arXiv subjects

Nikolay V. Alekseechkin

Publications and source records attributed to Nikolay V. Alekseechkin.

11 recordsLinked to original sources

arXiv2025

Crystallization of metallic glass as a grain-boundary nucleated process: experimental and theoretical evidence for the grain structure of metallic glasses

Experimental DSC and Avrami curves for the crystallization of metallic glasses demonstrate nucleation at grain boundaries and thus indicate their grain structure, which refutes the generally accepted idea of glass as a homogeneous frozen liquid obtained as a result of avoiding crystallization. Under certain conditions, this nucleation mechanism results in the appearance of two-peak DSC curves and three-step Avrami plots which are observed experimentally. To clarify these conditions, isothermal and non-isothermal surface-nucleated crystallization of a spherical particle is considered within the framework of a simple analytical model of nucleation and growth.

cond-mat.mtrl-sci↗

arXiv2023

On the thermodynamic theory of curvature-dependent surface tension

An exact equation for determining the Tolman length (TL) as a function of radius is obtained and a computational procedure for solving it is proposed. As a result of implementing this procedure, the dependences of the TL and surface tension on radius are obtained for the drop and bubble cases and various equations of state. As one of the results of the thermodynamic study, a new equation for the dependence of surface tension on radius (curvature effect), alternative to the corresponding Tolman equation and associated with the spinodal point, is obtained. The Kelvin type equation for the equimolecular radius is shown to be exact over the entire metastability region and serves as the basis for the TL equation. The expansions of surface tension near the spinodal and binodal points show that the correction to Rusanov s linear asymptotics in the first case is a series in cubes of the radius, whereas a series in curvature holds in the second case. As a result of the analysis of these expansions, the fundamental impossibility to determine the curvature effect analytically from the binodal point is established; the computational procedure determines it from the spinodal point. It is shown that just the characteristics of the system on the spinodal, mainly the TL value at zero radius, determine the curvature effect. In general, the theory reveals a close connection between surface and bulk properties.

physics.chem-ph↗

arXiv2021

Kinetics of grain-boundary nucleated transformations in rectangular geometries and one paradox relating to Cahn's model

Volume-fraction expressions are obtained for the systems of an infinite number of parallel planes arranged both regularly and randomly. As a special case of random arrangement, a non-Poissonian point process (the second-order Erlang process) of arrangement of planes is considered for the first time. The exact volume-fraction expression obtained for this case shows that it cannot be derived by the Cahn method, i. e. the extended-volume approach is applicable only to Poisson processes. The volume fraction equations for regular planes are used to study cubic grain structures, both regular and random. It is shown that the Cahn equation underestimates the transformation kinetics in both regular and random structures with four different size distributions of cubes; the degree of underestimation depends on the size distribution, being the largest in the regular structure. The paradox of packing is described: the structures composed of the same elements (random parallelepipeds) transforming in the same way, but packed differently, give different transformation rates.

cond-mat.mtrl-sci↗

arXiv2020

Kinetics of the surface-nucleated transformation of spherical particles and new model for grain-boundary nucleated transformations

Equations for the transformed volume fraction of a spherical particle with nucleation on its surface, both nonisothermal and isothermal, are derived in the framework of Kolmogorov method adapted for this problem. Characteristic parameters governing the transformation kinetics are determined; the latter is studied with particular emphasis on the Avrami exponent temporal behavior. It is shown that the surface-nucleated transformation qualitatively differs from the bulk-nucleated one at large values of the characteristic parameters due to the one-dimensional radial growth of the new phase occurring after the complete transformation of the surface itself at the early stage of the process. This effect also manifests itself in the considered ensemble of size-distributed particles and in the grain-boundary nucleated transformations. The logarithmic normal distribution inherent for the particles obtained by grinding is employed for numerical calculations and shown to stretch temporally the volume-fraction and Avrami-exponent dependences for the ensemble of identical particles. A new model for grain-boundary nucleated transformations alternative to the Cahn model of random planes is offered; it is based on the ensemble of size-distributed spherical particles with the possibility for a growing nucleus to cross grain boundaries. The kinetics of this process is shown to be governed by the same characteristic parameter, as for a single particle, and qualitatively differs from the Cahn-model one. In particular, the logarithmic volume-fraction plot at large values of the governing parameter ends by a characteristic bend observed on experimental curves for the crystallization of bulk metallic glasses. This peculiarity together with the form of the plot as a whole directly indicates to the grain (polycluster) structure of metallic glasses and nucleation at intercluster boundaries.

