Fractional molecular field theory(FMFT)is a phenomenological theory that describes phase transitions in crystals with randomly distributed components,such as the relaxor-ferroelectrics and spin glasses.In order to ver...Fractional molecular field theory(FMFT)is a phenomenological theory that describes phase transitions in crystals with randomly distributed components,such as the relaxor-ferroelectrics and spin glasses.In order to verify the feasibility of this theory,this paper fits it to the Monte Carlo simulations of specific heat and susceptibility versus temperature of two-dimensional(2D)random-site Ising model(2D-RSIM).The results indicate that the FMFT deviates from the 2D-RSIM significantly.The main reason for the deviation is that the 2D-RSIM is a typical system of component random distribution,where the real order parameter is spatially heterogeneous and has no symmetry of space translation,but the basic assumption of FMFT means that the parameter is spatially uniform and has symmetry of space translation.展开更多
The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifur...The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models.Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions.To elucidate the idea,we apply this analytical approach to three representative phase field equations:the Allen-Cahn equation,the Cahn-Hilliard equation,and the Allen-Cahn-Ohta-Kawasaki system.The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.展开更多
In contrast to conventional transformers, power electronic transformers, as an integral component of new energy power system, are often subjected to high-frequency and transient electrical stresses, leading to heighte...In contrast to conventional transformers, power electronic transformers, as an integral component of new energy power system, are often subjected to high-frequency and transient electrical stresses, leading to heightened concerns regarding insulation failures. Meanwhile, the underlying mechanism behind discharge breakdown failure and nanofiller enhancement under high-frequency electrical stress remains unclear. An electric-thermal coupled discharge breakdown phase field model was constructed to study the evolution of the breakdown path in polyimide nanocomposite insulation subjected to high-frequency stress. The investigation focused on analyzing the effect of various factors, including frequency, temperature, and nanofiller shape, on the breakdown path of Polyimide(PI) composites. Additionally, it elucidated the enhancement mechanism of nano-modified composite insulation at the mesoscopic scale. The results indicated that with increasing frequency and temperature, the discharge breakdown path demonstrates accelerated development, accompanied by a gradual dominance of Joule heat energy. This enhancement is attributed to the dispersed electric field distribution and the hindering effect of the nanosheets. The research findings offer a theoretical foundation and methodological framework to inform the optimal design and performance management of new insulating materials utilized in high-frequency power equipment.展开更多
Thixocasting requires manufacturing of billets with non-dendritic microstructure.Aluminum alloy A356 billets were produced by rheocasting in a mould placed inside a linear electromagnetic stirrer.Subsequent heat treat...Thixocasting requires manufacturing of billets with non-dendritic microstructure.Aluminum alloy A356 billets were produced by rheocasting in a mould placed inside a linear electromagnetic stirrer.Subsequent heat treatment was used to produce a transition from rosette to globular microstructure.The current and the duration of stirring were explored as control parameters.Simultaneous induction heating of the billet during stirring was quantified using experimentally determined thermal profiles.The effect of processing parameters on the dendrite fragmentation was discussed.Corresponding computational modeling of the process was performed using phase-field modeling of alloy solidification in order to gain insight into the process of morphological changes of a solid during this process.A non-isothermal alloy solidification model was used for simulations.The morphological evolution under such imposed thermal cycles was simulated and compared with experimentally determined one.Suitable scaling using the thermosolutal diffusion distances was used to overcome computational difficulties in quantitative comparison at system scale.The results were interpreted in the light of existing theories of microstructure refinement and globularisation.展开更多
Single dendrite and multi-dendrite growth for Al-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking p...Single dendrite and multi-dendrite growth for Al-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking phenomenon can be observed. For multi-dendrite growth, there exists the competitive growth among the dendrites during solidification. As solidification proceeds, growing and coarsening of the primary arms occurs, together with the branching and coarsening of the secondary arms. When the diffusion fields of dendrite tips come into contact with those of the branches growing from the neighboring dendrites, the dendrites stop growing and being to ripen and thicken.展开更多
