K. Yu. Khromov

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.

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...

On the theory of interactions and thermodynamic properties of carbon atoms in hcp and fcc iron

General expressions are derived for deformational interactions of interstitial atoms in an hcp interstitial alloy MeXc taking into account Me-X interactions of any range. These expressions are used for obtaining quantitative estimates of both deformational and chemical interactions of carbon atoms in hcp iron-carbon alloys. The results show that the interactions of interstitial atoms in hcp alloys noticeably differ from analogous interactions in cubic alloys, being more anisotropic, more extended, and more sharply oscillating with increasing distance. Analytical expressions are obtained for the thermodynamic contribution of interstitial atoms in disordered MeXc alloys using both the simple mean field approximation and more exact cluster methods. Comparison of the results of such calculations for austenite with the results of simulation based on the Monte Carlo technique and with experimental data shows that the accuracy of the mean field approximation for MeXc alloys is very low due to strong repulsion of neighboring interstitial atoms. On the other hand, the accuracy of cluster methods remains high for all temperatures and concentrations under consideration.

On the Theory of Austenite-Cementite Phase Equilibria in Steels

A microscopic model is proposed, which describes the structure and thermodynamic properties of cementite (an ordered iron carbide with a composition of Fe3C1 − δ) and the phase equilibria between cementite and austenite (a disordered solid solution of carbon in face-centered cubic iron). Based on this model, chemical and stress-induced (deformational) interactions of carbon atoms in cementite and austenite structures are quantitatively evaluated. The “lattice” contributions in the equations of phase equilibria, which are related to changes in the crystal structure as a result of the cementite-austenite phase transition, are estimated. The proposed model well describes available data on the thermodynamics of cementite and austenite and provides a basis for the further microscopic investigation of high-temperature phase transformations in steels.

Characteristic features of anharmonic effects in the lattice dynamics of fcc metals

The dispersion in the entire Brillouin zone and the temperature dependence (right up to the melting temperature) of the anharmonic frequency shift and phonon damping in a number of fcc metals is investigated on the basis of microscopic calculations. It is found that the anharmonic effects depend sharply on the wave vector in the directions Г-X, X-W, and Г-L and, in contrast to bcc metals, the magnitude of the effects is not due to the softness of the initial phonon spectrum. It is shown that the relative frequency shifts and the phonon damping near melting do not exceed 10–20%. The relative role of various anharmonic processes is examined, and the relation between the results obtained and existing experimental data is discussed.

Thermal expansion and the equation of state of Ir and Rh

Abstract The simplest anharmonic characteristics of Ir and Rh are discussed in the framework of a previously developed simple pseudopotential model which describes the elastic moduli, the phonon spectra and the lattice heat capacity in the harmonic approximation of these metals successfully. The microscopic Gruneisen parameters, the dependences of the elastic moduli on pressure, the coefficient of thermal expansion and the equations of state at the finite temperatures have been calculated. The ab initio calculations of the energy-band structure and the equation of state for Ir at T = 0 have been done to test the model for adequacy at high pressures. The values of different contributions (zero-point oscillations, quasiharmonic, etc.) in the considered thermodynamic characteristics of Ir and Rh are discussed.

Generalized Ginzburg-Landau functionals for studies of phase transformations between FCC, BCC, and HCP structures in metals and alloys

Generalized Ginzburg-Landau functionals describing transitions between bcc, fcc, and hcp structures are studied using four weakly nonuniform transformation parameters: three tensile strains along the principal crystallographic axes and a “phonon” parameter describing relative slip of close-packed planes. Several versions of transformation paths indicated for each of the three transformations considered, which appear to be the most realistic; explicit expressions for atomic displacements are given for each of these paths. It is shown that the gradient terms in these functionals can be explicitly expressed in terms of the dynamic matrix of the crystal on a transformation path; these dynamic matrices can be determined using interpolations of experimental data on phonon spectra between the initial and final phases. The results are used for estimating the characteristics of interphase boundaries between ferrite and cementite in steels. It is found that the width of such interfaces considerably exceeds the interatomic distance, while the estimated values of the gradient terms are in reasonable agreement with the available experimental data.

Peculiarities of anharmonic lattice dynamics and thermodynamics of alkaline-earth metals

Abstract Calculations are performed for a broad range of properties in the fcc and bcc phases of Ca and Sr. Detailed information on the magnitude and character of the temperature dependence of anharmonic effects in the lattice dynamics over the entire Brillouin zone (frequency shifts, phonon damping and Grüneisen parameters) is given. A detailed comparison of the computational results for the heat capacity and thermal expansion with the experimental data is carried out; the theoretical results are in good agreement with the experiment.

Construction of a dynamical matrix for an HCP crystal using phonon data at the symmetry points of the Brillouin zone and elastic constants

General analytical expressions are obtained for the dynamical matrix D(k) and the elastic constants Cik in an HCP crystal in terms of the Born-von Karman (BvK) parameters. An analytical method is proposed for constructing D(k) on the basis of data about the phonon frequencies ωi(N) at the symmetry points of the Brillouin zone and the elastic constants Cik. A number of relations between the values of ωi(N) and Cik are presented for conventional interaction models. It is shown that the standard method for determining BvK parameters by fitting them to experimental phonon spectra in HCP lattices is, as a rule, ambiguous, whereas the analytical method proposed allows one to find all the solutions of the problem. The methods developed are illustrated by the construction of dynamical matrices for Tb, Sc, Ti, and Co.

Phonon-deformational generalized ginzburg-landau functionals for describing martensite transitions between FCC and BCC structures in metals

A method is developed for theoretical description of martensite transitions between fcc and bcc phases of metals based on generalized Ginzburg-Landau functionals (GGLFs), in which the transformation parameters are the “phonon” parameter describing relative slips of close-packed atomic planes and fcc lattice deformations in the region of a martensite inclusion. General expressions are proposed for calculating the deformational contributions to the GGLF. Local strains and local elastic moduli in the region of martensite inclusions are estimated numerically. The possibility of constructing phenomenological expressions for the GGLF using interpolations of available experimental data on the structure and elastic moduli in the fcc and bcc phases is discussed.