Polarizable Ion Model Research Articles

Structure and transport properties of LiF–BeF2 mixtures: Comparison of rigid and polarizable ion potentials#

Molecular dynamics simulations are performed to study the structure and dynamics of the LiF–BeF2 system over a range of compositions using the transferable rigid-ion model (TRIM). The densities obtained with the TRIM potential are approximately 17–20% lower than the experimental values while polarizable ion models (PIM) give densities within 5% of the experimental value. The TRIM and PIM potentials give essentially identical radial distribution functions (RDFs) for Li–F and Be–F ion pairs though the Be–Be pair correlation differ significantly and reflect the corresponding density differences. The variation in the radial distribution functions with concentration, particularly the anion–anion pair correlation function, reflects the reorganization of the fluoride ions as the addition of BeF2 in the mixture promotes the formation of the tetrahedral fluoroberyllate network. Along the 67 mole% LiF isopleth, diffusivities and Nernst–Einstein ionic conductivities from simulations using the PIM and TRIM potentials are in good agreement for temperatures up to 925 K. The viscosity data using the PIM model is also found to be in good agreement with the TRIM results presented here along the 873 K isotherm for compositions ranging from 0 to 50 mole% BeF2. The main conclusion from this study is that the non-polarizable, TRIM provides reasonable results for the structural correlations and transport properties of the LiF–BeF2 system in comparison with first-principles-based, PIM. Behaviour of ionic conductivity as a function of temperature, calculated using a rigid ion model is compared with experiment and with a polarizable ion model for the LiF–BeF2 system at 33 mole% BeF2. Simulation snapshots of the LiF–BeF2 melt at concentrations of 10 and 70 mole% BeF2 along the 1500K isotherm are shown on the right. The green, blue and red coloured spheres represent the lithium, beryllium and fluorine, respectively.

From molten salts to room temperature ionic liquids: Simulation studies on chloroaluminate systems

An interaction potential including chloride anion polarization effects, constructed from first-principles calculations, is used to examine the structure and transport properties of a series of chloroaluminate melts. A particular emphasis was given to the study of the equimolar mixture of aluminium chloride with 1-ethyl-3-methylimidazolium chloride, which forms a room temperature ionic liquid EMI+–AlCl−4. The structure yielded by the classical simulations performed within the framework of the polarizable ion model is compared to the results obtained from entirely electronic structure-based simulations: An excellent agreement between the two flavors of molecular dynamics is observed. When changing the organic cation EMI+ by an inorganic cation with a smaller ionic radius (Li+, Na+, K+), the chloroaluminate speciation becomes more complex, with the formation of Al2Cl−7 in small amounts. The calculated transport properties (diffusion coefficients, electrical conductivity and viscosity) of EMI+–AlCl−4 are in good agreement with experimental data.

A dipole polarizable potential for reduced and dopedCeO2 obtained from first principles

In this paper we present the parameterization of a new interionic potential for stoichiometric, reduced anddoped CeO2. We use a dipole polarizable potential (DIPPIM: the dipole polarizable ion model) andoptimize its parameters by fitting them to a series of density functional theory calculations.The resulting potential was tested by calculating a series of fundamental properties forCeO2 and by comparing them against experimental values. The values for all the calculatedproperties (thermal and chemical expansion coefficients, lattice parameters, oxygenmigration energies, local crystalline structure and elastic constants) are within 10–15% ofthe experimental ones, an accuracy comparable to that of ab initio calculations. This resultsuggests the use of this new potential for reliably predicting atomic scale properties ofCeO2 in problems where ab initio calculations are not feasible due to their size limitations.

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.

The structure of molten AgCl, AgI and their eutectic mixture as studied by molecular dynamics simulations of polarizable ion model potentials

The structure of molten AgCl, AgI, and their eutectic mixture Ag(Cl(0.43)I(0.57)) is studied by means of molecular dynamics simulations of polarizable ion model potentials. The corresponding static coherent structure factors reproduce quite well the available neutron scattering data. The qualitative behavior of the simulated partial structure factors and radial distribution functions for molten AgCl and AgI is that predicted by the reverse Monte Carlo modeling of the experimental data. The AgI results are also in qualitative agreement with those calculated from ab initio molecular dynamics.

