Article
Materials Science, Multidisciplinary
Sepideh Kavousi, Mohsen Asle Zaeem
Summary: A quantitative phase-field model is developed to predict solute trapping in solidification processes relevant to additive manufacturing, showing good agreement with experimental data and theoretical models up to diffusive velocities. The model accurately predicts partition coefficient and kinetic undercooling for a wide range of solidification velocities, with less sensitivity to diffusive interface width.
Article
Materials Science, Multidisciplinary
Yijia Gu, Xiaoming He, Daozhi Han
Summary: In this study, a phase-field model was developed for the rapid solidification of dilute binary alloys. The influences of simplifications on interface kinetics, solute trapping, and thermal diffusion were quantified, highlighting the importance of thermal diffusion and interface kinetics for quantitative modeling of alloy solidification processes. Using the rapid solidification of a melt-spun ribbon as an example, it was shown that the phase-field model with all three aspects considered can accurately predict solidification structures by capturing the complex interplay among temperature, solute concentration, and interfacial velocity.
COMPUTATIONAL MATERIALS SCIENCE
(2021)
Article
Materials Science, Multidisciplinary
Chuanzhen Ma, Ruijie Zhang, Zixin Li, Xue Jiang, Yongwei Wang, Cong Zhang, Haiqing Yin, Xuanhui Qu
Summary: In this study, the phase field and Lattice Boltzmann Method were used to predict dendrite morphology, solute precipitation, and diffusion during solidification process. It was found that solidification shrinkage and shrinkage-flow have significant effects on dendritic morphology and solute segregation. The study also observed the increase in solute concentration in the channel when continuous feeding of melt was applied in crystal growth.
COMPUTATIONAL MATERIALS SCIENCE
(2022)
Article
Multidisciplinary Sciences
Ang Zhang, Bin Jiang, Zhipeng Guo, Jinglian Du, Qigui Wang, Fusheng Pan, Shoumei Xiong
Summary: The study investigates the thermal-solute-convection interaction during solidification through a high-performance numerical scheme. By utilizing a multilevel data structure and acceleration strategy, the computing efficiency is significantly improved, allowing for discussions on Al-Cu dendrite growth and its impact on microstructure evolution.
ADVANCED THEORY AND SIMULATIONS
(2021)
Article
Mathematics, Applied
Junfeng Xu, Markus Rettenmayr, Peter K. Galenko
Summary: The developed model describes diffusion-limited and diffusionless solidification of a eutectic alloy, providing new expressions for solute distribution coefficient and liquidus lines slope. The model's predictions are compared with experimental data for Fe-B alloy solidification, showing good agreement especially for low and high undercoolings. The influence of model parameters on growth kinetics during eutectic solidification is discussed.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Materials Science, Multidisciplinary
Xiying Liu, Chunwen Guo, Hongliang Zhao, Yuheng Fan, Xianglei Dong, Junjie Li, Qiudong Li
Summary: This study investigates the growth direction selection of inclined columnar dendrites during directional solidification of Mg-4 wt% Li alloy with HCP crystal structure using phase-field simulations. The results show that the growth direction of dendrites varies with pulling velocity and primary dendrite spacing, and is influenced by solute interaction between neighboring dendrites. At high pulling velocities, the solute interaction weakens or fails, leading to a deviation from the previous model.
MATERIALS TODAY COMMUNICATIONS
(2022)
Article
Materials Science, Multidisciplinary
Xianqiang Fan, Natalia Shevchenko, Catherine Tonry, Samuel J. Clark, Robert C. Atwood, Sven Eckert, Koulis Pericleous, Peter D. Lee, Andrew Kao
Summary: Solute channel formation can occur in various processes and is influenced by the interaction between an external magnetic field and thermoelectric currents at solid/liquid interfaces. In this study, we used in situ synchrotron X-ray imaging and numerical simulations to investigate the characteristics of flow and solute transport under thermoelectric magnetohydrodynamic (TEMHD) effects. Our observations suggest that macroscopic and microscopic TEMHD flows are the primary mechanisms controlling plume migration and channel bias. We also discovered that grain orientation can modify solute flow through anisotropic permeability. These findings led to the proposed strategy of using a time-modulated magnetic field for solute channel-free solidification.
