Born-Mayer Potential Research Articles

Calculation of the energies of core structures of the ½〈111〉 screw dislocation in b.c.c. Mo by the tight-binding recursion method

Abstract The tight-binding recursion method is used to investigate the structure of the screw dislocation core in the b.c.c. transition metal Mo. The short-range repulsive energy between adjacent atoms is described by a Born-Mayer potential and taken into account in the total energy calculation. It is shown that the stable core structure of the 1/2 screw dislocation is of non-degenerate unpolarized type. The physical reason for the relative stability of the non-degenerate core with respect to the degenerate core is discussed. The cut-off parameter r c in the self-energy expression of the screw dislocation is calculated to be 0-32b, where b is the magnitude of the Burgers vector.

Lattice dynamics of lithium-intercalated iron phosphorus trisulphide

We review the recent investigations on the lattice dynamics of lithium-intercalated FePS 3. These studies represent an extension of those made for the pure material and have been performed by means of a force-constant model generated by a set of short-range two-body potentials. The intercalated phases have been investigated for the three stoichiometric compositions Li 0.5FePS 3, LiFePS 3 and Li 1.5FePS 3 with the aim of analysing the evolution of the host lattice normal modes as a function of the concentration, and finding the dispersion of the new phonon branches induced by lithium. The above special values of lithium concentration have been chosen because the size of the unit cell remains the same as in the host material. The interaction between lithium and sulphur includes only nearest neighbours and is also described by a two-body potential. The Li-Li interaction is described by a Born-Mayer potential. The choice of this simplified model is dictated by the limited number of experimental data: these are the Raman and infrared data for the host material and only the infrared data for the intercalated phases. The force constants of lithium are fitted to these data and the phonon dispersion curves are calculated along the symmetry directions of the Brillouin zone. A spectroscopic method for monitoring lithium migration in the host material is proposed.

Lattice dynamics of molybdenum and tungsten

The directional properties of the Born–Mayer potential associated with the interaction of the s- and d- state wave functions are shown in the framework of the model potential theory for the lattice dynamics of molybdenum and tungsten. The numerical calculations give a better understanding of the occurrence of the soft modes in both metals.

Surface vibrations, soft modes, and structural phase transitions of (001) slabs of KMnF3 and KZnF3.

We have treated the surface relaxation and surface dynamics of the fluoridic perovskites ${\mathrm{KMnF}}_{3}$ and ${\mathrm{KZnF}}_{3}$ in the framework of shell models, in which the short-range interactions are represented by Born-Mayer potentials. A variety of surface-localized modes have been found for both kinds of (001) surfaces of ${\mathrm{KMnF}}_{3}$ and ${\mathrm{KZnF}}_{3}$ (K-F and Mn/Zn-${\mathrm{F}}_{2}$ surfaces), in the unrelaxed as well as relaxed geometries. For the K-F surface of ${\mathrm{KMnF}}_{3}$ a soft mode was obtained at the M\ifmmode\bar\else\textasciimacron\fi{} point of the two-dimensional Brillouin zone. The surface reconstruction associated with this mode is discussed.

Round Robin computer simulation of ejection probability in sputtering

We have studied the ejection of a copper atom through a planar copper surface as a function of recoil velocity and depth of origin. Results were obtained from six molecular dynamics codes, four binary collision lattice simulation codes, and eight Monte Carlo codes. Most results were found with a Born-Mayer interaction potential between the atoms with Gibson 2 parameters and a planar surface barrier, but variations on this standard were allowed for, as well as differences in the adopted cutoff radius for the interaction potential, electronic stopping, and target temperature. Large differences were found between the predictions of the various codes, but the cause of these differences could be determined in most cases. A fairly clear picture emerges from all three types of codes for the depth range and the angular range for ejection at energies relevant to sputter ejection, although a quantitative discussion would have to include an analysis of replacement collision events which has been left out here.

