空位对Hf-Ta-C体系的结构、力学性质及电子性质影响的第一性原理研究

doi:10.15541/jim20210179

无机材料学报 ›› 2022, Vol. 37 ›› Issue (1): 51-57.DOI: 10.15541/jim20210179

所属专题：【虚拟专辑】计算材料

空位对Hf-Ta-C体系的结构、力学性质及电子性质影响的第一性原理研究

彭军辉¹^,²(), TIKHONOV Evgenii¹()

1.西北工业大学材料学院, 材料发现国际中心, 西安 710072
2.太原工业学院材料工程系, 太原 030008

收稿日期:2021-03-20 修回日期:2021-04-30 出版日期:2022-01-20 网络出版日期:2021-12-30
通讯作者: TIKHONOV Evgenii, 助理教授. E-mail: tikhonov.e@nwpu.edu.cn
作者简介:彭军辉(1989-), 男, 博士研究生. E-mail: pjh1989@yeah.net
基金资助:
外国人才引进与学术交流项目(B08040)

Vacancy on Structures, Mechanical and Electronic Properties of Ternary Hf-Ta-C System: a First-principles Study

PENG Junhui¹^,²(), TIKHONOV Evgenii¹()

1. International Center for Materials Discovery, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an 710072, China
2. Department of Materials Engineering, Taiyuan Institute of Technology, Taiyuan 030008, China

Received:2021-03-20 Revised:2021-04-30 Published:2022-01-20 Online:2021-12-30
Contact: TIKHONOV Evgenii, assistant professor. E-mail: tikhonov.e@nwpu.edu.cn
About author:PENG Junhui(1989-), male, PhD candidate. E-mail: pjh1989@yeah.net
Supported by:
Foreign Talents Introduction and Academic Exchange Program of China(B08040)

摘要/Abstract

摘要：

本研究理论预测了三元Hf-Ta-C空位有序结构以及空位对力学性质的影响。采用第一性原理进化晶体结构预测软件USPEX, 预测得到了5种热力学稳定和3种亚稳的(Hf, Ta)C_1-_x空位有序结构, 这些结构都属于岩盐结构。采用第一性原理方法, 计算了(Hf, Ta)C_1-_x空位有序结构的力学性质, 并分析了力学性质随空位浓度的变化。(Hf, Ta)C_1-_x都具有较高的体模量、剪切模量、杨氏模量和维氏硬度;各(Hf, Ta)C_1-_x的Hf/Ta比相同时, 其模量、硬度等随空位浓度增大而减小。最后, 计算了(Hf, Ta)C_1-_x的电子态密度, 发现其均具有强共价性和弱金属性。本研究结果对于了解Hf-Ta-C体系的空位结构及其力学性质和应用, 具有重要参考价值。

关键词: Hf-Ta-C体系, 空位有序结构, 维氏硬度, 第一性原理方法

Abstract:

In this study, the first-principles method was used to predict the vacancy ordered structures of ternary Hf-Ta-C system and the effect of vacancy on its mechanical properties. Crystal structure of (Hf, Ta)C_1-_x under ambient pressure were predicted by first-principles evolutionary using USPEX software. This calculation found 5 stable and 3 metastable vacancy ordered structures which all share the rock-salt structure. Then, mechanical properties of (Hf, Ta)C_1-_x vacancy ordered structures were calculated by the first-principles method, and change of mechanical properties with the concentration of vacancy was analyzed. They all showed high bulk modulus, shear modulus, elastic modulus, and Vickers hardness. Their moduli and hardness decreased with the increase of the concentration of vacancy at the same Hf/Ta ratio. Finally, their electronic density of states are calculated, revealing that their chemical bonding is a mixture of strong covalence and weak metallic. Data from this study are promising for understanding vacancy ordered structures, mechanical properties and applications of Hf-Ta-C system.

Key words: Hf-Ta-C system, vacancy ordered structure, Vickers hardness, first-principles method

中图分类号:

O411

彭军辉, TIKHONOV Evgenii. 空位对Hf-Ta-C体系的结构、力学性质及电子性质影响的第一性原理研究[J]. 无机材料学报, 2022, 37(1): 51-57.

