Interionic Pair Potentials Research Articles

Local minimum in pair potentials of polyvalent metals: A limitation of pseudopotential theory

Local minimum appearing in the interionic pair potentials, when derived from local model pseudopotential, for Al (and some other polyvalent metals) remains as a long standing problem of clear understanding of its origin, although some attempts have been made by a few authors. The origin of this feature of local minimum is systematically investigated for the first time in this paper considering both the core size and the conduction electron density as variables. Interionic pair potential is derived from Ashcroft’s empty core model because it depends on these two variables only. Results of this investigation show monovalent metals do not exhibit a local minimum at all but trivalent Al and some other polyvalent metals do exhibit at their normal densities. Here, the combined effect of the core size and the conduction electron density results whether the local minimum will appear or not. More interestingly, for smaller core size, conduction electron density plays major role and for larger core size the core radius plays the major role in determining the depth of the local minimum.

Interionic Pair Potential, hard sphere diameter and entropy of mixing of NaCd compound forming binary molten alloys under the framework of Pseudopotential theory

The observed asymmetric behaviour of mixing of NaCd liquid alloys around equiatomic composition with smaller negative values for free energy of mixing at compound forming concentration, i.e. GMXS = -4.9KJ at Ccd =0.66 has aroused our interest to undertake a theoretical investigation of this system.A simple statistical mechanical theory based on compound formation model has been used to investigate the energetics of formation of intermetallic compound Cd2Na in the melt through the study of entropy of mixing.Besides, the interionic interactions between component atoms Na and Cd of the alloys have been understood through the study of interionic pair potential фij(r), calculated from pseudopotential theory in the light of CF model.Our study of фij(r) suggest that the effective interaction between Na-Na atoms decreases on alloying with Cd atom, being minimum for compound forming alloy( Cd 0.66 Na 0.34 ).The nearest neighbor distance between Na-Na atoms does not alter on alloying. Like wise Na-Na, effective interaction between Cd-Cd atom decreases from pure state to NaCd alloys, being smaller at compound forming concentration Cd 0.66 Na 0.34.The computed values of SM from pseudopotential theory are positive at all concentrations, but the agreement between theory and experimental is not satisfactory. This might be happening due to parameterisation of σ3 and Ψcompound.

Semi-ab initio interionic potential for gadolinia-doped ceria

In the current work, a set of semi-ab initio interionic pair potentials in a concise functional form with parameters for gadolinia-doped ceria (GDC) systems is derived via the Chen–Mobius lattice inversion and ab initio quantum-chemical calculation. The quality of the proposed potentials is verified by molecular dynamics simulations of CeO 2 and A 2O 3 (A = Ce and Gd) on their static properties, doped concentrations and temperature dependence of lattice constants, mean-square displacements, pair correlation functions and elastic constants. Simulation results are consistent with corresponding experimental data, showing that the new form is valid over a wide range of interionic separations and applicable for describing structural properties of ionic solids.

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

Ab initio interionic potentials for UN by multiple lattice inversion

Based on the Chen–Möbius lattice inversion and a series of pseudopotential total-energy curves, interionic pair potentials for UN were derived. By means of molecular dynamic (MD), we have examined this interionic potentials. Comparing with the experimental data, the thermal expansion coefficient and the compressibility were well reproduced by this potentials.

Interionic pair potential and entropy of mixing of Al–Mg compound forming binary molten alloys

The observed asymmetric behaviour of mixing properties of AlMg liquid alloys around equiatomic composition with smaller negative values for excess free energy of mixing (−0.15 kJ mol −1) has aroused our interest to undertake a theoretical investigation of this system. A simple statistical mechanical theory based on compound formation model ( μA + νB ⇌ A μ B ν ) has been used to investigate the energetics of formation of intermetallic compound Al 3Mg 2 in the melt, through the steady of thermodynamic property such as entropy of mixing. Besides, the interionic interactions between component atoms (Al and Mg) of the alloy have been understood through the study of interionic pair potential ϕ ij ( r), calculated from pseudopotential theory in the light of CF model. Our study of ϕ ij ( r) suggests that the effective interaction between Al–Al atom in the pure state is found to be smaller than those obtained in Al 0.425Mg 0.575 and Al 0.625Mg 0.375 alloys. Φ Al–Al in the case of Al 0.625Mg 0.375 alloys lies in between pure state (Al) and Al 0.425Mg 0.575 .The nearest neighbour distance does not change appreciably on alloying, whereas the effective interaction between Mg–Mg atoms increase in the order Al 0.625Mg 0.375 < Al 0.425Mg 0.575 < Mg pure, being minimum in CF alloys. The computed values of S M from pseudopotential theory are positive at all concentrations, but the agreement between theory and experimental is not satisfactory. This might be happening due to parameterization of σ 3 and Ψ compound.

