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

doi:10.15541/jim20230518

Abstract

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

CLC Number:

O6-04
TQ174

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.

Figures/Tables 13

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

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

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

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

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

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

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)

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

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

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

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

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

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

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