Maria C. Abramo

Ionic radii and diffraction patterns of molten alkali halides

The mean spherical approximation for a fluid of charged hard spheres of different radii is applied to the evaluation of diffraction patterns for the whole family of molten alkali halides. The ionic radii entering the model are determined from the liquid‐state compressibility. The liquid‐state radii are shown to be characteristic temperature‐dependent lengths for each ion through the family of salts, and a good one‐parameter fit of the whole set of compressibilities at each temperature is obtained through the assumption that the radius ratios are those for basic radii yielded by the Born–Mayer theory of alkali halide crystals. The analysis also provides new evidence against the older sets of crystal ionic radii. Calculations of partial structure factors and of x‐ray diffraction patterns are then reported for all the salts and compared with the results of x‐ray and neutron diffraction experiments wherever possible. The model emerges as having semiquantitative value in the prediction of x‐ray diffraction fro...

Equilibrium properties of charged hard spheres of different diameters in the electrolyte solution regime: Monte Carlo and integral equation results

Extensive Monte Carlo (MC) and integral equation calculations of thermodynamic and structural properties for the 1‐1 aqueous electrolyte regime of the primitive model are reported. The salt concentration covers the range 0.1–2 M. The ratio of the radii of the two ionic species α covers the range 0.1–0.8. The MC results are compared to the results of the HNC, MSA, and EXP approximations. The excess internal energies calculated in the HNC are found to be in good agreement with the MC values. In the MSA the energy turns out to be too high for large α and too small for small α. For α=0.4 the MSA value is accurate as compared to the simulation. Similar remarks hold for the osmotic coefficient. The radial distribution functions (RDF) calculated in the EXP approximation agree fairly well with the MC results at all molarities and radius ratios investigated, except for α=0.1, where the agreement is only qualitative. The MSA yields RDF which are in qualitative agreement with the MC only at high concentrations and f...

Structural properties and medium‐range order in calcium‐metasilicate (CaSiO3) glass: A molecular dynamics study

Structural properties and medium‐range order (MRO) in calcium metasilicate (CaSiO3) glass are investigated at different concentrations of calcium oxide through the molecular dynamics technique. Calculations are based on the Born–Mayer–Huggins potential, and show that the experimental Ca–Ca partial structure factor, which documents the existence in the glass of Ca MRO, can qualitatively be reproduced within such a model. The characteristics of Ca MRO are then examined in the context of the overall structure of the system. At equimolar concentrations of CaO and SiO2, the simulation evidentiates the formation in the glass of clusters of CaO6 octahedra in which Ca ions are roughly lying on a plane, in a configuration that closely resembles the one of crystalline CaSiO3. On the other hand, the ‘network’ structure and MRO of pure SiO2 glass appear sensibly affected by the presence of Ca ions, with considerable loose of connectivity between SiO4 tetrahedral units, and reduction of the first sharp diffraction pea...

Solution and thermodynamic consistency of the GMSA for hard sphere mixtures

The explicit numerical solution of the Generalized Mean Spherical Approximation (GMSA) for a two-component hard sphere mixture is obtained by employing an iterative procedure which starts from the known analytic Percus-Yevick (PY) result. The parameters which enter the theory are fitted to a set of thermodynamic data generated from parametrized forms of computer simulation results, so as to ensure the thermodynamic consistency of the theory. The radial distribution functions so obtained compare very favourably with the available Monte Carlo results, and systematically improve on the PY gij (r). A possible scheme for obtaining the thermodynamic consistency without having recourse to external data sources is also proposed. The q → 0 limit of the concentration-concentration structure factor S cc(q) is also investigated, this allowing a better understanding of the role played by the diameter ratio, R, and the concentration of the two species, in the enhancement or reduction of disorder in the mixture, especia...

MSA and GMSA for charged hard spheres of different diameters: Comparison with RHNC and MC calculationsa)

The excess internal energies and the radial distribution functions of systems of charged hard spheres with two species of different diameters are calculated by using the mean spherical approximation (MSA) and the generalized mean spherical approximation (GMSA). The results obtained are compared with reference hypernetted chain (RHNC) and Monte Carlo (MC) calculations performed by other authors. The MSA estimates of the excess internal energies are often very close to the computer simulation values. The MSA radial distribution functions, on the whole, compare qualitatively well with the MC gij(r), being less satisfactory when the difference in the diameters of the particles is large. The GMSA appears to improve in a systematic manner over the MSA and, when the whole range of the physical situations investigated in this paper is considered, the agreement of this theory with the MC simulation can be considered very good. Similar remarks apply to the RHNC, so that it is possible to conclude that the GMSA and ...