Electronic theory for adsorbate (N, O) induced reconstruction at the Ni(100) surface

Using for the binding electrons a tight-binding type theory and for the repulsive interatomic interaction a Born-Mayer potential the adsorbate induced clock-reconstruction of the Ni(100) surface has been studied. Most remarkably we obtain for decreasing adsorbate radius an abrupt onset of the clock-reconstruction phase. This reconstruction results mainly from the interaction between the adsorbate and second layer atoms and is predicted to occur for C and N, but not for O and S, for example. The reconstruction is accompanied by a large outward relaxation of the atoms of the surface layer and a second surface layer corrugation.

Chemisorption geometry of O at the Ni(100)-surface

We study the position and chemisorption energy of O on Ni(100) as a function of coverage and including atomic relaxations. A Hubbard like tight-binding Hamiltonian and the Hartree-Fock approximation is used. The repulsive interaction between atoms is described by a Born-Mayer type potential. Results are given for atomic relaxations and for the binding energy of O at various chemisorption sites. Our results do not indicate the pseudo-bridge position as a stable one.

Approximations for the inner branch of potential curves of diatomic molecules

Three potential energy functions are examined with respect to their ability to reproduce the inner branch of the potential curve for 43 molecular states. Two of the states turn out to be unusual. In the remaining 41 cases, it is found that a potential proposed by the author gives the least error in 28 cases and is close to the least error in another six. The potential curves of NaAr(X) and XeCl(X) are very different from those of the other 41 states considered in this paper. The Born–Mayer potential appears to provide a reasonable representation of the inner branch of the potential curve for XeCl(X).

Anistropic Born-Mayer potential in lattice dynamics of vanadium

A microscopic theory of the lattice dynamics of the transition metal vanadium is developed based on the Animalu's transition metal model potential (TMMP). The Born-Mayer potential associated with the distribution of the transition metald-electrons is treated as anisotropic. Good agreement with experimental phonon dispersion curves is obtained particularly with regards to symmetry and crossover of longitudinal branches in the [111] direction.

Coherency Strain Modeling of Elastic Moduli in CU/NB Multilayers

AbstractAn anomalous decrease in the elastic moduli of Cu/Nb multilayers has been observed via acoustic wave measurements. The decrease occurs for (111) fcc Cu and (110) bcc Nb layered structures with repeat periods between 1 and 5 nm. The coherency strain model has been used to simulate modulus enhancement in noble/transition metal multilayers. This approach addresses the atomic displacements corresponding with the lattice distortions of biaxially stressed layers. Elastic moduli are derived with respect to higher order differentials of a Born-Mayer type potential for nearest neighbor ions. The elastic moduli anomalies of Cu/Nb multilayers will be modelled within this conceptual framework.

The interaction between ions and the activation barrier of elementary events of crystal growth and evaporation

The activation barrier of the elementary processes of the growth and evaporation of an NaCl-type ionic crystal in contact with its vapour such as surface diffusion, incorporation and detachment, are examined in terms of the sum of the pair potential energy between adions and lattice ions. Lattice-sum studies of the Coulombic part of the potential energy was evaluated exactly using integral transform which is equivalent to the solution of the Poisson equation derived earlier. The Coulombic potential-energy function experienced by adions decays rapidly to zero within a distance less than one interionic separation above the surface. Three forms of non-Coulombic potential energy were evaluated by direct lattice summation. Both the pair potential-energy function derived from ab initio quantum mechanics and the effective Born–Mayer potential-energy function are short-ranged. Moreover, at a binding site, the ab initio potential energy experienced by an adion is attractive and slightly larger than that of the Coulombic part, whilst the Born–Mayer potential function gives rise to a small but repulsive contribution to the total potential energy. The total potential energy of an adion was shown not to be proportional to the number of nearest neighbours, despite being effectively short-ranged. The non-Coulombic potential energy derived from a combination of the Mott–Littleton polarisation energy and overlap repulsion is long-ranged, and at an equilibrium adsorption site it is attractive and is very large compared with the Coulombic potential-energy function. All non-Coulombic potential energies are dependent on the type of charge of the adion. The activation barrier to incorporation, either directly from the vapour phase or after surface diffusion, is zero, whilst the barrier to detachment is determined by the total potential energy of the surface ion. The activation barrier for surface diffusion, as calculated from the variation of adion potential energy along a diffusion path, is shown to be contributed almost exclusively from the Coulombic part. Of the two possible diffusion paths, the lateral path along the unit cell (path 1) has a larger activation barrier than the preferred diffusion path diagonal to the unit cell (path 2) which has a barrier of almost half the size. The corresponding diffusion will be more restricted on the surface of bivalent metal sulphates because of the larger charges of lattice ions.

