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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
