An effective Fourier spectral phase-field approach for ferroelectric materials - Durdiev, Dilshod; Wendler, Frank (Computational Materials Science, 2023)
In this article, we propose an efficient iterative numerical algorithm applying a Fourier spectral method to accurately compute the coupled elasto–electrostatic equilibrium equations in ferroelectric microstructures. The method is implemented for a phase-field model for domain pattern formation and domain kinetics evolution in tetragonal perovskite ferroelectrics, that uses spontaneous polarization as order parameter and includes the piezoelectric effect in the constitutive equation. The scheme is based on a two-scale homogenization approach, introducing local perturbations for stress and dielectric displacement. Green's functions are derived in Fourier space for the coupled constitutive equations. Furthermore, using model parameters for BaTiO3 we investigate domain formation in 2D and 3D, and the polarization switching process starting from a critical nucleus subjected to an applied electric field and compressive stress. The simulation results based on the proposed method reveal that for polarization switching under external fields, intermediately appearing domains with 90° rotated polarization are formed, that reduce electrostatic or elastic strain energy.
CRIS-Team Scopus Importer:2022-12-16
Keywords: Domain wall; Ferroelectrics; Fourier spectral method; Phase-field model

An inverse problem of finding a time-dependent coefficient in a fractional diffusion equation - Durdiev, Durdimurod; Durdiev, Dilshod (Turkish Journal of Mathematics, 2023)
This article is concerned with the study of unique solvability of an inverse coefficient problem of determining the coefficient at the lower term of a fractional diffusion equation. The direct problem is the initial-boundary problem for this equation with usual initial and homogeneous Dirichlet conditions. To determine the unknown coefficient, an overdetermination condition is given as the Neumann condition at the left end of the spatial interval. The theorems of existence and uniqueness of inverse problem solution are obtained. Furthermore, we propose a numerical algorithm based on a finite-difference scheme to accurately compute the inverse problem of simultaneously determining a time-dependent coefficient in a fractional diffusion equation, together with its solution. A test example using the developed numerical algorithm is presented herein.
CRIS-Team Scopus Importer:2023-08-25
Keywords: finite difference method; fractional diffusion equation; Inverse problem; overdetermination condition

Determining thermal activation parameters for ferroelectric domain nucleation in BaTiO3 from molecular dynamics simulations - Durdiev, Dilshod; Zaiser, Michael; Wendler, Frank; Tsuzuki, Takahiro; Azuma, Hikaru; Ogata, Shuji; Kobayashi, Ryo; Uranagase, Masayuki (Applied Physics Letters, 2024)
Polarization switching in ferroelectric hysteresis of BaTiO3 proceeds by localized nucleation and subsequent growth of domains of reverse polarization. While this process is driven by the applied electric field, thermal activation can play an important role in domain nucleation. As a consequence of the stochastic nature of thermal activation, coercive fields in small systems exhibit a significant scatter. It is demonstrated that the statistics of coercive fields observed in molecular dynamics simulations is consistent with the statistical distribution expected for field-assisted thermally activated nucleation of reverse polarization domains. The excellent quantitative agreement between the simulation data and the theory of thermally activated processes provides strong evidence that polarization switching occurs by nucleation-and-growth rather than loss of the local minimum of the Gibbs free energy function. In a pristine crystal, switching is controlled by the field at which thermal fluctuations can create a critical nucleus in the bulk (homogeneous nucleation). The analysis of crystals with various vacancy-type defects demonstrates that such defects may enable heterogeneous nucleation at reduced fields. In both cases, the statistical analysis gives access to the respective activation energies, their field dependence, and the sizes of the critical nuclei.
CRIS-Team Scopus Importer:2024-04-05

Effects of mono/Di-Vacancies on domain growth of BaTiO3: An atomistic computer simulation study - Tsuzuki, Takahiro; Ogata, Shuji; Kobayashi, Ryo; Uranagase, Masayuki; Shimoi, Seiya; Tsujimoto, Saki; Wendler, Frank; Durdiev, Dilshod (International Conference on Electrical, Computer, Communications and Mechatronics Engineering, ICECCME 2021, 2021)
BaTiO3 is one of the well-known ferroelectric and piezoelectric materials, which has been widely used in various devices. However, the microscopic mechanism of the ferroelectric domain growth is not understood well. We investigated the effects of point defects, mono- and di-vacancies of Ba, Ti, and O, on the domain growth of BaTiO3 using molecular dynamics simulation with the core-shell inter-atomic potential. We found the following: s (1) One kind of monovacancy, VO1, located on the TiO plane perpendicular to the applied electric field direction, acts to hinder the polarization inversion induced by the applied electric field. The monopole electric field produced by VO1 either hinders or assists the local polarization inversion in accordance with the local intensity of the total electric field. (2) The 1st-neighbor divacancies VBa-VO and VTi-VO as compared to the 2nd-neighbor divacancies asymmetrically affect the domain growth with respect to the applied electric field, making the hysteresis behavior of applied electric field vs. polarization relation. The domain grows even at a small electric field when the directions of the applied electric field and the divacancy dipole are mutually the same. (3) The domain growth speed towards the applied electric field direction is about 2 orders of magnitude higher than that towards the perpendicular direction.
CRIS-Team Scopus Importer:2021-12-03
Keywords: Barium titanate; Molecular dynamics simulation; Point defect

