Born-Mayer Potential Research Articles

Phonon contibution for th elow temperature specific heat of solid C60 and K3C60

We present the result of a theoretical analysis of the phonon contribution to the specific heat for both pure C 60 and alkaline doped K 3 C 60 fullerenes. This is based on the construction of the phonon density of states through the solution of the dynamical matrix, using a Born-Mayer type potential, for the different points in the Brillouin zone. Our results show the contribution to the specific heat for the different modes and in particular we study the low-lying modes coming from intramolecular motions appearing at low temperatures.

Crystalline structure and symmetry dependence of acoustic nonlinearity parameters

A quantitative measure of elastic wave nonlinearity in crystals is provided by the acoustic nonlinearity parameters. The nonlinearity parameters are defined for arbitrary propagation modes for solids of arbitrary crystalline symmetry and are determined along the pure mode propagation directions for 33 crystals of cubic symmetry from data reported in the literature. The magnitudes of the nonlinearity parameters are found to exhibit a strong dependence on the crystalline structure and symmetries associated with the modal direction in the solid. Calculations based on the Born–Mayer potential for crystals having a dominant repulsive contribution to the elastic constants from the interatomic pair potential suggest that the origin of the structure dependence is associated with the shape rather than the strength of the potential. Considerations based on variations in crystal symmetry during loading along pure mode propagation directions of face-centered-cubic solids provide a qualitative explanation for the dependence of the acoustic nonlinearity parameters on modal direction.

High-frequency structural relaxation in sodium silicates — a molecular dynamic study

The dynamic behavior of sodium silicate liquid and glassy structures were investigated by means of molecular dynamic simulations. Particle interactions were modeled using the central force Born-Mayer potential. Simulations were carried out over approximately half a nanosecond. Dynamic susceptibility spectra describing the response of the alkali cations to thermal activation are reported for various temperatures. The diffusion of alkali cations was found to be solid-like, i.e., occurring as sudden jumps separated by long waiting periods, even above the glass transition temperature. The intermediate scattering functions approximately follow a stretched exponential behaviour, with a stretching exponent of 0.8. The characteristic relaxation times for cation motion depend on the probing wave vector according to a power law, with an exponent close to −2.

Relaxation and dynamics of the (110) surfaces of the cesium chloride structure crystals CsCl, CsBr and CsI

We have treated the relaxation and the dynamics of the (110) surfaces of the cesium halogens CsCI, CsBr and CsI in the framework of shell models, in which the short range interactions are represented by Born-Mayer potentials. The relaxation in the surface layer is small (~ 0.01 a 0) and diminishes rapidly away from the surface. The calculated normal vibrations of twenty-five layer slabs are presented in three-dimensional diagrams, which provide a very direct and pictorial display of the surface localization of vibrational states. For all three compounds a rich structure of surface modes and surface resonances is found, which is dependent on the amount of overlap of the bulk bands.

Relaxation and dynamics of the (111) surfaces of the fluorides CaF2 and SrF2

The authors have treated the relaxation and the dynamics of the (111) surfaces of the fluorides CaF2 and SrF2 in the framework of shell models, in which the short-range interactions are represented by Born-Mayer potentials. The relaxation in the outer layer of the crystal, consisting of three closely spaced F-Ca/SrF layers, is significant. The calculated normal vibrations of a 19-layer slab are presented in 3-dimensional diagrams of the normalized surface squared amplitude, which provide a very direct and pictorial display of the surface localization of vibrational states. For CaF2 the calculations are compared with the HREELS data of Longueville et at. (1990).

Lattice dynamics of b.c.c. alkaline-earth metals: Barium

The attractive short-range component of the interatomic potential screens the conventional Born-Mayer potential in the framework of the resonance pseudopotential model. The elastic constants are evaluated at the long-wavelength limit of the phonon spectrum and the obtained results are compared with previous experimental values. The numerical calculations show that the attractive component of the potential explains the soft modes in this body-centred cubic (b.c.c.) alkaline-earth metal barium.

