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Determination of the high c/a ratio of hexagonal metals with a semi-empirical tight-binding method

COMPUTATIONAL MATERIALS SCIENCE 2000年第2-4期17卷 249-254页

作者： Béré, A Chen, J Hairie, A Nouet, G Paumier, E Inst Sci Mat & Rayonnement UPRESA CNRS 6004 Lab Etud & Rech Mat F-14050 Caen France

A semi-empirical tight-binding potential is developed to reproduce the high c/a ratio of zinc and cadmium. In this scheme, we show that the calculation of the electronic energy by the standard recursion method with the Harrison model for the hopping integrals and their radius dependence is not able to predict c/a values higher than the ideal one gamma(0) = root 8/3 = 1.633. Only, the recursion method limited to first neighbours has permitted to get the right c/a ratio of zinc and cadmium. The calculated energies of different structures (2H, 4H, 6H and 3C) show that the hexagonal compact structure (2H) is always most stable. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： density matrix O(N) method electronic energy tight-binding recursion method hexagonal metals zinc cadmium

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Spin dynamics of the one-dimensional J-J' model and spin-Peierls transition in CuGeO3

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JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 1997年第11期66卷 3617-3635页

作者： Yokoyama, H Saiga, Y Department of Physics Tohoku University Aramaki Aoba Aoba-ku Sendai 980-77

Spin dynamics as well as static properties of the one-dimensional J-J' model (S = 1/2, J > 0 and 0 less than or equal to alpha = J'/J less than or equal to 0.5) are studied by the exact diagonalization and the recursion method of finite systems up to 26 sites. Especially, the dynamical structure factor S(q, omega) is investigated carefully for various values of alpha. As a increases beyond the gapless-gapful critical value alpha(c) = 0.2411, there appear features definitely different from the Heisenberg model but the same with the Majumdar-Ghosh model. Some of these features depend only on the value of alpha and not on delta: a parameter introduced for the coupling alternation. By comparing these results with a recent inelastic neutron scattering spectrum of an inorganic spin-Peierls compound CuGeO3 [M. Arai et al.: Phys. Rev. Lett. 77 (1996) 3649], it is found that the frustration by J' in CuGeO3 is unexpectedly strong (alpha = 0.4-0.45), and at least alpha must be larger than alpha(c) to some extent. The value of J is evaluated at similar to 180 K consistent with other estimations. The coupling alternation is extremely small. This large frustration is a primary origin of the various anomalous properties CuGeO3 possesses. For comparison we refer also to alpha'-NaV2O5.

关键词： spin dynamics neutron scattering spin-Peierls transition CuGeO3 J-J' model Heisenberg model Haldane-Shastry model Majumdar-Ghosh model exact diagonalization recursion method

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Theoretical study on magnetic ground state in the perovskite CeCoO₃

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PHYSICA B-CONDENSED MATTER 2008年第10-11期403卷 1715-1718页

作者： Zhang, Xiu'e Sun, Aimin NE Normal Univ Coll Phys & Elect Engn Lanzhou 730070 Peoples R China

The unrestricted Hartree-Fock approximation on a realistic multiband lattice model has been applied to study the various spin states of cobalt perovskite CeCOO3. We have studied various magnetically ordered states of an enlarged double cell, including the low-spin state (t(2g)(6)e(g)(1)), high-spin state (t(2g)(5) e(g)(2)), as well as all combinations among the two states. Our results show that the magnetic ground state mainly depends on the competition between the crystal field strength Dq and Hund's coupling j, For a fixed j, the magnetic ground state is the high-spin antiferromagnetically ordered state. (c) 2007 Elsevier B.V. All rights reserved.

关键词： recursion method Hartree-Fock approximation density of state spin state magnetic ground state tetravalent ions Ce

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Theoretical study on magnetic ground state in the layered perovskite SrCeCoO₄

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OPTOELECTRONICS AND ADVANCED MATERIALS-RAPID COMMUNICATIONS 2014年第5-6期8卷 506-510页

作者： Zhang Xiu'e Kang Yonggang Inst Disaster Prevent Sanhe 065201 Hebei Peoples R China

By using the unrestricted Hartree-Fock approximation and the real-space recursion method, we have investigated various magnetic structures in an enlarged double cell of layered perovskite SrCeCoo(4). These include the low-spin state (t(2g)(6)e(g)(1)), high-spin state (t(2g)(5)e(g)(2)), as well as all combinations among the two states. Our results show that the magnetic ground state mainly depends on the competition between the crystal field strength D-q and Hund's coupling j, For a fixed j the magnetic ground state is the high-spin antiferromagnetically ordered state.

关键词： recursion method Hartree-Fock approximation Density of state Layered perovskite Spin state Magnetic ground state

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Possible magnetic ground state of the half doped perovskite compound R_0.5Ce_0.5CoO₃ (R=Ca, Sr)

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PHYSICA B-CONDENSED MATTER 2010年第4期405卷 1150-1153页

作者： Hu Shuntian Zhang Xiu'e Kang Yonggang Inst Disaster Prevent Sci & Technol Sanhe 065201 Hebei Peoples R China

By using the unrestricted Hartree-Fock approximation and the real-space recursion method, we have investigated various magnetic structures in an enlarged double cell of the half doped compound R0.5Ce0.5CoO3 (R=Ca, Sr). These include the low-spin state (LS : t(2g)(5)e(g)(1)), the intermediate-spin state (IS : t(2g)(4.5)e(g)(1.5)), and the high-spin state (HS : t(2g)(4)e(g)(2)) as well as all possible combinations among these three states. The densities of states are computed and stabilities of various states are analyzed as functions of the model parameters. For a fixed Hund's coupling j, it is shown that the ground state of R0.5Ce0.5CoO3 (R=Ca, Sr) transforms from the antiferromagnetic high-spin state to the ferromagnetically ordered high-spin low-spin state as the crystal-field splitting Dq increases. (C) 2009 Elsevier B.V. All rights reserved.