PENG Junhui, TIKHONOV Evgenii. Vacancy on Structures, Mechanical and Electronic Properties of Ternary Hf-Ta-C System: a First-principles Study[J]. Journal of Inorganic Materials, 2022, 37(1): 51-57.

图/表 7

图1 晶体结构预测及(Hf,Ta)C1-x空位有序结构

Fig. 1 Crystal structure prediction and (Hf, Ta)C1-x vacancy ordered structure (a) Enthalpy convex-hull of ternary Hf-Ta-C system (black sphere indicating stable structure, while others indicating metastable structure, and red square representing the structure with high enthalpy above the convex-hull, but not considered here); (b) Simulated X-ray diffractions of (Hf, Ta)C1-x vacancy ordered structures with a copper Kα X-ray source

表1 (Hf, Ta)C1-x空位有序结构的空间群、晶格常数、高于凸包线的焓值、形成焓(ΔHf)、原子配位数(CN)、空位浓度(x)

Table 1 Space groups, lattice constants, enthalpy above the convex-hull, formation enthalpy (ΔHf), concentration of vacancy (x) and coordination number (CN) of Hf or Ta for ternary (Hf, Ta)C1-x vacancy ordered structures

Compound	Space group	Lattice constants/nm	Above convex-hull /(eV·atom^-1)	ΔH_f /(eV·atom^-1)	CN	x
Hf₅TaC₅	Cm	a=0.567, b=0.976, c=0.929, β=145.1°	0	-0.8925	5, 5	1/6
Hf₃TaC₃	P-1	a=0.567, b=0.648, c=0.565 α=89.4°, β=69.6°, γ=91.3°	0.0007	-0.8408	5/4, 4	1/4
Hf₆Ta₂C₇	P-1	a=0.565, b=0.562, c=0.653 α=90.4°, β=72.4°, γ=99.8°	0	-0.8868	6/5, 5	1/8
Hf₂TaC₂	P-1	a=0.566, b=0.554, c=0.560 α=119.4°, β=98.4°, γ=102.4°	0.0012	-0.7842	4, 4	1/3
Hf₄Ta₂C₅	P-1	a=0.559, b=0.561, c=0.559 α=109.1°, β=100.1°, γ=60.3°	0	-0.8604	5, 5	1/6
Hf₃Ta₃C₅	Cm	a=0.558, b=0.963, c=0.644, β=125.2°	0.0009	-0.8161	5, 5	1/6
Hf₂Ta₄C₅	C2/m	a=0.551, b=0.963, c=0.551, β=71.3°	0	-0.7735	5, 5	1/6
HfTa₅C₅	Cm	a=0.548, b=0.954, c=0.548, β=109.2°	0	-0.7033	5, 5	1/6

表2 (Hf, Ta)C1-x空位有序结构的弹性常数(Cij)、体模量(B)、剪切模量(G)、杨氏模量(E)、泊松比(μ)、维氏硬度(Hv)和Pugh比(G/B)

Table 2 Calculated elastic constants (Cij) and mechanical properties-bulk modulus (B), shear modulus (G/), elastic modulus (E), Poisson’s ratio (μ), Vickers hardness (Hv) and Pugh’s ratio (G/B) of (Hf, Ta)C1-x vacancy ordered structures