In this paper,a numerical investigation about the metal transfer of GMAW is investigated based on the phase field model.Be different of most published work,we take the thermocapillary effect and mixture energy into th...In this paper,a numerical investigation about the metal transfer of GMAW is investigated based on the phase field model.Be different of most published work,we take the thermocapillary effect and mixture energy into the process of phase transfer and interface change which is different from volume of fluid( VOF) method.We discretize the whole model with a continuous finite element method and we also apply a penalty formulation to the continuity condition enhancing the stability of the pressure.Metal transfer of GMAW with constant and pulse current is computed as numerical examples which agrees well with the data of high-speed photography.The result shows that the computing process of the phase field model is stability and it has a higher precision in predicting the diameter of droplet.展开更多
Liquid permeability of the mushy zone is important for porosity formation during the solidification process. In order to investigate the permeability of the mushy zone, an integrated model was developed by combining t...Liquid permeability of the mushy zone is important for porosity formation during the solidification process. In order to investigate the permeability of the mushy zone, an integrated model was developed by combining the phase field model and computational fluid dynamics (CFD) model. The three-dimensional multigrain dendrite morphology was obtained by using the phase field model. Subsequently, the computer-aided design (CAD) geometry and mesh were generated based on calculated dendrite morphologies. Finally, the permeability of the dendritic mushy zone was obtained by solving the Navier-Stokes and continuity equations in ANSYS Fluent software. As an example, the dendritic mushy zone permeability of Al-4.5wt%Cu alloy and its relationship with the solid fractions were studied in detail. The predicted permeability data can be input to the solidification model on a greater length scale for macro segregation and porosity simulations.展开更多
A new phase field method for two-dimensional simulations of binary alloy solidification was studied. A model basing on solute conservative in every unit was developed for solving the solute diffusion equation during s...A new phase field method for two-dimensional simulations of binary alloy solidification was studied. A model basing on solute conservative in every unit was developed for solving the solute diffusion equation during solidification. Two-dimensional computations were performed for ideal solutions and Ni-Cu dendritic growth into an isothermal and highly supersaturated liquid phase.展开更多
A model has been established to simulate the realistic spatio-temporal microstructure evolution in recrystallization of a magnesium alloy using the phase field approach. A set of rules have been proposed to decide the...A model has been established to simulate the realistic spatio-temporal microstructure evolution in recrystallization of a magnesium alloy using the phase field approach. A set of rules have been proposed to decide the real physical value of all parameters in the model. The thermodynamic software THERMOCALC is applied to determine the local chemical free energy and strain energy, which is added to the free energy density of grains before recrystallization. The Arrhenius formula is used to describe boundary mobility and the activity energy is suggested with a value of zinc segregation energy at the boundary. However, the mobility constant in the formula was found out by fitting to a group of grain size measurements during recrystallization of the alloy. The boundary range is suggested to decide the gradient parameters in addition of fitting to the experimental boundary energy value. These parameter values can be regarded as a database for other similar simulations and the fitting rules can also be applied to build up databases for any other alloy systems. The simulated results show a good agreement with reported experimental measurement of the alloy at the temperatures from 300 to 400℃ for up to 100 min but not at 250℃. This implies a mechanism variation in activity energy of the boundary mobility in the alloy at low temperature.展开更多
Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems.In this study,the growth process of multiple dendrites in Al-2-mole-%-Si binary al...Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems.In this study,the growth process of multiple dendrites in Al-2-mole-%-Si binary alloy under isothermal solidification was simulated using phase field model.The simulation results showed the impingement of arbitrarily oriented crystals and the competitive growth among the grains during solidification.With the increase of growing time,the grains begin to coalesce and impinge the adjacent grains.When the dendrites start to impinge,the dendrite growth is obviously inhibited.展开更多
<正> The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within themean-field theory based on Bogoliubov inequality for the Gibbs free energy.The ground-state phase diagr...<正> The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within themean-field theory based on Bogoliubov inequality for the Gibbs free energy.The ground-state phase diagram and thetricritical point are obtained in the transverse field Ω/zJ-longitudinal crystal D/zJ field plane.We find that there are thefirst order-order phase transitions in a very small range of D/zJ besides the usual first order-disorder phase transitionsand the second order-disorder phase transitions.展开更多
