【作者】 唐明君；

【导师】 何林；

【作者基本信息】 四川师范大学 ， 理论物理， 2008， 硕士

【摘要】 在高压下固体物质结构（晶格结构和电子结构）的改变会对它们的弹性、电学以及光学等性质产生影响。研究固体物质在高压下的物理性质对人们认识自然有推动作用。本文分两个部分分别就Al₂O₃和Cu在高压下的一些物理性质进行研究。第一部分内容是基于第一性原理计算方法,得到了三种Al₂O₃理想晶体结构的能带结构以及能隙（或禁带宽度）随压力的变化关系;同时计算并分析了光学性质（包括高压下的光吸收系数、介电函数的虚部与实部、反射谱与吸收谱以及能量损失谱）;进一步分析了高压下三种Al₂O₃理想晶体结构的电子态密度和力学性质。这些计算的目的是尝试对在冲击实验中观测到的蓝宝石电导率突增以及光学透明性降低现象的认识提供一些可能的物理机理。本部分的主要工作和结果如下:1)基于密度泛函理论框架下的第一性原理平面波超软赝势方法,结合局域密度近似（LDA）,计算了纯Al₂O₃理想晶体的三个结构相（Corundum相、Rh₂O₃（II）相以及CaIrO₃相）在高压下的电子能带结构,并根据此导出了Al₂O₃的三个结构相的能隙随压力变化关系。从这个计算结果发现在0K时,Corundum相到Rh₂O₃（II）相以及Rh₂O₃（II）相到CaIrO₃相的结构相变将导致Al₂O₃的带隙分别减少大约7-8%以及18-20%。另外,还发现在CaIrO₃相区,带隙随压力是微弱地减小,而在Corundum和Rh₂O₃（II）相区,带隙随压力是明显地增加。2)通过冲击实验观测到的蓝宝石电导率突增的温压条件与Al₂O₃在高温高压下Rh₂O₃（II）结构和CaIrO₃结构的相边界线比较,可以说明,蓝宝石电导率突增与压力大约为130GPa以及温度大约为1500K的Rh₂O₃（II）相到CaIrO₃相的结构相变存在密切关系。估算表明,在这个温压条件下,Rh₂O₃（II）到CaIrO₃的结构相变将导致蓝宝石电导率增加的量值大约为△lnσ～6.49。这些信息说明实验观测到的蓝宝石电导率突增可能是起因于在这个温压条件下蓝宝石从Rh₂O₃（II）到CaIrO₃的相变所引起的能隙明显地减少。而且,带隙随压力变化关系可以被用于解释实验中得到的蓝宝石电导率数据轨迹。这指明,在91-220GPa的冲击压力范围内,电子导电是蓝宝石主要的电导机理。3)基于Al₂O₃的CaIrO₃相与MgSiO3的后钙钛矿相在晶体结构和Raman光谱上的相似性,Al₂O₃的能带结构计算结果建议,MgSiO3从钙钛矿到后钙钛矿的相变也可能导致MgSiO3的能隙减少,这对探索在下地幔底部具有异常高的电导率的机理有重要意义。4)利用密度泛函理论框架下的第一性原理平面波超软赝势方法,结合局域密度近似（LDA）,还计算了纯Al₂O₃理想晶体的三个结构相在高压下的光吸收系数。结果指明,在0-220GPa的压力范围内以及在冲击波高压实验中所采用的光波段内（大约200-1000nm）,Al₂O₃吸收系数始终为零。这说明冲击实验在大约130-172GPa范围内所观测到的蓝宝石光学透明性降低与它的相变无关。5)本文的计算数据强化了Al₂O₃从Corundum到Rh₂O₃（II）的结构相变可能引起它的电导率变化的建议,但不支持这个相变可能改变蓝宝石光学透明性的推测。本论文第二部分运用分子动力学方法,采用嵌入原子模型（EAM）描述原子之间的相互作用势,在0-35GPa压强范围,对面心立方（FCC）结构金属铜中空位密度对其弹性性质的影响进行了计算模拟。为使缺陷可以在整个空间运动,采用了周期性边界条件。模拟均在0K温度下进行,对于温度的控制,采用的是Nose-Hoover方法,对于应力的控制则采用了Parrinello-Rahman等压方法。本部分的主要工作和结果如下:1)运用分子动力学方法对8×8×8原子数为2048的系统从0GPa到35GPa应力范围内的弹性系数进行了研究,得到了弹性系数随压强线性变化的关系。利用Murnagahan等温状态方程对压强和体积关系进行了拟合,得到铜在零压下的体模量。2)分别对5×5×5、6×6×6、7×7×7、8×8×8的四种晶胞中各拿走一个点阵上的原子形成空位时各体系在零温零压下的弹性系数进行模拟计算,得到金属铜的弹性系数随空位浓度的变化规律。3)对8×8×8的晶胞中含一个空位的系统在0-35GPa应力范围的弹性系数进行了模拟,并与无空位时相同大小的晶胞的弹性系数进行比较,得到相同空位浓度下,压强对有缺陷晶体弹性性质的影响。更多还原

