Statistical Derivation of Basic Equations of Diffusional Kinetics in Alloys with Application to the Description of Diffusion of Carbon in Austenite

Basic equations of diffusional kinetics in alloys are statistically derived using the master equation approach. To describe diffusional transformations in substitution alloys, we derive the "quasi-equilibrium" kinetic equation which generalizes its earlier versions by taking into account possible "interaction renormalization" effects. For the interstitial alloys Me-X, we derive the explicit expression for the diffusivity D of an interstitial atom X which notably differs from those used in previous phenomenological treatments. This microscopic expression for D is applied to describe the diffusion of carbon in austenite basing on some simple models of carbon-carbon interaction. The results obtained enable us to make certain conclusions about the real form of these interactions, and about the scale of the "transition state entropy" for diffusion of carbon in austenite.Comment: 26 pages, 5 postscript figures, LaTe

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 $\Gamma$-X, X-W, and $\Gamma$-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.Comment: 4 pages, 5 figures, LaTe

Studies of concentration and temperature dependencies of precipitation kinetics in iron-copper alloys using kinetic monte carlo and stochastic statistical simulations

The earlier-developed ab initio model and the kinetic Monte Carlo method (KMCM) are used to simulate precipitation in a number of iron-copper alloys with different copper concentrations x and temperatures T. The same simulations are also made using the improved version of the earlier-suggested stochastic statistical method (SSM). The results obtained enable us to make a number of general conclusions about the dependencies of the decomposition kinetics in Fe-Cu alloys on x and T. We also show that the SSM describes the precipitation kinetics in a fair agreement with the KMCM, and employing the SSM in conjunction with the KMCM enables us to extend the KMC simulations to the longer evolution times. The results of simulations seem to agree with available experimental data for Fe-Cu alloys within statistical errors of simulations and the scatter of experimental results. Comparison of results of simulations to experiments for some multicomponent Fe-Cu-based alloys enables us to make certain conclusions about the influence of alloying elements in these alloys on the precipitation kinetics at different stages of evolution.Comment: 18 pages, 17 postscript figures, LaTe

Transition from a one-dimensional to a quasi-one-dimensional state in interacting quantum wires

Upon increasing the electron density in a quantum wire, the one-dimensional electron system undergoes a transition to a quasi-one-dimensional state. In the absence of interactions between electrons, this corresponds to filling up the second subband of transverse quantization, and there are two gapless excitation modes above the transition. On the other hand, strongly interacting one-dimensional electrons form a Wigner crystal, and the transition corresponds to it splitting into two chains (zigzag crystal). The two chains are locked, so their relative motion is gapped, and only one gapless mode remains. We study the evolution of the system as the interaction strength changes, and show that only one gapless mode exists near the transition at any interaction strength.Comment: 4 pages, 2 figure

Color superconductivity in the static Einstein Universe

We study the behavior of quark and diquark condensates in dense quark matter under the influence of a gravitational field adopting as a simple model the static $D-$dimensional Einstein Universe. Calculations are performed in the framework of the extended Nambu--Jona-Lasinio model at finite temperature and quark density on the basis of the thermodynamic potential and the gap equations. Quark and diquark condensates as functions of the chemical potential and temperature at different values of the curvature have been studied. Phase portraits of the system have been constructed

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

A simple pseudopotential model is proposed, which allows the phonon spectra and temperature dependence of the lattice heat capacity of Ir and Rh be described with a high enough 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 determination of the characteristics (momenta) of the phonon density of states from the experimental values of the total heat capacity of 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 (more than by a factor of 1.5) decrease in the effective Debye temperature with increasing termperature. The temperature dependence of the mean square amplitude of atomic displacements in Ir and Rh has been calculated. Basing on the band calculations the manifestation of the Kohn singularities in the phonon spectra of Ir are discussed.Comment: 15 pages, LaTeX2e, 12 figures in postscrip

Anharmonicity of BaTiO_3 single crystals

By analyzing the dielectric non-linearity with the Landau thermodynamic expansion, we find a simple and direct way to assess the importance of the eighth order term. Following this approach, it is demonstrated that the eighth order term is essential for the adequate description of the para/ferroelectric phase transition of BaTiO_3. The temperature dependence of the quartic coefficient \beta is accordingly reconsidered and is strongly evidenced by the change of its sign above 165 C. All these findings attest to the strong polarization anharmonicity of this material, which is unexpected for classical displacive ferroelectrics.Comment: 4 figures, to be published in Phys. Rev.

Exact Curie temperature for the Ising model on Archimedean and Laves lattices

Using the Feynman-Vdovichenko combinatorial approach to the two dimensional Ising model, we determine the exact Curie temperature for all two dimensional Archimedean lattices. By means of duality, we extend our results to cover all two dimensional Laves lattices. For those lattices where the exact critical temperatures are not exactly known yet, we compare them with Monte Carlo simulations.Comment: 10 pages, 1 figures, 3 table