Hf-N体系的晶体结构预测和性质的第一性原理研究

为了寻找具有优异力学性能的新型超高温陶瓷材料, 结合进化算法和第一性原理, 系统研究了Hf-N二元体系所有稳定存在的化合物及其晶体结构. 除了实验已知的岩盐结构的HfN之外, 本文还找到了Hf₆N(R-3), Hf₃N(P6₃22), Hf₃N₂(R-3m), Hf₅N₆(C2/m)和Hf₃N₄(C2/m)五种新结构, 基于准简谐近似原理计算了这些稳定结构的声子谱以验证其动力学稳定性, 常温甚至更高温度下的吉布斯自由能以验证其高温热力学稳定性. 结果表明, 这些结构是动力学稳定的, 且在1500 K以下都是热力学稳定的. 同时, 本文还列出了在搜索过程中出现的空间对称性较高、能量较低的亚稳态结构, 包括Hf₂N(P4₂/mnm), Hf₄N₃(C2/m), Hf₆N₅(C2/m), Hf₄N₅(I4/m), Hf₃N₄(I-43d)和Hf₃N₄(Pnma). 之后计算了上述所有结构的力学性质(弹性常数、体模量、 剪切模量、 杨氏模量、硬度), 随着N 所占比例的增加, 硬度呈现的整体趋势是先增大后下降, 在Hf₅N₆处取得最大值, 为21 GPa. 其中Hf₃N₂和Hf₄N₅也展现出了较高的硬度, 都为19 GPa. 最后, 计算了这些结构的电子态密度和晶体轨道汉密尔顿分布, 从电子结构的角度分析了力学性能的成因. 研究结果显示, 较强的Hf-N共价键和较低的结构空位率是Hf₅N₆具有优异力学性能的主要原因.

Novel compounds in the hafnium nitride system: first principle study of their crystal structures and mechanical properties

Motivated by exploring new high temperature ceramics which have excellent mechanical properties, we systematically search for all the stable compounds and their crystal structures in the binary Hf-N system by combining the evolutionary algorithm with first principle calculation. In addition to the well-known rock-salt HfN, we find five other novel compounds, i.e., Hf₆N(R-3), Hf₃N(P6₃22), Hf₃N₂(R-3m), Hf₅N₆(C2/m), and Hf₃N₄(C2/m). Then, their phonon frequencies are calculated so that the dynamical stabilities are known. Their high temperature thermodynamic stabilities are further confirmed and the Gibbs free energies are calculated in thequasi-harmonic approximation. All of these structures are thermodynamic stable when the temperature is lower than 1500 K. However, as temperature increases, the structuresHf₅N₆(C2/m) and Hf₃N₄(C2/m) become meta-stable. Meanwhile, some meta-stable structures, including Hf₂N (P4₂/mnm), Hf₄N₃ (C2/m), Hf₆N₅(C2/m), Hf₄N₅(I4/m), Hf₃N₄ (I-43d), and Hf₃N₄ (Pnma), each of which has higher symmetry and lower formation enthalpy, are all listed. At the same time, our results of Hf₃N₄ testify that C2/m structure is stabler than Pnma and I-43d structures when the temperature is lower than 2000 K, which is different from the conclusion given by Bazhanov Bazhanov D I, Knizhnik A A, Safonov A A, Bagatur'yants A A, Stoker M W, Korkin A A 2005 J. Appl. Phys. 97 044108]. The results also show that the difference in Gibbs free energy between C2/m and Pnma Hf₃N₄ structure decreases with temperature increasing. Thus, we speculate that the C2/m Hf₃N₄ transforms into Pnma Hf₃N₄ when the temperature is above 2000 K. The mechanical properties, including the elastic constant, bulk modulus, shear modulus, Young's modulus and hardness, are systematically investigated. The hardness first increases, reaching a maximum at Hf₅N₆ (21 GPa), and then decreases with increasing nitrogen content. Besides, Hf₃N₂ and Hf₄N₅ both exhibit relatively high hardness value of 19 GPa, while the hardness of HfN is 15 GPa. Finally, the electron densities of states and crystal orbital Hamilton populations are calculated so that the mechanic origins can be analyzed from the electronic structures of these phases. The crystal orbital Hamilton populations show that the strength of Hf-N covalent bonding increases with increasing nitrogen content, however, it has an exceptional peak for Hf₃N₂, which can be used to explain the relatively high hardness of this structure. Beside covalent bonding strength, structural vacancy can also affect their mechanical properties. It is concluded that the strong covalent bonding and low structural vacancy both can explain the good mechanical performance of Hf₅N₆.