The method of linear combination of pseudoatomic orbitals is applied to calculated the surface electronic structure of semiconductors- Besides the form factors of pseudo-potential, the method does not introduce any adjustable parameters. The electronic states and wave functions of the ideal and relaxed (111) surfaces of Si and GaAs arc calculated. The results of Si is compared with Appelbaum and Hamann's results of self-consistent calculation, it is found that both results are consistent well about the position of surface energy levels and distribution of surface electronic charges. It is shown that the surface energy levels shift upward when the Si or Ga atoms at the surface move inward, and shift downwarol when the As atoms at the surface move outward. At the same time the properties of the wave function of surface states often show more obvious changes.
The method of linear combination of pseudoatomic orbitals is applied to calculated the surface electronic structure of semiconductors- Besides the form factors of pseudo-potential, the method does not introduce any adjustable parameters. The electronic states and wave functions of the ideal and relaxed (111) surfaces of Si and GaAs arc calculated. The results of Si is compared with Appelbaum and Hamann's results of self-consistent calculation, it is found that both results are consistent well about the position of surface energy levels and distribution of surface electronic charges. It is shown that the surface energy levels shift upward when the Si or Ga atoms at the surface move inward, and shift downwarol when the As atoms at the surface move outward. At the same time the properties of the wave function of surface states often show more obvious changes.
The flavour singlet structure functions of deep inelastic scattering processes can yield more decisive tests of QCD than the non-singlet. We give analytical expression for flavour singlet structure functions through analysing the lepton-nucleon deep inelastic scattering processes by means of QCD and using Jacobi polynomials. This expression contains 4 to 5 parameters and shows the changes of the singlet structure functions with x and Q2 very well. In QCD leading order, the conclusion is in reasonable agreement with experimental data.
The flavour singlet structure functions of deep inelastic scattering processes can yield more decisive tests of QCD than the non-singlet. We give analytical expression for flavour singlet structure functions through analysing the lepton-nucleon deep inelastic scattering processes by means of QCD and using Jacobi polynomials. This expression contains 4 to 5 parameters and shows the changes of the singlet structure functions with x and Q2 very well. In QCD leading order, the conclusion is in reasonable agreement with experimental data.
Detailed calculations of the properties of soliton propagation related to director motion in nematic liquid crystals under shear flow (including the presence of external magnetic or electric field) are given for the first time. Analytic soliton solutions are obtained when wave velocity is large. The properties of soliton solution, the energy of soliton and the interference patterns of polarized (monochromatic or white) light caused by the movement of such solitons are calculated and discussed. Eecent experiments of Refs. [12] and [13] are analysed and the dark lines observed in liquid crystal MBBA are shown to correspond to the type A soliton presented in this paper.
Detailed calculations of the properties of soliton propagation related to director motion in nematic liquid crystals under shear flow (including the presence of external magnetic or electric field) are given for the first time. Analytic soliton solutions are obtained when wave velocity is large. The properties of soliton solution, the energy of soliton and the interference patterns of polarized (monochromatic or white) light caused by the movement of such solitons are calculated and discussed. Eecent experiments of Refs. [12] and [13] are analysed and the dark lines observed in liquid crystal MBBA are shown to correspond to the type A soliton presented in this paper.
It was pointed out that the potential acting on an election at the boundary of an atom inside a solid should not vanish in a TF model of calculation. A strict deduction shows that it approaches to the value -e2/r0. When this term is taken into account, the calculated pressure values lie near those measured in a large range of compressions-Thus, equations of states for the metals U, Pb, Au, Ag, Cu, Fe, K, Al, Na and Li can be derived for the compression ratios from 1 to 10 at the temperature of absolute zero. Results are in good agreement with the corresponding current calculations in the high pressure limit. In the low pressure range, the agreement between calculated and observed ones are good within 10%. Particularly, for high-Z atomic number, for instance, the elements U and Ag, the agreement is excellent and at v=v0, P(v0)=0.Nevertheless, large deviations arise in the low-Z elements. This is due to the quantum effects of the Brillouin zones. As a recipe, normally a pseudo-potential is introduced. Accordingly, we do the same for the potential near the boundary of the atom-This leads to a better agreement within 10% again for all the elements mentioned above.In this paper, the method of numerical iteration for fitting the boundary conditions is improved by means of a new transformation of parameters. The accuracy in the numerical computation is thereby raised to 10-8.
