An iterative method is used to find the values of the Hamiltonian parameters for Yb^3＋ in a given low-symmetry crys- talline site. Samples of Yb^3＋ ：RETaO4 （RE = Gd, Y, and Sc） were prepared and their structures ...An iterative method is used to find the values of the Hamiltonian parameters for Yb^3＋ in a given low-symmetry crys- talline site. Samples of Yb^3＋ ：RETaO4 （RE = Gd, Y, and Sc） were prepared and their structures were determined. Based on the obtained structural data, their orbital-spin parameters and crystal field parameters were fitted by the superposition model （SM）. Using the crystal field parameters obtained by the SM fitting as the initial parameters, the Hamiltonian parameters were fitted iteratively. The calculated and experimental energy levels for Yb^3＋：RETaO4 are consistent, and the maximal mean-root-square deviation is only 2.84 cm^- 1, indicating that the method is effective to determine the Hamiltonian parameters of Yb^3＋ in low-symmetry crystalline sites.展开更多
A method to compute the numerical derivative of eigenvalues of parameterized crystal field Hamiltonian matrix is given, based on the numerical derivatives the general iteration methods such as Levenberg-Marquardt, New...A method to compute the numerical derivative of eigenvalues of parameterized crystal field Hamiltonian matrix is given, based on the numerical derivatives the general iteration methods such as Levenberg-Marquardt, Newton method, and so on, can be used to solve crystal field parameters by fitting to experimental energy levels. With the numerical eigenvalue derivative, a detailed iteration algorithm to compute crystal field parameters by fitting experimental energy levels has also been described. This method is used to compute the crystal parameters of Yb^3＋ in Sc2O3 crystal, which is prepared by a co-precipitation method and whose structure was refined by Rietveld method. By fitting on the parameters of a simple overlap model of crystal field, the results show that the new method can fit the crystal field energy splitting with fast convergence and good stability.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 90922003,51172236,and 50872135)the Knowledge Innovation Program of the Chinese Academy of Sciences (Grant No. YYYJ-1002)
文摘An iterative method is used to find the values of the Hamiltonian parameters for Yb^3＋ in a given low-symmetry crys- talline site. Samples of Yb^3＋ ：RETaO4 （RE = Gd, Y, and Sc） were prepared and their structures were determined. Based on the obtained structural data, their orbital-spin parameters and crystal field parameters were fitted by the superposition model （SM）. Using the crystal field parameters obtained by the SM fitting as the initial parameters, the Hamiltonian parameters were fitted iteratively. The calculated and experimental energy levels for Yb^3＋：RETaO4 are consistent, and the maximal mean-root-square deviation is only 2.84 cm^- 1, indicating that the method is effective to determine the Hamiltonian parameters of Yb^3＋ in low-symmetry crystalline sites.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.50772112 and 50872135)the Natural Science Foundation of Anhui Province of China(Grant No.08040106820)the Knowledge Innovation Program of the Chinese Academy of Sciences(Grant No.YYYJ-1002)
文摘A method to compute the numerical derivative of eigenvalues of parameterized crystal field Hamiltonian matrix is given, based on the numerical derivatives the general iteration methods such as Levenberg-Marquardt, Newton method, and so on, can be used to solve crystal field parameters by fitting to experimental energy levels. With the numerical eigenvalue derivative, a detailed iteration algorithm to compute crystal field parameters by fitting experimental energy levels has also been described. This method is used to compute the crystal parameters of Yb^3＋ in Sc2O3 crystal, which is prepared by a co-precipitation method and whose structure was refined by Rietveld method. By fitting on the parameters of a simple overlap model of crystal field, the results show that the new method can fit the crystal field energy splitting with fast convergence and good stability.
