HfxTa1-xC体系力学性能及熔化曲线的第一性原理研究

doi:10.15541/jim20230518

无机材料学报 ›› 2024, Vol. 39 ›› Issue (7): 761-768.DOI: 10.15541/jim20230518 CSTR: 32189.14.10.15541/jim20230518

所属专题：【结构材料】超高温结构陶瓷(202409)；【材料计算】计算材料(202409)

Hf_xTa_1-_xC体系力学性能及熔化曲线的第一性原理研究

吴玉豪(), 彭仁赐, 程春玉, 杨丽(), 周益春()

西安电子科技大学先进材料与纳米科技学院, 陕西省空天高电子轨道材料与防护技术重点实验室, 西安 710126

收稿日期:2023-11-06 修回日期:2024-02-28 出版日期:2024-07-20 网络出版日期:2024-03-08
通讯作者: 周益春, 教授. E-mail: yichunzhou@xidian.edu.cn;
杨丽, 教授，E-mail: lyang-xd@xidian.edu.cn
作者简介:吴玉豪(2000-), 男, 硕士研究生. E-mail: hsarfr@163.com
基金资助:
国家自然科学基金(11890684);国家自然科学基金(12302125);中央高校基本科研业务费(20101237677);中央高校基本科研业务费(ZYTS23079)

First-principles Study on Mechanical Properties and Melting Curve of Hf_xTa_1-_xC System

WU Yuhao(), PENG Renci, CHENG Chunyu, YANG Li(), ZHOU Yichun()

Shaanxi Key Laboratory of High-Orbits-Electron Materials and Protection Technology for Aerospace, School of Advanced Materials and Nanotechnology, Xidian University, Xi’an 710126, China

Received:2023-11-06 Revised:2024-02-28 Published:2024-07-20 Online:2024-03-08
Contact: ZHOU Yichun, professor. E-mail: yichunzhou@xidian.edu.cn;
YANG Li, professor. E-mail: lyang-xd@xidian.edu.cn
About author:WU Yuhao (2000-), male, Master candidate. E-mail: hsarfr@163.com
Supported by:
National Natural Science Foundation of China(11890684);National Natural Science Foundation of China(12302125);Fundamental Research Funds for the Central Universities of China(20101237677);Fundamental Research Funds for the Central Universities of China(ZYTS23079)

摘要/Abstract

摘要：

Hf_xTa_1-_xC具有高熔化温度、高硬度、高强度, 以及导电、导热性好等优异性能, 是2000 ℃以上热防护领域极有潜力的候选材料, 但其力学性质与熔化温度随组分变化规律尚不清晰。本研究基于特殊准随机结构(SQS)方法和第一性原理计算, 从共价键强度、价电子浓度(VEC)的微观角度系统地探讨了Hf_xTa_1-_xC系固溶体力学性质随组分的变化机理。力学性质计算结果表明: 5种组分(HfC、Hf_0.75Ta_0.25C、Hf_0.5Ta_0.5C、Hf_0.25Ta_0.75C与TaC)中, Hf_0.25Ta_0.75C固溶体具有最高的弹性模量和剪切模量, 这主要归因于: (1)该组分具有最高的共价键强度; (2)来自C的p轨道和来自Hf或Ta的d轨道之间的特殊键合在VEC=8.75(Hf_0.25Ta_0.75C)附近被完全填充, 它们强烈抑制形状变化。研究还使用基于从头算分子动力学(AIMD)的分子动力学Z方法计算了Hf_xTa_1-_xC系固溶体的熔化曲线。结果显示Hf_xTa_1-_xC系固溶体熔化温度反常增加的现象的确存在, 且在Hf_0.5Ta_0.5C处熔化温度最高(4270 K), 这主要归因于构型熵与共价键强度的协同作用。本研究结果为高熔化温度及高力学性能Hf_xTa_1-_xC系固溶体组分的实验选择及其耐高温涂层应用等提供了理论指导, 也为其他过渡金属碳化物研究提供了参考。

关键词: Hf_xTa_1-_xC, 第一性原理, 力学性质, 熔化温度

Abstract:

