Polarizable Ion Model Research Articles

Molecular dynamics studies of molten NaI II. Mass-, charge- and number-density fluctuations

Molecular dynamics simulations of molten NaI have been performed using both rigid-ion and polarizable-ion models. The mass-, charge- and number-density autocorrelation functions have been calculated together with their frequency spectra. The liquid-state analogues of longitudinal optic and acoustic phonons are identified at longer wavelengths. The acoustic modes are weak and broad. The major differences between the rigid-ion model and the polarizable-ion model are that(1) there is a substantial difference between their static charge—charge structure factors, SQQ(q), and(2) the normalized charge-charge dynamical structure spectra at longer wavelengths differ in intensity and frequency of the optic mode. The mode for the polarizable-ion model occurs at a lower frequency and is less well resolved.

Molecular dynamics studies of molten NaI I. Quasi-elastic neutron scattering

AbstractThe quasi-elastic neutron scattering spectrum of molten NaI has been calculated using molecular dynamics simulation. The wave-vector dependences of the coherent and incoherent partial contributions to the spectrum are reported. A comparison is made between the spectra obtained from rigid-ion and polarizable-ion model simulations. The spectra are contrasted with those obtained by neutron scattering.

Application of the polarizable-ion model on crystals with the corundum structure

This paper reports the results of charge, polarizability and force constant calculations at k̄ = 0 on crystals with the corundum structure. Published vibrational frequencies are used in the normal coordinate treatment. The calculated electronic parameters are discussed.

Anisotropy of Lattice Dynamical Properties in ZrS2 and HfS2

The frequencies of A 2u phonons of the layer compounds ZrS 2 and HfS 2 are determined from two phonon resonant Raman scattering. The analysis based on the polarizable ion model by van der Valk and Haas suggests that the long-range Coulomb interaction plays an important role in the anisotropy of lattice dynamics. The A 1g phonon spectrum of ZrS 2 exhibits anomalous line shape induced by the hybridization of the A 1g phonon with the A 2u (LO).

Phonon side bands in the absorption spectra ofNi2+andCo2+in CdI2and PbI2

The absorption and magnetic CD spectra of the 3A2g → 1Eg electronic transition of CdI2:Ni2+ and PbI2:Ni2+ and of the a4T1g → b2T1g, 2A1g transition of CdI2:Co2+ were measured. The spectra show a complicated fine structure caused by the coupling with nonlocalized vibrational modes of the host lattice. The theory of this effect is presented. The obsd. vibronic structure images the phonon d. of states in the Brillouin zone, modified by matrix elements and selection rules. The contributions of the different phonon branches (acoustic, Raman, and IR-active modes) are calcd. The spectra show a strong anisotropy, which is due to the presence of static dipoles at the anions; the magnitude of the anisotropy is calcd. with use of the polarizable-ion model. The vibronic fine structure is used to deduce the max. of the phonon d. of states of CdI2 and PbI2, and to est. the phonon dispersion curves. [on SciFinder(R)]

Review article: ion pair potentials for alkali halides and some applications to liquids and defect studies

Abstract We review the basis on which interionic potentials for alkali halides are obtained. We find that the sizes of the van der Waals terms are known poorly and that the polarizable ion models lack the necessary thermodynamic corrections, however small they may be, to fit low temperature properties of the solid. Although the quantum statistical calculations indicated some damping of van der Waals interactions due to ionic overlap, a systematic study of the basic and modified approaches shows them to be unsatisfactory.

Structure of molten alkali chlorides

Abstract The structure of molten alkali chlorides has been studied by molecular dynamics simulation. A comparison is made of rigid-ion and shell models of the interionic potentials. It is shown that the effect of the polarizability of the ions is small when the two ions have similar sizes but is substantial when the cation is relatively small and unpolarizable. For NaCl the use of polarizable-ion potentials yields significantly better agreement with experiment whereas for RbCl it does not appear to be important for the structure. The excess number and excess charge fluctuations for the polarizable-ion model of NaCl are presented.

