三元Hf-C-N体系的空位有序结构及其力学性质和电子性质的第一性原理研究

First-principles study of vacancy ordered structures,mechanical properties and electronic properties of ternary Hf-C-N system

采用第一性原理方法,研究了三元Hf-C-N体系的空位有序结构及其力学性质和电子性质.首先采用第一性原理和进化算法,预测得到8种可能存在的热力学稳定的Hf-C-N空位有序结构;这些结构都具有岩盐结构,与实验发现的无序固溶体的结构类型一致.本文的预测结果证明了Hf-C-N空位化合物能够以有序结构形式存在,空位与C,N原子都位于[Hf6]八面体间隙,这一结构特点与Hf C_x的相同.然后采用第一性原理方法,计算了Hf-C-N空位有序结构的力学性质,发现除C∶N=1∶4外,相同C/N下,随着空位浓度的增大,Hf-C-N的体模量、剪切模量、弹性模量、Pugh比、维氏硬度等降低;而Hf6CN4(空位浓度为1/6)的维氏硬度高于Hf_5CN_4(无空位),表现出空位硬化现象.最后,计算了Hf-C-N空位有序结构的态密度和晶体轨道哈密顿分布,发现其具有强共价性和金属性;且随着空位浓度增大,总体键强减弱,因而模量减小.

The thermal-mechanical properties of transition metal carbonitrides can be affected by the concentration and ordering of vacancies besides the C/N atomic ratio.However,there are few reports on the vacancy ordered structure of ternary transition metal carbonitrides.In the present paper,the first-principles method is used to study the vacancy ordered structures,mechanical properties,electronic properties and the effect of vacancies on the ternary Hf-C-N system.Firstly,the crystal structures of Hf-C-N system is examined by the first-principles and evolutionary algorithms implemented in USPEX under ambient pressure,and eight thermodynamical stable vacancy ordered structures are found,each of which has a rock-salt structure,and is also dynamical and mechanical stable,which are verified by the calculations of their phonon dispersion curves and elastic constants.The vacancies are occupied at the[Hf6]octahedral interstices,which replace the positions of non-metal atoms.Their crystallographic data such as space group,lattice constants are also predicted.To the best of our knowledge,there is no report on the Hf-C-N vacancy ordered structures and these structures investigated here in this work are all found for the first time.Then their mechanical properties are calculated.The Hf-C-N vacancy ordered structures all have very high bulk,shear and elastic modulus and hardness.It is found that except for C∶N=1∶4,for the Hf-C-N system with the same C/N ratio the moduli,Vickers hardness values,and Pugh’s ratios decrease with the increase of the concentration of vacancy.However,the Vickers hardness of Hf6CN4(the concentration of vacancy is equal to 1/6)is higher than that of Hf5CN4(no vacancy),that is so-called vacancy hardening.Finally,the electronic density of states and the crystal orbital Hamilton populations are calculated.The chemical bonding of Hf-C-N vacancy ordered structure is analyzed,which is a mixture of covalence and metallic and is similar to that of binary transition metal carbides and nitrides.With the increase of the concentration of vacancy,the total bond strength decreases,and then the modulus decreases for Hf-C-N compound.