cond-mat.mtrl-sci↗

arXiv2018

Thermodynamics and kinetics of nucleation in binary solutions

A new approach that is a combination of classical thermodynamics and macroscopic kinetics is offered for studying the nucleation kinetics in condensed binary solutions. The theory covers the separation of liquid and solid solutions proceeding along the nucleation mechanism, as well as liquid-solid transformations, e.g., the crystallization of molten alloys. The cases of nucleation of both unary and binary precipitates are considered. Equations of equilibrium for a critical nucleus are derived and then employed in the macroscopic equations of nucleus growth; the steady state nucleation rate is calculated with the use of these equations. The present approach can be applied to the general case of non-ideal solution; the calculations are performed on the model of regular solution within the classical nucleation theory (CNT) approximation implying the bulk properties of a nucleus and constant surface tension. The way of extending the theory beyond the CNT approximation is shown in the framework of the finite-thickness layer method. From equations of equilibrium of a surface layer with coexisting bulk phases, equations for adsorption and the dependences of surface tension on temperature, radius, and composition are derived. Surface effects on the thermodynamics and kinetics of nucleation are discussed.

physics.chem-ph↗

arXiv2017

Surface effects in nucleation

The classical nucleation theory (CNT) concept of a nucleus as a fragment of the bulk new phase fails for nanosized nuclei. An extension of CNT taking into account the properties of the transition region between coexisting bulk phases is proposed. For this purpose, the finite-thickness layer method which is an alternative to Gibbs one is used; the transition region is considered as a separate (surface) phase. An equation for the nucleation work is derived which is basic for the multivariable theory of nucleation. Equations of equilibrium following from it are employed for considering the dependences of surface tension on radius and temperature for droplets; Kelvin formula for the equilibrium vapor pressure is extended to small radii. It is shown that the ratio of the isothermal nucleation rate to that of CNT can achieve several orders of magnitude due to the curvature effect (the dependence of surface tension on curvature). The analysis of different dependences of the Tolman length on radius, d(R), suggests that (i) the curvature effect is determined by the value of d(0) which is positive and relates to the limiting (spinodal) vapor supersaturation and (ii) the function d(R) decreases with increasing radius; at the same time, this effect is weakly sensitive to the form of the function d(R) and its asymptotic value. The second differential of the work is obtained as a quadratic form with contributions from both the bulk and surface phases. It is used for calculating the fluctuations of surface layer parameters such as the surface tension and the specific surface area as well as the fluctuations of nucleus parameters.

physics.chem-ph↗

arXiv2015

Thermodynamics and kinetics of binary nucleation in ideal-gas mixtures

The nonisothermal single-component theory of droplet nucleation (Alekseechkin, 2014) is extended to binary case; the droplet volume V, composition x, and temperature T are the variables of the theory. An approach based on macroscopic kinetics (in contrast to the standard microscopic model of nucleation operating with the probabilities of monomer attachment and detachment) is developed for the droplet evolution and results in the derived droplet motion equations in the space (V,x,T) - equations for V_dot, x_dot, and T_dot. The work W(V,x,T) of the droplet formation is calculated; it is obtained in the vicinity of the saddle point as a quadratic form with diagonal matrix. Also the problem of generalizing the single-component Kelvin equation for the equilibrium vapor pressure to binary case is solved; it is presented here as a problem of integrability of a Pfaffian equation. The equation for is shown to be the first law of thermodynamics for the droplet, which is a consequence of Onsagers reciprocal relations and the linked-fluxes concept. As an example of ideal solution for demonstrative numerical calculations, the o-xylene-m-xylene system is employed. Both nonisothermal and enrichment effects are shown to exist; the mean steady-state overheat of droplets and their mean steady-state enrichment are calculated with the help of the 3D distribution function. The qualitative peculiarities of the nucleation thermodynamics and kinetics in the water-sulfuric acid system are considered in the model of regular solution. It is shown that there is a small kinetic parameter in the theory due to the small amount of the acid in the vapor and, as a consequence, the nucleation process is isothermal.

