S. V. Titov

Temperature dependence of the heat capacity and times of the establishment of vacancy equilibrium in simple crystals

The concentration range of vacancies that affect the temperature dependence of the heat capacity at constant volume Cv has been determined. The times of the establishment of vacancy equilibrium in spherical samples of simple crystals with different radii due to the thermal motion of atoms have been calculated for the process as close as possible to the equilibrium one with a decrease in the temperature from the melting point to the current value T. The free energy of an imperfect crystal has been determined taking into account contributions from interatomic interactions in terms of the Lennard-Jones potential functions and vibrational energies. The properties of an imperfect crystal have been calculated within the Lifshitz approximation linear in the density of vacancies with the frequency distribution function of the perfect crystal with the corresponding corrections, which reflect local vibrations of atoms around vacancies. The free energy of a defect-free perfect crystal has been determined from the calculated frequencies of normal vibrations with the inclusion of up to four nearest neighbors. It has been shown that disregard of acoustic (out-of-phase) parts of the spectrum in the calculation of the heat capacity Cv with increasing temperature leads to a decrease (increase) in Cv from the values calculated for the total vibrational spectrum. A nonequilibrium state of the imperfect crystal can lead to negative values of the heat capacity at constant volume.

Characteristics of atomic vibrational motion in a one-component defective crystal

Vibrations of atoms in a defective argon crystal are considered. Frequencies are calculated in the harmonic approximation and Mie and Einstein approximations. The vibrations are calculated for a set of local clusters differing in the position of a vacancy at different distances from a selected atom. Probabilities for these clusters are calculated within a quasichemical approximation of the lattice gas model. It is shown that when combined contributions from lateral interactions and vibrational motions are allowed for in the free crystal energy, there is an increase in the lattice constant upon a rise in temperature in all approximations. It is found that the frequencies calculated using the Mie model become closer to the frequency distribution in the harmonic approximation as the degree of crystal defectiveness increases.

Role of local environment relaxation in calculating the rates of elementary processes in vapor-liquid systems

The role of local environment relaxation is studied in calculating the rates of elementary processes in vapor-liquid systems consisting of dipole molecules. It is accepted that the intermolecular interaction potential of reaction system components includes dipole-dipole and Lennard-Jones terms. Two limiting cases of short and long characteristic times of an elementary reaction are considered relative to the thermal progressive and rotational motions of neighboring dipole molecules. It is shown that the condition of long characteristic times for elementary reactions that correspond to the concept of activated complex activity distorts the properties of a system. Good correspondence is obtained for the temperature dependence of the water self-diffusion coefficient.

Calculating the effect of vacancies on the thermodynamic functions and frequencies of normal vibrations of a Lennard-Jones monoatomic crystal

Four main functions of a Lennard-Jones defect argon crystal with an FCC lattice are considered in the context of the lattice gas model: Helmholtz free energy, entropy, internal energy, and heat capacity at a constant volume (allowing for normal vibrations of a solid). Properties of the defect crystal are calculated from the distribution function of the frequencies of an ideal crystal, and corrections to it that reflect local atomic vibrations around vacancies, in the context of the Lifshits linear approximation according to vacancy density. To find the free energy of a defect-free ideal crystal, frequencies of normal vibrations of the crystal are calculated with allowance for the interactions of the four nearest neighbors. The nonlocality of the chemical potentials of the atoms of a solid is discussed, and the influence of contributions from various segments of the vibrational spectrum to the values of thermodynamic functions is investigated. It is shown that ignoring the acoustic or antiphase segments of the spectrum when calculating the free energy leads to increasing of its deviation from the one calculated using the full vibrational spectrum with an increase in temperature. It is concluded that the nonequilibrium state of the defect crystal can lead to negative values of heat capacity at a constant volume.

A molecular model of water based on the lattice gas model

A lattice gas model is used to describe the vapor-liquid state of water molecules. The orientationally directed interaction of the water molecules via their tetrahedral structure and dipole-dipole interaction are considered in the theory, along with the Lennard-Jones contributions to the potential of molecular interaction, which stabilize the system with dipole interaction. We studied how the radius of the molecular interaction potential affects the equilibrium characteristics of the system (the phase separation curves of the vapor-liquid system, and the relationship between the fluid density and the chemical potential value).

Lennard-Jones crystal: Complete vibrational spectrum, its local approximation, and thermodynamic functions

Different methods of taking into account the vibrational partition function in Helmholtz free energy for imperfect crystals of inert gases are compared. These methods are based on the complete vibrational spectrum of the fcc lattice or on few local frequencies. Thermodynamic properties of the Lennard- Jones crystal are considered in the framework of the lattice gas model with the potential interaction in the quasi-chemical approximation. In frequency calculations in the quasi-dimeric model, the role of local averaging, which leads to a threefold degeneracy of the vibrational contribution, is compared to the role of the direct diagonalization of the matrix of the second derivatives of potential energy in an imperfect cluster. The effects of different vibrational contributions on internal energy, entropy, and heat capacity at constant volume are considered as a function of temperature. The results of calculating thermal expansion in a vacuum for four inert gas crystals are compared with experimental data.

Role of local environment relaxation in calculating the reaction rates for nonideal reaction systems

An analysis of the equations for the rates of elementary stages in nonideal reaction systems demonstrates that the traditional notion of existence of the chemical potential of the activated complex in dense phases is inconsistent with the actual times of molecular motions and with the procedure of statistical averaging of the molecular distributions. Expressions relating the rate constants of elementary chemical reactions for experiments at atmospheric pressure and under supercritical conditions are derived.

Estimating the sizes of small single crystals satisfying the Wolf theorem

Geometric estimates of the characteristic sizes of simple single crystals with tetragonal, cubic, and octahedral shapes of the surface are obtained. The Wolf theorem with independent contributions from each face to the surface tension can be applied to these if the edge size is at least ~53 lattice constants. Energy estimates of the individuality of free energy contributions from each face are consistent with this estimate. The resulting minimum edge sizes also agree with an independent estimate obtained earlier using the contributions from fluctuations in the near-surface region of the phase.

Thermodynamic properties of water in the lattice gas model with сonsideration of the vibrational motions of molecules

A molecular model developed earlier for a polar fluid within the lattice gas model is supplemented by considering the vibrational motions of molecules using water as an example. A combination of point dipole and Lennard-Jones potentials from SPC parametrization is chosen as the force field model for the molecule. The main thermodynamic properties of liquid water (density, internal energy, and entropy) are studied as functions of temperature. There is qualitative agreement between the calculation results and the experimental data. Ways of refining the molecular theory are discussed.

Equilibrium density fluctuations and the rate of a Langmuir-Hinshelwood type reaction on microcrystal particles

We investigate the effect of restricting the area of planes of microcrystals and equilibrium density fluctuations in components of binary mixtures on partial isotherms of the adsorption of binary mixtures of molecules and the rate of a surface reaction of the Langmuir-Hinshelwood type. Adsorption of components of mixture is considered in a large canonical assembly, and the rate of an elementary step is calculated in kinetic regime. The value of a section of the surface on a plane contains a number of adsorption centers in the range of 10 to 105. The effect of the structure of a heterogeneous surface on the rate of the considered reaction is studied. The effect of the density fluctuations of adsorbed molecules on partial adsorption isotherms and fluctuations in the rate of reaction on heterogeneous surfaces is discussed. It is shown that the greatest effect of density fluctuations on the rate of a step is observed at low fillings of each plane of a particle and at the almost complete filling of a plane.