Vladimir Ankudinov

Russian Academy of Sciences | RAS · Institute of High Pressure Physics

The Phase Field Crystal (PFC) model incorporates microscopic structural details into a mesoscopic continuum theory. Methods for fast propagation of PFC interfaces are discussed in this book. They can handle a wide range of cooling rates, thermal gradients, supersaturations and supercoolings, including applications to the microstructural pattern for...

A phase field model for small and large driving forces on solidification and melting of a pure metal or binary alloy is formulated. A traveling wave solution of the phase field equation predicts the non-linear behavior in the velocity of the crystal/liquid interface at the large driving force. This non-linearity has the dependence of velocity with...

A mathematical model of selective laser melting (SLM) of fine-grained metallic powders under the pulse laser annealing conditions has been developed. The processed powder bed is considered in the approximation of continuous medium where its effective thermophysical properties depend on local porosity. The model allows simulation of unsteady distrib...

Interface energy and kinetic coefficient of crystal growth strongly depend on the face of the crystalline lattice. To investigate the kinetic anisotropy and velocity of different crystallographic faces we use the hyperbolic (modified) phase field crystal model which takes into account relaxation of atomic density (as a slow thermodynamic variable)...

Using the phase field crystal model (PFC model), an analysis of slow and fast dynamics of solid-liquid interfaces in solidification and melting processes is presented. Dynamical regimes for cubic lattices invading metastable liquids (solidification) and liquids propagating into metastable crystals (melting) are described in terms of the evolving am...

Studying Arctic ice formation stays in the focus of research groups over the past decades in the context of ice cover changes, thermal budget and climate agenda in general. Nevertheless, the phenomenon's underlying mechanisms are still not completely understood and described. The main reason for the lack in understanding is the limited experimental...

The process of glass transition during the quenching in the domain with the cold wall has been numerically simulated. We have implemented the temperature-dependent form of the previously proposed theoretical model, which combined the heat transfer in the domain and the gauge theory of glass transition, assuming the presence of topologically stable...

The paper presents a numerical simulation of the glass transition process under conditions of rapid quenching with unsteady heat transfer and fixed gradient cooling rate. A temperature-dependent form of the previously proposed theoretical model was used. This model combines the gauge theory of glass transition, assuming the presence of topologicall...

These authors contributed equally to this work. Abstract: One of the classes of the kinetic phase-field model in the form of the two-mode hyperbolic phase-field crystal model (modified PFC model) is used for the study of the noise effect of the crystalline structure. Special attention is paid to the origin of the defect's microstructure in the crys...

A novel method based on molecular dynamics (MD) is developed to make the kinetic phase-field (PF) model quantitative in predicting non-equilibrium crystal growth during rapid solidification. MD-calculated variations of the diffuse solid-liquid (SL) interface width versus interface velocity are used to parameterize the kinetic PF model. Two approach...

The phase‐field model for the description of the solidification processes with the glass‐crystal competition is suggested. The model combines the first‐order phase transition model in the phase‐field formalism and gauge‐field theory of glass transition. We present a self‐consistent system of stochastic motion equations for unconserved order paramet...

Calculating viscosity in multicompoinent metallic melts is a challenging task for both classical and ab initio molecular dynamics simulations methods. The former may not to provide enough accuracy and the latter is too resources demanding. Machine learning potentials provide optimal balance between accuracy and computational efficiency and so seem...

Studying Arctic ice formation stays in the focus of research groups over the past decades in the context of ice cover changes, thermal budget and climate agenda in general. Nevertheless, the phenomenon’s underlying mechanisms are still not completely understood and described. The main reason for the lack in understanding is the limited experimental...

A novel method based on molecular dynamics (MD) is developed to make the kinetic phase-field (PF) model quantitative in predicting non-equilibrium crystal growth during rapid solidification. MD-calculated variations of the diffuse solid-liquid (SL) interface width versus interface velocity are used to parameterize the kinetic PF model. Two approach...

The phase-field model for the description of the solidification processes with the glass-crystal competition is suggested. The model combines the first-order phase transition model in the phase-field formalism and gauge-field theory of glass transition. We present a self-consistent system of stochastic motion equations for unconserved order paramet...

Calculating viscosity in multicompoinent metallic melts is a challenging task for both classical and \textit{ab~initio} molecular dynamics simulations methods. The former may not to provide enough accuracy and the latter is too resources demanding. Machine learning potentials provide optimal balance between accuracy and computational efficiency and...

A revised study of the growth and melting of crystals in congruently melting Al50Ni50 alloy is carried out by molecular dynamics (MD) and phase field methods. An Embedded Atom Method (EAM) potential of Purja Pun and Mishin [Philosophical Magazine 89 (2009) 3245] is used to estimate the material's properties (density, enthalpy, and self-diffusion) o...