Hf_xTa_1-_xC is a very promising candidate for thermal protection materials above 2000 ℃ due to its excellent properties such as high melting point, high hardness, high strength, high electrical conductivity, and high thermal conductivity. However, the rules of its mechanical properties and melting temperature varying with the composition remain elusive. Firstly, the mechanism of the variation of mechanical properties of Hf_xTa_1-_xC system solid solutions with its components was systematically investigated from the microscopic point of view of covalent bond strength and valence electron concentration (VEC) based on the special quasirandom structures (SQS) method and first-principles calculations. It revealed that among the five components of solid solutions (i.e., HfC, Hf_0.75Ta_0.25C, Hf_0.5Ta_0.5C, Hf_0.25Ta_0.75C and TaC), the Hf_0.25Ta_0.75C solid solution possessed the largest elastic modulus and shear modulus. It was mainly attributed to two reasons: (1) the component possessing the strongest covalent bonding strength among the above ternary compounds; (2) the special bonding states between the p-orbital from C and the d-orbital from Hf or Ta strongly resisting the deformation and being completely filled near VEC=8.75 (for Hf_0.25Ta_0.75C). Secondly, the melting curves of the Hf_xTa_1-_xC system solid solutions were calculated using the ab initio molecular dynamics (AIMD)-based molecular dynamics Z method. It showed that there existed indeed the phenomenon for anomalous increase in the melting temprature of Hf_xTa_1-_xC system solid solutions, and the highest melting temperature of 4270 K was predicted on Hf_0.5Ta_0.5C, which was mainly attributed to the synergistic effect of the conformational entropy and the strength of the covalent bond. The results provide a theoretical guidance for the experimental selection of the optimal components of high melting temprature and high mechanical properties for Hf_xTa_1-_xC system solid solutions in the thermal barrier coating applications, as well as a reference for the study of other transition metal carbides.

Key words: Hf_xTa_1-_xC, first-principles, mechanical property, melting temperature

中图分类号:

O6-04
TQ174

吴玉豪, 彭仁赐, 程春玉, 杨丽, 周益春. Hf_xTa_1-_xC体系力学性能及熔化曲线的第一性原理研究[J]. 无机材料学报, 2024, 39(7): 761-768.

WU Yuhao, PENG Renci, CHENG Chunyu, YANG Li, ZHOU Yichun. First-principles Study on Mechanical Properties and Melting Curve of Hf_xTa_1-_xC System[J]. Journal of Inorganic Materials, 2024, 39(7): 761-768.

图/表 13

图1 (a) Hf0.75Ta0.25C, (b) Hf0.5Ta0.5C, (c) Hf0.25Ta0.75C, (d) HfC和(e) TaC结构弛豫后得到的稳定结构

Fig. 1 Stable crystal structures after structural relaxation of (a) Hf0.75Ta0.25C, (b) Hf0.5Ta0.5C, (c) Hf0.25Ta0.75C, (d) HfC, and (e) TaC

表S1 HfC、Hf0.75Ta0.25C、Hf0.5Ta0.5C、Hf0.25Ta0.75C、TaC的晶格常数、内聚能(Ecoh)和混合能(Emix)

Table S1 Lattice constants, cohesive enthalpy ( E c o h), and mixing enthalpy ( E m i x ) of HfC, Hf0.75Ta0.25C, Hf0.5Ta0.5C, Hf0.25Ta0.75C and TaC

Compound	Lattice constant/Å	E_coh/(eV·atom^-1)	E_mix/(eV·atom^-1)
HfC	a=b=c=9.293	-10.525
Hf_0.75Ta_0.25C	a=9.197, b=9.197, c=9.198	-10.696	-0.21
Hf_0.5Ta_0.5C	a=9.112, b=9.108, c=9.109	-10.842	-0.22
Hf_0.25Ta_0.75C	a=9.034, b=9.034, c=9.023	-10.977	-0.15
TaC	a=b=c=8.957	-11.102

表1 HfC、Hf0.75Ta0.25C、Hf0.5Ta0.5C、Hf0.25Ta0.75C、TaC的弹性常数

Table 1 Elastic constants of HfC, Hf0.75Ta0.25C, Hf0.5Ta0.5C, Hf0.25Ta0.75C, and TaC

