?K and pressure range of 0–10?GPa. The phonon softening process of HMX is investigated. We have proven that the Debye frequency and thermal conductivity tend to 0 at the phonon softening point. A physical picture of the phonon–phonon interaction, phonon lifetime and phonon softening is built up.