V.I. Zubov

Calculations of the thermal expansion, cohesive energy and thermodynamic stability of a Van der Waals crystal - fullerene C60

The temperature dependence of the intermolecular distance and the cohesive energy in the high-temperature modification of C60 solid fullerene was studied on basis of the correlative method of unsymmetrized self-consistent field. The central intermolecular potential of Girifalco and its approximation by Yakub were used. We conclude about the decisive role of anharmonic effects at high temperatures. The discrepancy between the calculated and experimental values of intermolecular distance does not exceed 0.8% on the whole temperature interval. The temperature of loss of thermodynamic stability was obtained (≈ 1915 K) and a possible melting temperature was estimated (≈ 1400 K).

Statistical-mechanical investigation of the saturated vapor pressure, the enthalpy of sublimation and thermodynamic stability of the fcc phase of the C70 fullerite

Abstract Using the correlative method of the unsymmetrized self-consistent field for strongly anharmonic crystals and the virial expansion for a gas we have calculated the temperature dependence of the saturated vapor pressure P sat and the enthalpy of sublimation ΔH sub for the FCC modification of the fullerite C 70 . The potential of Verheijen et al. [ Science , 1992, 166 , 287] with parameters calculated on the basis of theoretical estimates by Pan et al . [ J. Phys. Chem ., 1991, 95 , 2944] and experimental data of Baker et al. [ Chem. Phys. Lett. , 1991, 184 , 182] and Vaughan et al. [ Science , 1991, 254 , 1350] have been utilized for the intermolecular forces. The temperature of loss of stability has been estimated for the two-phase crystal-vapor system. A comparison has been made between the results obtained with different sets of parameters and the values calculated earlier for the C 60 . The correspondence with available experimental data is satisfactory. Over the whole range of temperatures studied the dependence of the logarithm of the vapor pressure on the inverse of the temperature is close to linear: log P sat ≈ A − B T − CT , while ΔH sub decreases about 20%. Using the scaling law an estimate of the triple point parameters is given for the C 70 : T tr ≈ 1500 K, P tr ≈ 655 torr.

Intermolecular correlations and mean square relative displacements in C60 fullerite

We study molecular properties of the high-temperature modification of fullerites. In the present work we calculate the intermolecular correlations and the mean square relative displacements in C 60 . The Girifalco intermolecular potential is utilized. The calculations have been made in the whole interval from the equilibrium point with orientationally ordered phase up to the spinodal temperature. To take into account the lattice anharmonicity we use the correlative method of unsymmetrized sell-consistent field. Its second order allows one to investigate correlations in fcc lattice between the nearest, second, third and fourth neighbors. The anharmonicity has strong effect on the intermolecular correlations at T > 700 K, causing their drastic rise near the spinodal point. The dependence of the correlation moments on the distance between molecules and on the crystallographic direction is considered. We compare our results with those for solid Ar and discuss the influence of a special feature of the interaction potentials on the intermolecular correlations and the mean square molecular displacements.

Thermal and elastic properties of solid sodium based on an effective interionic potential

Basing on the Schiff effective interionic potential which has oscillatory character we have calculated a complete set of equilibrium thermodynamic properties of solid sodium at normal pressure above the martensitic transition temperature. To take into account the anharmonicity which is strong at high temperatures we use the correlative method of unsymmetrized self-consistent field elaborated previously. Our results are in agreement with measured values and with available data of computer simulations. We discuss the thermodynamic stability of the b.c.c. lattice of sodium and the mechanism of its loss. The metastability of a hypothetical f.c.c. lattice with Schiff potential is discussed.

Isotherms, thermodynamic properties and stability of the FCC phase of the C60 fullerite: A theoretical study

We are pursuing statistical-mechanical investigations of thermodynamic properties of the high-temperature modification of the C60 fullerite taking into account the intramolecular degrees of freedom and the strong anharmonicity of lattice vibrations. In our theoretical calculations we employed the correlative method of an unsymmetrized self-consistent field for strongly anharmonic crystals using the available experimental information about the vibrational spectrum of this molecule. The Girifalco potential and the Yakub approximation are used. In the present work we have calculated isotherms of this fullerite and a complete set of its equilibrium properties, including the components of the elastic tensors. Each isotherm has two branches V1(P) 0, while at the right one, BT(P, V2) < 0; the latter represents the absolute instability of the states V2(P). We have also investigated the thermodynamic stability of this fullerite and the mechanism of loss of stability depending on the temperature. Our results for thermal and elastic properties are in good agreement with experimental data available at low pressures and temperatures.

