论文总字数：30508字

摘 要

本文采用基于密度泛函理论的第一性原理计算方法，对不同等静压力下β-CaSiO₃和α-CaSiO₃的力学性质、热力学性质、各向异性和声学性质进行了研究。基于平面波超软赝势方法，交换关联函数采用广义梯度近似(GGA)中的质子平衡方程(PBE)，计算了两种硅酸钙晶体在不同压力下的弹性常数、柔性常数、体积模量、剪切模量、杨氏模量、泊松比来判断硅酸钙的力学性质，比如延展性，脆性，硬度和塑性等。根据等静压条件下机械稳定性判据。其次，探究了两种硅灰石晶格常数晶胞体积随压强的变化情况。此外，还计算了两种晶型硅灰石在不同方向上的杨氏模量，分析了两种晶型硅灰石的各向异性。通过最低热导率和声学常数来探究了热物理性质和声学性质。最后，通过分析原子态密度和总态密度图得到两种晶型硅灰石的电学性质。研究结果表明：两种硅酸钙在研究压力范围内，满足机械稳定性条件；并且在压力为6Gpa的条件下，杨氏模量最大，刚性最大；在压力为10Gpa的条件下泊松比最大，表明其塑性最好；晶格参数和晶胞体积随压强的增大而减小；导带区一般由未占据的Ca-3d形成，在费米能级(0eV)附近O-2p贡献最大。

关键词：第一性原理 硅酸钙 热物理性质 力学性质 电子结构

Thermal, mechanical and electronic structure properties of different polytypes of wollastonite

ABSTRACT

The first principles calculations based on density functional theory was applied to carry out the research on the thermal, mechanical and electronic structure properties of two polytypes of wollastonite, β-CaSiO₃ and α-CasiO₃, under different isostatic pressures. The interactions between atoms are approximated by plane wave pseudopotential method, and the PBE function was used for the generalized gradient approximation (GGA). Under circumstance of different pressures, we calculated the elastic index, flexible index, bulk modulus, shear modulus, Young's modulus, and Poisson's ratio of two polytypes of calcium silicate crystals. Furthermore, the mechanical properties of calcium silicate, such as ductility, brittleness, hardness and plasticity, were decided. It is judged that two types of calcium silicate meet the mechanical stability conditions within the investigative pressure range according to the mechanical stability under isostatic pressuring condition.Next, we explored the change of lattice constants with pressure for two types of wollastonite crystals.Furthermore, we also calculated the Young's modulus of two wollastonite crystal forms in different directions , and analyzed the anisotropy of the two wollastonite crystal forms. The thermal properties and acoustic properties are also calculated by means of the minimum thermal conductivity and acoustic constants. In the end, the electrical property of two wollastonite crystal forms are obtained by analyzing the atomic density and total density diagrams.The results of the study indicate that the two types of calcium silicate meet the mechanical stability conditions within the study pressure range; and that the Young's modulus is the largest and the rigidity is the largest when the pressure is 6 Gpa; the Poisson's ratio is the largest when the pressure is 10 Gpa , Indicating that its plasticity is the best; lattice parameters and unit cell volume decrease with increasing pressure; the conduction band is generally formed by unoccupied Ca-3d, and O-2p contributes the most near the Fermi level (0eV).

Key Words: First principle calculations; wollastonite; Thermal properties; Mechanical properties; Electronic structures

目 录

摘 要 I

ABSTRACT II

第一章 绪论 1

1.1文献综述 1

1.1.1 硅灰石结构参数随压力的变化的情况 1

1.1.2 硅灰石在不同压力下的相变，力学常数及其力学性质 1

1.1.3 硅灰石的热力学性质 2

1.1.4 硅灰石晶体随压力的各向异性情况 2

1.1.5 硅灰石的光学性质 2

1.1.6 硅灰石的应用和前景 3

1.2 理论基础 3

1.2.1 第一性原理 3

1.2.2 Materials studio软件及CASTEP模块 3

1.2.3 密度泛函理论（DFT) 4

1.2.4 赝势 4

第二章 实验方案 6

2.1 晶胞参数优化方法 6

2.2 力学常数计算方法 7

3.3 电学性能计算方法 7

第三章 两种硅灰石在等静压条件下的力学、热物理性质 8

3.1 结构性质 8

3.2 两种硅灰石晶体的力学性能 8

3.2.1 两种硅灰石结构的机械稳定性 8

3.2.2 弹性模量及力学性质 9

3.2.3 弹性各向异性随压强的变化 14

3.3 两种硅酸钙晶体的结构变化 18

3.4 热物理性质 19

3.4.1 德拜温度 20

3.4.2 最低热导率 21

3.4.3 声学Grüneisen常数 22

3.5 电学性质 23

第四章 结论 25

参考文献 26

致谢 28

第一章 绪论

1.1文献综述

1.1.1 硅灰石结构参数随压力的变化的情况

硅灰石^[1]的结构为链状，有两种变体，分别是高温变体和低温变体。高低温变体的转化温度约为1125℃，两种变体的晶体结构特点如下表所示：

表1-1 硅灰石的两种变体

图1-1 硅灰石两种变体晶胞结构图 (a) α-CaSiO₃晶体结构图 (b) β-CaSiO₃晶体结构图

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