In this paper we investigate the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential.By the energy method and the theory of Campanato spaces,...In this paper we investigate the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential.By the energy method and the theory of Campanato spaces,we prove the existence and the uniqueness of classical solutions in 3-dimensional space.展开更多
In this paper we consider the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential. By the L^P type estimates and the theory of Morrey spaces,...In this paper we consider the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential. By the L^P type estimates and the theory of Morrey spaces,we prove the Holder continuity of the solutions.Then we obtain the existence of global classical solutions.The present work can be viewed as an extension to the previous work on the Cahn-Hilliard equation with concentration dependent mobility and potential.展开更多
By incorporating the contribution of solute atoms to the Helmholtz free energy of solid solution,a linear relation is derived between Young's modulus and the concentration of solute atoms.The solute atoms can eith...By incorporating the contribution of solute atoms to the Helmholtz free energy of solid solution,a linear relation is derived between Young's modulus and the concentration of solute atoms.The solute atoms can either increase or decrease Young's modulus of solid solution,depending on the first-order derivative of the Helmholtz free energy with respect to the concentration of solute atoms.Using this relation,a closed-form solution of the chemical stress in an elastic plate is obtained when the diffusion behavior in the plate can be described by the classical Fick's second law with convection boundary condition on one surface and zero flux on the other surface.The plate experiences tensile stress after short diffusion time due to asymmetrical diffusion,which will likely cause surface microcracking.The results show that the effect of the concentration dependence of Young's modulus on the evolution of chemical stress in elastic plates is negligible if the change of Young's modulus due to the diffusive motion of solute atomsis is not compatible in magnitude with Young's modulus of the pure material.Also,a new diffusion equation is developed for strictly regular binary solid solution.The effective diffusivity is a nonlinear function of the concentration of solute atoms.展开更多
Lu3Al5O12（LuAG） thin films with different Tb^3＋ concentration were prepared on carefully cleaned （111 ） silicon wafer by a Peehini process and dip-coating technique. Heat treatment was performed in the temperatur...Lu3Al5O12（LuAG） thin films with different Tb^3＋ concentration were prepared on carefully cleaned （111 ） silicon wafer by a Peehini process and dip-coating technique. Heat treatment was performed in the temperature range from 800 to 1100 ℃. The crystal structure was analyzed by XRD. The results show that LuAG film starts to crystallize at about 900 ℃, and the particle size increases with the sintering temperature. Excitation and emission spectra of Tb^3＋ doped LuAG films were measured. The effects of heat-treatment temperature and doping concentration of Th3 ＋ on the luminescent properties were also investigated. For a comparison study, Th^3＋-doped LuAG powders were also prepared by the same sol-gel method.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No.11001103)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.200801831002)+1 种基金the China Postdoctoral Science Foundation (Grant No.20100481229)the Fundamental Research Funds for the Central Universities
文摘In this paper we investigate the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential.By the energy method and the theory of Campanato spaces,we prove the existence and the uniqueness of classical solutions in 3-dimensional space.
基金The NSF(11001103)the SRFDP(200801831002) of China
文摘In this paper we consider the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential. By the L^P type estimates and the theory of Morrey spaces,we prove the Holder continuity of the solutions.Then we obtain the existence of global classical solutions.The present work can be viewed as an extension to the previous work on the Cahn-Hilliard equation with concentration dependent mobility and potential.
文摘By incorporating the contribution of solute atoms to the Helmholtz free energy of solid solution,a linear relation is derived between Young's modulus and the concentration of solute atoms.The solute atoms can either increase or decrease Young's modulus of solid solution,depending on the first-order derivative of the Helmholtz free energy with respect to the concentration of solute atoms.Using this relation,a closed-form solution of the chemical stress in an elastic plate is obtained when the diffusion behavior in the plate can be described by the classical Fick's second law with convection boundary condition on one surface and zero flux on the other surface.The plate experiences tensile stress after short diffusion time due to asymmetrical diffusion,which will likely cause surface microcracking.The results show that the effect of the concentration dependence of Young's modulus on the evolution of chemical stress in elastic plates is negligible if the change of Young's modulus due to the diffusive motion of solute atomsis is not compatible in magnitude with Young's modulus of the pure material.Also,a new diffusion equation is developed for strictly regular binary solid solution.The effective diffusivity is a nonlinear function of the concentration of solute atoms.
基金Project supported by the National High Technology Research and Development Programof China(863 Program) (2002 AA324070) and the National Natural Science Foundation of China (50332050)
文摘Lu3Al5O12（LuAG） thin films with different Tb^3＋ concentration were prepared on carefully cleaned （111 ） silicon wafer by a Peehini process and dip-coating technique. Heat treatment was performed in the temperature range from 800 to 1100 ℃. The crystal structure was analyzed by XRD. The results show that LuAG film starts to crystallize at about 900 ℃, and the particle size increases with the sintering temperature. Excitation and emission spectra of Tb^3＋ doped LuAG films were measured. The effects of heat-treatment temperature and doping concentration of Th3 ＋ on the luminescent properties were also investigated. For a comparison study, Th^3＋-doped LuAG powders were also prepared by the same sol-gel method.