Radius-ratio effects in the structure of fluids of charged hard spheres

The mean spherical model for a binary fluid of charged hard spheres with arbitrary radii has been solved numerically. The results are used to illustrate several aspects of the dependence of the structure of an ionic liquid on the relative sizes of the ionic components.

Free energy determination of phase coexistence in model C60: A comprehensive Monte Carlo study

The free energy of the solid and fluid phases of the Girifalco C60 model are determined through extensive Monte Carlo simulations. In this model the molecules interact through a spherical pair potential, characterized by a narrow and attractive well, adjacent to a harshly repulsive core. We have used the Widom test particle method and a mapping from an Einstein crystal in order to estimate the absolute free energy in the fluid and solid phases, respectively; we have then determined the free energy along several isotherms, and the whole phase diagram, by means of standard thermodynamic integrations. The dependence of the simulation’s results on the size of the sample is also monitored in a number of cases. We highlight how the interplay between the liquid–vapor and the liquid–solid coexistence conditions determines the existence of a narrow liquid pocket in the phase diagram, whose stability is assessed and confirmed in agreement with previous studies. In particular, the critical temperature follows closel...

Dynamic structure factors and neutron scattering in molten salts

A simple form for the partial dynamic structure factors in a molten binary salt, based on Moris memory function formalism and satisfying the usual moment sum rules, is proposed and applied in numerical calculations for a rigid-ion model of molten sodium chloride. Suitable linear combinations of the partial density fluctuations, having the character of acoustic- and optic-type collective motions at long wavelength and of independent particle behaviour of the two components at short wavelength and of independent particle behaviour of the two components at short wavelength, lead to an approximate diagonalization of the matrix of dynamic structure factors. The corresponding longitudinal current spectra, at any given wavevector, peak at different frequencies even though no well defined structure corresponding to optic-type motions would be present in the neutron scattering spectrum for wavevectors q>or approximately=1AA-1.

Determination of the critical consolution point of a Lennard-Jones mixture through a thermodynamically self-consistent structural theory

Abstract We show that a structural theory of fluids embodying a thermodynamic consistency constraint can be solved up to extremely near the “critical” consolution point of a Lennard-Jones liquid mixture. The predicted thermodynamic quantities are in close agreement with molecular dynamics (MD) simulation data. The MD experiments also signal incipient segregation of the mixture in the thermodynamic region where the theoretically estimated concentration fluctuation correlations tend to diverge; the “critical” temperature is then accurately determined from the theory. Comparison with other structural liquid state theories, and a preliminary determination of the critical exponent γ, are also reported.

On the determination of phase boundaries via thermodynamic integration across coexistence regions

Specialized Monte Carlo methods are nowadays routinely employed, in combination with thermodynamic integration (TI), to locate phase boundaries of classical many-particle systems. This is especially useful for the fluid-solid transition, where a critical point does not exist and both phases may notoriously go deeply metastable. Using the Lennard-Jones model for demonstration, we hereby investigate on the alternate possibility of tracing reasonably accurate transition lines directly by integrating the pressure equation of state computed in a canonical-ensemble simulation with local moves. The recourse to this method would become a necessity when the stable crystal structure is not known. We show that, rather counterintuitively, metastability problems can be alleviated by reducing (rather than increasing) the size of the system. In particular, the location of liquid-vapor coexistence can exactly be predicted by just TI. On the contrary, TI badly fails in the solid-liquid region, where a better assessment (to within 10% accuracy) of the coexistence pressure can be made by following the expansion, until melting, of the defective solid which has previously emerged from the decay of the metastable liquid.Specialized Monte Carlo methods are nowadays routinely employed, in combination with thermodynamic integration (TI), to locate phase boundaries of classical many-particle systems. This is especially useful for the fluid-solid transition, where a critical point does not exist and both phases may notoriously go deeply metastable. Using the Lennard-Jones model for demonstration, we hereby investigate on the alternate possibility of tracing reasonably accurate transition lines directly by integrating the pressure equation of state computed in a canonical-ensemble simulation with local moves. The recourse to this method would become a necessity when the stable crystal structure is not known. We show that, rather counterintuitively, metastability problems can be alleviated by reducing (rather than increasing) the size of the system. In particular, the location of liquid-vapor coexistence can exactly be predicted by just TI. On the contrary, TI badly fails in the solid-liquid region, where a better assessment (to within 10% accuracy) of the coexistence pressure can be made by following the expansion, until melting, of the defective solid which has previously emerged from the decay of the metastable liquid.