A molecular dynamics simulation of lithium fluoride: Volume phase and nanosized particle

The PC GAMESS package was used to obtain interionic pair potentials for lithium fluoride. A molecular dynamics simulation of the volume phase and nanosized LiF particle was performed. The temperatures of fusion and self-diffusion coefficients of the volume phase and lithium fluoride nanoparticle were found; for the volume phase, they were close to the experimental data. The temperature of fusion of a particle ∼2 A in diameter decreased by ∼600 K. The possibility of a considerable increase in ionic conductivity over the temperature range 520–1122 K was demonstrated for nanosized LiF.

The ab-initio calculation of crystal structure and lattice dynamics of perfect and defective MeX (Me+ = Rb+, K+, Na+; X-= F-, Cl-)

In this work, the interionic pair potentials X-- X-, Me+- X-(Me+ = Rb+, K+, Na+; X- = F-, Cl-) within the framework of shell model were obtained using the self consistent field Rhoothaan-Hartree-Fock approximation allowing the correlation correction in second order Moller-Plesset form. Further, nonempirical pair potentials were used for the calculations of the structure and lattice dynamics of perfect and imperfect alkali halides crystals. Impact analysis of anion vacancies influence on crystal vibrational spectrum was carried out with the help of recursive technique calculations of symmetrized and localized density of vibrational states in the perfect and vacancies including crystal.

Interionic pair potentials and partial structure factors of compound-forming quaternary NaSn liquid alloy: First principle approach

In this paper formulae for partial structure factors have been used to study partial structure factors of compound-forming quaternary liquid alloys by considering Hoshino’s m-component hard-sphere mixture, which is based on Percus-Yevic equation of Hiroike. Formulae are applied to NaSn (Na, Sn, NaSn, Na3Sn) which is considered as a quaternary liquid mixture with the formation of two compounds simultaneously. We have compared the total structure factors for ternary and quaternary alloys with experimental total structure factors which are found to be in good agreement. This suggests that, for suitable stoichiometric composition, two compounds are formed simultaneously. The hard-sphere diameters needed have been calculated using Troullier and Martins ab-initio pseudopotentials.

Atomic order and interionic pair potentials in Cu–Sn liquid alloys

A statistical mechanical theory based on compound formation (CF) model has been used to investigate the energetics of the formation of intermetallic compounds, Cu 3Sn in the melt of Cu–Sn liquid alloys through the study of concentration dependence of various thermodynamic as well as microscopic functions such as excess free energy of mixing ( G M xs ) , heat of mixing ( H M), entropy of mixing ( S M), concentration fluctuations in the long wavelength limit ( S cc(0)) and chemical short range order parameter ( α 1). Besides, the interionic interactions between component atoms (Cu and Sn) of the alloy have been understood through the study of interionic pair potentials ( ϕ i− j ( r)), calculated from pseudopotential theory in the light of CF model. Our theoretical investigation not only reproduces the concentration dependence of G M xs , H M and S M but also suggests the existence of compounds, Cu 3Sn in Cu–Sn liquid alloys at C Cu = 0.75. The maximum deviation of S cc(0) from ideal values [ S cc(0) − S cc(0, id)] and minimum negative value of α 1 around C Cu = 0.75 substantiates above findings. Our study of ϕ i− j ( r) suggests that the effective interaction between Cu–Cu atoms decreases on alloying with Sn atoms. ϕ Cu–Cu( r) for CF Cu 0.75Sn 0.25 alloy lies in between the pure state (Cu) and Cu 0.5Sn 0.5 alloy whereas the effective interaction between Sn–Sn atoms increases in the order, pure < Cu 0.5Sn 0.5 < Cu 0.75Sn 0.25; being maximum in CF alloys. The computed values of S M from pseudopotential theory are positive at all concentrations but the agreement between theory and the experiment is not satisfactory. This might be happening due to parameterization of σ 3 and ψ comp.