It was pointed out that the potential acting on an election at the boundary of an atom inside a solid should not vanish in a TF model of calculation. A strict deduction shows that it approaches to the value -e2/r0. When this term is taken into account, the calculated pressure values lie near those measured in a large range of compressions-Thus, equations of states for the metals U, Pb, Au, Ag, Cu, Fe, K, Al, Na and Li can be derived for the compression ratios from 1 to 10 at the temperature of absolute zero. Results are in good agreement with the corresponding current calculations in the high pressure limit. In the low pressure range, the agreement between calculated and observed ones are good within 10%. Particularly, for high-Z atomic number, for instance, the elements U and Ag, the agreement is excellent and at v=v0, P(v0)=0.Nevertheless, large deviations arise in the low-Z elements. This is due to the quantum effects of the Brillouin zones. As a recipe, normally a pseudo-potential is introduced. Accordingly, we do the same for the potential near the boundary of the atom-This leads to a better agreement within 10% again for all the elements mentioned above.In this paper, the method of numerical iteration for fitting the boundary conditions is improved by means of a new transformation of parameters. The accuracy in the numerical computation is thereby raised to 10-8.
In this article, the Green Function method has been employed to investigate the infrared spectrum of one-dimensional twobloek crystal A-E. Assuming that the Green Functions of the blocks are known, we first derive the matrices and the Green Functions of the crystal and then investigate some quantities important to infrared spectrum of the crystal, including (1) the density of states, (2) the eigenfrequencies of the crystal, (3) the normal displacements of atoms in the crystal, (4) infrared absorption intensity and (5) peak width.
In this article, the Green Function method has been employed to investigate the infrared spectrum of one-dimensional twobloek crystal A-E. Assuming that the Green Functions of the blocks are known, we first derive the matrices and the Green Functions of the crystal and then investigate some quantities important to infrared spectrum of the crystal, including (1) the density of states, (2) the eigenfrequencies of the crystal, (3) the normal displacements of atoms in the crystal, (4) infrared absorption intensity and (5) peak width.
By using the elastic dipole model of strained crystals, we regard every atom in a binary crystal as an elastic dipole, which has various effective moment. On various kinds of atoms, different force will be acted by the stress field due to other stronger internal stress sources such as dislocation, inclusion, etc. Thus different displacement will take place and some domains of various shape depending on the relative magnitude of permanent moment and induced moment will form. In the present paper, the domain patterns produced by internal stress field of edge dislocation, screw dislocation, inclusion and crowdion are obtained by calculation, they look like rosettes Under proper condition the patterns of these domains might be observed. The result also shows the effect of pressure on phase transition.
By using the elastic dipole model of strained crystals, we regard every atom in a binary crystal as an elastic dipole, which has various effective moment. On various kinds of atoms, different force will be acted by the stress field due to other stronger internal stress sources such as dislocation, inclusion, etc. Thus different displacement will take place and some domains of various shape depending on the relative magnitude of permanent moment and induced moment will form. In the present paper, the domain patterns produced by internal stress field of edge dislocation, screw dislocation, inclusion and crowdion are obtained by calculation, they look like rosettes Under proper condition the patterns of these domains might be observed. The result also shows the effect of pressure on phase transition.