The ring-banded spherulite is a special morphology of polymer crystals and has attracted considerable attention over recent decades. In this study, a new phase field model with polymer characteristics is established t...The ring-banded spherulite is a special morphology of polymer crystals and has attracted considerable attention over recent decades. In this study, a new phase field model with polymer characteristics is established to investigate the emergence and formation mechanism of the ring-banded spherulites of crystalline polymers. The model consists of a nonconserved phase field representing the phase transition and a temperature field describing the diffusion of the released latent heat. The corresponding model parameters can be obtained from experimentally accessible material parameters.Two-dimensional calculations are carried out for the ring-banded spherulitic growth of polyethylene film under a series of crystallization temperatures. The results of these calculations demonstrate that the formation of ring-banded spherulites can be triggered by the self-generated thermal field. Moreover, some temperature-dependent characteristics of the ring-banded spherulites observed in experiments are reproduced by simulations, which may help to study the effects of crystallization temperature on the ring-banded structures.展开更多
All the quantitative phase field models try to get rid of the artificial factors of solutal drag, interface diffusion and interface stretch in the diffuse interface. These artificial non-equilibrium effects due to the...All the quantitative phase field models try to get rid of the artificial factors of solutal drag, interface diffusion and interface stretch in the diffuse interface. These artificial non-equilibrium effects due to the introducing of diffuse interface are analysed based on the thermodynamic status across the diffuse interface in the quantitative phase field model of binary alloys. Results indicate that the non-equilibrium effects are related to the negative driving force in the local region of solid side across the diffuse interface. The negative driving force results from the fact that the phase field model is derived from equilibrium condition but used to simulate the non-equilibrium solidification process. The interface thickness dependence of the non-equilibrium effects and its restriction on the large scale simulation are also discussed.展开更多
Electrocaloric effect(ECE)of ferroelectrics has attracted considerable interest due to its potential application in environmentally friendly solid-state refrigeration.The discovery of giant ECE in ferroelectric thin f...Electrocaloric effect(ECE)of ferroelectrics has attracted considerable interest due to its potential application in environmentally friendly solid-state refrigeration.The discovery of giant ECE in ferroelectric thin films has greatly renewed the research activities and significantly stimulated experimental and theoretical investigations.In this review,the recent progress on the theoretical modeling of ECE in ferroelectric and antiferroelectric materials are introduced,which mainly focuses on the phase field modeling and first-principles based effective Hamiltonian method.We firstly provide the theoretical foundation and technique details for each method.Then a comprehensive review on the progress in the application of two methods and the strategies to tune the ECE are presented.Finally,we outline the practical procedure on the development of multi-scale computational method without experiemtal parameters for the screening of optimized electrocaloric materials.展开更多
In phase field fracture models the value of the order parameter distin- guishes between broken and undamaged material. At crack faces the order param- eter interpolates smoothly between these two states of the materia...In phase field fracture models the value of the order parameter distin- guishes between broken and undamaged material. At crack faces the order param- eter interpolates smoothly between these two states of the material, which can be regarded as phases. The crack evolution follows implicitly from the time inte- gration of an evolution equation of the order parameter, which is coupled to the mechanical field equations. Among other phenomena phase field fracture mod- els are able to reproduce crack nucleation in initially sound materials. For a 1D setting it has been shown that crack nucleation is triggered by the loss of stability of the unfractured, spatially homogeneous solution, and that the stability point depends on the size of the considered structure. This work numerically investi- gates to which extend size effects are reproduced by the 2D phase field model. Exemplarily, a finite element study of the hole size effect is performed and the simulation results are compared to exnerimental data.展开更多
In this article, we study the phase-field model of solidification for numerical simulation of dendritic crystal growth that occurs during the casting of metals and alloys. Phase-field model of solidification describes...In this article, we study the phase-field model of solidification for numerical simulation of dendritic crystal growth that occurs during the casting of metals and alloys. Phase-field model of solidification describes the physics of dendritic growth in any material during the process of under cooling. The numerical procedure in this work is based on finite difference scheme for space and the 4th-order Runge-Kutta method for time discretization. The effect of each physical parameter on the shape and growth of dendritic crystal is studied and visualized in detail.展开更多
