Rigid Ion Research Articles

Theoretical analysis of phonon dynamical behaviour of Cesium Chloride at various temperatures

We have developed a new model to investigate the complete lattice dynamics of cesium chloride at 78 K and at room temperature (298 K). The new model, van der Waals three body force shell model (VTSM) incorporates the effect of van der Waals interactions and three-body interactions in the frame work of rigid shell model where short range interactions are effective up to the second neighbour. A good agreement has been obtained between theory and experiment for dependant properties also. Cesium halides have been given a keen interest to most of the workers in the field of lattice dynamics due to the paramount importance of such binary solids, as the nature and physical properties of such crystal reveals to an understanding of their vibrational, thermo-dynamical, elastic, optical, thermal and numerous physical properties. The availability of a lot of measured data on elastic constants (1-4), dielectric constants (5,7), phonon dispersion curves (6,7,8), Debye temperature variations (9-11), two phonon IR and Raman spectra (12-15), third and fourth order elastic constants and their pressure derivatives (16,17), for all of them (CsCl, CsBr, CsI) and their interpretations by means of theoretical models (18-25) with moderate success, has motivated the present author to the basic need for a lattice dynamical model for the satisfactory description of their interesting properties. Various experimental and theoretical workers have given evolution for the study of phonon behaviour of CsCl structure. The first and most important model considered the ions of the crystal to be rigid, undeformable and unpolarizable spherical particle is rigid ion model (RIM) of Kellermann (25) which could not interpret well the dynamical, optical and elastic properties. Further efforts have been put as deformation dipole model (DDM) of Karo and Hardy (19) and rigid shell model (RSM) of Dick and Overhauser (26) and Woods et al. (23) by two different groups of workers. The DDM allows only the redistribution of charges in deformed electron cloud while the shell model considers the relative displacement. Therefore both effects (deformation and displacement) are present in ionic crystals. A general way to remove this deficiency is to include the deformation of electron shells in the framework of RSM. The most prominent amongst them are breathing shell model (BSM) of Schroder (20), the deformable shell model (DSM) of Basu and Sengupta (21), three-body force shell model (TSM) of Verma and Singh (27) and further Singh et al. (1) used extended three-body-force shell model (ETSM) which is an amalgamation of RSM and DDM. It is emergent from the descriptions that the most realistic model for the lattice dynamics and statics of these crystals can be developed by introducing the effect of van der Waals interactions (VWI), and three body interactions (TBI) in the framework of RSM, where the short-range interactions have been considered up to the second neighbours. The development of such a lattice dynamical model is the chief aim of the present work. This model is known as van der Waals three body force shell model (VTSM). A formal description of VWI and three-body interactions in the framework of RSM has been described in section 2. The present model VTSM in a way as outline above has been applied to investigate the complete lattice dynamics of cesium halides (CsCl, CsBr, CsI). The motivation behind the choice of the present system of solids lies in the fact that they are characterized by high energy gap, some discrepancies in PDCs and Cauchy violations. The effect of TBI and VWI are quite significant and play a vital role in the description of lattice dynamics of cesium halides. The proposed investigations have been carried out by adopting a simple method to determine a consistent set of 14-parameters )

Temperature-dependent Raman scattering study of K 2MoO 4

This research reports a temperature-dependent Raman scattering study of dipotassium molybdate (K 2MoO 4) in the 18–913 K temperature range. This study indicates that K 2MoO 4 crystal exhibits a temperature-induced first-order phase transition at around 578 K from monoclinic phase to incommensurate phase. The phase transition is connected with tilting and/or rotations of the MoO 4 tetrahedra that lead to a disorder in the MoO 4 sites. An orthorhombic phase (α′-phase) of K 2MoO 4 was obtained when the low-temperature monoclinic structure was heated or when high-temperature hexagonal structure was cooled. A lattice dynamic calculation was performed by using the classical rigid ion model, in order to predict both wavenumbers and atomic displacements (eigenvectors) for the vibrational modes of the monoclinic phase of K 2MoO 4 and K 2WO 4.

