A. V. Trefilov

Structure, elastic moduli, and thermodynamics of sodium and potassium at ultrahigh pressures

The equations of state at room temperature as well as the energies of crystal structures up to pressures exceeding 100 GPa are calculated for Na and K . It is shown that the allowance for generalized gradient corrections (GGA) in the density functional method provides a precision description of the equation of state for Na, which can be used for the calibration of pressure scale. It is established that the close-packed structures and BCC structure are not energetically advantageous at high enough compressions. Sharply non-monotonous pressure dependences of elastic moduli for Na and K are predicted and melting temperatures at high pressures are estimated from various melting criteria. The phase diagram of K is calculated and found to be in good agreement with experiment.

Inter-ionic potentials and structure factors in liquid alkali metals

The inter-ionic potentials phi (r) in the alkali metals and the possibilities of estimating them from data on the structure factors S(k) are discussed. The dependences of phi (r) on the density and on the form of the pseudopotential model used are investigated. The structure factor is calculated in the Percus-Yevick (PY) approximation which has been shown previously to describe the region of the main peak of S(k) very accurately. phi (r) and S(k) are found to be rather sensitive to the choice of the pseudopotential and the approximation for screening. The form of S(k) is determined primarily by the effective packing fraction, i.e. by the ratio of the effective volume of the repulsive core of phi (r) to the atomic volume, and is less sensitive to variations of the attractive part of phi (r). Potentials phi (r) are presented corresponding to the pseudopotential model discussed earlier which gives a very accurate description of all the atomic properties of solid alkali metals. The S(k) calculated with these phi (r) are shown to be in good agreement with the available data for liquid alkali metals over wide ranges of temperatures and densities.

An experimental and theoretical study of martensitic phase transitions in Li and Na under pressure

By using the methods of acoustic emission and neutron-structure analysis, the effect of pressure p on low-temperature phase transitions in Li and Na is investigated. In Li, within the investigated interval of p <or approximately=3 GPa, the transition temperature rises with pressure, and the low-temperature phase has a 9R structure. In Na, on the contrary, pressure suppresses the transition, so that it disappears even at p=0.1-0.2 GPa but the 9R phase is the low-temperature one too. The shape of acoustic emission signals suggests the presence of pretransition phenomena and differences in the kinetics of transitions in Li and Na. Calculations performed explain the difference in the influence of pressure on structural stability of Li and Na by the effect of proximity of the Fermi level to peaks in the electronic density of states, which appears under pressure in Li but is absent from Na. The same effects account for a premartensitic softening of the shear constant, observed under compression of Li.

The effect of proximity of the Fermi level to singularities in the electron state density on elastic and thermodynamic properties of metals and alloys

The authors investigate the effect of the proximity of the Fermi surface (FS) to a singularity in the electron state density on atomic properties of a nearly free-electron metal. Expressions for thermodynamic potentials in the improved version of the pseudopotential perturbation theory are given which generalise the conventional formulae to the case of small distances eta between the FS and the Brillouin zone (BZ) face and also take into account the Fermi liquid interaction effects. The case of the FS proximity to the BZ edge is also considered. The character of the eta dependence of atomic properties is illustrated by model calculations for disordered Li1-xMgx alloys in the BCC, FCC and HCP structures. They calculate the concentration dependencies of the elastic constants cik and their volume derivatives delta cik/ delta u, the low-temperature phonon and electron contributions to the specific heat Cv and to the thermal expansion coefficient beta T, and the equilibrium lattice parameters. All the quantities have peculiar anomalies at small eta which can be rather large, especially in delta cik/ delta u and beta T. The results are compared with the available experimental data.

On the accuracy of the liquid theory approximate methods for the description of liquid metal thermodynamics

The accuracy of the various liquid theory methods for calculating the thermodynamic properties of liquid metals is investigated. The calculations have been made for liquid Na, Rb, Mg and Al over wide ranges of temperature T and density n using (i) the variational method and hard-sphere reference system (the HSV method), (ii) the Barker-Henderson (BH) method, (iii) the Weeks-Chandler-Andersen (WCA) method and (iv) the expressions for energy and pressure in terms of the radial distribution function found in the Percus-Yevick approximation (the PYEP method). The results of the calculations are compared with each other and with experiment. The pseudopotential model is used which describes all the atomic properties of the alkali metals to a high precision, those of Mg rather well, and of Al fairly well. It has been shown that the simple HSV approximation suitable for a semi-quantitative description of the liquid metal properties is insufficient for quantitative calculations of differential characteristics, such as melting temperatures, entropies of fusion, entropies of liquid alloy mixing, etc. The PYEP and BH methods allow the authors to calculate some thermodynamic potentials rather precisely but the computational difficulties prevent them from being used for calculating other thermodynamic properties. The WCA method has been found to combine high accuracy with sufficient simplicity of calculations and seems, therefore, to be the most promising one for quantitative calculations of liquid metal thermodynamics. They also discuss the problems of applicability of the methods considered at various T and n (particularly in the vicinity of the critical point), of the dependence of their accuracy on the metal valency and the sensitivity of the results to the type of pseudopotential model used.