关键词： recursion method Hartree-Fock approximation Density of state Perovskite compound Spin state Magnetic ground state

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Configuration and self-averaging in disordered systems

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INDIAN JOURNAL OF PHYSICS 2016年第6期90卷 649-657页

作者： Chowdhury, S. Jana, D. Sadhukhan, B. Nafday, D. Baidya, S. Saha-Dasgupta, T. Mookerjee, A. Univ Calcutta Dept Phys 92 Acharya Prafulla Chandra Rd Kolkata 700009 WB India Presidency Univ Dept Phys 86-1 Coll St Kolkata 700073 WB India SN Bose Natl Ctr Basic Sci Dept Condensed Matter & Mat Sci JD 3 Kolkata 7000098 WB India Lady Brabourne Coll Dept Phys 1-2 Suhrawardy St Kolkata 700017 WB India

The main aim of this work is to present two different methodologies for configuration averaging in disordered systems. The recursion method is suitable for the calculation of spatial or self-averaging, while the augmented space formalism averages over different possible configurations of the system. We have applied these techniques to a simple example and compared their results. Based on these, we have reexamined the concept of spatial ergodicity in disordered systems. The specific aspect, we have focused on, is the question "Why does an experimentalist often obtain the averaged result on a single sample?'' We have found that in our example of disordered graphene, the two lead to the same result within the error limits of the two methods.

关键词： recursion method Augmented space formalism Spatial ergodicity

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A simple derivation of the recursion relation for ⟨r^N⟩ in energy eigenstates

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AMERICAN JOURNAL OF PHYSICS 2000年第10期68卷 959-960页

作者： Balasubramanian, S Univ Madras Dept Theoret Phys Madras 600025 Tamil Nadu India

A simple derivation based on the generalized Hellmann-Feynman theorem is given for the three-term recursion relation for (r(N)) in the energy eigenstates of a hydrogenic atom and the harmonic oscillator in one, two, a... 详细信息

关键词： atomic structure recursion method quantum theory eigenvalues and eigenfunctions harmonic oscillators teaching 03.65

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RECURSIVE method IN ONE-DIMENSIONAL ISING-MODEL

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JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 1980年第7期13卷 2465-2477页

作者： MARCHI, E VILA, J Univ. Nacional de San Luis San Luis Argentina

The authors introduce a new recursive method which allows one to solve exactly one-dimensional Ising problems with higher-order interactions. The new method presents some important features, for example its exactness and the computational ease of its solution. They present a new method for evaluating the partition function. Moreover an application of this to the general approach is given and an analytic solution is found.

关键词： recursion method Ising model accuracy class Solutions new methods one-dimensional models Partition function

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WAVE VECTOR DEPENDENT SPIN SUSCEPTIBILITY OF IRON ABOVE THE CURIE-TEMPERATURE

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JOURNAL OF PHYSICS F-METAL PHYSICS 1983年第12期13卷 2655-2675页

作者： HASEGAWA, H Inst. for Solid State Phys. Univ. of Tokyo Tokyo Japan

Microscopic calculations are given of the wavevector- and temperature-dependent spin susceptibility, chi (q), of itinerant-electron magnets by generalising the approach initiated by Hubbard and Hasegawa (1979-1983). The expressions for chi (q) in the limit of q=0 and q=Q (the antiferromagnetic wavevector) are shown to reduce to the results obtained previously by the present author. Detailed calculations of chi (q) of paramagnetic iron are made using the density of states generated by the recursion method. The amplitude of local moments evaluated by summing chi (q) over the BCC Brillouin zone using the classical fluctuation-dissipation theorem is nearly in agreement with effective moments deduced from the susceptibility chi (0). The equal-time and spatial spin-spin correlation functions are also calculated, and discussed with reference to recent neutron diffraction experiments.

关键词： Density of states recursion method Curie temperature (ferromagnetic) local bending moment Neutron diffraction Correlation function Spin susceptibility Iron

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The integral formulas of the associated Legendre functions

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JOURNAL OF GEODESY 2012年第6期86卷 467-473页

作者： Yu, Jinhai Wan, Xiaoyun Zeng, Yanyan Chinese Acad Sci Grad Univ Coll Earth Sci Beijing 100049 Peoples R China

A new kind of integral formulas for is derived from the addition theorem about the Legendre Functions when - is an even number. Based on the newly introduced integral formulas, the fully normalized associated Legendre functions can be directly computed without using any recursion methods that currently are often used in the computations. In addition, some arithmetic examples are computed with the increasing degree recursion and the integral methods introduced in the paper respectively, in order to compare the precisions and run-times of these two methods in computing the fully normalized associated Legendre functions. The results indicate that the precisions of the integral methods are almost consistent for variant in computing , i.e., the precisions are independent of the choice of on the interval [0,1]. In contrast, the precisions of the increasing degree recursion change with different values on the interval [0,1], particularly, when tends to 1, the errors of computing by the increasing degree recursion become unacceptable when the degree becomes larger and larger. On the other hand, the integral methods cost more run-time than the increasing degree recursion. Hence, it is suggested that combinations of the integral method and the increasing degree recursion can be adopted, that is, the integral methods can be used as a replacement for the recursive initials when the recursion method become divergent.

关键词： Legendre function Integral formula recursion method

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