Specific heat of rare earth cobaltates RCoO 3 (R = La, Pr and Nd)

We have reported the temperature dependence (5 K ≤ T ≤ 1000 K) of the lattice contribution to the specific heat of rhombohedral LaCoO 3 and orthocobaltates RCoO 3 (R = Pr and Nd). The strong electron phonon interactions are present in these compounds and lattice distortions can affect them substantially. Thus Rigid Ion Model (RIM) is used for the first time to study the cohesive and thermal properties of the cobaltates RCoO 3 with rare earth cation (R = La, Pr and Nd). The values of specific heat calculated by us have shown remarkably good agreement with corresponding experimental data. In addition, the results on the temperature dependence of cohesive energy ( ϕ), molecular force constant ( f), Reststrahlen frequency ( υ), Debye temperature ( θ D ) and Gruneisen parameter ( γ) are also reported.

The influence of dipole polarisation on threshold displacement energies in UO2

Molecular dynamics simulations of radiation damage in nuclear materials have traditionally been performed using rigid ion empirical potential models. The inclusion of dipole polarisability via the shell model offers the possibility to incorporate more of the underlying physics into simulations of radiation damage via cascade simulations. Here we assess the impact of dipole polarisability on the evolution of radiation damage in UO2 by performing molecular dynamics simulations to determine the threshold displacement energies using both a standard rigid ion potential and the equivalent model including dipole polarisability. The inclusion of dipole polarisability reduces the threshold displacement energies by 20–30% relative to the rigid ion model, suggesting a significant increase in the number of defects created during the collisional phase of the cascade. However, a reduction in the activation energies for migration due to inclusion of polarisability may increase the rate of subsequent interstitial–vacancy recombination. The overall level of radiation damage will, therefore, be determined by the relative effectiveness of these two opposing processes.

Elastic and thermodynamic properties of AVO 3 (A=Sr, Pb) perovskites

We have investigated the elastic and thermodynamic properties for the perovskite type metavanadate SrVO 3 and the multiferroic PbVO 3, probably for the first time by the means of a Modified Rigid Ion Model (MRIM). We present the elastic constants ( C 11, C 12, C 44) and other elastic properties like Bulk modulus ( B), Young′s modulus ( E), shear modulus ( G), Poisson′s ratio ( σ) and wave velocity ( υ l, υ s, υ m). Besides we have reported the thermodynamic properties molecular force constant ( f), Reststrahlen frequency ( ν), cohesive energy ( ϕ), Debye temperature ( θ D) and Gruneisen parameter ( γ). We have also computed the variation of heat capacity ( C P) and there by volume thermal expansion coefficient ( α) in a wide temperature range. We found that the computed properties reproduce well with the available data in literature. To our knowledge some of the properties are reported for the first time.

Molecular dynamics simulation of UO 2 nanocrystals surface

In this article we investigated surface of nanocrystals (NCs) of uranium dioxide (UO 2) using molecular dynamics (MD) under isolated (non-periodic) boundary conditions in the approximation of rigid ions and pair potentials (RIPI). It is shown that a cubic shape of NCs is metastable and equilibrium is reached in the process of structural relaxation to the octahedral shape during long simulations of 1000 ns (200 million MD steps), which increase with the size of NC. We measured the size dependences of the lattice parameter and the surface energy density of cubic and octahedral NCs with volumes up to 1000 nm 3 (50 000 particles) at temperatures of 2200 K and 2300 K. For the surfaces {1 0 0} and {1 1 1} we obtained the energy densities σ 100 = 1.60 ± 0.02 J/m 2, σ 111 = 1.14 ± 0.03 J/m 2 and surface tension constant γ 111 = 0.841 ± 0.008 J/m 2. The resulting ratio of σ 100/ σ 111 = 1.41 ± 0.04 within the error coincides with the experimental value of 1.42 ± 0.05 measured for microscopic cavities in UO 2 monocrystals.

