Dynamics Of Interphase Boundaries Research Articles

“Digital Core” Technology and Supercomputer Computing

This article is focused on the modeling of multiphase hydrodynamic flows within “digital core” technology for the needs of the oil and gas industry. The essence of this technology is direct numerical simulation of the flows on the scale of the pore space of oil and gas reservoir rocks with direct resolution of the structure of this space and the dynamics of interphase boundaries. The importance of the development of high-performance computing facilities (supercomputers) for the successful implementation of this technology is emphasized. Work carried out by the Keldysh Institute of Applied Mathematics, RAS, in the field of mathematical models, computational algorithms, and their software implementation is described.

Dynamics and statics of interphase and domain boundaries at diffusionless phase transitions

We consider the interface dynamics of diffusionless first-order phase transitions in the case of an arbitrary dimension. We examine the generalized dynamics of interphase boundaries in the presence of mechanical stress. The displacement patterns due to interphase and domain boundaries are calculated in the case of martensitic phase transitions.

Temperature-induced motion of interphase boundaries in confined ferroelectrics

Abstract Thermally induced dynamics of interphase boundaries are considered in confined ferroelectrics at a first-order phase transition. The size dependence of the temperature of the stability limit of the paraelectric phase and the phase transition temperature is calculated for a semi-infinite plate with one finite size (thickness). The velocity of the interphase boundary is presented as a function of its thickness for the thermally induced motion. The result is in agreement with the experiment on PbTiO3. It is shown that close to the phase transition the interphase boundary should change the direction of its motion at a critical thickness of the sample, reflecting the first-order character of the ferroelectric phase transition.

Finite-size effects in dynamics of paraelectric–ferroelectric interfaces induced by latent heat transfer

A theory of the thermally induced dynamics of interphase boundaries in the case of latent heat transfer is presented for confined ferroelectrics. Two distinct types of interface motion, thermally induced, have been observed in experiment in ferroelectric perovskites: (a) slow motion usually governed by the polarization relaxation mechanism and presented by polarization kink migration, and (b) rapid motion that takes place over short periods of time and has not been sufficiently clarified. We show that latent heat transfer may cause the observed rapid motion of the interphase boundary during the phase transition temperature passage. On cooling the heat generated during the phase transition accelerates the interphase boundary. The dependence of the interface velocity on the crystal size is calculated for the latent heat transfer mechanism of the interface motion. The theoretical result is in agreement with the experiment according to which the interface velocity decreases with increasing crystal size.

Competition between Relaxation Kinetics and Heat Transfer in the Dynamics of Phase Transition Fronts

The velocity of the interphase boundary motion caused by latent heat transfer at ferroelectric phase transitions is calculated. The criterion for separating of two mechanisms for the front motion - the latent heat transfer and the relaxation of the order parameter - is obtained for ferroelectrics. Electric field dynamics of interphase boundaries have been studied. The expression for the front velocity of the threshold field type is derived. The transition from a metastable phase to a thermodynamically stable phase takes place via fluctuations leading to the formation of nuclei of the new phase (heterophase fluctuations) (I). In order to describe systems which undergo a symmetry-breaking first-order phase transition, the nucleation and growth processes must be accounted for. The growth is associated with the propagation of interphase boundaries separating the high-temperature parent phase and the low-temperature product phase. In solid diffusiohless transformations the growth may be slow enough for the observation by polarization microscope technique. In particular, in ferroelectrics sharp interphase boundaries can be observed (2-121. Crystals with sharp interfaces most often have kinetically controlled rather than diffusion-limited growth. Usually the interphase dynamics are governed entirely by the time evolution of the order parameter (13-201, and the temperature can be considered to be a constant. Thus the heat is assumed to be removed rapidly enough that no temperature change occurs as the latent heat of the phase transition appears at the interphase boundary. However as the interface moves it acts as a heat source with a strength proportional to the latent heat and the forward rate of motion, giving rise to a jump in the thermal gradient. The heat generated during the interphase boundary motion can accelerate the interface which, in turn, increases the heat production rate. A system involved in this avalanche-like process can be stabilized by the heat removal via the heat conductivity and the heat exchange with the thermal bath. This problem is less important in metallic systems. If one deals with substances which conduct heat very well, the temperature may be treated as a constant and so no kinetic equation additional to one for the order parameter is necessary. But for materials which do not conduct heat so well, we may need a second equation to determine the temperature distribution. Therefore the interphase boundary motion can be determined by the rate of heat transfer in the system. In the recent review (12) our theory of the kink motion of the interphase boundary (14,16,17) has been examined. The necessity of taking into account processes of dissipati(;n of energy released (or additionaly absorbed) during the time of transition has been analysed (12). The electric-field driven kinetics of ferroelectric interphase boundaries have not been studied up to now. In this paper we obtain a criterion of necessity of considering the heat transfer effect on the interphase boundary propagation. We show here that at first-order phase transitions in ferroelectrics-semiconductors the thermal conductivity is not a controlling process and

Conspicuous domination of polarization relaxation in kinetics of first-order phase transitions in perovskites.

We justify the application of the theory of the kink-type motion for interphase boundaries for perovskites at first-order phase transitions and obtain a criterion for separating two mechanisms for the front motion---the latent heat transfer and the relaxation of the order parameter. Calculations of the velocity of the interphase boundary motion caused by latent heat transfer at ferroelectric phase transitions show the domination of relaxation kinetics during the ferroelectric-paraelectric phase transitions in perovskites of the ${\mathit{ABO}}_{3}$ type. This allows us to conclude that the dynamics of interphase boundaries in perovskites are governed by the polarization evolution. \textcopyright{} 1996 The American Physical Society.

Kinetics of phase transitions in solid solutions of ferroelectric perovskites.

The dynamics of interphase boundaries at first-order phase transitions in ferroelectric solid solutions are considered. The width and velocity of the interphase boundary as functions of concentration are calculated for the ferroelectric perovskite solid solutions K(Ta,Nb)${\mathrm{O}}_{3}$ (KTN) and Pb (Zr,Ti)${\mathrm{O}}_{3}$ (PZT), which are taken as examples. It is shown that the velocity depends very strongly on concentration in the vicinity of the phase transition.

Nonlinear field-induced dynamics of interphase boundaries at some diffusionless phase transitions.

Magnetic- and electric-field effects on the width, surface tension, and velocity of the interphase boundary are calculated for solid-solid and nematic-isotropic first-order phase transitions described by the Landau expansion with a cubic term. The exact solution of the Ginzburg\char21{}Landau\char21{}de Gennes equation including an external field is obtained. The results are compared with the experimental data in nematic liquid crystals and ferroelectrics.