Variational principles for two kinds of extended Korteweg—de Vries equations

Variational principles are constructed using the semi-inverse method for two kinds of extended Korteweg—de Vries (KdV) equations, which can be regarded as simple models of the nonlinear oceanic internal waves and atmospheric long waves, respectively. The obtained variational principles have also been proved to be correct.     

Ab initio total energy calculation of the dynamical stability of noble metal carbides

The structural, electronic, vibrational and thermodynamical properties of transition metal carbides RuC, RhC, PdC and AgC are investigated using the plane-wave pseudopotentials method within the generalized gradient approximation (GGA) in the frame of density functional theory (DFT). There is a good agreement between present theoretical and available experimental theoretical data in the case of ground state properties such as lattice parameter and bulk modulus. The electronic band structure of these compounds show that all compounds except RuC in zinc blende phase are metallic in nature. RuC in zinc blende phase is semiconducting in nature with an indirect band gap. The phonon properties of RhC, PdC and AgC are investigated for the first time. The phonon frequencies in the phonon dispersion curves are positive throughout the Brillouin zone for zinc blende RuC and AgC and rocksalt RhC and PdC indicating dynamical stability for these compounds in the said phases. Temperature variation of thermodynamical properties for noble metal carbides are calculated and discussed.     

First principles lattice dynamical calculation of semiboride Be2B and its ternary alloys XBeB (X=Na, Mg, Al)

We present results of first principles total energy calculations of the structure, electronic and lattice dynamics for beryllium semiboride and its three ternary alloys using generalized gradient and local density approximations under the framework of density functional theory. The generalized gradient approximation is used for all compounds except MgBeB using the Perdew-Burke-Ernzehorf exchange correlation functional while local density approximations use the Perdew-Zunger ultrasoft exchange correlation functional. The calculated ground state structural parameters are in good agreement with those of experimental and previous theoretical studies. The electronic band structure calculations show that Be₂B may transform to a semiconductor after Al substitution. A linear response approach to density functional theory is used to calculate phonon dispersion curves and vibrational density of states. The phonon dispersion curves of Be₂B and AlBeB are positive indicating a dynamical stablility of the structure for these compounds. The phonon dispersion curves of NaBeB and MgBeB show the imaginary phonons throughout the Brillouin zone, which confirms dynamical instability as indicated in band structures for these alloys. We also present the partial phonon density of states for different species of Be₂B and AlBeB to bring out the details of the participation of different atoms in the total phonon density of state, particularly the role played by Al atom. The first time calculated phonon properties are clearly able to bring out the significant effect of isoelectronic substitution in Be₂B.     

锐钛矿(TiO2)半导体的氧空位浓度对导电性能影响的第一性原理计算

基于低温重氧空位锐钛矿半导体的态密度计算,在同等条件下研究取不同大小模型的锐钛矿做适量浓度的氧空位存在,分别对进入导带的相对平均电子数和氧空位类杂质的散射迁移率进行计算,之后对电导率进行类比,发现锐钛矿半导体的导电性能对适量浓度低的氧空位有利可行得到了证明.同时,低温重氧空位的条件下,锐钛矿半导体的电导率不仅与氧空位浓度有关,而且和进入导带的平均电子数有关,和氧空位散射的电子迁移率有关的正确结论. 关键词： 锐钛矿半导体 氧空位浓度 电导率 第一性原理计算     

Magnetic properties in zinc-blende CdS induced by Cd vacancies

The magnetic property induced by neutral Cd and S vacancies in CdS bulk and thin film are investigated, using first principles simulation. For bulk CdS, the magnetism originates from Cd, instead of S, vacancies. The ferromagnetism with a Curie temperature above room temperature can be expected. For CdS thin film, both Cd and S vacancies does not yield any magnetism at the (111) surface, while local magnetic moments at the outermost S plane of the (001) surface is ascribed to the surface effect. The ferromagnetism at S-terminated (001) surface can account for the experimental observation.     

Mechanical and electronic properties of stoichiometric silicene and germanene oxides from first‐principles

Using first‐principles calculations, we investigate the fully oxidized silicene and germanene with stoichiometric ratio Si:O/Ge:O = 1:1. For both compounds, the zigzag ether‐like conformation (z‐sSiO/z‐sGeO) is found to be the most energetically favorable structure. These z‐sSiO and z‐sGeO nanosheets have prominent elastic characteristics, which even exhibit an unconventional auxetic behavior with negative Poisson ratios. After oxidation, the semi‐metallic nanosheets are transformed into semiconductors with narrow direct band gaps. Due to the anisotropic mechanical and electronic properties, the z‐sSiO and z‐sGeO possess an axially high intrinsic charge mobility up to the order of 10⁴ cm²/Vs, which is comparable to that of graphene nanoribbons. Our studies demonstrate that the silicene and germanene oxides have peculiar mechanical and electronic properties, which endow these nanostructures for potential applications in nanoelectronics and devices. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