Article
Physics, Condensed Matter
Roberto E. Rozas, Vladimir Ankudinov, Peter K. Galenko
Summary: A revised study of the growth and melting of crystals in congruently melting Al50Ni50 alloy is carried out using molecular dynamics (MD) and phase field (PF) methods. The material properties are estimated using an embedded atom method (EAM) potential, which shows better agreement with experimental data compared to previous works. The kinetics of melting and solidification are quantitatively evaluated using the 'crystal-liquid interface velocity-undercooling' relationship, and the results are described by the kinetic PF model and hodograph equation.
JOURNAL OF PHYSICS-CONDENSED MATTER
(2022)
Article
Materials Science, Multidisciplinary
Hui Xing, Hanxu Jing, Xianglei Dong, Lei Wang, Yongsheng Han, Rui Hu
Summary: This paper investigates columnar cellular growth with kinetic effects in rapid directional solidification of alloys using a quantitative phase-field model. The study finds that kinetic effects play important roles in the morphological transition and spacing selection of cellular arrays. The inclusion of kinetic effects results in an increase of solute in the solid phase and solute enrichment in the interdendritic liquid channel.
MATERIALS TODAY COMMUNICATIONS
(2022)
Article
Engineering, Mechanical
Matti Lindroos, Tatu Pinomaa, Kais Ammar, Anssi Laukkanen, Nikolas Provatas, Samuel Forest
Summary: A coupled phase field and crystal plasticity model is used to analyze the formation of dislocation structures and residual stresses during the rapid solidification of additively manufactured 316L stainless steel. The study reveals the significant influence of microsegregation related to the intra-grain cellular microstructure on the microstructure and mechanical properties.
INTERNATIONAL JOURNAL OF PLASTICITY
(2022)
Article
Materials Science, Multidisciplinary
Tong-Zhao Gong, Yun Chen, Wei-Ye Hao, Xing-Qiu Chen, Dian-Zhong Li
Summary: This study investigated the effects of carbide forming element diffusion, primary austenite grain size, and cooling rate on solute segregation and carbide precipitation during the solidification of an Fe-C binary alloy using the phase-field method coupled with a thermodynamic database. The results showed that increasing the ratio of solute diffusivity in solid and liquid, refining the grain size of primary austenite to below a critical value, and increasing the cooling rate can reduce solute segregation and precipitation of primary carbide. Two characteristic parameters were introduced to quantitatively evaluate solute segregation, providing potential ways to control solute segregation and primary carbide precipitation in bearing steels.
Article
Multidisciplinary Sciences
Tatu Pinomaa, Matti Lindroos, Paul Jreidini, Matias Haapalehto, Kais Ammar, Lei Wang, Samuel Forest, Nikolas Provatas, Anssi Laukkanen
Summary: Rapid solidification leads to unique microstructural features and formation of crystalline defects. Understanding the formation mechanisms of these defects is crucial for material's mechanical properties and performance features. This study conducts a multiscale modelling analysis to investigate the rapid solidification induced crystalline defects and compares them to past experiments.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Chemistry, Physical
Binting Huang, Jishi Yang, Zhiheng Luo, Yang Wang, Nan Wang
Summary: The rapid solidification process often leads to high-density microstructure defects and residual thermal stress in metals. Twin boundaries, which are potentially beneficial, have been observed in rapidly solidified nanocrystalline microstructures. This study proposes a pathway for forming twin boundaries and provides a detailed derivation of strain inhomogeneities and the deformation twinning phase field method. By calculating the cooling-induced thermal strain inhomogeneity and growth thresholds for deformation twinning, it is shown that residual thermal strain hotspots in the microstructure can reach the threshold for deformation twinning when there is a significant difference in shear elastic property between grain boundaries and the bulk material.
Article
Materials Science, Multidisciplinary
Y. Liu, K. Zweiacker, C. Liu, J. T. McKeown, J. M. K. Wiezorek
Summary: The evolution of rapid solidification microstructure and solidification interface velocity of hypereutectic Al-20at.%Cu alloy after laser melting has been studied experimentally. It was found that the formation of microstructure was dominated by eutectic, alpha-cell, and banded morphology grains, and the growth modes changed with increasing interface velocity.
