Hf-N体系的晶体结构预测和性质的第一性原理研究

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

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Hf N之外,本文还找到了Hf_6N(R-3),Hf_3N(P6322),Hf_3N_2(R-3m),Hf_5N_6(C2/m)和Hf_3N_4(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Hf_2N(P42/mnm),Hf_4N_3(C2/m),Hf_6N_5(C2/m),Hf4N5(I4/m),Hf_3N_4(I-43d)和Hf_3N_4(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Hf_5N_6处取得最大值,为21 GPa.其中Hf_3N_2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Hf_5N_6具有优异力学性能的主要原因.

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 Hf N,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 structures Hf5N6（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-43 d 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 P nma Hf3N4 structure decreases with temperature increasing.Thus,we speculate that the C2/m Hf3N4 transforms into P nma 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 Hf N 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.