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

On the inter ionic potentials of molten salts

Inter ionic pair potentials including the effect of ion polarization have been re-examined after the brief survey of their study. The cause of major defect of the polarizable ion model, the polarization catastrophe , has been examined. New expression of screened ion potentials including ion polarization has been proposed to avoid the catastrophe. The application to molten CuI has been demonstrated as an example

Static dielectric properties of polarizable ion models: Molecular dynamics study of molten AgI and NaI

The fluctuation-dissipation theorem for the static dielectric response function of systems of ions with inducible point dipoles is derived. It is shown that the static longitudinal dielectric function is determined by spatial correlations of both charge and dipole-moment density fluctuations. Moreover, it is deduced that the long-wavelength behavior of the charge structure factor for polarizable ion systems is different from that for systems of rigid ions. Molecular dynamics simulation results of rigid and polarizable ion models for molten AgI and NaI are reported.

Polarization effects on the dielectric properties of molten AgI

The results are reported of molecular dynamics simulations of the static longitudinal dielectric and response functions for molten AgI at 923 K using two ionic models. The first one is a rigid ion model, while in the second the induced dipole moments of the anions are added to the effective pair potentials of the first. It is derived theoretically that the dielectric functions for the polarizable ion model are determined by spatial correlations of charge and dipole moment densities. The charge structure factor at long wavelengths is also studied.

Molecular Dynamics Study of Polarization Effects on AgI

Three different models of AgI are studied by molecular dynamics simulations. The first one is the rigid ion model (RIM) with the effective pair potential of the Vashishta and Rahman form and the parametrization proposed by Shimojo and Kobayashi. The other two are polarizable ion models in which the induced polarization effects have been added to the RIM effective pair potential. In one of them (PIM1), only the anions are assumed to be polarizable by the local electric field. In the other one (PIM2s), the silver polarization is also included, and a short-range overlap-induced polarization opposes the electrically induced dipole moments. This short-range polarization is proved to be necessary to avoid overpolarization when both species are assumed to be polarizable. The three models reproduce the superionic character of alpha-AgI at 573 K and the liquid behavior of molten AgI at 923 K. The averaged spatial distribution of the cations in the alpha-phase obtained for PIM1 appears to be in better agreement with experimental data analysis. The PIM1 also reproduces the structure factor prepeak at about 1 A(-1) observed from neutron diffraction data of molten AgI. The three models retain in the liquid phase the superionic character of alpha-AgI, as the mobility of the cations is significantly larger than that for the anions. The ionic conductivity for the polarizable ion models is in better agreement with experimental data for alpha-AgI and molten AgI.

Molecular dynamics study of polarizable point dipole models for molten sodium iodide

The structure, the ionic transport properties, and the dynamics of long-wavelength charge-density fluctuations, for two polarizable point dipole models of molten NaI, have been studied by molecular dynamics simulations. These models are based on a rigid ion potential to which the induced dipole polarization of the anions is added. The polarization is added in such a way that point dipoles are induced on the anions by both local electric field and short-range damping interactions that oppose the electrically induced dipole moments. The two polarizable ion models differ only in the range of the damping polarization interactions. The influence of the induced anion polarization on the different properties of simulated molten NaI is discussed.

Lattice dynamics and the phase transition from the cubic phase to the tetragonal phase in the LaMnO3 crystal within the polarizable-ion model

The paper reports on the results of ab initio calculations of the static and dynamic properties of the LaMnO3 crystal with a perovskite structure in the cubic, rhombohedral, and orthorhombic phases. The calculations are performed within the ionic crystal model, which takes into account the deformability and polarizability of the ions. It is revealed that the spectrum of lattice vibrations in the cubic phase contains unstable vibrational modes, which occupy the phase space in the entire Brillouin zone. The eigenvectors of the softest mode at the boundary point R of the Brillouin zone are associated with the displacements of the oxygen ions and correspond to the “rotation” of the MnO6 octahedron. The condensation of one, two, and three components of this mode leads to the tetragonal, orthorhombic, and rhombohedral distortions of the structure. The structural phase transition is described in terms of the local mode approximation with the use of the double perovskite unit cell, in which the MnO6 octahedron is explicitly separated. The parameters of the model Hamiltonian are determined. The static properties are investigated by the Monte Carlo method. The calculated temperature of the phase transition from the cubic phase (9800 K) is considerably higher than the melting temperature of the crystal under investigation. The calculated frequencies of long-wavelength lattice vibrations in the experimentally observed orthorhombic and rhombohedral phases are in reasonable agreement with experimental data.