In this paper, we analyzed the physical essence for producing a series of step structures or oscillating effect of dc Josephson current within one flux quantum period φ0 by placing Josephson junction, two-junction SQUID and the supercon ducting ring containing a single junction in a cavity, when one of the eigen-frequencies ωr of which is equal to Josephson frequency and the Q-Value is sufficiently high. We point out that the frequency effect of the feedback field would produce a series of induced steps for Josephson junction or two-junction SQUID, as ω = ωr, the oscillating electric-magnetic field excited by the junction current reacts on the junctions themself. Furthermore, a series of new step structures should occur within the φ0 since the amplitude of the feedback field is modulated by applied magnetic field as the modulation of the amplitude of the feedback field is coupled with that of the radiation. For the superconducting ring containing a single junction, as nω=ωr, the feedback radiation of stationary electric-magnetic wave will give rise constrained oscillation of the supereurrent with a smaller period than the φ0.
In this paper, we analyzed the physical essence for producing a series of step structures or oscillating effect of dc Josephson current within one flux quantum period φ0 by placing Josephson junction, two-junction SQUID and the supercon ducting ring containing a single junction in a cavity, when one of the eigen-frequencies ωr of which is equal to Josephson frequency and the Q-Value is sufficiently high. We point out that the frequency effect of the feedback field would produce a series of induced steps for Josephson junction or two-junction SQUID, as ω = ωr, the oscillating electric-magnetic field excited by the junction current reacts on the junctions themself. Furthermore, a series of new step structures should occur within the φ0 since the amplitude of the feedback field is modulated by applied magnetic field as the modulation of the amplitude of the feedback field is coupled with that of the radiation. For the superconducting ring containing a single junction, as nω=ωr, the feedback radiation of stationary electric-magnetic wave will give rise constrained oscillation of the supereurrent with a smaller period than the φ0.
The ionic electrical conduction in sintered Bi2O3-Y2O3 system for samples containing 20-30 mol% Y2O3 was investigated by means of measurement of ac conductivity and the emf of oxygen gas concentration cell using the specimen tablet as electrolyte. The experimental po2 range from 1 to 10-21 atm for ionic electrical conduction measurement-These materials showed high oxygen ionic conduction, the conductivities for samples containing 22.5-30mol% Y2O3 are many times higher than those of stabilized zirconia ZrO based solid electrolyte at corresponding temperatures. When these materials are used to construct an oxygen concentration cell, the E/E0 is equal to 1 or approaches 1. These values show that the samples containing 22.5 to 30 mol% Y2O3 are nearly pure ionic conductors. The p-type hole conductivity is very small at higher po2 values, so it is negligible. The n-type electronic conduction was investigated by means of coulomb titration technique for Y2O3 27.5 mol% sample We obtained that lg pe＇=-767000/T +665. The pe＇ is equal to 2.6×10-61 atm at 800℃. The n-type electronic conduction is vary small, so that it is also negligible.These materials are proved to be good high ionic conductors.
The ionic electrical conduction in sintered Bi2O3-Y2O3 system for samples containing 20-30 mol% Y2O3 was investigated by means of measurement of ac conductivity and the emf of oxygen gas concentration cell using the specimen tablet as electrolyte. The experimental po2 range from 1 to 10-21 atm for ionic electrical conduction measurement-These materials showed high oxygen ionic conduction, the conductivities for samples containing 22.5-30mol% Y2O3 are many times higher than those of stabilized zirconia ZrO based solid electrolyte at corresponding temperatures. When these materials are used to construct an oxygen concentration cell, the E/E0 is equal to 1 or approaches 1. These values show that the samples containing 22.5 to 30 mol% Y2O3 are nearly pure ionic conductors. The p-type hole conductivity is very small at higher po2 values, so it is negligible. The n-type electronic conduction was investigated by means of coulomb titration technique for Y2O3 27.5 mol% sample We obtained that lg pe＇=-767000/T +665. The pe＇ is equal to 2.6×10-61 atm at 800℃. The n-type electronic conduction is vary small, so that it is also negligible.These materials are proved to be good high ionic conductors.
