负膨胀材料Zn(CN)_2和Cd(CN)_2的晶格振动分析

Lattice Vibrational Analysis of the Negative Thermal Expansion Materials of Zn(CN)_2 and Zn(CN)_2

运用群论理论对负膨胀系数材料Zn(CN)2和Cd(CN)2的晶格振动进行了对称性分类,利用第一性原理密度泛函理论计算了它们布里渊区中心点的声子频率和Grüneisen参数,根据计算得到的各个模式所对应的本征矢对各个振动模式进行了指认,根据各模式Grüneisen参数讨论了负膨胀机理。在11个光学振动模式中,一个属于Zn/Cd原子的晶格振动模,位于223 cm-1/154 cm-1;5个属于C≡N刚性单元平移振动模;3个属于C≡N刚性单元天平动;2个属于C≡N刚性单元内振动。有7个振动模为拉曼活性,4个振动模为红外活性,两个振动模红外和拉曼均为非活性。C≡N刚性单元的3个低频平移振动模和全部天平动模的Grüneisen参数为负,对负热膨胀的产生有贡献,振动频率为47 cm-1的平移振动模具有最大的负Grüneisen参数,对负膨胀贡献最大。

We have classified the phonons of different symmetries in the negative thermal expansion materials of Zn（CN）2 and Cd（CN）2 based on group theoretical analyses and calculated the Brillouin zone center phonon frequencies and corresponding Gruneisen parameters by the first-principles plane-wave pseudopotential method based on density functional theory. Each mode is assigned according to the eigenvector analysis and the mechanism of negative thermal expansion is explained based on Gruneisen parameter calculations. There are 5 translational, 3 librational and 2 internal （stretching） modes of the C≡N units and 1 lattice mode of metal ions. Among these modes, 7 are Raman active, 4 are infrared active and 2 are both Raman and infrared inactive. The lowest 3 translational and all librational modes have negative Grtineisen parameters, responsible for the negative thermal expansion. However, the lowest phonon mode at 47 cm-1 for Zn（CN）2 and 39 cm-1 for Cd（CN）2 have the largest Grianeisen parameters and hence give rise to dominant contribution to the negative thermal expansion （NTE）.