Based on the Karma model and the Eggleston regularization technique of the strong interfacial energy anisotropy, a phase-field model was established for HCP materials. An explicit finite difference numerical method wa...Based on the Karma model and the Eggleston regularization technique of the strong interfacial energy anisotropy, a phase-field model was established for HCP materials. An explicit finite difference numerical method was used to solve phase field model and simulate the dendrite growth behaviors of HCP materials. Results indicate that the dendrite morphology presents obvious six-fold symmetry, and discontinuity in the variation of interface orientation occurs, resulting in a fact that the corners were formed at the tips of the main stem and side branches. When the interfacial energy anisotropy strength is lower than the critical value(1/35), the steady-state tip velocity of dendrite increases with anisotropy as expected. As the anisotropy strength crosses the critical value, the steady-state tip velocity drops down by about 0.89%. With further increase in anisotropy strength, the steady-state tip velocity increases and reaches the maximum value at anisotropy strength of 0.04, then decreases.展开更多
A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth m...A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth morphology were investigated, respectively. These results indicate that the nucleus grows into a hexagonal symmetry faceted dendrite. When the mesh grid is above 640×640, the size has no much effect on the shape. With the increase in the anisotropy value, the tip velocities of faceted dendrite increase and reach a balance value, and then decrease gradually. With the increase in the supersaturation value, crystal evolves from circle to the developed faceted dendrite morphology. Based on the Wulff theory and faceted symmetry morphology diagram, the proposed model was proved to be effective, and it can be generalized to arbitrary crystal symmetries.展开更多
Numerical simulations based on a new regularized phase-field model were presented, to simulate the solidification of hexagonal close-packed materials with strong interfacial energy anisotropies. Results show that the ...Numerical simulations based on a new regularized phase-field model were presented, to simulate the solidification of hexagonal close-packed materials with strong interfacial energy anisotropies. Results show that the crystal grows into facet dendrites,displaying six-fold symmetry. The size of initial crystals has an effect on the branching-off of the principal branch tip along the<100> direction, which is eliminated by setting the b/a(a and b are the semi-major and semi-minor sizes in the initial elliptical crystals, respectively) value to be less than or equal to 1. With an increase in the undercooling value, the equilibrium morphology of the crystal changes from a star-like shape to facet dendrites without side branches. The steady-state tip velocity increases exponentially when the dimensionless undercooling is below the critical value. With a further increase in the undercooling value, the equilibrium morphology of the crystal grows into a developed side-branch structure, and the steady-state tip velocity of the facet dendrites increases linearly. The facet dendrite growth has controlled diffusion and kinetics.展开更多
We review recent studies by different experimental means of ultrathin films,exhibiting thickness-driven spin reorientation transitions(SRTs).The stage is set by determining,via phenomenological thermodynamic descripti...We review recent studies by different experimental means of ultrathin films,exhibiting thickness-driven spin reorientation transitions(SRTs).The stage is set by determining,via phenomenological thermodynamic description,of the relevant phase diagrams for the possible types of SRT with and without applied magnetic field.Suitable representation may be chosen such that best use is made of the linear character(under thickness variation) of the system's path in anisotropy space.The latter involves higher-order bulk and surface anisotropies in a substantial way.We examine sensitive experimental techniques for the detection and quantification of SRTs,such as hysteresis measurements with magneto-optical Kerr effect(MOKE),micromagnetic studies utilizing scanning electron microscopy with polarization analysis(SEMPA),photoemission electron microscopy(PEEM) and spin-polarized low-energy electron microscopy(SPLEEM) as well as ac magnetic susceptibility measurements via MOKE.Key issues are conclusively discussed including the identification of reliable experimental fingerprints about whether a given SRT proceeds via a phase of coexistence or via a cone(canted) phase.We demonstrate how the application of the general theoretical ideas to carefully designed measurements leads to the determination of the most important material parameters in any ultrathin-film SRT,namely,the surface(interface) magnetic anisotropy constants.The review concludes by our personal outline for future promising work on SRTs.展开更多
基金Project(10834015)supported by the National Natural Science Foundation of ChinaProject(12SKY01-1)supported by the Doctoral Fund of Shangluo University,China
文摘Based on the Karma model and the Eggleston regularization technique of the strong interfacial energy anisotropy, a phase-field model was established for HCP materials. An explicit finite difference numerical method was used to solve phase field model and simulate the dendrite growth behaviors of HCP materials. Results indicate that the dendrite morphology presents obvious six-fold symmetry, and discontinuity in the variation of interface orientation occurs, resulting in a fact that the corners were formed at the tips of the main stem and side branches. When the interfacial energy anisotropy strength is lower than the critical value(1/35), the steady-state tip velocity of dendrite increases with anisotropy as expected. As the anisotropy strength crosses the critical value, the steady-state tip velocity drops down by about 0.89%. With further increase in anisotropy strength, the steady-state tip velocity increases and reaches the maximum value at anisotropy strength of 0.04, then decreases.