physics.chem-ph↗

arXiv2014

Multivariable theory of droplet nucleation in a single-component vapor

The multivariable theory of nucleation [N. V. Alekseechkin, J. Chem. Phys. 124, 124512 (2006)] is applied to the droplet nucleation in a supersaturated single-component vapor; the droplet volume V, temperature T, and volume change rate U=V_dot are the variables of the theory. A new approach based on macroscopic kinetics is developed for the droplet evolution and results in the derived equations for U_dot, V_dot, and T_dot. It is shown that there is no the viscosity effect in the employed ideal gas approximation, so the variable U can be omitted. The nonisothermal effect (the discrepancy between the actual and isothermal nucleation rates) earlier studied numerically is analytically examined here. The calculated steady state distribution function of droplets shows their average overheating relatively the vapor temperature. An inert background gas is shown to diminish the nonisothermal effect in comparison with a pure vapor case.

physics.chem-ph↗

arXiv2013

Comment on "generalized Gibbs' approach" [J. Chem. Phys. 119, 6166 (2003); 124, 194503 (2006)]

"Generalized Gibbs' approach" of Schmelzer et al [J. Chem. Phys. 119, 6166 (2003); 124, 194503 (2006)] results in wrong conditions of equilibrium of a critical embryo with the ambient phase. The presented analysis shows the shortcomings of this approach and proves the thermodynamic conditions of equilibrium. Also, a generalized adsorption equation is obtained in different forms.

physics.chem-ph↗

arXiv2013

Nucleation kinetics of vapor bubbles in a liquid with arbitrary viscosity

The theory of vapor bubbles nucleation in single-component liquids developed in [J. Phys. Chem. B 116, 9445 (2012)] for the case of high viscosity (the (V,/rho,T)- theory) is extended to the case of arbitrary viscosity. For this purpose, Langevin's approach in the theory of Brownian motion, or Kramers' model of chemical reactions, is employed. The obtained expression for the bubbles nucleation rate is valid for arbitrary relations between the kinetic parameters controlling the nucleation process: viscosity, inertia of a liquid, the rate of evaporation into a bubble and the rate of heat exchange between the bubble and ambient liquid. So, the presented theory together with the (V,/rho,T)- theory gives a complete description of the vapor-bubbles nucleation kinetics in one-component liquids. Limiting cases with respect to the mentioned parameters are considered, in particular, the low viscosity limit. It is shown that the low- and high-viscosity nucleation rates differ from each other qualitatively and quantitatively. The possibility of application of the theory to cavitation in superfluid helium-4 is discussed.

cond-mat.soft↗

arXiv2012

Thermodynamics and kinetics of vapor bubbles nucleation in one-component liquids

The multivariable theory of nucleation [J. Chem. Phys. 124, 124512 (2006)] is applied to the problem of vapor bubbles formation in pure liquids. The presented self-consistent macroscopic theory of this process employs thermodynamics (classical, statistical and linear non-equilibrium), hydrodynamics and interfacial kinetics. As a result of thermodynamic study of the problem, the work of formation of a bubble is obtained and parameters of the critical bubble are determined. The variables V (the bubble volume), ρ(the vapor density), and T (the vapor temperature) are shown to be natural for the given task. An algorithm of writing the equations of motion of a bubble in the space {V, ρ, T} - equations for V, ρ, and T - is offered. This algorithm ensures symmetry of the matrix of kinetic coefficients. The equation for written on the basis of this algorithm is shown to represent the first law of thermodynamics for a bubble. The negative eigenvalue of the motion equations which alongside with the work of the critical bubble formation determines the stationary nucleation rate of bubbles is obtained. Various kinetic limits are considered. One of the kinetic constraints leads to the fact that the nucleation cannot occur in the whole metastable region; it occurs only in some subregion of the latter. Zeldovich theory of cavitation is shown to be a limiting case of the theory presented. The limiting effects of various kinetic processes on the nucleation rate of bubbles are shown analytically. These are the inertial motion of a liquid as well as the processes of particles exchange and heat exchange between a bubble and surrounding liquid. The nucleation rate is shown to be determined by the slowest kinetic process at positive and moderately negative pressures in a liquid. The limiting effect vanishes at high negative pressures.

cond-mat.soft↗