Peculiarities of phonon spectra and lattice heat capacity in Ir aned Rh

Abstract A simple pseudopotential model is proposed, which allows the phonon spectra and temperature dependences of the lattice heat capacity of Ir and Rh to be described with a sufficiently high accuracy. A careful comparison of the calculated and experimental values of the lattice heat capacity is carried out, with the procedure of the identification of the phonon contribution to the heat capacity and the determination of the characteristics (momenta) of the phonon density of states from the experimental values of the total heat capacity of a metal at a constant pressure being described in detail. The results of the theoretical calculations explain, in particular, such peculiar feature of Ir and Rh, unusual for cubic metals, as a sharp (by a factor of more than 1.5) decrease in the effective Debye temperature with increasing temperature. The temperature dependence of the mean square amplitude of atomic displacements in Ir and Rh has been calculated. On the basis of the band calculations the manifestatio...

Phonon spectra, interatomic interaction potentials and simulation of lattice defects in iridium and rhodium

Abstract The method of inelastic neutron scattering has been used to measure the frequencies of the transverse branch of phonons in Ir in the (001) and (110) directions. The results obtained are used to fit the interatomic interaction potential φ(r) for Ir, which describes with high accuracy the Ir lattice properties, including energy characteristics of point defects. The analogous potential is plotted for Rh. Specific features of φ(r) in Ir and Rh are discussed; in particular, “rigidity” at small distances and weakly pronounced Friedel oscillations. Elastic properties, phonon spectra, the formation energies of vacancies, interstitial atoms, and stacking faults, as well as the migration energies of vacancies, and interstitial atoms in Ir and Rh, are calculated.

Anharmonic effects in thermodynamics and vacancy characteristics in alkali metals

Anharmonic contributions to free energy, pressure, specific heat, Cpan(T), and thermal expansion, ( Delta v/v)an, have been calculated for five alkali metals. A pseudopotential model that gives a rather accurate description of the atomic properties of these metals is used. In the range of T where vacancy concentration is negligible the calculated contributions Cvan amount to 0.3-0.5 of the difference Cp-Cv and most of them are in good agreement with experiment. The volume dependence of Cvan is very weak and anharmonic pressure Pan is quite small. The contribution ( Delta v/v)an is determined mainly by the bulk modulus quasiharmonic variation due to thermal expansion. The lattice defect heat capacities Cd (T) of Na, K, Rb, and Cs have been determined from the experimental specific heat Cp and the calculated Cvan and Cp-Cv. The vacancy concentrations nv and formation energies E1vF have been estimated from the Cd(T). The values of nv obtained are larger, and those of E1vF smaller, than most previous estimates.

On the microscopic model of Fe and Ni: the possible breakdown of the ferromagnetic fermi-liquid picture

A new model of strong itinerant ferromagnetism, taking into account the presence of a narrow density-of-states peak at EF, which is due to merging of van Hove singularities, is proposed. The states of the peak (eg-type states for Fe) are treated within the framework of the Hubbard model with strong correlations. The role of the non-quasi-particle states, which lie near EF and are not described by the theory of the ferromagnetic Fermi liquid, is investigated. In particular, experimental data on the spin polarization of conduction electrons and T-dependence of resistivity are discussed.

Anomalies of phonon spectra and anharmonic effects in metals and alloys due to proximity of the Fermi level to singular points of band structure

A study is made of special features of phonon spectra ω k and of anharmonic effects in metals and alloys which occur when the distances η between the Fermi level and singular points of the electron density of states are small. Explicit expressions are derived for the contributions to ω k and to the anharmonic properties that are nonanalytic in η in the case when the pseudopotential of the electron-ion interaction is small. It is found that the magnitudes of the temperature derivatives of the elastic moduli and of optical phonon frequencies near electron topological transitions increase for small η as η −1/2 at moderate temperatures