基金Projects(11102164,11304243)supported by the National Natural Science Foundation of ChinaProject(2014JQ1039)supported by the Natural Science Foundation of Shannxi Province,China+1 种基金Project(3102016ZY027)supported by the Fundamental Research Funds for the Central Universities of ChinaProject(13GH014602)supported by the Program of New Staff and Research Area Project of NWPU,China
文摘A numerical simulation based on a regularized phase field model is developed to describe faceted dendrite growth morphology. The effects of mesh grid, anisotropy, supersaturation and fold symmetry on dendrite growth morphology were investigated, respectively. These results indicate that the nucleus grows into a hexagonal symmetry faceted dendrite. When the mesh grid is above 640×640, the size has no much effect on the shape. With the increase in the anisotropy value, the tip velocities of faceted dendrite increase and reach a balance value, and then decrease gradually. With the increase in the supersaturation value, crystal evolves from circle to the developed faceted dendrite morphology. Based on the Wulff theory and faceted symmetry morphology diagram, the proposed model was proved to be effective, and it can be generalized to arbitrary crystal symmetries.
基金Project(10834015) supported by the National Natural Science Foundation of ChinaProject(12SKY01-1) supported by the Doctoral Fund of Shangluo University,ChinaProject(14JK1223) supported by the Scientific Research Program of Shaanxi Provincial Education Department,China
文摘Numerical simulations based on a new regularized phase-field model were presented, to simulate the solidification of hexagonal close-packed materials with strong interfacial energy anisotropies. Results show that the crystal grows into facet dendrites,displaying six-fold symmetry. The size of initial crystals has an effect on the branching-off of the principal branch tip along the<100> direction, which is eliminated by setting the b/a(a and b are the semi-major and semi-minor sizes in the initial elliptical crystals, respectively) value to be less than or equal to 1. With an increase in the undercooling value, the equilibrium morphology of the crystal changes from a star-like shape to facet dendrites without side branches. The steady-state tip velocity increases exponentially when the dimensionless undercooling is below the critical value. With a further increase in the undercooling value, the equilibrium morphology of the crystal grows into a developed side-branch structure, and the steady-state tip velocity of the facet dendrites increases linearly. The facet dendrite growth has controlled diffusion and kinetics.
基金supported by the State Key Programme for Basic Research of China (Grant No. 2010CB923401)National Natural Science Foundation of China (Grant Nos. 10834001,10974087 and 11023002)Natural Science Foundation of Jiangsu (Grant No. BK2012300)
文摘We review recent studies by different experimental means of ultrathin films,exhibiting thickness-driven spin reorientation transitions(SRTs).The stage is set by determining,via phenomenological thermodynamic description,of the relevant phase diagrams for the possible types of SRT with and without applied magnetic field.Suitable representation may be chosen such that best use is made of the linear character(under thickness variation) of the system's path in anisotropy space.The latter involves higher-order bulk and surface anisotropies in a substantial way.We examine sensitive experimental techniques for the detection and quantification of SRTs,such as hysteresis measurements with magneto-optical Kerr effect(MOKE),micromagnetic studies utilizing scanning electron microscopy with polarization analysis(SEMPA),photoemission electron microscopy(PEEM) and spin-polarized low-energy electron microscopy(SPLEEM) as well as ac magnetic susceptibility measurements via MOKE.Key issues are conclusively discussed including the identification of reliable experimental fingerprints about whether a given SRT proceeds via a phase of coexistence or via a cone(canted) phase.We demonstrate how the application of the general theoretical ideas to carefully designed measurements leads to the determination of the most important material parameters in any ultrathin-film SRT,namely,the surface(interface) magnetic anisotropy constants.The review concludes by our personal outline for future promising work on SRTs.