UNISOFT– a program package for lattice-dynamical calculations

The program package UNISOFT has been developed for lattice-dynamical calculations. Phonon dispersion curves can be calculated for any crystal structure with up to 20 atoms per primitive cell. The interaction between each individual pair of atoms can be modelled by one or more interaction types such as longitudinal and transverse springs (Born–von Karman model), Born–Mayer potential, Lennard-Jones potential, van der Waals potential, Coulomb potential, shell model. In addition to the model calculation part, UNISOFT contains several auxiliary programs dealing with group-theoretical analysis, neighbourhood analysis, plot of the phonon dispersion, calculation of partial derivatives, check of rotational invariance, calculation of local electrical fields and gradients, calculation of phonon intensities. In combination with a spectrometer for inelastic neutron scattering, UNISOFT provides a tool for the optimization of experiments as well as for a first interpretation of the results.

Temperature dependence of ultrasonic attenuation in dielectric crystals

Starting with second-nearest-neighbour distance and hardness parameter of the substance and Coulomb and Born-Mayer potentials, thermal-relaxation time, average Gruneisen numbers, nonlinearity constants and attenuation are evaluated from 50 to 500 K along two principal directions of propagation for both longitudinal and transverse waves in NaF, NaCl and NaBr. The variation of thermal-relaxation time follows theT−n law (1<n<3). The attenuation also varies according toTn law (0.2<n<1.3 below 200 K and 1<−n<2 above 200 K). The results are compared with experimental and theoretical values available in the literature. It is also concluded that ultrasonic attenuation is a very important property of the substances.

The role of alternative geometries in alkali–halide clusters

The relative importance of the cubic structures that were proposed to explain magic numbers for alkali–halide cluster ions from cluster sources is examined via total-energy calculations on nine-atom cluster ions of various optimized geometries. The relative energies of the planar, tetrahedral, quasioctahedral, lowest energy nonplanar nine-atom clusters for LiF, LiI, NaI, KI, RbI, CsI, NaF, NaCl, NaBr, and NaI are computed using Martin’s Coulomb plus the Born–Mayer potential model. The most stable structure is invariably a slightly puckered plane. The relative energies of these clusters for LiF have also been tested using Hartree–Fock and density functional theory. Other comparisons are made for NaCl clusters and eight-atom LiF clusters. The computationally more tractable Born–Mayer potentials rather accurately predict the relative energies of the clusters in the ab initio calculations. The largest problem is too strong a repulsion between like atoms which overestimates the energy difference between the planar and quasioctahedral structure proposed by Morgan et al. These calculations suggest a greater population of noncubic structures for the larger and more polarizable alkali–halide cluster ions in beams from cluster sources.

Average phonon decay rate in anharmonic insulators.