The convergence of the energy cluster expansion in LinCl(n-1)+

Non-additivity in the energies of Li n Cl(n-1)+ ion clusters (n = 2→4) has been studied by means of ab initio SCF calculations. Four-body energies contribute less than 2 per cent to the total interaction energies, while in the only Li4Cl3+ structure considered the five-body energy is negligibly small. However three-body energies are not small but are similar in size to the non-coulomb two-body energies. We have investigated to what extent these non-additive effects can be explained in terms of a simple polarizable ion model.

Lattice dynamics of wurtzite-type crystals including the effect of the electronic extension

Birman has given a physical meaning to the Ewald method and has given a potential including the effect of the electronic extension with the use of this method. Thus we can easily take into account the effect of the electronic extension with the use of the Birman method without considering any other new procedures. On the basis of the polarizable-ion model, after applying the Birman method we have calculated macroscopic quantities (wave number, elastic constant, and piezoelectric constant), and examined the contribution of this effect to them. The result is that the effect is not so small that it can be neglected, and enables better agreement with the observed macroscopic quantities to be obtained.

Phononspectroscopy and lattice dynamical calculations of anhydrite and gypsum

Detailed experimental and theoretical studies of the k=0 vibrational spectra of anhydrite and gypsum are reported. The dielectric constants and the infrared reflection and Raman spectra of the single crystal have been measured. The frequencies of the phonon spectrum, the contribution of potential terms to potential energy and detailed mode assignments have been determined based on a polarizable-ion model. The relative experimental intensity of the spectra, the observed crystal field effects, the rotatory lattice modes of the H2O molecule and the mixed character of translatory and rotatory modes of the Ca, SO4, and H2O groups are discussed based on the theoretical vibrational modes and the potential energy distribution. The principal moments of inertia of the water molecule and the Lennard-Jones potential constants for nonbonded oxygen-oxygen interactions are presented.

Woodcock potential for alkali hydrides

A generalized pair potential of Woodcock corresponding to a simple polarizable ion model, which includes both an inverse power function due to Born and Lande and an exponential function due to Born and Mayer, has been used to compute the rotational constants and cohesive energy of five alkali hydrides. The effect of exponent n of the Woodcock potential function upon the polarization coefficient a of the function, rotational constant αe and cohesive energy, W, has been discussed. It is concluded that the Woodcock potential has limited validity for the alkali hydrides.

The structure and vibrational frequencies of ionic clusters

The table configurations of ionic clusters having the compositions (MX)n and (MX2)n are determined by numerically minimizing the total energy. Both rigid ion and polarizable ion models are used to describe the two particle interactions. Clusters of a given size and composition are found to have many stable configurations. In order to find as many stable configurations as possible, classifications based on the arrangement of small stable subunits are often helpful. In general, (MX)n clusters have high symmetry and often resemble small portions of NaCl or wurtzite lattices. (MX2)n clusters, on the other hand, often occur in forms having no symmetry, indicating their tendency to form disordered solids even with purely ionic interactions between atoms. Certain cluster sizes, for example n=5,7,11, and 13 for NaCl, have low binding energies which present barriers to crystal growth. The second derivatives of the total energy with respect to atomic displacements were evaluated numerically and the dynamical matrix diagonalized to give the vibrational frequencies of each cluster. Comparison is made with previously reported experimental infrared absorption spectra of (LiF)n and with new spectra of (PdCl2)n.

Matrix isolated alkali halide monomers and clusters

The far infrared absorption spectra of sodium and cesium halide monomers and clusters isolated in solid argon are reported. For low concentrations of alkali halide vapor in argon, four absorption lines were usually seen. The strongest and highest frequency line could be assigned to the monomer. The three remaining lines were due to planar rhombic dimers. For higher concentrations of alkali halide vapor, new absorption lines appeared which seem to be due to trimer and tetramer formation. The equilibrium configurations of alkali halide molecules containing from two to eight atoms were calculated by minimizing the total energy. Both rigid and polarizable ion models were used to describe the two particle interaction. The second derivative of the total energy with respect to the atomic displacements was then calculated and the resulting dynamical matrix diagonalized to give the infrared absorption spectrum.

