【作者】 周波；

【导师】 贺德衍；

【作者基本信息】 兰州大学 ， 凝聚态物理， 2009， 博士

【摘要】 随着高效而且准确的数值算法的发展,基于密度泛函理论的第一性原理方法成为凝聚态物理、量子化学和材料科学中的重要研究手段。以平面波赝势方法和局域密度近似理论为基础的密度泛函理论提供了一个简单的第一性原理计算框架,其准确性和强大的预测能力已被许多研究者所证实。最近提出的高效线性响应理论使在任意倒易点阵阵点上计算力常数矩阵成为可能,而计算量仅仅跟自洽计算相当。根据线性响应理论可以准确地得到整个布里渊区的声子色散、晶体材料的拉曼与红外光谱,对实验具有重要的指导意义。钒是一个典型的多价过渡金属元素,可形成多种氧化物,其中V₂O₅受到了最多的关注。特殊的晶体结构和电化学性质使得V₂O₅在很多领域有着非常广泛的应用。本文利用第一性原理方法对V₂O₅的三种相结构的电子能带、晶格振动特性等进行了细致地研究,得到了一系列与实验相符的结果,并首次对α相向β相转变过程中拉曼光谱的变化做出了理论的预测。本论文所开展的主要工作和所获得的主要创新性成果有:1.综合密度微扰理论和固体物理学相关知识,建立了完整的第一性原理方法计算单晶材料拉曼光谱的方法,并对该计算方法的具体实现做了初步地研究。2.计算了α-,β-,γ-V₂O₅的电子能带结构。所得到的α-V₂O₅的带隙值（2.30eV）与实验测量值一致;得到的β-V₂O₅的间接带隙为1.66 eV,并发现β-V₂O₅的电子迁移率高于α-V₂O₅;通过对计算得到的α-,β-,γ-V₂O₅能带结构的对比,得到了V₂O₅能带结构与晶体结构的关系。3.首次计算了α-,β-V₂O₅的声子色散曲线和拉曼光谱,细致地研究了α-V₂O₅到β-V₂O₅的相变过程中拉曼光谱的变化。所得到的拉曼光谱的计算结果与实验数据相符合,为利用拉曼光谱研究钒氧化合物提供了重要的理论指导。更多还原

【Abstract】 With the progress in density functional theory（DFT） and its numerical methods, DFT based first-principles calculation has become a routine method for condensed matter theory,quantum chemistry and material science.The plane-wave pseudopotential method and the local-density approximation（LDA） to density-functional theory（DFT） have provided a simple framework whose accuracy and predictive power have been convincingly demonstrated in a large variety of systems.Recently,very efficient linear-response techniques have been proposed which allow one to obtain dynamical matrices at arbitrary wave vectors with computational effort comparable to the self-consistent calculation for the unperturbed bulk.It is by now possible to obtain accurate phonon dispersions on a fine grid of wave vectors covering the entire Brillouin zone（BZ）,which can compare directly with neutron-diffraction data.The Raman spectra and infrared spectra obtained from linear response method are helpful for experiments.Vanadium is a typical transition metal element with much active chemical properties.It can form many kinds of oxides,among which,vanadium pentoxides attract most of focus from experimental and theoretical study because of its special and variant structures.The main progresses of this work are lists as follows:First,we summarize the process of calculating Raman sepctrac from first principles method,which is besed on density functional perturbation theory.The density functional perturbation theory is built on the framework of density function. We give a detailed description of this method,from a programmer aspect.We also state out the process of how to use ABINIT software package to calculate the Raman spectra of cystals.Second,the band structure ofα-,β-,γ-V₂O₅ have been obtained.The band gap ofα-V₂O₅ is 2.30 eV,which is the same as measured from experiments.The band gap ofβ-V₂O₅ is 1.66 eV.Compared from band structure,β-V₂O₅ has the highest electronic mobility than others.We also study the relation of band structure and the crystal structureThird,we obtained the Raman sepctrum ofα-,β-V₂O₅,using DFPT method.The calculated spectra fit the experiments very well.And we first present the phonon dispersion ofα-,β-V₂O₅.These data are valuable for interepting the experimental Raman sepctrum of vanadium oxide compounds.Then we fully study the transient process fromα- toβ-V₂O₅.更多还原