Electrical resistivity of NaSn compound forming liquid alloy using ab initio pseudopotentials

The electrical resistivity of the compound forming liquid alloy NaSn is studied as a function of concentration. Hard-sphere diameters of Na and Sn are obtained through the inter-ionic pair potentials evaluated using Troullier and Martins ab initio pseudopotential, which have been used to calculate partial structure factors S ( q ) . Considering the liquid alloy to be a ternary mixture, Ziman's formula for calculating the resistivity of binary liquid alloys, modified for complex formation, has been used. Form factors are calculated using ab initio pseudopotentials. The results suggest that the Ziman formalism, when used with ab initio pseudopotentials, is quite successful in explaining the electrical resistivity data of compound forming binary liquid alloys.

A theory of transport properties in molten salts

Expressions for diffusion constants in molten salts have been obtained in terms of the inter-ionic pair potentials and the pair distribution functions. Numerical attempts for diffusion constants in molten alkali halides are carried out and results agreed fairly with those obtained by molecular-dynamics simulation and with some experimental data. Based on the coupling of generalized Langevin equation and damped Einstein oscillator equation, ions' velocity autocorrelation functions have also been described and are numerically applied for molten potassium fluoride. The deviation from the Nernst-Einstein relation was also discussed in detail. In Appendixes A x B x C, the short-time expansion of velocity correlation functions in relation to the partial conductivities and the diffusion constants were obtained up to the term of t(4) and these were compared with a model function described by the form of cos(omegat)sech(ttau).

Electrical resistivity of NaPb compound-forming liquid alloy using abinitio pseudopotentials

The study of electrical resistivity of compound-forming liquid alloy, NaPb, is presented as a function of concentration. Hard sphere diameters of Na and Pb are obtained through the interionic pair potentials evaluated using Troullier and Martinsab initio pseudopotential, which have been used to calculate the partial structure factors S(q). Considering the liquid alloy to be a ternary mixture, Ziman formula, modified for complex formation has been used for calculating resistivity of binary liquid alloys. Form factors are calculated usingab initio pseudopotentials. The results suggest that Ziman formalism, when used withab initio pseudopotentials, are quite successful in explaining the electrical resistivity data of compound-forming binary liquid alloys.

Model development and analysis of temperature-dependent lithium sputtering and sputtered Li+ transport for tokamak plasma-facing applications

We developed and applied models for overall (atom+ion) sputtering and sputtered Li+ transport of liquid lithium tokamak divertor surfaces. The model/analysis has four parts: (1) a temperature-dependent data-calibrated empirical/code (TRIM) model of lithium sputtering by D+ and Li+ as a function of incident particle energy and angle; (2) temperature and energy-dependent molecular dynamics (MolDyn) modeling using an effective interionic pair potential of surface-reflected redeposited Li+; (3) analytical model of reflected lithium charge state; and (4) analytic model of Li+ near-surface emission/redeposition cascade. We predict: (1) strong temperature dependence of sputter yields, (2) reflection coefficients of order 50% (thermal energies) and 10% (hyperthermal energies), (3) reflected lithium charge fractions of 10–30% near 1eV incidence, and (4) enhanced but non-runaway Li emission for the studied surface temperature range between 473 and 653K.

Molecular Prototypes for Simple SiO2 Potentials

A popular class of interionic pair potentials for simulation of the properties of condensed-phase SiO 2 uses two calibrations: first-principles electronic structure results for a small cluster and experimental crystallinedata. The clusters are argued to be broadly valid prototypes for the local structural and bonding behavior of condensed-phase SiO 2 . This approach introduces an issue: the extent to which there is prototypical computed behavior for small silicates irrespective of cluster size, symmetry constraints, methodological refinement, and accuracy of implementation (basis set). By extension, the issue of commonality vs diversity in small silicates arises. We address those issues by comparative study of 12 systems containing one or two Si atoms in combination with H, O, and bare protons. We use several different levels of theoretical refinement and various basis sets. Though some chemical trends are clear, there is no clear single prototype for condensed-phase SiO 2 (including no clear preference to tetrahedral symmetry). We find a wide diversity of bond lengths, bond angles, and interaction energies and significant methodological consequences that go largely ignored in the potential-fitting literature.