The deconfinement phase transition with external magnetic field is investigated in the Friedberg-Lee model. We expand the potentiM around the two locM minima of the first-order deconfinement phase transition and extra...The deconfinement phase transition with external magnetic field is investigated in the Friedberg-Lee model. We expand the potentiM around the two locM minima of the first-order deconfinement phase transition and extract the ground state of the system in the frame of functional renormalization group. By solving the flow equations we find that the magnetic field displays a catalysis effect and it becomes more difficult to break through the confinement.展开更多
Discrete materials such as powders and granular materials have been widely used due to their specific characteristics. The precise evaluation is accordingly becoming important, and various numerical schemes have been ...Discrete materials such as powders and granular materials have been widely used due to their specific characteristics. The precise evaluation is accordingly becoming important, and various numerical schemes have been developed. However, the interactions among the constituent particles are still difficult to model precisely. Especially, contact conditions, which vary with material properties and circumstances, are difficult to formulate. In this study, a computational model for simulating adhesive particles on contact in a many-particle system is proposed. The interaction between the particles was represented by a two-body repulsive force that depends on the distance between particles and an additional adhesive force at the contact point. A phase-field variable was introduced to express the surface of each particle, and the adhesive force was formulated using the phase-field distribution. As a result, the adhesion of particles was properly expressed. For a mono-particle system, neighboring particles adhered and uniformly aggregated, while for a dual-particle system, several characteristic patterns were obtained depending on the initial arrangement of the particles. Repulsive contact was also considered as a specific case, and the corresponding results were obtained.展开更多
Phase-field modeling for three-dimensional foam structures is presented. The foam structure, which is generally applicable for porous material design, is geometrically approximated with a space-filling structure, and ...Phase-field modeling for three-dimensional foam structures is presented. The foam structure, which is generally applicable for porous material design, is geometrically approximated with a space-filling structure, and hence, the analysis of the space-filling structure was performed using the phase field model. An additional term was introduced to the conventional multi-phase field model to satisfy the volume constraint condition. Then, the equations were numerically solved using the finite difference method, and simulations were carried out for several nuclei settings. First, the nuclei were set on complete lattice points for a bcc or fcc arrangement, with a truncated hexagonal structure, which is known as a Kelvin cell, or a rhombic dodecahedron being obtained, respectively. Then, an irregularity was introduced in the initial nuclei arrangement. The results revealed that the truncated hexagonal structure was stable against a slight irregularity, whereas the rhombic polyhedral was destroyed by the instability. Finally, the nuclei were placed randomly, and the relaxation process of a certain cell was traced with the result that every cell leads to a convex polyhedron shape.展开更多
By employing the phase-field-crystal models, the atomic crystallization process of hexagonal and square crystals is investigated with the emphasis on the growth mechanism and morphological change. A unified regime des...By employing the phase-field-crystal models, the atomic crystallization process of hexagonal and square crystals is investigated with the emphasis on the growth mechanism and morphological change. A unified regime describing the crystallization behavior of both crystals is obtained with the thermodynamic driving force varying. By increasing the driving force,, both crystals (in the steady-state) transform from a faceted polygon to an apex-bulged polygon, and then into a symmetric dendrite. For the faceted polygon, the interface advances by a layer-by-layer (LL) mode while for the apex-bulged polygonal and the deridritic crystals, it first adopts the LL mode and then transits into the multi-layer (ML) mode in the later stage. In particular, a shift of the nucleation sites from the face center to the area around the crystal tips is detected in the early growth stage of both crystals and is rationalized in terms of the relation between the crystal size and the driving force distribution. Finally, a parameter characterizing the complex shape change of square crystal is introduced.展开更多
基金Project supported by the Open Project of the Key Laboratory of Xinjiang Uygur Autonomous Region,China(Grant No.2021D04015)the Yili Kazakh Autonomous Prefecture Science and Technology Program Project,China(Grant No.YZ2022B021).