A modification of structural phase-field crystal (XPFC) model for an arbitrary pair interaction potential is presented. Formation of 1D and 2D structures for the Lennard-Jones (LJ) potential was studied numerically. The equilibrium lattice parameters for the presented structures were found consistent to the correspondent LJ-distance parameters. The...

A modification of the structural phase-field crystal (XPFC) model for a Lennard-Jones (LJ) pair interaction potential is presented. Formation of 1D and 2D structures for the LJ-potential was studied numerically. The equilibrium lattice parameters for the obtained structures were found consistent to the correspondent LJ-distance parameters. The latt...

В работе рассмотрена двухмодовая математическая модель кристаллического фазового поля (КФП), описывающая микроскопическую структурную динамику и упорядочение вещества в процессе кристаллизации из однородной фазы. Модель представлена нелинейным дифференциальным уравнением десятого порядка по пространству и второго по времени, для решения которого бы...

The crystallization of a supercooled metastable homogeneous phase into a hexagonal periodic lattice has been studied within the phase-field crystal model. The numerically determined velocities of the crystallization front of the hexagonal (honeycomb) lattice are compared to the analytical traveling wave solution. The growth of the hexagonal (honeyc...

The phase-field crystal (PFC) method is known as a relatively new continuum approach for describing the microstructural dynamics of materials during structural and phase transitions. In contrast to molecular dynamics (MD) or density functional theory (DFT) methods, PFC allows description processes on diffusion time scales while maintaining an atomi...

A three-dimensional model of a partially melted powder bed with particles stochastically distributed in size and space coordinates has been developed. Numerical simulation of temperature distributions in stainless steel AISI 316L and Al-12Si powders in vacuum, air and argon has been performed to analyze unsteady heat transfer in a porous medium. Th...

A three-dimensional model of a partially melted powder bed with particles stochastically distributed in size and space coordinates has been developed. Numerical simulation of temperature distributions in stainless steel AISI 316L and Al-12Si powders in vacuum, air and argon has been performed to analyze unsteady heat transfer in a porous medium. Th...

The phase-field crystal (PFC-model) is a powerful tool for modelling of the crystallization in colloidal and metallic systems. In the present work, the modified hyperbolic phase-field crystal model for binary systems is presented. This model takes into account slow and fast dynamics of moving interfaces for both concentration and relative atomic nu...

A theoretical model is proposed that describes the kinetics of the formation and evolution of competing phases, one of which is a disordered system of topologically stable excitations (vortices) and the second one is an ordered (crystalline) phase. This model is intended to be the simplest model which can demonstrate such important characteristics...

Two different phase‐field crystal (PFC) free excess energy expansions have been analyzed with respect to the order of a truncation term and to the accuracy of a pair correlation functions fitting. The coefficients of the correlation function in PFC model was found for the aluminum crystal based on the molecular dynamics data. A machine learning (ML...

A phase‐field crystal model (PFC model) which takes into account exponential relaxation of the atomic flux and its fluctuations is developed. The model corresponds to a system undergoing phase transformation described with a partial differential equation of hyperbolic type. Such a model covers slow and rapid regimes of interface propagation at smal...

Modeling of crystal micro‐structures and their dynamics during fast phase transitions can be performed by the phase‐field crystal (PFC) model in the hyperbolic formulation (Modified Phase Field Crystal [MPFC] model). This method is suitable for a continual modeling of the atomic density field at diffusion time intervals (slow diffusion dynamics) an...

The paper presents the results of comparing the microstructure of alloys of the Al – Ge system of eutectic and near- eutectic compositions synthesized at melt cooling rates of 102 and 105 K/s. It was shown by scanning electron microscopy that at a cooling rate of 102 K/s, crystallization starts with grain growth of the excess component and ends wit...

We analyze the crystal growth kinetics of rapidly solidifying glass-forming Cu50Zr50 alloy melts. Formulating a dendrite growth model we predict all features of crystallization kinetics in Cu50Zr50 from thermodynamically controlled growth (governed by the change in Gibbs free energy on solidification) to the kinetically limited regime (governed by...

Interface energy and kinetic coefficient of crystal growth strongly depend on the face of the crystalline lattice. To investigate the kinetic anisotropy and velocity of different crystallographic faces we use the hyperbolic (modified) phase field crystal model which takes into account atomic density (as a slow thermodynamic variable) and atomic flu...

Recent advancements in the phase field theory predict slow and fast regimes of crystal growth from melts and solutions [1]. We analyze kinetics of crystal interfaces invading undercooled melts using traveling wave solutions derived from phase field theory of fast phase transformations. These solutions are compared with data kinetics of molecular dy...

Kinetics of crystal growth in undercooled melts is analyzed by methods of theoretical modeling. Special attention is paid to rapid growth regimes occurring at deep undercoolings at which non-linearity in crystal velocity appears. A traveling wave solution of the phase field model (PFM) derived from the fast transitions theory is used for a quantita...