Article
Materials Science, Multidisciplinary
Mehran Golizadeh, Francisca Mendez Martin, Stefan Wurster, Johann P. Mogeritsch, Abdellah Kharicha, Szilard Kolozsvari, Christian Mitterer, Robert Franz
Summary: A combination of traditional and advanced high-resolution characterization techniques were applied to study modified layers on the surface of three composite Al-Cr arc cathodes with identical nominal composition, revealing the formation of metastable phases due to high cooling rates involved during solidification. The modified layers mainly consisted of Cr solid solution, high temperature cubic Al8Cr5, supersaturated Al solid solution, and icosahedral quasicrystal. The average cooling rate was estimated to be 10(6) K/s based on measurements and simulations.
JOURNAL OF MATERIALS SCIENCE & TECHNOLOGY
(2021)
Article
Materials Science, Multidisciplinary
M. Reinartz, M. Kolbe, D. M. Herlach, M. Rettenmayr, L. Toropova, D. Alexandrov, P. K. Galenko
Summary: Experiments were conducted on the International Space Station to study the dendritic growth of Al-35 at%Ni alloy under primary solidification. The velocity versus undercooling relationship showed an anomalous behavior, with the velocity decreasing at low undercoolings and increasing at higher undercoolings. A special mechanism was identified through the different crystals having scales and dendritic morphology. This unusual behavior was confirmed experimentally and explained theoretically using analytical solutions for crystal growth.
Article
Mathematics, Applied
Liubov Toropova, Markus Rettenmayr, Peter K. Galenko, Dmitri Alexandrov
Summary: A theory of stable dendrite growth in an undercooled binary melt under intense convection is proposed, combining convective conditions with conductive heat and mass transfer boundary conditions to cover the entire range of melt undercooling. By deriving a selection criterion and undercooling balance condition, the theory successfully determines the combination of dendrite tip velocity and tip diameter. The results are in good agreement with experimental data on Al-Ge crystallization.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Junfeng Xu, Tao Zhang, Peter K. Galenko
Summary: This article introduces an analytical model to understand the rod growth of eutectic in the bulk undercooled melt, aiming to predict transitions in eutectic patterns under different growth velocities, and presents mathematical simplifications for solving Bessel functions as the most important priority for model calculation.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Dmitri Alexandrov, Peter K. Galenko
Summary: This article explores the hydrodynamic problem of oblique flow of a viscous incompressible fluid around the tip of a dendritic crystal. Approximate analytical solutions of Oseen's hydrodynamic equations in 2D and 3D cases using special curvilinear coordinates are obtained. The study reveals significant changes in the projections of fluid velocity with variations in flow slope and Reynolds number, and shows a limiting transition to previously known solutions for rectilinear fluid flow around a dendrite.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Multidisciplinary Sciences
Peter K. Galenko, Junfeng Xu
Summary: This study investigates the formation mechanism of metastable solid phases in rapidly solidified eutectic systems. It proposes a diffusionless growth model to suppress eutectic decomposition and analyzes atomic diffusion in the growth of rod eutectics. A simplified calculating method for the Bessel function in the growth equation is also obtained, which can be applied to other rod eutectic growth models.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Multidisciplinary Sciences
Yindong Fang, Peter K. Galenko, Dongmei Liu, Klaus Hack, Markus Rettenmayr, Stephanie Lippmann
Summary: The thermodynamic description of the fcc phase in the Al-Cu system has been revised to predict metastable fcc/liquid phase equilibria. Experimental and modeling results were used to determine solidus and liquidus concentrations and to validate the new description. The methodology can be applied to other alloy systems.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Multidisciplinary Sciences
V Ankudinov, P. K. Galenko
Summary: This article presents a modified phase-field crystal model for simulating crystallization in colloidal and metallic systems. Through the study of chemical segregation dynamics, a structure diagram for the model is obtained, which shows qualitative agreement with the known equilibrium diagram based on thermodynamic functions.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Article
Multidisciplinary Sciences
E. Kharanzhevskiy, P. K. Galenko, M. Rettenmayr, S. Koch, R. Wonneberger, M. Zamoryanskaya, M. A. Yagovkina, D. A. Kirilenko, V. A. Bershtein, P. N. Yakushev, L. M. Egorova, K. N. Orekhova, V. G. Lebedev, A. Egorov, A. S. Senchenkov
Summary: This study investigates the structure formation during solidification of a Pd-Ni-Cu-P melt and finds that changes in heat transfer conditions lead to nonlinear changes in the structure characteristics. The experimental results show that a decrease in the cooling rate of the alloy increases the size, proportion, and composition of nanoinclusions in an amorphous matrix.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
Review
Crystallography
Liubov Toropova, Peter K. Galenko, Dmitri Alexandrov
Summary: In this paper, a theory of stable dendritic growth in undercooled melts with conductive and convective boundary conditions is developed. The analytical theory is constructed by separately considering the conductive and convective mechanisms. The laws for total undercooling and selection criteria for stable growth mode are derived for each mechanism. The case of simultaneous occurrence of these heat and mass transfer mechanisms is also studied by combining the conductive and convective laws using power stitching functions. The generalized selection theory is validated through comparison with experimental data for Al24Ge76 and Ti45Al55 undercooled melts.