We observed experimentally that at least two optical absorption peaks appear between 3500-6500? after bombardment of LiNbO3 crystal surface by low-energy ion. Also the relative dark conductivity increase by two order of magnitudes, the fact suggests that the additional optical absorption and conductiviting active center creates after ion-bombardment. During bombardment, owing to the prior sputtering of some atom and atom groups in the crystal, a substantial deviation of stoichiometry occur in the surface layer, which has a direct effect upon the optical and electrical properties of LiNbO3 crystal.The measurements of XPS (X photoelectron energy spectroscopy) prove that the structure of this surface layer conforms to the vacancy model of LiNbO3 defect structure. We propose a possible mechanism of the formation of this kind of active center in LiNbO3. By this model, we can explain qualitatively the result obtained from LiNbO3 crystals after bombardement by the mixed ions of Ar+/O+.
We observed experimentally that at least two optical absorption peaks appear between 3500-6500? after bombardment of LiNbO3 crystal surface by low-energy ion. Also the relative dark conductivity increase by two order of magnitudes, the fact suggests that the additional optical absorption and conductiviting active center creates after ion-bombardment. During bombardment, owing to the prior sputtering of some atom and atom groups in the crystal, a substantial deviation of stoichiometry occur in the surface layer, which has a direct effect upon the optical and electrical properties of LiNbO3 crystal.The measurements of XPS (X photoelectron energy spectroscopy) prove that the structure of this surface layer conforms to the vacancy model of LiNbO3 defect structure. We propose a possible mechanism of the formation of this kind of active center in LiNbO3. By this model, we can explain qualitatively the result obtained from LiNbO3 crystals after bombardement by the mixed ions of Ar+/O+.
The phase transitions of LiKSO4 have been investigated by means of X-ray powder diffraction and thermal analysis above room temperature. It is established that the crystal structure of LiKSO4 between the melting point and 675℃ is isostructural with the high temperature phase of α-K2SO4 and its space group is probably P63/mmc. Cooling below Ti=675℃ , there appears an incommensurately modulated structure analogous to the incommensurate phase in K2WO4, K2MoO4, etc. The parameter κ changes with temperature from 0.492(640℃ ) to 0.500(470℃ ). At 470℃ , I→C phase transition (lock-in) takes place, after which the crystal structure becomes the superstructure lattice of the room temperature phase. At 439℃ the superstructure disappears yielding to the room temperature phase (P63).
The phase transitions of LiKSO4 have been investigated by means of X-ray powder diffraction and thermal analysis above room temperature. It is established that the crystal structure of LiKSO4 between the melting point and 675℃ is isostructural with the high temperature phase of α-K2SO4 and its space group is probably P63/mmc. Cooling below Ti=675℃ , there appears an incommensurately modulated structure analogous to the incommensurate phase in K2WO4, K2MoO4, etc. The parameter κ changes with temperature from 0.492(640℃ ) to 0.500(470℃ ). At 470℃ , I→C phase transition (lock-in) takes place, after which the crystal structure becomes the superstructure lattice of the room temperature phase. At 439℃ the superstructure disappears yielding to the room temperature phase (P63).
Based on the intersection between Gauss electron beam and the largest cross-sectior of the particles, a method is proposed for calculating the X-ray intensity emitted frond particles. The intensity of the characteristic X-rays from particles of the shape of spheroid, cuboid, elliptic cylinder or elliptic spheroid has been calculated for Al, Cu and Au at 20keV and 25keV. Monte Carlo evaluation of the electron scattering was performed using the model put forward in reference (1).
Based on the intersection between Gauss electron beam and the largest cross-sectior of the particles, a method is proposed for calculating the X-ray intensity emitted frond particles. The intensity of the characteristic X-rays from particles of the shape of spheroid, cuboid, elliptic cylinder or elliptic spheroid has been calculated for Al, Cu and Au at 20keV and 25keV. Monte Carlo evaluation of the electron scattering was performed using the model put forward in reference (1).
Considering characteristies of fast discharge, the equilibrum equation of axisym-metric plasma with free boundary is solved by means of integration. Combining with circuit equations, the equilibrum configurations of plasma and. their variations with time are obtained in the case of plasma strongly coupling with the external circuit.