放射性核素铀在针铁矿中的占位研究

用第一性原理研究放射性同位素铀在针铁矿(α-FeOOH)中的占位情况, 分别考虑铀原子替代针铁矿中的铁的替位缺陷和铀的多种八面体和多种四面体间隙缺陷. 计算发现了三个最稳定的缺陷构型, 它们分别对应于一个铀替位缺陷(S) 及其中的一个铀的八面体(O)和四面体(T)间隙缺陷, 其形成能分别为-13.49, -3.86, -1.60 eV. 也研究了两个相邻的铀原子在针铁矿中的占位情况, 发现双铀原子很容易掺入到相邻的SS或OS位, 它们的形成能分别为-27.392和-16.214 eV, 结合能分别为-0.417和1.131 eV. 表明双原子铀在针铁矿中会以SS形式发生偏聚而较难以OS形式偏聚. 关键词： 铀 针铁矿 占位 第一性原理     

高压下三元金属间化合物SrAlSi的电学和晶格动力学特性

基于密度泛函理论的第一性原理方法,系统研究了三元金属间化合物SrAlSi在高压下的电子性质和晶格动力学性质.三元金属间化合物SrAlSi具有和MgB₂类似的六角蜂巢状结构,Sr原子取代了Mg原子的位置,Al、Si原子无序地占据B原子的位子.通过对SrAlSi三元金属间化合物能带和三维费米面的计算,发现在压力的作用下SrAlSi费米面附近的能带发生电子拓扑变化,压力可以导致电子拓扑结构相变(ETTs).通过晶格动力学研究发现,在压力的作用下,SrAlSi的光学支沿着A-L-H方向逐渐软化,声学支逐渐变硬,说明金属间化合物SrAlSi在压力作用下结构不是很稳定,随着压力的继续增大,会有新的结构出现.     

Cr,Mo,Ni在α-Fe(C)中占位、键合性质及合金化效应的第一性原理研究

基于密度泛函理论第一性原理方法,采用广义梯度近似下的PW91泛函形式,计算了合金元素Cr,Mo,Ni固溶于α-Fe(C)的电子结构,从晶格畸变、结合能、态密度、重叠布居及差分电荷密度等计算结果出发探讨了合金元素在α-Fe(C)中占位、键合性质及其合金化效应,结果表明:Cr优先占据铁素体晶胞顶角位置,而Mo,Ni优先占据体心位置;Cr与晶胞的结合能最大,晶胞最稳定,Ni次之,Mo最低;Cr,Mo,Ni在晶胞中都存在金属键、共价键和微弱离子键的共同作用,成键轨道主要是Cr3d与Fe3d,Mo4d与Fe3d,Ni3d与Fe3d,C2p的交互作用形成的;Cr与晶胞原子间的键合作用强,晶胞的稳定性好,对增强钢材的机械性能帮助较大,Ni的键合作用较弱,但还是能保持晶胞的稳定性,Mo虽然键合作用强,但反键作用也非常强,使晶胞的稳定性大大降低,对钢材的机械性能危害较大.     

激发态过程的多体理论方法

描述多电子体系的绝大部分参量可实验测量,如吸收光谱、发光光谱和激子效应等,都涉及电子激发态的正确描述。密度泛函理论(DFT)框架内的局域密度近似(LDA)作为第一性原理基态理论,即基于Kohn-Sham方程的解,是研究多粒子体系基态性质非常有力的工具。然而,体系激发态的第一性原理理论及其计算要比基态的理论计算复杂得多。关键问题在于描写基态和激发态时,粒子间的交换关联相互作用并不相同,而对于非均匀相互作用多粒子体系的交换关联能至今仍不清楚。不过,近年来关于激发态问题的研究,先后发展了许多描述电子激发态的理论,最重要的是基于准粒子概念和Green函数方程的多体微扰理论和含时间密度泛函理论(TDDFT)以及与此相关的描述电子-空穴相互作用的Bethe-Salpeter方程在凝聚态物理问题中的应用。其中最关键的物理量是粒子的自能算符Σ,它描述Hartree近似之外的交换和关联效应。虽然这些理论不可避免地也要引入某些近似,如对于Σ的一个好的近似就是Hedin的GW近似方法。对许多实际凝聚态体系的计算机模拟结果表明,GW近似是描述激发态问题相当成功的理论方法。将Hartree-Fock(HF)理论与LDA相结合,但采用非局域屏蔽交换代替HF方法中的局域非屏蔽交换相互作用,建立广义的KS方程(GKS),得到所谓屏蔽交换局域密度近似(sX-LDA)方法。我们在平面波自洽场方法PWscf程序包的基础上,发展了PW scf-sX-LDA方法,也是处理激发态问题及材料设计的有效方法。将评述激发态过程多体理论各种方法的发展和意义,讨论这些多体理论方法之间的联系和差异,并在此基础上介绍它们在解决半导体带带跃迁(或带隙偏小问题)、半导体及其微结构中的激子效应等重要领域的应用和成果。