Ultrasonic Attenuation in Alloys

= 1.00, 0.70, 0.60, 0.45 and 0) due to phonon-phonon (p-p) interaction and thermoelastic loss in a wide temperature region along (110) crystallographic direction for longitudinal and shear waves. Ultrasonic Gruneisen parame- ters, nonlinearity constants and ultrasonic attenuation due to p-p interac- tion and thermoelastic loss were determined from 50 K to 500 K using the Born-Mayer and electrostatic potentials. The results were compared with available experimental results.

Compressibility, specific heat capacity, and Grüneisen parameter for C60/C70

We have measured the specific heat capacity c p of C 60 /C 70 between 110 and 310 K and its compressibility κ up to 1.1 GPa (11 kbar) at 293 K, a range in t and p which overlaps reported ranges of stability of both the rotationally disordered high T, low p fcc phase and the low T high p orientationally ordered sc phase. No sharp anomaly is observed in c p at the transition. The bulk modulus B near p = 0 was 8.4 GPa, rapidly increasing to about 16 GPa near 1 GPa. For our data, the intermolecular forces could be modeled by either a Lennard-Jones or a Born-Mayer potential, but this was not the case if literature data for compression vs. p were used.

Phonons and elastic constants for scandium, zirconium and magnesium

The generalised exponential potential and the Born-Mayer potential are employed to describe the paired and the unpaired interactions in the hexagonally closed pack (hcp) metals. These forces are found to explain simultaneously the phonon dispersion and the elastic behaviours of the metals like Scandium (Sc), Zirconium (Zr) and Magnesium (Mg). The input data for lattice constants inverse compressibility and cohesive energy give rise to such results on the said behaviour of the metals which compare satisfactorily with the experimental values.

Relativistic effect on the interatomic platinum–oxygen potential and its consequences in high energy O2/Pt(111) scattering

The influence of relativity on the binding in the Pt–O molecule is investigated using density functional calculations and proves to be quite important, not only for the potential well but also for the repulsive wall. Using a Born–Mayer fit to this interatomic gas phase potential, we perform a classical trajectory study on high energy O2/Pt(111) scattering (Ei=80 eV). The Born–Mayer form of the interatomic potential leads to a higher degree of dissociation for O2/Pt(111) than for O2/Ag(111) which is also experimentally found. The role of relativity turns out to be significant. The dissociation mechanism, however, does not change when going from O2/Ag(111) to O2/Pt(111). The molecules were found to first gain primarily rotational energy, which is largely transfered to vibration at the turning point of the second atom, in the case of finally dissociating molecules. Since the calculated dissociation in the case of platinum is still less than found experimentally, we investigate the influence of better fits to the interatomic potential, as well as inclusion of the potential well. It is possible to improve agreement with the experimental results by directly reducing the long range of the Born–Mayer potential.

Magnetism-induced surface reconstruction

Surface reconstruction in antiferromagnetic transition metals with a nearly half-filled d band, such as Cr, is investigated on a basis of a simple model, in which the interaction between two atoms consists of two parts; one is the attractive interaction which originates from d band energy including formation energy of magnetic moments. The other one is the repulsive interaction which is described by a Born-Mayer potential. As an example, a bcc(001) surface is investigated. It is found that the surface reveals a c(2 × 2) surface reconstruction with atomic displacements perpendicular to the surface, accompanied by a c(2 × 2) antiferromagnetic ordered structure and uniform expansion of the first interlayer spacing. It is also pointed out that, in weakly magnetic cases, vacancies make a c(2 × 2) structure on the bcc(001) surface at finite temperatures.