INVERSE PROBLEM OF DETERMINING THE TIME-DEPENDENT BEAM STIFFNESS COEFFICIENT IN THE BEAM VIBRATION EQUATION USING THE FINITE DIFFERENCE METHOD - Durdimuratovich, Durdiev Umidjon; Durdiev, Dilshod (Eurasian Journal of Mathematical and Computer Applications, 2024)
In this study, we consider the inverse problem of determining the time-dependent beam stiffness coefficient q(t) and transverse bending vibrations u(x, t) of a homogeneous beam using the finite difference method. The problem is governed by a fourth-order partial differential equation, which is discretized in space and time using numerical techniques to obtain an accurate and stable solution. An additional condition in the form of an integral is also included to determine q(t). The results obtained for different discretization grid points are compared, and a simple test example is presented to demonstrate the accuracy and agreement of the numerical solutions with analytical solutions. The paper provides a comprehensive overview of the methodology used to solve the inverse problem, and presents a detailed analysis of the results obtained.
CRIS-Team Scopus Importer:2024-06-14
Keywords: beam vibration equation; direct problem; finite difference method; inverse problem

Microscopic structure and migration of 90° ferroelectric domain wall in BaTiO3determined via molecular dynamics simulations - Azuma, Hikaru; Ogata, Shuji; Kobayashi, Ryo; Uranagase, Masayuki; Tsuzuki, Takahiro; Durdiev, Dilshod; Wendler, Frank (Journal of Applied Physics, 2023)
BaTiO3 is a well-known piezoelectric material with commercial uses. The ferroelectric state of BaTiO3 generally comprises electrically polarized domains separated by domain walls (DWs). The DW alters local polarization vectors by an angle of 90° for 90° DW or 180° for 180° DW. The DW is crucial to piezoelectric properties such as response time and fatigue. Furthermore, the DW structure and its dynamics in BaTiO3 are not well understood. Hence, for the first time, we theoretically obtained the atomistic structure of the 90° DW via molecular dynamics simulations at 300 K with the core-shell interatomic potential, using a large-scale system with a side length of 2.8 × 10 3 Å. The width of the 90° DW thereby obtained was approximately 30 Å, which was 20 Å wider than that of the 180° DW. Under the external electric field E → ext parallel to the DW, we observed an extension of a domain having a polarization vector with a positive component along the E → ext-direction. The migration velocity of the 90° DW was approximately two times that of the 180° DW at the same E ext in the range 7 - 20 MV / m. For E ext ≥ 15 MV / m, the migration velocity of the 90° DW in the direction with a positive component along the polarization vector of the extending domain was substantially higher than that in the opposite direction. The physical causes of the difference in the migration velocities of the 90° DW in the two directions were analyzed.
CRIS-Team Scopus Importer:2023-03-24

Parameterization of a phase field model for ferroelectrics from molecular dynamics data - Durdiev, Dilshod; Wendler, Frank; Zaiser, Michael; Azuma, Hikaru; Tsuzuki, Takahiro; Ogata, Shuji; Ogawa, Tomohiro; Kobayashi, Ryo; Uranagase, Masayuki (Acta Materialia, 2025)
In this work, molecular dynamics (MD) simulations of ferroelectric BaTiO3 are used to generate parameters for a phase-field (PF) model. The MD simulations provide important input parameters, such as elastic and piezoelectric properties, as well as domain wall (DW) widths and velocities. A parameterization technique is proposed to incorporate the MD results into the PF simulations, allowing for the generation of relevant parameters. Anisotropic interface energy coefficients are used to match the widths of both the 180° and 90° DWs in the PF simulations to the MD data. The velocities of the DWs are calculated and compared to the results obtained from MD simulations, demonstrating excellent agreement. Furthermore, we investigate the disparity between coercive fields obtained from PF simulations and MD simulations. Initially, our PF simulations yield coercive fields approximately twice as high as those observed in MD simulations. To address this discrepancy, we introduce a nucleus into the PF simulation system. The parameters of this nucleus are derived from a statistical analysis of coercive field data from MD simulations. By incorporating the nucleus model, we achieve a coercive field in PF simulations that closely aligns with the MD results. Validation of the parameterized PF model using MD data obtained with different initial conditions and thermodynamic constraints shows good agreement, further confirming the model's accuracy.
CRIS-Team Scopus Importer:2024-11-15
Keywords: Ferroelectrics; Molecular dynamics; Nucleus; Phase-field model

