Hf-Ta-C-N四元化合物的结构、力学及电子性质的第一性原理研究

doi:10.19596/j.cnki.1001-246x.8543

摘要/Abstract

摘要：

基于进化算法和第一性原理计算，预测四元化合物Hf_xTa_8-xC₇N(x=1~7)的晶体结构。与二元HfC和TaC的晶体结构相似，这些四元Hf_xTa_8-xC₇N晶体结构属于岩盐结构。计算结果表明：随着有效价电子浓度(VEC)的增大，Hf_xTa_8-xC₇N的体模量逐渐增大；当VEC等于8.875时，剪切模量和杨氏模量达到最大值；维氏硬度在VEC等于8.25时达到最大值。因此，可以通过VEC的设计，得到具有综合力学性质优异的四元Hf_xTa_8-xC₇N化合物。计算Hf_xTa_8-xC₇N的电子性质，并分析力学性质与电子性质之间的关系。

关键词: Hf_xTa_8-xC₇N, 晶体结构预测, 有效价电子浓度, 第一性原理计算

Abstract:

Based on evolutionary algorithm and first-principles calculation, crystal structures of quaternary compound Hf_xTa_8-xC₇N (x=1-7) were predicted. Similar to binary HfC and TaC, these compounds have a rock-salt structure. The calculation of mechanical properties shows that: With the increase of valence electron concentration (VEC), the bulk modulus of Hf_xTa_8-xC₇N increased gradually; At VEC=8.875, the shear modulus and elastic modulus are the largest; The Vickers hardness reaches the maximum at VEC=8.25. Therefore, the quaternary Hf_xTa_8-xC₇N compounds with excellent comprehensive mechanical properties can be obtained with the design of VEC. Finally, electronic properties of Hf_xTa_8-xC₇N compounds were calculated. Relations between mechanical properties and electronic properties were analyzed.

Key words: Hf_xTa_8-xC₇N, crystal structure prediction, effective valence electron concentration, first-principles calculation

程翔, 冯军伟, EvgeniiTikhonov. Hf-Ta-C-N四元化合物的结构、力学及电子性质的第一性原理研究[J]. 计算物理, 2023, 40(1): 40-46.

Xiang CHENG, Junwei FENG, Tikhonov EVGENII. First-principles Study of Structures, Mechanical Properties and Electronic Properties of Quaternary Hf-Ta-C-N System[J]. Chinese Journal of Computational Physics, 2023, 40(1): 40-46.

图/表 6

表1 HfxTa8-xC7N(x=1~7)的空间群、晶格常数、形成焓ΔHf、高出凸包线的能量和有效价电子浓度(VEC)

Table 1 Space groups, lattice constants, enthalpy of formation ΔHf, enthalpy above convex-hull, and valence electron concentrations (VEC) of HfxTa8-xC7N (x=1-7)

Compound	Space group	Lattice constants/Å	ΔH_f/(eV·atom^-1)	instability/(eV·atom^-1)	VEC
Hf₇TaC₇N	P4mm	a=4.603, b=4.603, c=9.245	-1.041 5	0.004 1	8.25
Hf₆Ta₂C₇N	Pmmm	a=4.575, b=4.600, c=9.166	-0.993 7	0.010 7	8.375
Hf₅Ta₃C₇N	Pmm2	a=4.560, b=4.564, c=9.145	-0.945 1	0.013 3	8.5
Hf₄Ta₄C₇N	Pmm2	a=4.538, b=4.548, c=9.094	-0.897 5	0.007 1	8.625
Hf₃Ta₅C₇N	P4mm	a=4.515, b=4.515, c=9.091	-0.842 4	0.005 9	8.75
Hf₂Ta₆C₇N	Pmm2	a=4.495, b=4.503, c=9.030	-0.781 2	0.007 9	8.875
HfTa₇C₇N	P4mm	a=4.488, b=4.488, c=8.959	-0.702 8	0.022 6	9

图1 晶体结构(a)HfTa7C7N；(b)Hf2Ta6C7N；(c)Hf3Ta5C7N；(d)Hf4Ta4C7N；(e)Hf5Ta3C7N；(f)Hf6Ta2C7N；(g)Hf7TaC7N

Fig.1 Crystal structures of (a) HfTa7C7N, (b) Hf2Ta6C7N, (c) Hf3Ta5C7N, (d) Hf4Ta4C7N, (e) Hf5Ta3C7N, (f) Hf6Ta2C7N and (g) Hf7TaC7N

表2 HfxTa8-xC7N(x=1~8)的键长和原子体积

Table 2 Bond lengths and volume per atom of HfxTa8-xC7N(x=1-8)

Compound	Bond length/Å				Volume per atom/Å³
Compound	Hf-C	Hf-N	Ta-C	Ta-N	Volume per atom/Å³
Hf₇TaC₇N	2.285~2.328	2.302~2.364	2.199~2.303	2.353	12.243 5
Hf₆Ta₂C₇N	2.273~2.309	2.288~2.306	2.259~2.323	2.300	12.055 2
Hf₅Ta₃C₇N	2.273~2.349	2.280~2.373	2.164~2.301	2.335	11.892 5
Hf₄Ta₄C₇N	2.233~2.289	2.269~2.344	2.158~2.301	2.274~2.359	11.731 4
Hf₃Ta₅C₇N	2.258~2.322	2.258	2.163~2.259	2.352~2.413	11.583 0
Hf₂Ta₆C₇N	2.248~2.285	2.248	2.178~2.272	2.251~2.349	11.423 4
HfTa₇C₇N	2.238~2.244	2.272	2.184~2.275	2.244~2.264	11.275 4
Hf₈C₇N	2.309~2.322	3.324			12.432 8

图2 HfxTa8-xC7N (x=1~8)的力学性质与VEC之间的关系(a) 体模量(B)；(b) 剪切模量(G)；(c) 杨氏模量(E)；(d) 维氏硬度(HV)；(e) Pugh比(G/B)；(f) 断裂韧性(KIC)

Fig.2 Mechanical properties as functions of VEC for HfxTa8-xC7N (x=1-8) (a) Bulk modulus (B); (b) shear modulus (G); (c) elastic modulus (E); (d) Vickers hardness (HV); (e) Pugh's ratio (G/B) and (f) fracture toughness (KIC)

图3 HfxTa8-xC7N (x=1~8)的晶体轨道哈密顿分布(-COHP)(Fermi能级位于0 eV。)

Fig.3 Crystal orbital Hamilton populations (-COHP) of HfxTa8-xC7N (x=1-8) (The Fermi level is set at 0 eV.)

图4 HfxTa8-xC7N (x=1~8)的晶体轨道哈密顿分布积分值(-ICOHP)与VEC之间的关系

Fig.4 Integrated crystal orbital Hamilton populations (-ICOHP)as a function of VEC for HfxTa8-xC7N (x=1-8)

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