文摘Fractional molecular field theory(FMFT)is a phenomenological theory that describes phase transitions in crystals with randomly distributed components,such as the relaxor-ferroelectrics and spin glasses.In order to verify the feasibility of this theory,this paper fits it to the Monte Carlo simulations of specific heat and susceptibility versus temperature of two-dimensional(2D)random-site Ising model(2D-RSIM).The results indicate that the FMFT deviates from the 2D-RSIM significantly.The main reason for the deviation is that the 2D-RSIM is a typical system of component random distribution,where the real order parameter is spatially heterogeneous and has no symmetry of space translation,but the basic assumption of FMFT means that the parameter is spatially uniform and has symmetry of space translation.
基金supported as part of the Computational Materials Sciences Program funded by the U.S.Department of Energy,Office of Science,Basic Energy Sciences,under Award No.DE-SC0020145Y.Z.would like to acknowledge support for his effort by the Simons Foundation through Grant No.357963 and NSF grant DMS-2142500.
文摘The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems.Here,we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models.Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions.To elucidate the idea,we apply this analytical approach to three representative phase field equations:the Allen-Cahn equation,the Cahn-Hilliard equation,and the Allen-Cahn-Ohta-Kawasaki system.The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.
基金supported in part by the National Key R&D Program of China (No.2021YFB2601404)Beijing Natural Science Foundation (No.3232053)National Natural Science Foundation of China (Nos.51929701 and 52127812)。
文摘In contrast to conventional transformers, power electronic transformers, as an integral component of new energy power system, are often subjected to high-frequency and transient electrical stresses, leading to heightened concerns regarding insulation failures. Meanwhile, the underlying mechanism behind discharge breakdown failure and nanofiller enhancement under high-frequency electrical stress remains unclear. An electric-thermal coupled discharge breakdown phase field model was constructed to study the evolution of the breakdown path in polyimide nanocomposite insulation subjected to high-frequency stress. The investigation focused on analyzing the effect of various factors, including frequency, temperature, and nanofiller shape, on the breakdown path of Polyimide(PI) composites. Additionally, it elucidated the enhancement mechanism of nano-modified composite insulation at the mesoscopic scale. The results indicated that with increasing frequency and temperature, the discharge breakdown path demonstrates accelerated development, accompanied by a gradual dominance of Joule heat energy. This enhancement is attributed to the dispersed electric field distribution and the hindering effect of the nanosheets. The research findings offer a theoretical foundation and methodological framework to inform the optimal design and performance management of new insulating materials utilized in high-frequency power equipment.
文摘Thixocasting requires manufacturing of billets with non-dendritic microstructure.Aluminum alloy A356 billets were produced by rheocasting in a mould placed inside a linear electromagnetic stirrer.Subsequent heat treatment was used to produce a transition from rosette to globular microstructure.The current and the duration of stirring were explored as control parameters.Simultaneous induction heating of the billet during stirring was quantified using experimentally determined thermal profiles.The effect of processing parameters on the dendrite fragmentation was discussed.Corresponding computational modeling of the process was performed using phase-field modeling of alloy solidification in order to gain insight into the process of morphological changes of a solid during this process.A non-isothermal alloy solidification model was used for simulations.The morphological evolution under such imposed thermal cycles was simulated and compared with experimentally determined one.Suitable scaling using the thermosolutal diffusion distances was used to overcome computational difficulties in quantitative comparison at system scale.The results were interpreted in the light of existing theories of microstructure refinement and globularisation.