Article
Physics, Condensed Matter
Roberto E. Rozas, Vladimir Ankudinov, Peter K. Galenko
Summary: A revised study of the growth and melting of crystals in congruently melting Al50Ni50 alloy is carried out using molecular dynamics (MD) and phase field (PF) methods. The material properties are estimated using an embedded atom method (EAM) potential, which shows better agreement with experimental data compared to previous works. The kinetics of melting and solidification are quantitatively evaluated using the 'crystal-liquid interface velocity-undercooling' relationship, and the results are described by the kinetic PF model and hodograph equation.
JOURNAL OF PHYSICS-CONDENSED MATTER
(2022)
Article
Physics, Multidisciplinary
P. K. Galenko
Summary: Convection has an impact on the primary crystalline structure, especially on the velocity and tip radius of dendrite crystals. This study focuses on the influence of convective flow on the spacing between neighboring crystals within the dendrite ensemble. A binary alloy's solidification process is considered in a stagnant boundary layer model under a imposed thermal gradient, which affects the microstructure and chemical microsegregation of crystals. The model takes into account the convective flow in the solution of the solute diffusion transport equation, deriving the chemical composition in the solidifying liquid and crystalline solid. The results of the model align with the Scheil-Brody-Flemings model, experimental data, and computational results.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2023)
Article
Crystallography
Junfeng Xu, Peter K. Galenko
Summary: This paper presents a solidification growth model that combines the effect of eutectic transformation and off-eutectic composition, and discusses the influence of model and material parameters on solidification kinetics by comparing them with experimental data. The computational results show that the off-eutectic growth model agrees well with experimental data on the solidification kinetics of Ni-B and Ti-Si alloys.
Article
Crystallography
Tongzhuang Niu, Junfeng Xu, Zhirui Yao, Zengyun Jian, Peter K. Galenko
Summary: This article proposes a method for measuring and analyzing the volume and density changes in high-temperature alloy melts using high-speed photography and computer MATLAB program image analysis technology. These techniques will aid in understanding the variations in the volume and density of high-temperature melt samples during the phase transition process.
Article
Thermodynamics
Eugenya V. Makoveeva, Dmitri V. Alexandrov, Peter K. Galenko
Summary: A linear morphological stability analysis is conducted to investigate the solid-liquid phase interface during the solidification processes of a binary melt with convection. The study reveals the significant influence of convection intensity on stability and solidification, and identifies a criterion for concentration supercooling in steady-state solidification conditions. Various crystallization scenarios are defined based on the obtained dispersion relation and neutral stability curve.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2023)
Article
Physics, Multidisciplinary
V. E. Ankudinov, P. K. Galenko
Summary: The crystallization of a supercooled metastable homogeneous phase into a hexagonal lattice was studied using the phase-field crystal model. The growth of the hexagonal lattice was described by a second-order model where the amplitudes of the first and second sublattices were considered separately. The formation of the hexagonal lattice occurred after the metastable triangular phase, and the kinetics of the crystallization front depended on the symmetry of the growing phase and the driving force magnitude.