Dissociation energies of CaI, SrI, and BaI from high temperature mass spectrometry

Equilibrium effusion beams containing the gaseous molecules CaI, SrI, and BaI were generated by the reaction of HI with the corresponding metal oxides at 1500 to 1900 K. Beam composition data obtained by mass spectrometry were used to determine the equilibrium constants of gaseous reactions involving the monoiodides and certain reference molecules. Reaction enthalpies then were evaluated by second and third law methods, from which the dissociation energies D0° (Cal) =62.1±2.5, D0° (SrI) =63.6±1.4, and D0° (BaI) =71.4±1.0 kcal/mole were derived. The results are consistent with data obtained earlier for the diatomic metal fluorides, chlorides, and bromides, and they are compatible with the predictions of the Rittner polarizable-ion model. Various features of the chemical bonding are discussed. A correlation of the thermochemical properties across the entire halide series allows one to estimate reliable dissociation energies for BeBr, BeI, MgBr, and MgI.

Lattice dynamics of wurtzite-type crystals—II

We evaluated, in the preceding paper, the effective ionic charge and electronic polarizability for wurtzite-type crystals on the basis of the polarizable-ion model given by Born and Huang. With use of the quantities so evaluated, we here estimated the short-range force constants from observed frequencies, elastic constants, and piezoelectric constants after simplifying Born and Huang's procedures. The resulting set of force constants can reproduce the observed data except for the piezoelectric constants. This poor reproduction of the piezoelectric constants is due to the fact that the long-range force is emphasized in the polarizable-ion model.

Lattice dynamics of corundum

The short-range force constants and the contribution of the potential energy to the elastic constants have been calculated from explicit expressions for the elastic constants and for the optical frequencies. The large elastic constants of corundum are attributable to the contribution of the large short-range stretching forces. The frequencies of the phonon spectrum and the contribution of the potential energy to the frequencies have also been calculated based on a rigid-ion and polarizable-ion model. The effective charge of an oxygen ion is found to be −0.955e. The electronic polarizability of an aluminium and oxygen ion is found to be 0.05 and 1.36 A3, respectively.

The shape of the potential energy well of impurities in KCl:Li + and KF:M + ( M = Li, Na, K)

The shape of the potential well, which is seen by the Li + impurity in KF:Li + and KCl:Li + is calculated, using the polarizable point ion (PPI) model and the simple shell model (SSM), in combination with a number of potentials describing the short range interaction between the ions. For both systems an off-center system is predicted. It is found that the type of short range potential affects the direction along which the absolute potential energy minimum is located. Using the PPI model or the SSM only changes the depth of the minima and their distance from the lattice site but it does not affect the symmetry of the off-center systems. A preliminary calculation of the shape of the potential well in KF:Na + is presented.

Molten rubidium chloride a molecular dynamics study

Abstract The structure of molten rubidium chloride has been simulated by molecular dynamics using rigid ion and polarizable ion models. The partial pair radial distribution functions agree well with the experimental data. There are only small differences between the distribution functions predicted by the two models, the effect of polarization being primarily on the dynamical properties of the particles.

Lattice dynamics of wurtzite-type crystals

To deal with the lattice dynamics of wurtzite-type crystals, we have applied the polarizable-ion model following Born and Huang. On the basis of this we have calculated from macroscopic quantities the microscopic ones, namely the effective ionic charges and the electronic polarizabilities. Their values have led to the following relations: the anisotropy of the effective ionic charge has a regular correspondence with the structural anisotropy, and the electronic polarizability increases regularly with increasing unit-cell volume.

The analysis of the phonon spectrum of α quartz based on a polarizable ion model

The analysis of the phonon spectrum of α quartz based on a polarizable ion model