基金financially supported by the Educational Department of Liaoning Province (No.20060744)the Shenyang Nurturing Young Scientific Technological Talents Items (No.1081230-1-00)
文摘Single dendrite and multi-dendrite growth for Al-2 mol pct Si alloy during isothermal solidification are simulated by phase field method. In the case of single equiaxed dendrite growth, the secondary and the necking phenomenon can be observed. For multi-dendrite growth, there exists the competitive growth among the dendrites during solidification. As solidification proceeds, growing and coarsening of the primary arms occurs, together with the branching and coarsening of the secondary arms. When the diffusion fields of dendrite tips come into contact with those of the branches growing from the neighboring dendrites, the dendrites stop growing and being to ripen and thicken.
文摘In this paper,a numerical investigation about the metal transfer of GMAW is investigated based on the phase field model.Be different of most published work,we take the thermocapillary effect and mixture energy into the process of phase transfer and interface change which is different from volume of fluid( VOF) method.We discretize the whole model with a continuous finite element method and we also apply a penalty formulation to the continuity condition enhancing the stability of the pressure.Metal transfer of GMAW with constant and pulse current is computed as numerical examples which agrees well with the data of high-speed photography.The result shows that the computing process of the phase field model is stability and it has a higher precision in predicting the diameter of droplet.
基金financially supported by the National Key Research and Development Program of China(No.2016YFB0700503)National Natural Science Foundation of China(No.51701013)Beijing Laboratory of Metallic Materials and Processing for Modern Transportation
文摘Liquid permeability of the mushy zone is important for porosity formation during the solidification process. In order to investigate the permeability of the mushy zone, an integrated model was developed by combining the phase field model and computational fluid dynamics (CFD) model. The three-dimensional multigrain dendrite morphology was obtained by using the phase field model. Subsequently, the computer-aided design (CAD) geometry and mesh were generated based on calculated dendrite morphologies. Finally, the permeability of the dendritic mushy zone was obtained by solving the Navier-Stokes and continuity equations in ANSYS Fluent software. As an example, the dendritic mushy zone permeability of Al-4.5wt%Cu alloy and its relationship with the solid fractions were studied in detail. The predicted permeability data can be input to the solidification model on a greater length scale for macro segregation and porosity simulations.
基金the National Natural Science Foundation of China financially(Grant No.10176009)
文摘A new phase field method for two-dimensional simulations of binary alloy solidification was studied. A model basing on solute conservative in every unit was developed for solving the solute diffusion equation during solidification. Two-dimensional computations were performed for ideal solutions and Ni-Cu dendritic growth into an isothermal and highly supersaturated liquid phase.
基金the National Natural Science Foundation of China for the financial support under the grant Nos.50771028 and 50471024Education Ministry of China for an outstanding teacher research fund to this study.
文摘A model has been established to simulate the realistic spatio-temporal microstructure evolution in recrystallization of a magnesium alloy using the phase field approach. A set of rules have been proposed to decide the real physical value of all parameters in the model. The thermodynamic software THERMOCALC is applied to determine the local chemical free energy and strain energy, which is added to the free energy density of grains before recrystallization. The Arrhenius formula is used to describe boundary mobility and the activity energy is suggested with a value of zinc segregation energy at the boundary. However, the mobility constant in the formula was found out by fitting to a group of grain size measurements during recrystallization of the alloy. The boundary range is suggested to decide the gradient parameters in addition of fitting to the experimental boundary energy value. These parameter values can be regarded as a database for other similar simulations and the fitting rules can also be applied to build up databases for any other alloy systems. The simulated results show a good agreement with reported experimental measurement of the alloy at the temperatures from 300 to 400℃ for up to 100 min but not at 250℃. This implies a mechanism variation in activity energy of the boundary mobility in the alloy at low temperature.
基金supported by the Doctor Foundational Research Project in Shenyang Ligong University(Serial Number:0010).
文摘Phase field method offers the prospect of being able to perform realistic numerical experiments on dendrite growth in metallic systems.In this study,the growth process of multiple dendrites in Al-2-mole-%-Si binary alloy under isothermal solidification was simulated using phase field model.The simulation results showed the impingement of arbitrarily oriented crystals and the competitive growth among the grains during solidification.With the increase of growing time,the grains begin to coalesce and impinge the adjacent grains.When the dendrites start to impinge,the dendrite growth is obviously inhibited.