【Abstract】 The structural change of the solid materials under high pressures （including crystal and electronic structures） will affect their elastic, electrical and optical properties. Studying their physical properties under high-pressure is important for understanding nature. This paper is divided into two parts, studying on some physical properties of Al₂O₃ and Cu under high pressure respectively.In the first part of this thesis,using first-principles calculations, band structure and the pressure dependence of the band gap of perfect Al₂O₃, and investigate the optical properties （optical absorption coefficient, the real and imaginary parts of the dielectric function, reflection and absorption spectrum and the energy loss spectrum）, and study the electronic density of states and mechanical properties of Al₂O₃ without defects at high pressures. By these calculations, some possible physical mechanisms for the transparency loss and the onset of the electrical conductivity, observed by shock-wave experiments, are presented.The main work and results of this part are as follows:1) Based on the plane-wave pseudopotential method in the frame-work of the density function theory and the local density approximation of Ceperly and Adler by the parametrization of Perdew and Zunger （LDA-CA-PZ）, the author determines the pressure dependence of the band gap for the three perfect Al₂O₃ structure phases at 0 K, and the band-gap data may be obtained from the corresponding calculated energy-band structures. It is found that Corundum-Rh₂O₃（II） and Rh₂O₃（II）-CaIrO₃ transitions in alumina at 0 K cause about 7-8% and 18-20% band-gap reductions, respectively. The band gap decreases slightly with pressure in the CaIrO₃ phase region but increases in Corundum and Rh₂O₃（II） phase regions.2) While the onset point （the temperature and pressure condition） of the observed conductivity increase is compared with the phase boundary line between the Rh₂O₃（II） and CaIrO₃ structures, the conductivity increase of shocked Al₂O₃ at about 130 GPa is associated closely with this transition at about 130GPa and 1500 K. Estimations indicate that the conductivity increase （△lnσ）, produced by the band-gap reduction due to the Rh₂O₃（II）-CaIrO₃ transition at ¹30 GPa and ¹500 K, may be estimated through a relationship:△lnσ～6.49 if the effect of the Rh₂O₃（II）-CaIrO₃ transition on the band gap of Al₂O₃ is considered. This information implies that the onset of the conductivity increase is attributed possibly to a band-gap decrease due to the Rh₂O₃（II）-CaIrO₃ transition at ¹30 GPa and ¹500 K. Moreover, the band gap-pressure relations may just explain the trajectory of experimental conductivity data, which shows that the predominant conduction mechanism of sapphire at shock pressures of 91-220 GPa is electronic conduction.3) Because of similarities of the crystal structures and Raman spectra of Al₂O₃-CaIrO₃ and MgSiO3 post-perovskite, the calculations of Al₂O₃ suggest that a perovskite to post-povskite transition in MgSiO3 causes perhaps a band-gap reduction as well, which makes MgSiO3 post-perovskite possess the high conductivity. This has significant implications for exploring the source of fairly large electrical conductivity at the Earth’s lowermost mantle.4) Using the plane-wave pseudopotential method in the frame-work of the density function theory and the local density approximation of Ceperly and Adler by the parametrization of Perdew and Zunger （LDA-CA-PZ）, the author has performed static first-principles calculations of optical absorption coefficients of perfect Al₂O₃ under high pressures. Results indicate that optical absorption coefficients of Al₂O₃ at 0-220GPa are always zero within the wavelength range adopted in shock experiments （²50-1000nm）. The phase transitions in alumina at high pressure and temperature might not be responsible for its optical transparency degradation observed at shock pressures of about 130-172GPa.5) The calculated data reinforce the suggestion that the Corundum-Rh₂O₃（II） transition change the electrical conductivity of alumina but don’t support the inference that this transition causes its transparency loss.In the second section of this thesis, the effect of vacancy concentration on elastic properties of copper under high pressures （from 0GPa to 35 GPa） is studied by means of MD simulation. The embedded-atom model （EAM） is employed to describeinter-atomic interaction in face-centered cubic （FCC） copper. In order to avoid the influence of surface effect, the periodic boundary conditions is employed in.simulation, so that the defect can move in the infinite space. To control the constant temperature and stress, Nose-Hoover method and Parrinello-Rahman method are.used, respectively.The main work and results of this part are as follows:1). MD method with EAM potential were used to study the elastic constants.under pressures range from 0GPa to 35GPa in the cell with size of.8×8×8.The linear relation between the elastic constants and.pressure was obtained. The data were fitted to Murnagahan isothermal equation of.state （EOS） to get the bulk modulus. The P-V/Vo relation is compared with.experimental result.2). Four cells with 5×5×5、6×6×6、7×7×7、8×8×8 chosen. Each cell has one correspond to different vacancy concentration. The simulation condition is at 0K and 0GPa. The relation between elastic constants and the vacancy concentration was calculated3). The elastic constants of the cell, containing one vacancy, with dimensions of 8×8×8 under high pressures ranging from 0GPa to 35GPa were calculated. The comparison was made for the cell with one vacancy and the perfect cell with same size. Pressure effect on the elastic properties of imperfect crystal was obtained.更多还原