mgo和mgb2高压物性的第一性原理计算.doc

MgO和MgB2高压物性的第一性原理计算

作为地球形成的主要矿物质之一，方镁石（MgO）在压强高达227GPa时都始终以氯化钠（B1）结构稳定存在，研究它的弹性性质对解释地幔内部地震波速的变化以及构造地球内部矿物学理论模型具有重要的作用，也是经常用于发展固体物理第一性原理计算的模型材料。近年来，无论是在实验上还是理论上，研究材料在高压下的性质一直是个热门课题。2001年1月10日，日本青山学院大学教授秋光纯宣布二硼化镁具有超导电性，超导转变温度高达39K。发现二硼化镁超导电性迫使人们重新考虑，在BCS理论的框架内是否存在更高临界温度的超导体。二硼化镁结构简单，易于制备和加工，有着广阔的应用前景。本文主要包括两部分内容：
1) 利用平面波赝势密度泛函理论和准谐德拜模型研究了氧化镁（MgO）的晶格常数a、体弹性模量B0、状态方程以及弹性常数（C11、C12和C44）等基本性质参数。得到了压强0～130GPa范围内，温度分别为300K和800K的弹性常数（C11、C12和C44）、等温体弹性模量Bs、剪切模量G、德拜温度 和压缩波速VP、剪切波速VS。所得到的C12的等温线不同于Karki等人的理论计算结果。由于对材料增加压强和降低温度的效果几乎相同，我们认为本文结果应该更正确。另外，还研究了在300K、800K的弹性常数、弹性各向异性以及偏差 ，发现压强小于20GPa时，弹性各向异性为正值且随压强增加而降低，在20GPa时为零，呈现各向同性。MgO的偏差 绝对值随压强增加而增加，意味着MgO在高压下受到非中心多体力场作用。 
2) 利用基于线性缀加平面波的密度泛函理论研究了二硼化镁（MgB2）在压强0～60GPa下的态密度、能带结构以及晶体的弹性常数。比较分析了体积的压缩和晶格常数c/a的减小对能带结构的影响，得出c/a对导电性质的影响是主要的。另外，还研究了MgB2力学性质的各向异性，包括体弹性模量（B、Ba和Bc）、压缩波 和剪切波（ 、 ）与压强的关系。由于Mg原子层与B原子层之间的金属键相对B原子层内原子之间的共价键相对较弱，所以随着压强的增大呈现晶体力学性质的各向异性。
关键词：密度泛函，赝势，线性缀加平面波，弹性常数，能带结构，态密度
第First-Principles Calculations for the Properties of MgO and MgB2 at High Pressure
第
Major in Atomic and Molecular Physics
Postgraduate:  Zhao Jian-zhou     Tutor:  Chen Xiang-rong

As one of the main compositions of the earth minerals, periclase (MgO) is stable as sodium chloride (B1) structure at pressure up to 227 GPa. It has great usage of explain the change of earth-shock wave inside of the mantle and the model of mineral theory of composing the earth. It also used as the model of the first principles calculations of solid state physics. Recently, properties of material at high pressures and high temperatures have been the objects of intensive experimental and theoretical investigations. In Jan. 10, 2001, Professor of Aoyama-Gakuin University, Nagamatsu, Jun, announced magnesium diboride has properties of superconductivity, and its transition temperature up to 39 K. It forced people to reconsider whether it exist such superconductor with ever higher transition temperature. Magnesium diboride has simple structure, easy to preparation, and has wide exercise future. This paper conclude two part:
1) The thermodynamic properties and the equations of state (EOS) of rocksalt (RS) structure MgO are investigated at a wide range of pressure 0~170 GPa, using plane-wave pseudopotential density functional theory. We obtain the pressure dependences of the elastic constants, the adiabatic bulk modulus BS, the shear modulus G, aggregate acoustic velocities and the Debye temperature at several temperatures (300 K and 800 K) and pressures (0~130 GPa). Our calculated isotherm of C12 is different from the predicted result by Karki et al., who found that the isotherm for high temperature is above the isotherm for low temperature. Based on that the effect of increasing pressure on the material is the same as decreasing temperature of the material, we think that our calculated isotherm of C12 should be correct. The elastic anisotropy A is investigated at the temperatures of 300 K and 800 K. When P < 20 GPa，it is found that the elastic anisotropy of MgO decrease dramatically with increasing pressure, becoming elastically isotropic at the pressure of 20 GPa. The increase of the deviation   in absolute with pressure means that MgO is affected by the non-central many-body force at high pressure.
2) We have investigated the density of states, band structure, and elastic constants of magnesium diboride at pressure 0 ~ 60 GPa based on density functional theory with linear augmented plane wave. We compared the impact of volume compression and decrease of c/a ratio to the band structure, and conclude the conductivity is mainly affected by c/a. Beside, we investigated the mechanics anisotropy of MgB2, includes the relationship of bulk modulus (B, Ba and Bc), compression wave   and shear wave ( ,  ). As the metal bond between Mg atom layer and B atom layer is weaker than the covalent bond between the B atoms in a B atom layer, the mechanics anisotropy was shown obviously while pressure increased.
Key words: density functional theory, pseudopotential, Linear augmented plane wave, elastic constants, band structure, density of states