Simple Rigid Ion Model Research Articles

The structure of molten CuCl: Reverse Monte Carlo modeling with high-energy X-ray diffraction data and molecular dynamics of a polarizable ion model.

The results of the structural properties of molten copper chloride are reported from high-energy X-ray diffraction measurements, reverse Monte Carlo modeling method, and molecular dynamics simulations using a polarizable ion model. The simulated X-ray structure factor reproduces all trends observed experimentally, in particular the shoulder at around 1 Å(-1) related to intermediate range ordering, as well as the partial copper-copper correlations from the reverse Monte Carlo modeling, which cannot be reproduced by using a simple rigid ion model. It is shown that the shoulder comes from intermediate range copper-copper correlations caused by the polarized chlorides.

Vibrational properties of nanometricAB2 ionic clusters

A broad survey of harmonic dynamics inAB2 clusterswith up to N = 3000 atoms is performed using a simple rigid ion model, with ionic radii selected togive rutile as the ground state structure for the corresponding extended crystal.The vibrational density of states is already close to its bulk counterpart forN∼500, with characteristic differences due to surfaces, edges and vertices. Two methods areproposed and tested to map the cluster vibrational states onto the rutile crystal phonons.The net distinction between infrared (IR) active and Raman active modes that exists forbulk rutile becomes more and more blurred as the cluster size is reduced. It isfound that, in general, the higher the IR activity of the mode, the more this isaffected by the system size. IR active modes are found to spread over a widefrequency range for the finite clusters. Simple models based on either a crudeconfinement constraint or surface pressure arguments fail to reproduce the results ofthe calculations. The effects of the stoichiometry and dielectric properties of thesurrounding medium on the vibrational properties of the clusters are also investigated.

Phonon spectrum ofZnAl2O4spinel from inelastic neutron scattering and first-principles calculations

The phonon spectrum of ${\mathrm{ZnAl}}_{2}{\mathrm{O}}_{4}$ spinel was investigated jointly by inelastic neutron-scattering and first-principles calculations. The results permit an assessment of important mechanical and thermodynamical properties such as the bulk modulus, elastic constants, lattice specific heat, vibration energy, and Debye temperature. The observed generalized phonon density of states shows a gapless spectrum extending to a cutoff energy of \ensuremath{\sim}840 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. The theoretical results reproduce all of the features of the phonon density of states. The calculated Raman-and infrared-active phonon frequencies agree well with the data in the literature. A comparison of the lattice dynamics of ${\mathrm{ZnAl}}_{2}{\mathrm{O}}_{4}$ and ${\mathrm{MgAl}}_{2}{\mathrm{O}}_{4}$ spinels was carried out using a simple rigid-ion model, which shows that the major difference in the phonon frequencies of the two materials can be accounted for by the mass effects between the Zn and Mg ions.

Ferroelectric phase transitions: A first-principles approach

Fundamental aspects of the theoretical study of bulk ferroelectric phase transitions through the construction of model Hamiltonians from first-principles calculations are reviewed. It is demonstrated that density-functional-theory linear-response calculations and total-energy calculations with symmetry-constrained ionic relaxation are very useful in the determination of the local mode variable and of the parameters in an explicit expression for the model Hamiltonian. Results of first-principles pseudopotential calculations of the lattice constant, phonon frequencies, and distortion energies for the perovskite ferroelectric PbTiO3 are presented. From this information, the local mode variable is identified, a model Hamiltonian is constructed and its finite-temperature behavior is studied with mean-field theory and Monte Carlo simulation. Very rough agreement with the observed Tc is obtained and various improvements and refinements of the calculation proposed. A well-controlled method for investigation of the intrinsic limitations of the model Hamiltonian approach, based on application to a simple rigid ion model, is outlined and preliminary results described.

Cell-cluster and self-consistent calculations for a model sodium chloride crystal.

We have calculated the thermodynamic properties of a simple rigid-ion model of sodium chloride, using both cell and cell-cluster, and self-consistent- and improved self-consistent-phonon formalisms, to compare with recent Monte Carlo results. The cell-cluster results are good for the thermal expansivity and the bulk modulus, which involve the volume dependence of the free energy, but some discrepancies remain for the heat capacities. The improved self-consistent theory gives a better result for ${\mathit{C}}_{\mathit{v}}$, although the volume-dependent properties are less well described. The simple cell model is surprisingly successful in giving a description of the solid at high temperatures.

The phase behaviour of silver iodide. Constant stress molecular dynamics simulation

The constant stress molecular dynamics (MD) technique using the Parrinello-Rahman Lagrangian is used to investigate the phase behaviour of AgI using a simple rigid-ion model potential. The system of 216 or 256 ions spontaneously transforms from one pure phase to another upon superheating or supercooling and the known phase diagram of AgI is remarkably well mimicked. The high-pressure rocksalt phase has a diffuse fast-ion transition as does the α-phase supercooled below the α-β transition at 300 K, 0 GPa. Some authors have argued that a divergence in defect densities or a diffuse fast-ion transition in the β-phase drives the β-α transition. No evidence is found for this. A heat capacity, compressibility and diffusivity anomaly in the α-phase appears to confirm the order-disorder transition there proposed by Perrott and Fletcher. This perturbs the shape of the rocksalt-α-phase boundary as predicted earlier. Heats of transition are determined and the volume change across the β-α boundary is indeed negative as for real AgI. These results are a remarkable vindication of the MD technique, and should encourage application to further important model systems.

Density of phonon states in amorphous germanium and silicon

Abstract 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.