THERMOPHYSICAL PROPERTIES OF URANIUM DIOXIDE: A MOLECULAR DYNAMICS STUDY OF SOLID AND LIQUID PHASES OF STOICHIOMETRIC UO2

Thermodynamic and transport properties of solid and liquid uranium dioxide were studied using classical molecular dynamics simulation, with a newly parametrized interionic model potential. In addition to the static and transport properties which have been previously reported by the authors, this study further confirms that temperature dependence of the calculated thermophysical properties of uranium dioxide are in agreement with the available experimental data at both solid and liquid phases in providing an alternative rigid ion potential to the other model potentials in literature. Although lattice parameter and density have been underestimated, overall results give a fairly good description of the UO 2 system for wide range of temperature (0–4000 K). The transition to the superionic phase, Bredig transition, was successfully observed as a distinct λ-peak in specific heats at about 400 K below the experimental value. The results presented in our previous article and here show that the introduced alternative model potential for uranium dioxide is very promising and we are confident in the success of its use in future studies.

High-precision molecular dynamics simulation of UO 2–PuO 2: Pair potentials comparison in UO 2

Our series of articles is devoted to high-precision molecular dynamics simulation of mixed actinide-oxide (MOX) fuel in the approximation of rigid ions and pair interactions (RIPI) using high-performance graphics processors (GPU). In this first article ten most recent and widely used interatomic sets of pair potentials (SPP) are assessed by reproduction of solid phase properties of uranium dioxide (UO 2) – temperature dependences of the lattice constant, bulk modulus, enthalpy and heat capacity. Measurements were performed with 1 K accuracy in a wide temperature range from 300 K up to melting points. The best results are demonstrated by two recent SPPs MOX-07 and Yakub-09, which both had been fitted to the recommended thermal expansion in the range of temperatures 300–3100 K. They reproduce the experimental data better than the widely used SPPs Basak-03 and Morelon-03 at temperatures above 2500 K.

Synthesis of tailor‐made nanoporous polyaniline derived with PVA/alkaline metal system for metal complexation

AbstractNanoporous polyanilines (PANIs) have attracted attention due to well‐defined molecular structures and chemical versatility, which also complicate the mechanisms of interaction between metal ions and PANI. To further understand the complexation with metal ions, tailor‐made nanoporous PANIs were synthesized with self‐stabilized dispersion polymerization (SSDP) using the poly(vinyl alcohol) (PVA) and various alkaline metals for suitable target metal complexation. The effective complexation results for the removal of Cr ions were obtained by the nanoporous PANI derived from a PVA/Li system. The synthesized tailor‐made PANI‐emeraldine base (EB) was easily oxidized by a Cr(VI) oxidant resulting in an pernigraniline form with a rigid polymer template and effective metal ion binding sites, and then the reduced form of Cr(III) can be complexed with the resulting PANI. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011.

MOLECULAR DYNAMICS SIMULATION OF UO2: AN ALTERNATIVE RIGID ION MODEL POTENTIAL

A semi-empirical effective interionic potential model has been parameterized to investigate UO 2 by molecular dynamics simulation technique. The simulations were performed in the constant pressure–temperature ensemble between 300 K–3200 K at 100 K intervals. The pair distribution functions and coordination numbers signal the onset of structural changes at temperatures in accord with the Bredig transition and melting. The oxygen ion diffusion coefficients calculated from the mean square displacements markedly increase the liquid like value at T > 2100 K . The transition to the superionic state and melting are well reproduced within the limitations of a rigid ion potential.

Influence of La doping on elastic and thermodynamic properties of SrMoO 3

The elastic and thermodynamic properties for Sr 1− x La x MoO 3 ( x = 0.0, 0.05, 0.1, 0.15, and 0.2) with temperature have been investigated, probably for the first time, by using modified rigid ion model (MRIM). The computed results on the elastic constants ( C 11, C 12, and C 44) are the first report on them. Using these elastic constants we have computed other elastic properties such as B, β, G′, G, E, σ, B/ G ratio, Cauchy pressure ( C 12 − C 44) and Lame's parameters ( μ, λ). We have also reported the thermodynamic properties such as ϕ, f, θ D, θ D1, υ 0, υ 1, γ, and α. The values of Young's modulus, shear modulus and compressibility for SrMoO 3 are in good agreement with the available experimental data. The concentration ( x) dependence of θ D in Sr 1− x La x MoO 3 suggests that increased La doping drives the system effectively away from the strong electron–phonon coupling regime. Specific heat is reported in the wide temperature range and compared with the respective experimental data available in the literature. The thermal expansion coefficient of SrMoO 3 is in good agreement with the other theoretical data.