Spectroscopy and kinetics of ionic alkali halide excimers excited by a laser-produced plasma

Vapors of five alkali halides, CsF, RbF, KF, CsCl, and NaI, have been excited by soft x rays from a laser-produced plasma. In the cases of heavy alkalis and light halogens (CsF, RbF, and CsCl), the emission of ionic excimer continua is observed. The upper state of the alkali halide molecule (AX) is a bound state correlating to A2+ and X−, which decays by emission of photons to a weakly bound state correlating to A+ and X. For lighter alkalis or heavier halogens the alkali halide bound states A2+X− predissociate, and the fluorescence yield decreases dramatically. No ionic excimer emission is observed for KF and NaI; however, their emission spectra are characterized by molecular halogen and atomic and ionic emission lines. The qualitative trends in fluorescence yield and ionic excimer predissociation are predicted correctly by molecular potential-curve calculations based on modified Rittner and Born–Mayer potentials. The ionic alkali halide excimer states are produced by direct photoionization by the soft x rays from the laser-produced plasma. For sufficiently small differences in the equilibrium internuclear distance of the upper and the lower electronic states, the vibrational distribution in the excited state remains, to a good approximation, Maxwellian after excitation even on a time scale for which collisions with the ambient gas can be neglected. In a harmonic approximation the vibrational temperature in the upper ionized state, Tν′, depends only on the lower-state vibrational temperature, Tν″, the vibrational quanta of the upper state, ωe′, and of the lower state, ωe″, and the relative equilibrium internuclear distance. If the upper and the lower states are at the same equilibrium internuclear distance, the simple relation Tν′ = (ωe′/ωe″)Tν″ is obtained.

Ultrasonic Attenuation in Dielectric Crystals

Ultrasonic attenuation and non-linearity parameters have been evaluated for dielectric crystals RbCl, RbBr and RbI in a wide temperature range. Basic physical parameters, nearest neighbour distance and hardness parameters of the substance and Coulkb and Born-Mayer potentials have been used to obtain ultrasonic attenuation due to phonon-viscosity mechanism along (100) direction of propagation for longitudinal and shear waves. Results are as expected and it has been concluded that ultrasonic attenuation is a fundamental property of the substance.

Use of Harrison's potential in ZnS, NaCl and CsCl-structure solids

Harrison's overlap repulsive potential has been used for evaluating cohesive energies, bulk modulus and its pressure derivatives, Gruneisen parameter, and the volume derivatives of Gruneisen parameter for cuprous halides, silver halides and thallous halides. This potential has replaced the old and widely used Born-Mayer potential in ionic crystals. The Harrison repulsive potential has been represented by a quantum mechanical analytical potential form derived from the tight binding theory. The parameters involved in this potential form have been determined in terms of valence state energies of outermost d-electrons of Cu+, Ag+ and Tl+ ions. The results calculated in the present study have been found in good agreement with experimental data and better than those predicted from the Born potential model.

Analysis of polarizabilities, potentials, and geometries of alkali–halide dimers

An analysis of electronic polarizabilities, interionic potentials, and equilibrium geometries for 20 alkali–halide dimers such as Na2Cl2 is presented. The electronic polarizabilities of ions in dimers have been calculated by taking account of the electrostatic potential due to neighboring ions within the Seitz–Ruffa energy level analysis. The polarizabilities thus obtained for dimers are then used to evaluate the magnitudes of polarization energies and van der Waals dipole–dipole energies. For describing the overlap repulsive potential we have adopted two forms: (i) the revised version of the Born–Mayer potential and (ii) the Harrison form for the overlap repulsive energy. These potentials have been used to obtain the binding energies of monomers as well as dimers, spectroscopic constants of monomers, equilibrium geometries of dimers, and dimerization energies. The results have been discussed and compared with available experimental data.

LATTICE DYNAMICS OF α-LiIO3

The phonon dispersion curves of α- LiIO 3, which exhibit a characteristic molecular crystal behaviour, are calculated on the basis of a modified rigid-ion model in which a Born-Mayer potential is used for short-range repulsive interactions between Li ions and [Formula: see text] groups and a central force constant model is used for internal interactions in the [Formula: see text] group. The computed phonon frequencies are in good agreement with those of Raman, infrared and neutron measurements. The calculations show a strong mixing of the pre-normal modes given by Crettez et al.,4 therefore indicating that the long-range Coulomb force may change greatly the assignments previously obtained from a force-field model.

Phonon spectrum for barium ferrite.