On the Limit of the Thermodynamic Stability of Superheated Crystals and Mechanisms of Its Loss

Using the correlative method of unsymmetrized self-consistent field for strongly anharmonic crystals, the thermodynamic stability and the mechanism its loss is studied for crystals with various types of the chemical bond. The following interaction potentials are utilized: the Lennard-Jones pairwise potential together with Axilrod - Teller three-body one for simple van der Waals crystals (solid Ar), effective interionic pairwise potential proposed by Schiff for a metal (Na) and the Girifalco potential for fullerites (C60). In the first and third cases, the FCC lattice becomes unstable because the isothermal bulk modulus BT becomes zero. For fullerites, the shearing coefficient C44 goes to zero as well. Solid Na losses its stability when other shearing coefficient CT11 - CT12 becomes zero.Using the correlative method of unsymmetrized self-consistent field for strongly anharmonic crystals, the thermodynamic stability and the mechanisms of its loss is studied for crystals with various types of the chemical bond. The following interaction potentials are utilized: the Lennard-Jones pairwise potential together with the Axilrod-Teller three-body one for simple van der Waals crystals (solid Ar), the effective interionic pairwise potential proposed by Schiff for a metal (Na) [Phys. Rev. 186, 151 (1969)] and the Girifalco potential for fullerites (C 60 ) [J. Phys. Chem. 96, 858 (1992)]. In the first and third cases, the fcc lattice becomes unstable because the isothermal bulk modulus B T → 0. For fullerites, the shearing coefficient C 44 goes to zero as well. Solid Na loses its stability when the other shearing coefficient C T 11 - C T 12 becomes zero.

SELF-CONSISTENT THEORY OF ELASTIC PROPERTIES OF STRONGLY ANHARMONIC CRYSTALS II: PROPERTIES OF HEAVY RARE GAS SOLIDS

The method developed in the preceding papers has been used to calculate the full set of equilibrium thermodynamic properties of solid Ar, Kr and Xe at normal pressure. We have used various pairwise interatomic potentials taking into account the three-body Axilrod–Teller forces. For Ar and Kr the multiparameter potentials proposed by Barker et al. provide the best fit to available experimental data, and for Xe the old Lennard–Jones potential does this. Deviations from the Cauchy relations are discussed. Temperature dependencies of the stability coefficients and anisotropy have received much attention. In the unstable point that is about 1.35–1.45 times larger than the experimental melting temperature of each crystal, the isothermal bulk modulus goes to zero (and the thermal expansion coefficient and the isobaric specific heat tend to infinity). Other stability coefficients remain finite and positive.

SELF-CONSISTENT THEORY OF ELASTIC PROPERTIES OF STRONGLY ANHARMONIC CRYSTALS I: GENERAL TREATMENT AND COMPARISON WITH COMPUTER SIMULATIONS AND EXPERIMENT FOR FCC CRYSTALS

Based on the correlative method of an unsymmetrized self-consistent field,16–23 we have derived expressions for elastic constant tensors of strongly anharmonic crystals of cubic symmetry. Each isothermal elastic constant consists of four terms. The first one is the zeroth approximation containing the main anharmonicity (up to the fourth order). The second term is the quantum correction. It is important at temperatures below the De-bye characteristic temperature. Finally, the third and fourth terms are the perturbation theory corrections which take into account the influence of the correlations in atomic displacements from the lattice points and that of the high-order anharmonicity respectively. These corrections appear to be small up to the melting temperatures. It is sufficient for a personal computer to perform all our calculations with just a little computer time. A comparison with certain Monte Carlo simulations and with experimental data for Ar and Kr is made. For the most part, our results are between. The quasi-harmonic approximation fails at high temperatures, confirming once again the crucial role of strong anharmonicity.

ON THE DYNAMICAL PROPETIES OF A STRONGLY ANHARMONIC FACE-CENTERED CUBIC CRYSTAL

We study the interatomic correlations and mean square relative displacements (MSRD) in anharmonic crystals on the basis of the correlative method of unsymmetrized self-consistent field (CUSF). Here we present general formulae for crystals with the anharmonicity, including the strong one, up to the fourth anharmonic terms and perform calculations of the quadratic correlation moments (QCM) in a crystal with face centered cubic lattice, namely in solid Ar. The second order of CUSF allows one to investigate correlations in this lattice between the nearest, second, third and fourth neighbors. The anharmonicity was demonstrated to have strong effect on the interatomic correlations at temperatures above 0.4 of the melting temperature causing a drastic rise near the spinodal point. The dependence of QCM on the distance between atoms and on the crystallographic direction is discussed.

Statistical mechanical study of thermodynamic properties of a family of fullerites from C36 to C96 in the equilibrium with their vapors

Abstract The temperature dependence of saturated vapor pressure of fullerites C36–C96 and their thermodynamic properties along with the sublimation curves up to the spinodal are calculated. The saturated vapor pressures along all the range of temperatures are approximated by logP sat = A − (B/T) − CT. The coefficient A practically does not depend on the number of atoms in the molecule (varying only by 2.2%), B increases noticeably while C decreases from the C36 to the C96, both of them by approximately two. The isothermal bulk modulus B T and the shear modulus C44 vanish at the spinodal points.