Debye–Hückel theory for mixtures of rigid rodlike ions and salt

Like-charged surfaces are able to attract each other if they are embedded in an electrolyte solution of multivalent rodlike ions, even if the rods are long. To reproduce this ability the Poisson-Boltzmann model has recently been extended so as to account for the rodlike structure of the mobile ions. Our model properly accounts for intraionic correlations but still neglects correlations between different rodlike ions. For sufficiently long rods, the model shows excellent agreement with Monte Carlo simulations and exhibits two minima - a depletion and a bridging minimum - in the interaction free energy. In the present work, we generalize the Poisson-Boltzmann model to systems with polydisperse rod lengths and arbitrary charge distributions along the rods, including the presence of salt. On the level of the linearized Debye-Hückel model we derive a general criterion for whether an electrolyte with given distribution of rodlike ions is able to mediate attraction between like-charged surfaces. We numerically analyze two special cases, namely the influence of salt on symmetric and asymmetric mixtures of monodisperse rodlike ions. The symmetric mixture is characterized by the presence of both negatively and positively charged (but otherwise identical) rodlike ions. For the asymmetric mixture, the system contains rodlike ions of only one type. We demonstrate that the addition of salt retains the depletion minimum but tends to eliminate the bridging minimum.

A polarizable ion model for the structure of molten CuI

The results are reported of the molecular dynamics simulations of the coherent static structure factor of molten CuI at 938 K using a polarizable ion model. This model is based on a rigid ion potential to which the many body interactions due to the anions induced polarization are added. The calculated structure factor reproduces the clear sharp prepeak observed in neutron diffraction data. The corresponding partial structure factors and the related radial distribution functions calculated by molecular dynamics are compared with those found in the literature derived from a combination of neutron and x-ray diffraction data with the aid of the reverse Monte Carlo simulation technique, as well as those calculated by ab initio MD simulations.

Controlled porosity monolithic material as permselective ion exchange membranes

Ion exchange membranes (IEMs) are used in a variety of analytical devices, including suppressors, eluent generators and other components used in ion chromatography. Such membranes are flexible and undergo substantial dimensional changes on hydration. Presently the push to miniaturization continues; a resurgent interest in open tubular ion chromatography requires microscale adaptation of these components. Incorporating IEMs in microscale devices is difficult. Although both macroporous and microporous ion exchange materials have been made for use as chromatographic packing, ion exchange material used as membranes are porous only on a molecular scale. Because such pores have vicinal ion exchange sites, ions of the same charge sign as those of the fixed sites are excluded from the IEMs. Monolithic polymers, including ion exchangers derived therefrom, are presently extensively used. When used in a separation column, such a monolithic structure contains an extensively connected porous network. We show here that by controlling the amount of porogen added during the synthesis of monolithic polymers derived from ethylene dimethacrylate – glycidyl methacrylate, which are converted to an anion exchanger by treatment with trimethylamine, it is possible to obtain rigid ion exchange polymers that behave like IEMs and allow only one charge type of ions to pass through, i.e., are permselective. We demonstrate successful open tubular cation chromatography suppressor performance.

Molecular dynamics simulation of yttria-stabilized zirconia (YSZ) crystalline andamorphous solids

An empirically fitted atomic potential allows a classical moleculardynamics study of the static and dynamic properties of both crystallineand amorphous yttria-stabilized zirconia (YSZ) with typical diluteY2O3 concentrations(i.e. 3.0–12.0 mol% Y2O3) in the temperature range 300–1400 K. Based on the rigid ion model approximation, we find, regardlessof the distinctly different geometries, that the oxygen ionic conductivity shows a maximum at ∼ 8.0 mol%Y2O3, close to the experimental maximum. A lower absolute ionic conductivity is found for thehigh density YSZ amorphous solid, relative to crystalline YSZ, consistent with the trendsobserved in crystalline and stabilized amorphous thin films of YSZ reported inexperiments. Different from YSZ crystals, intriguing features of mutual diffusionamong the heavy cations and mobile anions are found in the amorphous phase.

