TAILIEUCHUNG - Báo cáo " Anharmonic effective potential, thermodynamic parameters, and EXAFS of hcp crystals "

Anharmonic effective potential, effective local force constant, thermal expansion coefficient, three leading cumulants, and EXAFS (Extended X-ray Absorption Fine Structure) of hcp crystals have been studied. Analytical expressions for these quantities have been derived. Numerical calculations have been carried out for Zn and Cd. They show a good agreement with experiment results measured at HASYLAB (DESY, Germany) and unnegligible anharmonic effects in the considered quantities. | VNU Journal of Science Mathematics - Physics 25 2009 213-219 Anharmonic effective potential thermodynamic parameters and EXAFS of hcp crystals Nguyen Van Hung Ngo Trong Hai Tong Sy Tien Le Hai Hung Faculty of Physics Hanoi University of Science VNU 334 Nguyen Trai Thanh Xuan Hanoi Vietnam Received 15 September 2009 Abstract. Anharmonic effective potential effective local force constant thermal expansion coefficient three leading cumulants and EXAFS Extended X-ray Absorption Fine Structure of hcp crystals have been studied. Analytical expressions for these quantities have been derived. Numerical calculations have been carried out for Zn and Cd. They show a good agreement with experiment results measured at HASYLAB DESY Germany and unnegligible anharmonic effects in the considered quantities. 1. Introduction EXAFS and its parameters are often measured at low temperatures and well analysed by the harmonic procedure 1 because the anharmonic contributions to atomic thermal vibrations can be neglected. But EXAFS may provide apparently different information on structure and on other parameters of the substances at different high temperatures 2-11 14 15 due to anharmonicity. This work is devoted to development of a new method for calculation and analysis of the high order anharmonic effective potential local force constant three leading cumulants thermal expansion coefficient and EXAFS of hcp crystals. Derivation of analytical expressions for these quantities is based on quantum statistical theory with the anharmonic correlated Einstein model 9 and Morse potential is used to characterize interaction between each pair of atoms. Numerical results for Zn and Cd are found to be in good agreement with experiment 16 and show unnegligible anharmonic effects in the considered quantities. 2. Formalism According to cumulant expansion approach the EXAFS oscillation function is given by 11 -2R 1 k c k -F ta eiF k exp 2ikR Y L2íị ls . n L n 1 where F k is the real atomic backscattering

• Báo cáo khoa học
• Anharmonic
• Mathematics
• Physics
• Scientific reports
• scientific studies
• natural sciences
• EXAFS analysis
• DebyeWaller factor
• Anharmonic correlated Einstein model
• Crystalline silicon
• Anharmonic EXAFS oscillation
• High – order anharmonic effective potential
• EXAFS cumulants of Nickel crystal
• Quantum perturbation theory
• University Tan Trao
• Influence of the nearest neighbors
• Summary of Material science Doctoral thesis
• The thermodynamic parameters
• Cumulants of some materials
• Anharmonic xafs method
• Experimental measurements in the XAFS method
• Mathematical science
• Physical science
• Statistical moment method
• Self consistent field method
• Anharmonic approximations
• Summary of Doctoral Thesis in Material science
• Doctoral Thesis in Material science
• Electronic material
• Anharmonic effective potential
• Local force constant
• Correlation effects
• XAFS of BCC crystals
• BCC crystals
• Anharmonic exafs
• Parameters of HCP crystal
• HCP crystals
• Comparison to experiment
• Experimental values
• curriculum
• science books
• Susceptibility
• Classical Anharmonic Oscillator
• Wave Equation
• Quantum Mechanical Theory
• Morse Potential
• Anharmonic Coordinates
• Geometrical Applications
• General Expression
• Geometrical Nets
• Osculating Circle
• Equations of Curvature
• Quasi exact solution
• Analytically solvable
• Levi Civita transformation
• Anharmonic oscillator potentials
• Harmonic oscillator
• Tạp chí khoa học
• Khoa học tự nhiên
• Debye Waller factor
• Effective potential
• Correlated Debye model