The Fourier spectral method for determining a heat capacity coefficient in a parabolic equation - Durdiev, Durdimurod; Durdiev, Dilshod (Turkish Journal of Mathematics, 2022)
In this paper, the comparison of finite difference and Fourier spectral numerical methods for an inverse problem of simultaneously determining an unknown coefficient in a parabolic equation with the usual initial and boundary conditions is proposed. We represent the detailed description of the methods and their algorithms. The research work conducted in this paper shows that the Fourier spectral method is highly accurate.
CRIS-Team Scopus Importer:2022-12-23
Keywords: Fourier spectral method; Inverse problem; Numerical algorithm; Overdetermination condition; Parabolic equation

Tuning Ferroelectric Properties of Barium Titanate by Lateral Strain: A Molecular Dynamics Simulation Study - Azuma, Hikaru; Shimoi, Seiya; Tsuzuki, Takahiro; Kobayashi, Ryo; Uranagase, Masayuki; Deguchi, Genki; Wendler, Frank; Durdiev, Dilshod; Ogata, Shuji (Physica Status Solidi-Rapid Research Letters, 2023)
BaTiO3 (BT), a lead-free ferroelectric material, is employed in energy-conversion devices, including actuators and capacitors. However, its ferroelectric properties, such as the piezoelectric coefficient and Curie temperature, fall short of those of harmful lead-based ferroelectrics, such as Pb(Zrx, Ti1−x)O3. In this study, a BT crystal is examined under biaxial strain (i.e., strain in the a- and b-directions of the unit cell) to investigate the alterations in its ferroelectric properties. The piezoelectric coefficient, Curie temperature, polarization magnitude, and coercive electric field are calculated under varying biaxial strains using molecular dynamics simulations. The simulations utilize a core–shell-type interatomic potential developed from first-principles electronic structure calculations. In the findings, it is revealed that 1) the Curie temperature, polarization magnitude, and coercive electric field increase, whereas the piezoelectric coefficient in the c-direction decreases under biaxial compression; 2) modifications in the ferroelectric properties depend on the area of ab-plane and not on its aspect ratio. Comprehensive analyses of the Ti-displacement distribution offer microscopic insights into strain-induced shifts in ferroelectric properties.
CRIS-Team Scopus Importer:2023-10-06
Keywords: BaTiO; ferroelectrics; molecular dynamics; piezoelectricities; strains

Vacancy-assisted ferroelectric domain growth in BaTiO3under an applied electric field: A molecular dynamics study - Tsuzuki, Takahiro; Ogata, Shuji; Kobayashi, Ryo; Uranagase, Masayuki; Shimoi, Seiya; Durdiev, Dilshod; Wendler, Frank (Journal of Applied Physics, 2022)
BaTiO3 is a well-known piezoelectric material, which is widely used in various devices. In general, the ferroelectric state of BaTiO3 is composed of polarized domains. The growth of these domains due to an applied electric field or stress is related to the piezoelectric performance. We investigated the effects of various point defects, monovacancies VBa, VTi, VO, and first- and second-neighbor divacancies VBa-VO, VTi-VO on polarized domain growth in BaTiO3 under an applied electric field by molecular dynamics simulations using the core-shell inter-atomic potential. We found that (i) the first-neighbor divacancy VBa-VO is the most effective in assisting the domain growth under an applied electric field (i.e., a smaller coercive electric field) in an asymmetrical manner with respect to the electric field direction. This is mainly due to the creation of an electric field around VBa-VO by significant Ti shifts toward VBa with the assistance of VO. (ii) Domain growth proceeds in a 1 + 2 dimensional manner. The domain growth velocity in the direction of the applied electric field is approximately two orders of magnitude higher than that in the perpendicular direction. (iii) Increasing the density of the divacancy VBa-VO further lowers the coercive electric field when the applied electric field is parallel to the divacancy dipoles. The present results will be essential for designing the type, orientation, and density of defects to modify the coercive electric field of BaTiO3 in defect engineering.
CRIS-Team Scopus Importer:2022-06-03