文摘<正> The transverse spin-2 Ising ferromagnetic model with a longitudinal crystal-field is studied within themean-field theory based on Bogoliubov inequality for the Gibbs free energy.The ground-state phase diagram and thetricritical point are obtained in the transverse field Ω/zJ-longitudinal crystal D/zJ field plane.We find that there are thefirst order-order phase transitions in a very small range of D/zJ besides the usual first order-disorder phase transitionsand the second order-disorder phase transitions.
基金Project supported by the National Key Basic Research Program of China(Grant No.2012CB025903)the National Natural Science Foundation of China(Grant No.11402210)+1 种基金the Northwestern Polytechnical University Foundation for Fundamental Research(Grant No.JCY20130141)the Ministry of Education Fund for Doctoral Students Newcomer Awards of China
文摘The ring-banded spherulite is a special morphology of polymer crystals and has attracted considerable attention over recent decades. In this study, a new phase field model with polymer characteristics is established to investigate the emergence and formation mechanism of the ring-banded spherulites of crystalline polymers. The model consists of a nonconserved phase field representing the phase transition and a temperature field describing the diffusion of the released latent heat. The corresponding model parameters can be obtained from experimentally accessible material parameters.Two-dimensional calculations are carried out for the ring-banded spherulitic growth of polyethylene film under a series of crystallization temperatures. The results of these calculations demonstrate that the formation of ring-banded spherulites can be triggered by the self-generated thermal field. Moreover, some temperature-dependent characteristics of the ring-banded spherulites observed in experiments are reproduced by simulations, which may help to study the effects of crystallization temperature on the ring-banded structures.
基金supported by the fund of the State Key Laboratory of Solidification Processing in NWPU,China (Grants Nos. 17-TZ-2007,03-TP-2008,and 24-TZ-2009)the Doctorate Foundation of Northwestern Polytechnical University
文摘All the quantitative phase field models try to get rid of the artificial factors of solutal drag, interface diffusion and interface stretch in the diffuse interface. These artificial non-equilibrium effects due to the introducing of diffuse interface are analysed based on the thermodynamic status across the diffuse interface in the quantitative phase field model of binary alloys. Results indicate that the non-equilibrium effects are related to the negative driving force in the local region of solid side across the diffuse interface. The negative driving force results from the fact that the phase field model is derived from equilibrium condition but used to simulate the non-equilibrium solidification process. The interface thickness dependence of the non-equilibrium effects and its restriction on the large scale simulation are also discussed.
基金the financial support from the National Natural Science Foundation of China(Grant No.11972320)Zhejiang Provincial Natural Science Foundation(Grant No.LZ17A020001).
文摘Electrocaloric effect(ECE)of ferroelectrics has attracted considerable interest due to its potential application in environmentally friendly solid-state refrigeration.The discovery of giant ECE in ferroelectric thin films has greatly renewed the research activities and significantly stimulated experimental and theoretical investigations.In this review,the recent progress on the theoretical modeling of ECE in ferroelectric and antiferroelectric materials are introduced,which mainly focuses on the phase field modeling and first-principles based effective Hamiltonian method.We firstly provide the theoretical foundation and technique details for each method.Then a comprehensive review on the progress in the application of two methods and the strategies to tune the ECE are presented.Finally,we outline the practical procedure on the development of multi-scale computational method without experiemtal parameters for the screening of optimized electrocaloric materials.
文摘In phase field fracture models the value of the order parameter distin- guishes between broken and undamaged material. At crack faces the order param- eter interpolates smoothly between these two states of the material, which can be regarded as phases. The crack evolution follows implicitly from the time inte- gration of an evolution equation of the order parameter, which is coupled to the mechanical field equations. Among other phenomena phase field fracture mod- els are able to reproduce crack nucleation in initially sound materials. For a 1D setting it has been shown that crack nucleation is triggered by the loss of stability of the unfractured, spatially homogeneous solution, and that the stability point depends on the size of the considered structure. This work numerically investi- gates to which extend size effects are reproduced by the 2D phase field model. Exemplarily, a finite element study of the hole size effect is performed and the simulation results are compared to exnerimental data.