The rate ${\ensuremath{\Gamma}}_{\mathrm{Qj}}$ for a phonon to decay by lowest-order anharmonic processes is proportional to T for Tg${\ensuremath{\Theta}}_{D}$. The Brillouin-zone average \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{} of ${\ensuremath{\Gamma}}_{\mathrm{Qj}}$ is discussed in detail. An approximate formula for \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{} is found which agrees accurately with an explicit calculation for an fcc crystal with nearest-neighbor Lennard-Jones interactions. The Brillouin-zone-average squared anharmonic matrix element is contained in a parameter called ${A}_{3}$ which is the sum of the squares of all third-order force constants. The other important parameter is ${\ensuremath{\omega}}^{2}$\ifmmode\bar\else\textasciimacron\fi{}, the mean-square frequency which is the trace of the dynamical matrix, or the sum of all diagonal (${K}_{\ensuremath{\alpha}\ensuremath{\alpha}}$(l,l)) second-order force constants.The result is a formula \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{}/(${\ensuremath{\omega}}^{2}$\ifmmode\bar\else\textasciimacron\fi{}${)}^{1/2}$=${\mathrm{CA}}_{3}$${k}_{B}$T (${\ensuremath{\omega}}^{2}$\ifmmode\bar\else\textasciimacron\fi{}${)}^{3}$, where c is (3\ensuremath{\pi}/8)(${d}_{3}$/${f}_{4}$) and ${d}_{3}$ and ${f}_{4}$ are complicated averages over the harmonic frequency spectrum. To an accuracy of \ensuremath{\approxeq}30%, C can be replaced by 1. Thus \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{} can be very easily estimated when second- and third-order force constants are known. An ``anharmonicity temperature'' ${\ensuremath{\Theta}}_{A}$ is defined by the formula \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{}/(${\ensuremath{\omega}}^{2}$\ifmmode\bar\else\textasciimacron\fi{}${)}^{1/2}$=T/${\ensuremath{\Theta}}_{A}$. When T=${\ensuremath{\Theta}}_{A}$, the broadening of the phonons is predicted to be as large on average as the frequency, a signal that perturbation theory is no longer valid.The theory is applied to fcc crystals with Lennard-Jones potentials, and rocksalt-structure crystals with Born-Mayer plus Coulomb potentials describing anharmonic interactions, but a shell model describing harmonic properties. In all cases ${\ensuremath{\Theta}}_{A}$ is found to be only 1 to 2 times greater than the melting temperature. This is compatible with experiment for rare-gas crystals but may overestimate the anharmonic strength in rocksalt-structure ionic materials by as much as a factor of 2. An average decay rate ${\ensuremath{\Gamma}}^{(\ensuremath{\kappa})}$ extracted from experimental thermal conductivity is typically an order-of-magnitude less than \ensuremath{\Gamma}\ifmmode\bar\else\textasciimacron\fi{}.

Tight-binding study of the structural stability of the (110) surface of the 5d-transition metals Ir, Pt and Au

The structural stability of the ground state of the (110) surface of Ir, Pt and Au is investigated for several reconstruction models. For the s,d-valence electrons we use a Slater-Koster parametrized tight-binding scheme, the Recursion Method and take into account the hybridization of the 5d-band with a nearly free electron band of mixed sp-character and allow electronic charge redistribution at the surface. The interatomic repulsive forces are determined by using a Born-Mayer potential. Results for the multilayer surface relaxation including row-pairing are also given. These relaxations are found to be most important for Au. The relaxed missing-row reconstructed surface is calculated to be the most stable registry for all three metals examined.

Measurement of the diffusion coefficient of sodium in neon at 530K

The diffusion coefficient D of sodium in neon has been measured at 530K. In a cylindrical discharge tube filled with neon at densities N of 1023 to 1024 m-3 a strong radial sodium density gradient is induced by means of a discharge current. In the afterglow of the discharge the decay rate of the fundamental diffusion mode is measured using dye laser absorption at the sodium D1 line. The value DN=(1.43+or-0.18)*1021 m-1 s-1 is found. The diffusion coefficient is calculated for temperatures between 300 and 600K using Lennard-Jones (n-6) interaction potentials with n=12, 8 and 7, and using a Born-Mayer potential. Potential parameters are taken from the literature. Best agreement with experiment is found for the Born-Mayer potential and for the Lennard-Jones (7-6) potential.