A polarizable ion model for the structure of molten AgI

The results are reported of the molecular dynamics simulations of the coherent static structure factor of molten AgI at 923 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 is in better agreement with recent neutron diffraction data than that obtained by using simple rigid ion pair potentials. The Voronoi-Delaunay method has been applied to study the relationship between voids in the spatial distribution of cations and the prepeak of the structure factor.

Lattice instability at phase transitions near the Lifshitz point in proper monoclinicferroelectrics

The temperature dependence of acoustic properties of theSn2P2(SexS1−x)6 uniaxial ferroelectric in the vicinity of the Lifshitz point (LP) was investigated byBrillouin spectroscopy and analysed in the Landau–Khalatnikov approximation. Ananomalous decrease of the longitudinal hypersound velocity in the paraelectricphase caused by fluctuation effects and crystal structure defects has been foundnear the LP. Besides this, a small softening of the transverse acoustic phonons isobserved, which is due to their linear interaction with the soft optic mode found forincommensurate phase transitions in proper ferroelectrics. The lattice instability analysis ofSn2P2S6 and Sn2P2Se6 crystals and their solid solutions in a polarizable ion model shows that a possible reason forthe absence of a soft acoustic mode is nonorthogonality of the spontaneous polarizationvector and modulation wavevector which both lie in the monoclinic symmetry plane.

Molecular Dynamics Study of Polarizable Ion Models for Molten AgBr

Three different polarizable ion models for molten AgBr have been studied by molecular dynamics simulations. The three models are based on a rigid ion model (RIM) with a pair potential of the type proposed by Vashishta and Rahman for alpha-AgI, to which the induced dipole polarization of the ions is added. In the first (PIM1) the dipole moments are only induced by the local electric field, while in the other two (PIM1s and PIM2s) a short-range overlap induced polarization opposes the electrically induced dipole moments. In the PIM1 and the PIM1s only the anions are assumed polarizable, while in the PIM2s both species are polarizable. Long molecular dynamics simulations show that the PIM2s is an unphysical model since, for some improbable but possible critical configurations, the ions become infinitely polarized. The results of using the PIM1, the PIM1s, as well as those of the simple RIM, have been compared for the static structure and ionic transport properties. The PIM1 reproduces the broad main peak of the total structure factor present in the neutron diffraction data, although the smoothed three-peak feature of this broad peak is slightly overestimated. The structural results for the PIM1s are intermediate between those for the RIM and the PIM1, but fail to reproduce the experimental features within the broad principal peak. Concerning the ionic transport properties, the value of the conductivity obtained using PIM1 is in good agreement with experimental values, while the self-diffusion coefficients and the conductivity for the PIM1s are lower than the corresponding values using the PIM1 and the RIM.

X–ray and neutron diffraction studies and MD simulation of atomic configurations in polyamorphic Y2O3-Al2O3systems

Supercooled liquids in the Y(2)O(3)-Al(2)O(3) system undergo a liquid-liquid phase transition between a high-temperature, high-density amorphous (HDA) polymorph form and one with lower density (LDA form) that is stable at lower temperature. The two amorphous polymorphs have the same chemical composition, but they differ in their density (ca. 4% difference) and in their heat content (enthalpy) and entropy determined by calorimetry. Here we present new results of structural studies using neutron and high-energy X-ray diffraction to study the structural differences between HDA and LDA polyamorphs. The combined datasets show no large differences in the average nearest-neighbour Al-O or Y-O bond lengths or coordination numbers between the low- and high-density liquids. However, the data indicate that substantial changes occur among the packing geometries and clustering of the Al-O and Y-O coordination polyhedra, i.e. within the second-nearest-neighbour shell defined by the metal-metal (i.e. Y-Y, Y-Al, Al-Al) interactions. Polarizable ion model molecular dynamics simulations of Y(2)O(3)-Al(2)O(3) liquids are used to help interpret the pair-correlation functions obtained from X-ray and neutron scattering data. Unexpectedly large density fluctuations are observed to occur during the simulation of nominally equilibrated systems. These are interpreted as being due to dynamic sampling of high- and low-density configurations within the single-phase liquid at temperatures above the critical point or phase transition line. Calculated partial radial distribution functions indicate that the primary differences between HDA and LDA configurations occur among the Y-Y correlations.