鉱物結晶学の多様化：新たな広がりと挑戦 ２．地球表層鉱物（地圏物質）鉱物の焦電性と原子の非調和熱振動

A structural approach was attempted to estimate rigid ion contributions to pyroelectric coefficients, employing atomic position vectors determined in the least-squares refinement of a polar mineral, cancrinite. The two sets of positions, obtained from the centers of gravity (centroids) and modes of asymmetric probability density functions (pdf) of atoms, were applied to calculate electric polarizations, whose temperature derivatives may correspond to the rigid ion contributions to the pyroelectric coefficient, γ(σ), normally measured under the condition of constant stresses and to the secondary pyroelectric coefficients, γ(2), respectively. The primary pyroelectric coefficient γ(ε) was given as the difference γ(σ)-γ(2).

Molecular dynamics of polarizable point dipole models for molten NaI. Comparison with first principles simulations

Molecular dynamics simulations of molten NaI at 995 K have been carried out using polarizable ion models based on rigid ion pair potentials to which the anion induced dipole polarization is added. The polarization is added in such a way that point dipoles are induced on the anions by both local electric field and deformation short-range damping interactions that oppose the electrically induced dipole moments. The structure and self-diffusion results are compared with those obtained by Galamba and Costa Cabral using first principles Hellmann-Feynman molecular dynamics simulations and using classical molecular dynamics of a shell model which allows only the iodide polarization

Investigations of Thermal Properties of Earth Mantle Silicates: ASiO3 (A = Mg, Ca)

We have investigated the thermal properties and specific heat of earth mantle silicates ASiO3 (A = Mg, Ca) by the means of rigid ion model (RIM) and compared them with the earlier experimental reports. The calculated specific heat of ASiO3 (A = Mg, Ca) obeys T3 law at low temperature (T < θD/50). The temperature dependence of the specific heat of MgSiO3 and CaSiO3 (0 K ≤ T ≤ 2000 K) is presented along with the elastic, cohesive and thermal properties, like Bulk modulus (B), cohesive energy (φ), molecular force constant (f), reststrahlen frequency (ν), Debye temperature (θD) and Gruneisen parameter (γ) at T = 300 K.

Phonon anomalies in intermediate valence compounds

Phonon anomalies in the intermediate valence compounds SmS, TmSe and YS were studied extensively using a three-body force rigid shell model. Three-body interactions were used because, due to valence fluctuations, the radii of rare-earth ions change significantly and, therefore, the amount of overlap with neighboring chalcogen ions also changes. Change in the radii of the rare-earth ions results in the deformation of the rare-earth ions, whereas change in the amount of overlap with the neighboring chalcogen ion gives rise to long-range three-body interactions between the transferred charges of the lattice. Both of these changes strongly influence the phonon dispersion curves, particularly along the zone boundary. Results obtained from the model are in agreement with the measured data for phonon dispersion as compared to the results obtained using a three-body rigid ion model. Results for Debye temperature variations and two-phonon IR/Raman spectra for these crystals have also been presented, probably for the first time, but could not be compared with experimental data due to their non-availability.

Vibrational properties of (Gd1−xYx)3Ga5O12 solid solutions

The vibrational properties of the (Gd1−xYx)3Ga5O12 (0≤x≤1) mixed garnet crystals are investigated at normal conditions by Raman and reflectivity infrared (IR)-spectroscopy while the end members of the series have been theoretically investigated by means of a rigid ion model. The IR experimental spectra were analyzed by means of the Kramers–Kronig relations and the Lorentz oscillator model. The obtained results are compared and discussed in detail with the theory, providing useful parameters for estimating and understanding the IR optical properties of mixed garnets. The majority of the expected Raman peaks is resolved and their symmetry assignment has been elucidated. The clear one mode behavior of the observed Raman and IR modes as a function of x confirms the formation of solid solutions, resulting from the replacement of the cations at the dodecahedral lattice sites. A softening of almost all Raman and IR modes is found as the unit cell volume increases (x decreases). Finally, the small dispersion of the Grüneisen parameters γi (ω) indicates that the binding forces are of the same nature and order of magnitude and that the binding strength between the various molecular units is quite comparable.