Ab initio interionic potentials for CaO by multiple lattice inversion

Using Chen–Möbius inversion, we derive the interionic pair potentials from pseudopotential total-energy curves of the CaO crystals in B1, B3 and two P4/mmm virtual structures. Based on these potentials, the static properties of CaO in the rocksalt phase are calculated. Moreover, the phase stability of B1–CaO has been described by the energy minimizations from the disordered to the ordered states. Furthermore, the pressure-induced phase transition, phonon dispersion curves and properties of (CaO) n clusters have also been investigated. Compared with experimental data, most of our results indicate that the present calculated potentials are effective for studying properties of CaO ionic crystal.

Representation of the nonideality of electrolyte solutions using the cluster expansion theory

An explicit model for electrolyte solutions has been developed in terms of the cluster expansion theory, with which the osmotic coefficient and activity coefficient in the dilute concentration range can be predicted using the Pauling ionic diameter. In this model, the electrolyte solution is modeled as an ion gas immersed in a dielectric continuum, and the ion is represented as a charged hard sphere. Based on the Debye–Hückel theory, the effects of solvent and mean field of surrounding ions have been considered by virtue of an effective interionic pair potential. The applicability of the model as well as the effective pair potential adopted have been tested on a HBr solution and fourteen 1:1 haloid electrolyte solutions. The results suggest that the cluster expansion theory with incorporated effective pair potential can qualitatively predict the activity and osmotic coefficient of electrolyte solutions.

Atomistic simulations of B1–B2 phase transition in KCl based on inversion pair potentials

Based on the Chen–Möbius lattice inversion, interionic pair potentials are derived from the pseudopotential total energies of KCl in B1, B2, B3 and one tetragonal structures. In terms of inversion potentials, four different transition pathways have been presented to describe the B1–B2 phase transition by using unit cells with different symmetric restrictions and sizes. Although the intermediate states are obviously different along the four pathways, the simulations indicate that the essence of phase transition is reflected by a Buerger mechanism. With more independent variables than the Buerger and WTM mechanisms, the present potentials predict that the transition path is formed by a series of states with different subgroup symmetries between Fm 3 ̄ m and Pm 3 ̄ m . This indicates that fewer symmetry restrictions will introduce intermediate structures with low symmetry along the transition path. One of the predicted intermediate structures is in good agreement with that found in the B1–B2 phase transition of AgCl. The exhibited transition characters also indicate that the present inversion pair potentials are appropriate in exploring the B1–B2 phase transition in KCl crystal.

Determination of the B1-B2 transition path in RbCl by Möbius pair potentials

Using Chen-Möbius lattice inversion, we derive the interionic pair potentials from pseudopotential total-energy curves of the RbCl polymorph. Based on the potentials, the B1-B2 transition pathways have been analysed by calculating the activation energy and saddle point at transition pressure. The intermediate structures along the transition path were obtained within the different symmetric restrictions. By comparing the four pathways under the different restricted conditions, the intermediate structures with space groups Cmcm and P2 1 / m were predicted to explain the B1-B2 phase transition in RbCl.

Energies and stabilities of sodium chloride clusters based on inversion pair potentials

Based on the Chen–Möbius inversion, the interionic pair potentials are derived from the pseudopotential total energies of NaCl crystals in B1, B3, and two P4/mmm structures. Based on the pair potentials, the geometries and binding energies of the most stable neutral and charged clusters have been obtained by the energy minimizations. The cluster relative stability has also been discussed by analyzing the binding energies and the energies required to remove one NaCl molecule from clusters. The results show the good agreement with the calculations by previous empirical potentials and ab initio method. This indicates that the present inversion interionic pair potentials are valid over a fair wide range to cover both neutral and charged sodium chloride clusters ( NaCl) n, Na n Cl n−1 + and (NaCl) n Cl −.