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

doi:10.15541/jim20210179

Abstract

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

CLC Number:

O411

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.

Figures/Tables 7

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

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

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

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

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

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)

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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