Compound	C₁₁/GPa	C₂₂ /GPa	C₃₃ /GPa	C₄₄ /GPa	C₅₅ /GPa	C₆₆ /GPa	C₁₂ /GPa	C₁₃ /GPa	C₂₃ /GPa	B /GPa	G /GPa	E /GPa	H_v /GPa	G/B	μ
Hf₅TaC₅	422.9	446.8	432.1	177.0	177.0	156.1	105.3	129.0	122.5	223.8	162.7	393.0	24.09	0.7271	0.2074
Hf₃TaC₃	382.3	407.8	403.3	156.7	156.7	121.6	102.9	123.1	121.8	209.3	141.4	346.1	19.88	0.6754	0.2244
Hf₆Ta₂C₇	454.5	482.0	472.3	180.9	180.9	171.3	122.2	135.9	114.0	239.1	170.6	413.4	24.23	0.7133	0.2119
Hf₂TaC₂	365.7	399.7	384.9	136.2	136.2	108.5	121.0	118.9	112.0	205.7	128.8	319.8	16.85	0.6265	0.2409
Hf₄Ta₂C₅	443.4	423.5	441.2	175.4	175.4	160.2	122.8	135.9	140.4	233.9	162.6	395.9	22.68	0.6949	0.2179
Hf₃Ta₃C₅	431.3	443.6	433.6	185.4	185.4	153.1	129.2	149.3	154.0	241.4	157.2	387.5	20.34	0.6513	0.2325
Hf₂Ta₄C₅	476.5	446.7	477.6	199.4	199.4	161.1	141.9	163.7	155.6	257.9	168.3	414.6	21.34	0.6525	0.2320
HfTa₅C₅	491.9	473.8	484.4	209.8	209.8	171.5	149.6	165.6	166.9	268.2	175.7	432.6	22.08	0.6551	0.2312

图2 (a) Hf5TaC5、(b) Hf3TaC3、(c) Hf6Ta2C7、(d) Hf2TaC2、(e) Hf4Ta2C5、(f) Hf3Ta3C5、(g) Hf2Ta4C5和(h) HfTa5C5的声子谱曲线

Fig. 2 Phonon dispersion curves of (a) Hf5TaC5, (b) Hf3TaC3, (c) Hf6Ta2C7, (d) Hf2TaC2, (e) Hf4Ta2C5, (f) Hf3Ta3C5, (g) Hf2Ta4C5, and (h) HfTa5C5 They are all dynamical stable because no imaginary frequencies were found in Brillouin zone

图3 (a) Hf5TaC5、(b) Hf3TaC3、(c) Hf6Ta2C7、(d) Hf2TaC2、(e) Hf4Ta2C5、(f) Hf3Ta3C5、(g) Hf2Ta4C5和(h) HfTa5C5的晶体结构

Fig. 3 Crystal structures of (a) Hf5TaC5, (b) Hf3TaC3, (c) Hf6Ta2C7, (d) Hf2TaC2, (e) Hf4Ta2C5, (f) Hf3Ta3C5, (g) Hf2Ta4C5, and (h) HfTa5C5 All sharing the rock-salt structure; Black square represents the structural vacancy

图4 空位对Hf-Ta-C体系力学性质的影响

Fig. 4 Effect of vacancy on mechanical properties for ternary Hf-Ta-C system (a) Bulk modulus (B); (b) Shear modulus (G); (c) Elastic modulus (E); (d) Vickers hardness (HV); (e) Pugh’s ratio (G/B); (f) Poisson’s ratio (μ)

图5 (a) Hf5TaC5、(b) Hf3TaC3、(c) Hf6Ta2C7、(d) Hf2TaC2、(e) Hf4Ta2C5、(f) Hf3Ta3C5、(g) Hf2Ta4C5和(h) HfTa5C5的态密度和分态密度(Fermi能级位于0 eV)

Fig. 5 Density of state (DOS) and partial DOS (PDOS) normalized by per (Hf, Ta)C1-x of (a) Hf5TaC5, (b) Hf3TaC3, (c) Hf6Ta2C7, (d) Hf2TaC2, (e) Hf4Ta2C5, (f) Hf3Ta3C5, (g) Hf2Ta4C5, and (h) HfTa5C5(The Fermi level being set at 0 eV) DOS is density of state / (states/eV); TDOS is total DOS; Hf, Ta, C are PDOS of Hf atom, Ta atom and C atom, respectively Colorful figures are available on the website

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空位对Hf-Ta-C体系的结构、力学性质及电子性质影响的第一性原理研究

Vacancy on Structures, Mechanical and Electronic Properties of Ternary Hf-Ta-C System: a First-principles Study

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