Considering characteristies of fast discharge, the equilibrum equation of axisym-metric plasma with free boundary is solved by means of integration. Combining with circuit equations, the equilibrum configurations of plasma and. their variations with time are obtained in the case of plasma strongly coupling with the external circuit.
It is shown that the algebra valued by the generalized Lax representation of nonlinear (evolution) system, i.e. the prolongation algebra y×D(λ), is in fact Kac-Moody type algebra where y is a finite dimensional Lie algebra and D(λ) the domain of value of the spectral parameter λ. The realization of the Kac-Moody algebra in a kind of 2 dimensional nonlinear (evolution) systems has been given by means of the realization of the Kac-Moody algebra in the principal chiral model due to Dolan.
It is shown that the algebra valued by the generalized Lax representation of nonlinear (evolution) system, i.e. the prolongation algebra y×D(λ), is in fact Kac-Moody type algebra where y is a finite dimensional Lie algebra and D(λ) the domain of value of the spectral parameter λ. The realization of the Kac-Moody algebra in a kind of 2 dimensional nonlinear (evolution) systems has been given by means of the realization of the Kac-Moody algebra in the principal chiral model due to Dolan.
Considering distorted octahedral crystal field-D3d point group symmetry of Mn2+ ion in CsMnBr2, crystal and using Zhao's SCF d-orbit of Mn2+ in complex, we have investigated electronic structure and absorption spectra of Mn2+ in MnBr64-. The spectral splittings at 18280cm-1, 21700cm-1, 26300cm-1, and 29650cm-1 have been interpreted by low symmetry crystal field. The theoretical calculations are in good agreement with experiment
Considering distorted octahedral crystal field-D3d point group symmetry of Mn2+ ion in CsMnBr2, crystal and using Zhao's SCF d-orbit of Mn2+ in complex, we have investigated electronic structure and absorption spectra of Mn2+ in MnBr64-. The spectral splittings at 18280cm-1, 21700cm-1, 26300cm-1, and 29650cm-1 have been interpreted by low symmetry crystal field. The theoretical calculations are in good agreement with experiment
The linearized Eliashberg equations for a superconductive system in strong exchange fields have been investigated. An iteration procedure has been used for including the asymmetry of the gap function φ(ω) with respect to ±ω and an approximate solu-tion has been obtained in the lowest order of the iteration equation. The results show that the asymmetry in the gap function can considerably change the critical exchange field as a function of temperature in moderate or stronger electron-phonon coupling (λ≥ 0.5) systems.
The linearized Eliashberg equations for a superconductive system in strong exchange fields have been investigated. An iteration procedure has been used for including the asymmetry of the gap function φ(ω) with respect to ±ω and an approximate solu-tion has been obtained in the lowest order of the iteration equation. The results show that the asymmetry in the gap function can considerably change the critical exchange field as a function of temperature in moderate or stronger electron-phonon coupling (λ≥ 0.5) systems.
We have used the perturbation theory to calculate the energy bands of the bipolaron and the free-polaron, in order to investigate the stabilities of the singlet and the triplet bipolaron states. By analyzing the specific heat and the magnetic susceptibility, we illustrate the importance of the triplet bipolaron state in understanding the experimental data.
We have used the perturbation theory to calculate the energy bands of the bipolaron and the free-polaron, in order to investigate the stabilities of the singlet and the triplet bipolaron states. By analyzing the specific heat and the magnetic susceptibility, we illustrate the importance of the triplet bipolaron state in understanding the experimental data.
A formula of the critical temperature for superconductors with small λ is derived from the Eliashberg equation.
A formula of the critical temperature for superconductors with small λ is derived from the Eliashberg equation.
Based on Scalapino-Huberman μ* model, the possibility of the temporally oscillating structures appearing in superconducting film under high quasi-particle injection is argued, the range of parameters in which these structures may occur is given.
Based on Scalapino-Huberman μ* model, the possibility of the temporally oscillating structures appearing in superconducting film under high quasi-particle injection is argued, the range of parameters in which these structures may occur is given.