文摘In this article, we study the phase-field model of solidification for numerical simulation of dendritic crystal growth that occurs during the casting of metals and alloys. Phase-field model of solidification describes the physics of dendritic growth in any material during the process of under cooling. The numerical procedure in this work is based on finite difference scheme for space and the 4th-order Runge-Kutta method for time discretization. The effect of each physical parameter on the shape and growth of dendritic crystal is studied and visualized in detail.
基金Supported by the National Natural Science Foundation of China under Grant No 11405122the China Postdoctoral Science Foundation under Grant No 2014M550483
文摘The deconfinement phase transition with external magnetic field is investigated in the Friedberg-Lee model. We expand the potentiM around the two locM minima of the first-order deconfinement phase transition and extract the ground state of the system in the frame of functional renormalization group. By solving the flow equations we find that the magnetic field displays a catalysis effect and it becomes more difficult to break through the confinement.
文摘Discrete materials such as powders and granular materials have been widely used due to their specific characteristics. The precise evaluation is accordingly becoming important, and various numerical schemes have been developed. However, the interactions among the constituent particles are still difficult to model precisely. Especially, contact conditions, which vary with material properties and circumstances, are difficult to formulate. In this study, a computational model for simulating adhesive particles on contact in a many-particle system is proposed. The interaction between the particles was represented by a two-body repulsive force that depends on the distance between particles and an additional adhesive force at the contact point. A phase-field variable was introduced to express the surface of each particle, and the adhesive force was formulated using the phase-field distribution. As a result, the adhesion of particles was properly expressed. For a mono-particle system, neighboring particles adhered and uniformly aggregated, while for a dual-particle system, several characteristic patterns were obtained depending on the initial arrangement of the particles. Repulsive contact was also considered as a specific case, and the corresponding results were obtained.
文摘Phase-field modeling for three-dimensional foam structures is presented. The foam structure, which is generally applicable for porous material design, is geometrically approximated with a space-filling structure, and hence, the analysis of the space-filling structure was performed using the phase field model. An additional term was introduced to the conventional multi-phase field model to satisfy the volume constraint condition. Then, the equations were numerically solved using the finite difference method, and simulations were carried out for several nuclei settings. First, the nuclei were set on complete lattice points for a bcc or fcc arrangement, with a truncated hexagonal structure, which is known as a Kelvin cell, or a rhombic dodecahedron being obtained, respectively. Then, an irregularity was introduced in the initial nuclei arrangement. The results revealed that the truncated hexagonal structure was stable against a slight irregularity, whereas the rhombic polyhedral was destroyed by the instability. Finally, the nuclei were placed randomly, and the relaxation process of a certain cell was traced with the result that every cell leads to a convex polyhedron shape.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.54175378,51474176,and 51274167)the Natural Science Foundation o Shaanxi Province,China(Grant No.2014JM7261)the Doctoral Foundation Program of Ministry of China(Grant No.20136102120021)
文摘By employing the phase-field-crystal models, the atomic crystallization process of hexagonal and square crystals is investigated with the emphasis on the growth mechanism and morphological change. A unified regime describing the crystallization behavior of both crystals is obtained with the thermodynamic driving force varying. By increasing the driving force,, both crystals (in the steady-state) transform from a faceted polygon to an apex-bulged polygon, and then into a symmetric dendrite. For the faceted polygon, the interface advances by a layer-by-layer (LL) mode while for the apex-bulged polygonal and the deridritic crystals, it first adopts the LL mode and then transits into the multi-layer (ML) mode in the later stage. In particular, a shift of the nucleation sites from the face center to the area around the crystal tips is detected in the early growth stage of both crystals and is rationalized in terms of the relation between the crystal size and the driving force distribution. Finally, a parameter characterizing the complex shape change of square crystal is introduced.