中文摘要：

本文采用第一性原理框架下的赝势平面波方法结合振动类德拜模型研究了α-，β-和γ-Si3N4在高温下的点阵常数，弹性常数和弹性模量．研究发现三种同质异相体的体模量都很高．β-Si3N4在低温下表现出脆性，在高温下则表现出延展性．γ-Si3N4在低温和高温下都是脆性的共价化合物．β→γ相变的相界斜率为正值，说明在较高温度时合成γ-Si3N4所需的压强也较高．α→τ相变的相界可以表示成P=16．29—1．835×10-2T＋9．33945×10-5T-2．16759×10-7T3＋2．91795×10-10T4．本文还分析了Si3N4同质异相体在高压下的态密度和能带．在α-Si3N4中主要是Si-s，P和N-s，P的轨道杂化对晶体的稳定性起作用．α和β-Si3N4都具有ГV-ГC类型的间接带隙（分别是4．9eV和4．4eV）而γ-Si3N4具有直接带隙（3．9eV）．研究还发现α—Si3N4和β-Si3N4的价带顶分别沿着，Г-M和，Г-A方向．本文的计算结果和已有的实验数据是一致的．

英文摘要：

The high-temperature lattice constants and elastic moduli of the silicon nitrides are calculated using the plane-wave pseudo- potential method combined with the vibrational Debye-like model. β-Si3N4 is ductile at low temperature and brittle at high temperature. γ-Si3N4 is found to be brittle and covalent in nature. We find a positive slope of the β→γ phase boundary, hence, at higher temperatures it requires higher pressures to synthesize γ-Si3N4. The α→γ phase boundary may be expressed as P = 16.29 - 1.835 × 10-2T ＋ 9.33945×10-5T2 - 2.16759×10-7T3 ＋ 2.91795×10-10T4. We also obtain the electronic structures and energy bands of Si3N4 with and without pressure. The interaction between Si-s, p and N-s, p plays a dominant role in the stability of α-SiaN4. The α- and β-Si3N4 have the ГV-ГC indirect band gaps （4.9 eV and 4.4 eV） while γ-Si3N4 has a direct band gap（3.9 eV）. The tops of the valence bands for α- and β-Si3N4 are along the Г-M and Г-A direction, respectively, Our results are consistent with the experimental data and the theoretical results.