We have shown in previous work that the calculation of the intrinsic ferrimagnetic (FMR) linewidth in barium ferrite on the basis of the Kasuya-LeCraw relaxation mechanism requires a knowledge of the magnon and phonon dispersion curves far from the center of the Brillouin zone. Therefore, in this article, we have calculated the full phonon spectrum for this crystal on the basis of the rigid-ion model in anticipation of future FMR-linewidth calculations. The short-range forces were approximated by the Born-Mayer potential, with parameters derived from compressibilities and effective radii of the constituent ions in binary divalent compounds exhibiting the NaCl structure and composed of ${\mathrm{Ba}}^{2+}$, ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$, ${\mathrm{Mn}}^{2+}$, and ${\mathrm{Fe}}^{2+}$. Our results are in good agreement with recent infrared-reflectivity data on barium ferrite in the frequency range of the magnon spectrum (the range needed for FMR-linewidth calculations). The extreme sensitivity of the lowest transverse-optic frequency to variation of one of the short-range repulsive parameters is indicative of possible soft-mode behavior. Experimental verification of this prediction would be possible by measuring the reflectivity of this material at various temperatures with the incident electric field parallel to the c axis of the crystal. We propose an explanation of the dynamics of the trigonal-site iron in barium ferrite based on our calculation.

Phenomenological description of the longitudinal vibrations of the quasi-one-dimensional solid PtCl: calculation of the valence defect frequencies

The longitudinal vibrations of the PtCl linear chain and those of various valence defects are described by a one-dimensional model in a first-nearest-neighbour interaction approximation. The analysis is performed as a function of the K2/K1 ratio (K1 and K2 representing the PtClIV-Cl and PtII-Cl force constants, respectively), which is shown to play an important role in the vibrational characteristics of the defects while the infrared frequencies are not strongly dependent on a particular ratio. A coherent description of the frequencies of the modes of the perfect chain and those of the polaronic defects is obtained for K2/K1=0.3. For this ratio the electron polaron and the electron bipolaron give rise to one Raman-active mode while at least two are predicted for the other investigated defects. The shapes of the Raman bands associated with the electron and hole polarons are explained by the chlorine isotopic effect. The vibration associated with the electron bipolaron is predicted to be at about 210 cm-1 where a broad line grows upon photolysis. An elementary calculation based upon a Born-Mayer potential for short-range interactions, adjusted from the interionic distances, leads to force constants of the same magnitude as those adjusted from the experimental frequencies.

THEORETICAL STUDY ON THE INCOHERENT TWIN BOUNDARIES IN AUSTENITIC STAINLESS STEEL

The structure of incoherent C=3 (112) twin boundaries in the austenitic stainless steel is investigated using the tight-binding recursion method and the model £cc iron crystal. To estimate the change in the total energy due to the atomic displacements, 15 pairs of recursion coefficients (an,bn; ns15) are calculated for the atomic clusters containing 2100 atoms:~he short-range repulsive energy contribution is also taken into account using the Born-Mayer potential. It is found that the significant rigid body translation occurs parallel to the boundary plane together with the excess volume displacements for the (112) incoherent twin boundaries in y-Fe. The occurence of the rigid body translation is shown to result from the reduced density of heavily distorted bonds and reduced local d-band deformation around the incoherent twin boundary.

Relaxation of optically excited F centers

The relaxation of optically excited F centers was studied by resonant secondary radiation (RSR), which occurs successively as Raman scattering, hot luminescence and ordinary luminescence. The RSR and its linear polarization were measured as a function of excitation photon energy mainly at 77 K, for F centers in seven alkali halides. Dynamic processes, including these optical processes were analyzed in terms of a semi-classical model based on the Franck-Condon principle in an A 1g anharmonic adiabatic potential derived from the Born-Mayer potential. It is proposed that, abruptly after the optical excitation, the F electron expands its orbital radius and changes its nature including decoupling from the T 2g Jahn-Teller mode. This model works particularly for KCl, RbCl and NaCl. The relaxation of F centers in KBr and KI is different from that in KCl, RbCl and NaCl. The difference is related to the characteristic differences in lattice dynamics, namely predominant coupling with localized modes and the T 2g frequency near that of the LO phonons. The relaxation of type II F A centers is attributed to two steps, one F-like and the other Li +-dominated.