We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, ...We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.展开更多
The structural parameters, the formation energies, and the elastic and thermodynamic properties of the （CuxNi1-x）3Sn phase with different structures are studied by the virtual crystal approximation （VCA） and super...The structural parameters, the formation energies, and the elastic and thermodynamic properties of the （CuxNi1-x）3Sn phase with different structures are studied by the virtual crystal approximation （VCA） and super-cell （SC） methods. The lattice constants, formation energies, and elastic constants obtained by SC and VCA are generally consistent with each other. It can be inferred that ttle VCA method is suitable for （CuxNil ,）3Sn ordered phase calculation. The calculated results show that the equilibrium structures of Cu3Sn and Ni3Sn are D0a and D019 respectively. （CuxNi1-x）3Sn D03 with various components are the mctastable phase at temperature of 0 K, just as D022 and L I2. With the temperature increase, tile free energy of the D03 is lower than those of D022 and L12, and D022 and L12 eventually turn into D03 in tile aging process. The （CuxNi1-x）3Sn D022 is first precipitated in a solid solution because its structure and cell volume are most similar to Ihose of a solid solution matrix. The LI2 and the D022 possess better mechanical stability than the D03. Also, they may play a more important role in the strengthening of Cu-Ni-Sn alloys. This study is valuable lk）r further research on Cu-Ni-Sn alloys.展开更多
In this paper, we investigated the structural, electronic and optical properties of InAs, InN and InP binary compounds and their related ternary and quaternary alloys by using the full potential linearized augmented p...In this paper, we investigated the structural, electronic and optical properties of InAs, InN and InP binary compounds and their related ternary and quaternary alloys by using the full potential linearized augmented plane wave（FP-LAPW）method based on density functional theory（DFT）. The total energies, the lattice parameters, and the bulk modulus and its first pressure derivative were calculated using different exchange correlation approximations. The local density approach（LDA） and Tran–Blaha modified Becke–Johnson（TB-m BJ） approximations were used to calculate the band structure.Nonlinear variations of the lattice parameters, the bulk modulus and the band gap with compositions x and y are found.Furthermore, the optical properties and the dielectric function, refractive index and loss energy were computed. Our results are in good agreement with the validated experimental and theoretical data found in the literature.展开更多
基金Supported by the National Nature Science Foundation.
文摘We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.
基金Project supported by the National Key Research and Development Program of China(Grant No.2016YFB0301402)the Project of Innovation-Driven Plan in Central South Universitythe State Key Laboratory of Powder Metallurgy,Central South University,Changsha,China
文摘The structural parameters, the formation energies, and the elastic and thermodynamic properties of the （CuxNi1-x）3Sn phase with different structures are studied by the virtual crystal approximation （VCA） and super-cell （SC） methods. The lattice constants, formation energies, and elastic constants obtained by SC and VCA are generally consistent with each other. It can be inferred that ttle VCA method is suitable for （CuxNil ,）3Sn ordered phase calculation. The calculated results show that the equilibrium structures of Cu3Sn and Ni3Sn are D0a and D019 respectively. （CuxNi1-x）3Sn D03 with various components are the mctastable phase at temperature of 0 K, just as D022 and L I2. With the temperature increase, tile free energy of the D03 is lower than those of D022 and L12, and D022 and L12 eventually turn into D03 in tile aging process. The （CuxNi1-x）3Sn D022 is first precipitated in a solid solution because its structure and cell volume are most similar to Ihose of a solid solution matrix. The LI2 and the D022 possess better mechanical stability than the D03. Also, they may play a more important role in the strengthening of Cu-Ni-Sn alloys. This study is valuable lk）r further research on Cu-Ni-Sn alloys.
基金supported by the Deanship of Scientific Research at King Saud University Group(Grant No.PRG-1437-39)
文摘In this paper, we investigated the structural, electronic and optical properties of InAs, InN and InP binary compounds and their related ternary and quaternary alloys by using the full potential linearized augmented plane wave（FP-LAPW）method based on density functional theory（DFT）. The total energies, the lattice parameters, and the bulk modulus and its first pressure derivative were calculated using different exchange correlation approximations. The local density approach（LDA） and Tran–Blaha modified Becke–Johnson（TB-m BJ） approximations were used to calculate the band structure.Nonlinear variations of the lattice parameters, the bulk modulus and the band gap with compositions x and y are found.Furthermore, the optical properties and the dielectric function, refractive index and loss energy were computed. Our results are in good agreement with the validated experimental and theoretical data found in the literature.