Optical properties and the crystal structure of anhydrous gadolinium-trichloride

The Raman and i.r. reflection spectra of GdCl3 have been studied in order to estabish the optically active fundamental frequencies. Gd3+−Cl−)-and (Cl−−Cl−)-force constants in GdCl3 and in LaCl3 and PrCl3 have been calculated on the basis of a simple rigid ion model. It is found that the apparently anomalous spectra of GdCl3 may be a result of a stronger (Cl−−Cl−)-coupling constant than in the hexagonal rare earth trichlorides with lower Z on the metal ion. This peculiar status of GdCl3 is related to the change of crystal structure in the series of Rare-Earth trichlorides from a hexagonal (La-…Gd-) Cl3 to an orthorhombic (TbCl3 DyCl3) structure. Some properties of the electronic spectra are also discussed in this context.

Transverse and longitudinal lattice frequencies and interionie potential in some AMF 3 perovskite fluoride crystals

The i.r. reflection spectra of the crystals RbMnF 3, RbFeF 3, KMgF 3, and CsMnF 3 were measured. The optical and dielectric constants were derived from the measured reflectivities. The transverse [ν(T)] and longitudinal [ν(L)] frequencies of the cubic crystals BbMnF 3, RbFeF 3 and KMgF 3 were obtained, from the real and imaginary dielectric constants, ϵ'( v) and ϵ''( v). The calculation of the ν(T) and ν(L) frequencies for y → (0, 0, 0) was made, on the basis of a simple rigid ion model which includes effective ionic charges and interionie repulsive force constants. The least squares calculation determined a set of potential constants and effective ionic charges, using the observed values of both the ν(T) and ν(L) frequencies. This simple rigid ion model may explain satisfactorily the lattice vibrations of AMF 3 cubic crystals. The short range force constant associated with the metal ion to fluorine ion indicates that this bond contains some amount of covalent character.

Effective Force Constant and Impurity Mode in the Low- and High-Frequency Limits

By employing an effective force constant introduced earlier in the framework of a rigid-ion model for the lattice dynamics we have discussed the asymptotic behavior of the high-frequency localized modes and the low-frequency resonance modes due to substitutional impurities in realistic cubic lattices. Simple expressions for the frequencies of these impurity modes and the linewidths of the resonance modes have been obtained. In the asymptotic description the motion of an impurity may be simulated by an Einstein oscillator which is vibrating in the rest of the host crystal assumed to be static. However, the dynamical correlation of the impurity with the other ions of the host lattice is found to be significant especially in the case of an impurity strongly coupled to the lattice. Numerical calculations have been made for CsI crystals doped with impurity ions of different species in the breathing-shell model. A good agreement between the theoretical and experimental results is observed. The values of the frequencies of the impurity modes and the linewidths of the resonant modes calculated in the asymptotic limits compare well with the experimental values. The discrepancy between the calculated and the experimental values in the majority of cases lie within 20%. In both the low- and high-frequency regions, the value of the effective force constant is seen to be independent of frequency. However, the value of the effective force constant in the high-frequency region is smaller in magnitude than that in the low-frequency region. Further, the value of the effective force constant does not depend on the kind of the ion in a unit cell in ionic crystal, i.e., the value is found to be practically the same whether we consider a positively charged impurity ion or a negatively charged impurity ion. The implication of these results is that one may employ a simple rigid-ion model for a realistic crystal lattice with central interactions for understanding the defect properties of solids in the low- and the very high-frequency regions.

Experimental studies of the magnetic and phonon excitations in cobalt fluoride

The excitations of cobalt fluoride have been studied with the technique of slow-neutron inelastic scattering. A triple-axis crystal spectrometer was used throughout in its constant Q mode of operation. Several of the branches of the phonon spectra were measured and are in reasonable agreement with calculations based on a very simple rigid ion model. The magnetic excitations are of interest because the Co2+ ion has unpaired orbital angular momentum which gives rise to several low-lying energy levels. Excitations have been observed from the ground state to the next three excited states in the antiferromagnetic phase and their dispersion and temperature dependence obtained below, near, and above the Néel temperature. The temperature dependences of the excitations to the different excited states are not the same. The measurements on the magnetic excitation branch of lowest frequency show that, contrary to current theories of magnetism, fairly well-defined magnetic excitations occur to at least 1.5TN Another excitation, which gave a weak scattering intensity, was also observed and it is suggested that this may be associated with a distortion of the crystal structure.

THE CRYSTAL DYNAMICS OF URANIUM DIOXIDE

The frequency/wave-vector dispersion relation for normal modes of vibration propagating along the [00ζ], [ζζ0], and [ζζζ] directions in uranium dioxide at 296 °K has been determined by studying the coherent one-phonon scattering of slow neutrons from a single-crystal specimen. Analysis of the results shows that a simple rigid-ion model of the crystal with axially symmetric forces between near-neighbor ions can provide qualitative agreement with experiment. A more complicated model, in which the ionic polarizabilities are taken into account, is needed to obtain quantitative agreement with the dispersion curves and with the known dielectric properties. Such a model provides an interpolation formula for computing the frequency distribution function and other related quantities, such as the Debye–Waller factors and lattice specific heat. Information concerning the anisotropy of the Debye–Waller factor for the oxygen ions and the configuration of the "magnetic" electrons in UO2 is derived by comparing these calculations with the appropriate experimental data. The optic-mode frequencies and dielectric constants of UO2 are shown to satisfy the Lyddane, Sachs, and Teller relation. The slopes of the acoustic-mode branches at small wave vectors are consistent with independently measured elastic constants.