Compound	C₁₁/GPa		C₄₄/GPa		C₁₂/GPa
Compound	This work	Ren et al.^[6]	This work	Ren et al.^[6]	This work	Ren et al.^[6]
HfC	516.2	540	175.5	171	102.9	112
Hf_0.75Ta_0.25C	554.1	601	185.9	187	114.8	117
Hf_0.5Ta_0.5C	627.2	654	182.5	182	108.9	120
Hf_0.25Ta_0.75C	687.8	706	182.6	183	120.1	124
TaC	679.2	674	170.9	167	137.5	172

图2 HfC、Hf0.75Ta0.25C、Hf0.5Ta0.5C、Hf0.25Ta0.75C和TaC的力学性质变化规律

Fig. 2 Mechanical properties of Hf, Hf0.75Ta0.25C, Hf0.5Ta0.5C, Hf0.25Ta0.75C, and TaC (a) Bulk modulus; (b) Shear modulus; (c) Pugh' ratio; (d) Young's modulus; (e) Hardness

图3 (a) HfxTa1-xC系固溶体的总态密度, 以及(b) TaC, (c) HfC, (d) Hf0.75Ta0.25C, (e) Hf0.5Ta0.5C和(f) Hf0.25Ta0.75C的分态密度

Fig. 3 (a) Total density of states (TDOS) for ternary HfxTa1-xC solid solution, and partial density of states (DOS) for (b) TaC, (c) HfC, (d) Hf0.75Ta0.25C, (e) Hf0.5Ta0.5C, and (f) Hf0.25Ta0.75C Colorful figures are available on website

图4 HfxTa1-xC的晶体轨道哈密顿分布积分(-ICOHP)随组分变化的规律

Fig. 4 Integrated crystal orbital Hamilton populations (-ICOHP) changed with composition for HfxTa1-xC

图S1 HfC的熔化过程示意图

Fig. S1 Schematic diagrams of the melting process of HfC (a) Original stable crystal structure (0 ps); (b) Melting begins (0.1 ps); (c) Complete melting (2.5 ps)

图S2 2000 K初始温度下TaC的温度、压力随时间的变化曲线

Fig. S2 Time dependent curves of TaC temperature and pressure at initial temperature of 2000 K

图S3 熔化过程的压力-温度等容曲线

Fig. S3 Pressure-temperature isovolumetric curves during melting process The highest melting point material searched by Bayesian global optimization with deep potential molecular dynamics (a) TaC; (b) HfC; (c) Hf0.75Ta0.25C; (d) Hf0.5Ta0.5C; (e) Hf0.25Ta0.75C

表S2 HfC、Hf0.75Ta0.25C、Hf0.5Ta0.5C、Hf0.25Ta0.75C和TaC的熔化温度及对应的压力

Table S2 Melting temperatures and corresponding pressures of HfC, Hf0.75Ta0.25C, Hf0.5Ta0.5C, Hf0.25Ta0.75C, and TaC

Compound	Pressure/GPa	Melting temperature/K
HfC	14.05	3402.1
Hf_0.75Ta_0.25C	14.82	3771.8
Hf_0.5Ta_0.5C	19.62	4720.2
Hf_0.25Ta_0.75C	19.31	4373.0
TaC	22.83	4285.3

图S4 HfC和TaC的熔化温度-压力曲线

Fig. S4 Melting temperature-pressure curves of HfC and TaC

图5 HfxTa1-xC的熔化温度和C11随组分的变化规律

Fig. 5 Melting temperature and C11 changed with composition for HfxTa1-xC

图S5 HfxTa1-xC的熔化温度随组分变化的规律

Fig. S5 Melting temperature changed with composition for HfxTa1-xC

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Hf_xTa_1-_xC体系力学性能及熔化曲线的第一性原理研究

First-principles Study on Mechanical Properties and Melting Curve of Hf_xTa_1-_xC System

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[15]	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.

HfxTa1-xC体系力学性能及熔化曲线的第一性原理研究

First-principles Study on Mechanical Properties and Melting Curve of HfxTa1-xC System

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Hf_xTa_1-_xC体系力学性能及熔化曲线的第一性原理研究

First-principles Study on Mechanical Properties and Melting Curve of Hf_xTa_1-_xC System