Study of the Nature and Mechanism of the Rhombohedral‐to‐Cubic Phase Transition in α‐AlF3 with Molecular Dynamics Simulations.

α-AlF3, which adopts a rhombohedrally distorted form of the ReO3 structure at room temperature, undergoes a phase transition to the cubic ReO3 structure at 466°C. The phase transition has been studied using molecular dynamics (MD) simulations performed with a polarizable ion model (PIM). The results are compared to information obtained from experimental diffraction data, and analogies to the tilting schemes of the structurally related perovskite phases are made. The cubic phase can be distinguished from the rhombohedral phase by following the Al-F-Al bond angles that describe the tilting of the AlF6 corner sharing octahedra as a function of temperature. The Al-F-Al chains are still bent in the so-called cubic phase, but the direction of tilting of the AlF6 octahedra varies continuously during the MD run, so that the time-averaged symmetry of the system is nearly cubic. The motion of the octahedra primarily involves a 360° rotation of the vector that describes the displacement of the F atom from its ideal position in a linear Al-F-Al chain. It is this 360° motion that distinguishes the cubic from the rhombohedral phase. The high-temperature phase is also associated with increased vibrations of the Al-F-Al chains. The results provide an explanation for the large thermal parameters observed experimentally for fluorine (in structures refined from diffraction data) above the phase transition. The simulation results suggest the possible existence of a third (orthorhombic) form of α-AlF3, which is energetically very similar to the rhombohedral phase at room temperature but differs in its octahedral tilting scheme.

Study of the Nature and Mechanism of the Rhombohedral-to-Cubic Phase Transition in α-AlF3 with Molecular Dynamics Simulations

α-AlF3, which adopts a rhombohedrally distorted form of the ReO3 structure at room temperature, undergoes a phase transition to the cubic ReO3 structure at 466°C. The phase transition has been studied using molecular dynamics (MD) simulations performed with a polarizable ion model (PIM). The results are compared to information obtained from experimental diffraction data, and analogies to the tilting schemes of the structurally related perovskite phases are made. The cubic phase can be distinguished from the rhombohedral phase by following the Al-F-Al bond angles that describe the tilting of the AlF6 corner sharing octahedra as a function of temperature. The Al-F-Al chains are still bent in the so-called cubic phase, but the direction of tilting of the AlF6 octahedra varies continuously during the MD run, so that the time-averaged symmetry of the system is nearly cubic. The motion of the octahedra primarily involves a 360° rotation of the vector that describes the displacement of the F atom from its ideal position in a linear Al-F-Al chain. It is this 360° motion that distinguishes the cubic from the rhombohedral phase. The high-temperature phase is also associated with increased vibrations of the Al-F-Al chains. The results provide an explanation for the large thermal parameters observed experimentally for fluorine (in structures refined from diffraction data) above the phase transition. The simulation results suggest the possible existence of a third (orthorhombic) form of α-AlF3, which is energetically very similar to the rhombohedral phase at room temperature but differs in its octahedral tilting scheme.

Collision rate constants for polarizable ions

Langevin described a model for the interaction between an ion and a neutral nearly a century ago and since then, many modifications have been introduced to adjust for specific circumstances. This work discusses the induced dipole–induced dipole interaction between an ion and a neutral without a permanent dipole and introduces an anisotropic adjustment. A point polarizable ion model (PPI) and an orientation dependent polarizable ion model (ODPI) are discussed and applied to systems where the ion is highly polarizable and the neutral is only weakly polarizable. Significant deviations from classical Langevin rate constants and significant differences between PPI and ODPI are observed.

The structure of molten AgCl revisited

We have studied the total structure of molten AgCl at 1073 K by means of two polarizable ion models via molecular dynamics simulations. The model potentials consisted of either the Vashishta–Rahman (VR) or the Born–Mayer rigid-ion potentials to which the anion-induced polarization contribution is added. Both model potentials reproduce well the main features of the structure of molten AgCl with that using the VR model potential giving marginally better results.