Anisotropy of defect introduction by electron irradiation in compound semiconductors

Two possible interpretations of the anisotropy for production of defects by electron irradiation in semiconductors with zinc-blende or Wurtzite structures, shadowing effect, and secondary atomic interactions, are quantitatively examined. For an electron beam perfectly aligned with a [111] hybrid bond direction, it is possible to derive an expression for a shadowing cross section which in principle measures the probability that an atom A masks its nearest neighbor B in the forward beam direction, and therefore that atoms A prevent the incident beam from interacting with atoms B and displacing them. Although these shadowing cross sections are several orders of magnitude larger than the displacement cross sections, we show that, due to electronic scattering and lattice vibrations, they are still much too weak to explain the experimentally observed anisotropies. To investigate the secondary atomic interactions, a simple dynamic model has been developed, where interactions are taken into account in the nearest neighbors atomic shell only. Interactions are described by elastic collisions in which the primary knock-on atom A loses a fraction ΔTB of its initial kinetic energy T0. ΔTB is obtained from an exact integration of classical equations of motion. It is assumed that atom A is definitively displaced if T0−ΔTB is larger than a certain isotropic threshold energy Td, which allows an anisotropic displacement cross section to be deduced. It is shown that this dynamic model predicts with a reasonable quantitative agreement the experimental results obtained in GaAs after irradiations along opposite [111] directions, when using a hard core or Born–Mayer potential to describe the atomic interactions. In particular, the observed reversal of the anisotropy at higher irradiation energies is predicted for the correct order of magnitude of the crossover energy, equal to about twice the threshold energy, and is shown to be the direct consequence of the tetrahedral coordination of the crystal. The magnitude of the anisotropy for irradiation energies larger than the crossover is a sensitive function of the interaction potential range. In the case of a hard core potential the fit gives a hard core radius equal to about twice the Bohr radius which is exactly the expected value for interatomic collisions in the energy range considered here. The paper is concluded by a brief survey of experimental data available for other compound semiconductors. Although they do not allow such a precise comparison as for GaAs, we show that they are entirely consistent with the dynamic model presented here.

Electrostrictive Coefficient of a Rocksalt-Type Oxide MgO

The electric-displacement-related electrostrictive coefficient Q h of a rocksalt-type oxide, MgO, has been determined as 0.16 m 4 C -2 by measuring the hydrostatic pressure dependence of the reciprocal permittivity ( Q h =(1/2)[∂(1/ e 0 e )/∂ p ]). Comparing the Q h values of several rocksalt- and perovskite-type fluorides and oxides, a general empirical rule is proposed that the electrostrictive coefficient of fluorides is larger than that of oxides with the same crystal structure and the Q h of the rocksalt is larger than that of the perovskite. A simple shell model can describe this general tendency in conjunction with the Born-Mayer potential, where the electrostrictive coefficient is represented in proportion to a 5 / Z 2 ( a : cation-anion distance; Z : ionic valence).

On the Core Behavior of Dislocations in the Covalent Semiconductors C, Si and Ge

We use a tight-binding (TB) type electronic theory to calculate the core structure and core energy of both screw and 60° dislocations in the covalent semiconductors C, Si and Ge. To represent the repulsive interaction between atomic sites i and j, arising mainly from the core orthogonalization, we introduce a Born-Mayer potential. From the total (attractive and repulsive) energy calculations, we investigate the stability of dissociated partial dislocations. We show that the glide-set dissociated dislocations are more stable than the corresponding shuffle-set perfect dislocation, in agreement with recent experimental observations. The calculated results are also compared with available experimental results on the structure images and the dynamic properties of dislocations. In addition, we investigate the electronic states (sp configuration) of the dangling-bond-like states (DBLS) near the core of the partial dislocations, and discuss the validity of using fixed sp3 hybrid orbitals for calculating the dislocations.