Thermodynamic driving forces and growth rates in rapid solidification are analysed. Taking into account the relaxation time of the solute diffusion flux in the model equations, the present theory uses, in a first case, the deviation from local chemical equilibrium, and ergodicity breaking. The second case of ergodicity breaking may exist in crystal...

The mathematical modeling of crystal structures and their dynamics during the structural transitions can be performed by the method of phase field crystal in the hyperbolic formulation (MPFC method). This method is suitable for a continual modeling of the atomic density field at diffusion time intervals. The unstable behavior of the solution near l...

The Phase Field Crystal model in hyperbolic formulation (modified PFC or MPFC), is investigated as one of the most promising techniques for modeling the formation of crystal patterns. MPFC is a convenient and fundamentally based description linking nano-and meso-scale processes in the evolution of crystal structures. The presented model is a powerf...

A mathematical model of selective laser melting (SLM) of fine-grained metallic powders under the conditions of pulse laser annealing has been developed. The processed powder bed is considered in approximation of a continuous medium where its effective thermophysical properties depend on local porosity. The model allows calculation of the unsteady d...

Modelling of selective laser melting (SLM) of Fe and stainless steel powders has been performed to analyze unsteady heat transfer in a porous medium under conditions of rapid phase transformations. The pulsed laser heat source develops high temperature gradients that lead to large solidification velocities, which can be used in acquisition of compl...

Effect of phase-field crystal model (PFC-model) parameters on the structure diagram is analyzed. The PFC-model is taken in a two-mode approximation and the construction of structure diagram follows from the free energy minimization and Maxwell thermodynamic rule. The diagram of structure's coexistence for three dimensional crystal structures [Body-...

The phase-field crystal method is suitable for simulations of the atomic densities on the diffusion time scales. This metohod and model can be used to calculate the structure phase diagrams for different crystal lattices and to model the wide spectrum of processes such as epitaxial grow, high speed crystal front propagation and so on.

Модель кристаллического фазового поля континуально описывает атомную плотность на диффузионных временах протекания реакций. В настоящей работе рассмотрены гомогенная структура (жидкость) и идеальный периодический кристалл, построенные из одномодового приближения модели кристаллического фазового поля. На основе аналитических решений модели построена...

The phase field crystal model provides a continual description of the atomic density over the diffusion time of reactions. We consider a homogeneous structure (liquid) and a perfect periodic crystal, which are constructed from the one-mode approximation of the phase field crystal model. A diagram of 2D structures is constructed from the analytic so...

There is a mesoscopic model of porous media observed.

The numerical model of mechanical loading and deformation of belleville washers is described in the article; the results of numerical analysis and experimental investigation of samples with the shape memory effect are compared. The nu-merical studies show the relationship between the operational characteristics of washers and their geometrical size...

In the first part of the paper, a model of laser annealing of powder materials (metals or allows) redeposited on a sub-strate is obtained. In order to describe motion of the melting (solidification) front, the method of mushy zone developed by V.T. Borisov and V.A. Zhuravlev is used. The final system of equations includes nonstationary partial diff...

The results of studying the porosity of ultrafine aluminum powder oxidized in the air are shown. The measurements were performed using the gas adsorption BET technique at low temperatures. The methodology is reviewed; the theory and calculation formulas are presented in the paper. The specific surface area is analyzed; the average size of pores whe...

The laser sintering of submicron metal powders has been studied in connection with unsteady heat transfer in a porous powder layer under conditions of rapid phase transformations. The multi-scale theoretical approach was used during the simulation. The heating and cooling rates and depth of the sintered layer are estimated by the micro-scale model...

Optimisation of laser sintering of submicron metal powders has been studied in connection with unsteady heat transfer in a porous powder layer under conditions of rapid phase transformations. The heating rate, cooling rate and depth of the sintered layer are estimated after analysis of geometrical characteristics of the metallic powder. The compute...

The article deals with the approach to the mathematical and physical description of heat transport in porous media. The attempt was made to build a geometrically adequate model describing a porous structure of powder, and analyse the connection between thermophysical properties and porosity.The task on heat conduction in metal porous media (tanta-l...

Optimization of laser sintering of submicron metal powders is studied in connection with unsteady heat transfer in a porous layer under simultaneous phase transformations. The heating/cooling rates and the depth of the sintered layer are estimated after analysis of geometrical characteristics of the metallic powder. Computer modeling revealed that...

The problem of unsteady heat transfer in a porous body has been studied for laser sintering of powders. The cooling rate and depth of the sintered layer are estimated after an analysis of geometrical characteristics of the metallic powder. With 2D computer modeling it was shown that the heating rate exceeds the cooling rate by 2 orders of magnitude...