【摘要】 本文采用基于第一性原理的密度泛函理论（DFT）和密度泛函微扰理论（DFPT）方法,计算了ZnCo₃（OH）₆Cl₂和ZnNi₃（OH）₆Cl₂两种六角结构晶体的结构,声子谱和模式密度,进而分析和比较了对称性,频率以及热力学性质。通过理论计算得到的声子谱没有虚频,可知该结构可以稳定存在;声子模式密度结果显示了不同种类原子的贡献大小。确定了拉曼活性振动模式的对称性和频率,并与量子自旋液体材料ZnCu₃（OH）₆Cl₂进行了比较,结果显示它们的主要拉曼峰位置比较接近。最后,计算和分析得到的热力学性质符合物理规律。更多还原

【Abstract】 In this paper, the method of density functional theory（DFT） and density functional perturbation theory（DFPT） based on the first principles are used to calculate the crystal structures, phonon spectra and density of modes for ZnCo₃（OH）₆Cl₂ and ZnNi₃（OH）₆Cl₂. Both of them have hexagonal crystal structures. Also, the symmetries and frequencies and thermodynamic properties are analyzed and compared. No imaginary frequencies are presented in the phonon spectra obtained from the theoretical calculation, which indicated that the crystal structures are stable; the results of density of modes showed the contribution of different kinds of atoms. The symmetries and frequencies of Raman active vibration modes are determined, and we also compared them with quantum spin liquid materials ZnCu₃（OH）₆Cl₂, the results showed that the main positions of Raman peak are close. Finally, the thermodynamic properties calculated and analyzed agree with the laws of physics.更多还原