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

. 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

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. Effect of vacancy on mechanical properties for ternary Hf-Ta-C system

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. Density of state (DOS) and partial DOS (PDOS) normalized by per (Hf, Ta)C_1-_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)

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Table 1. Space groups, lattice constants, enthalpy above the convex-hull, formation enthalpy (ΔH_f), concentration of vacancy (x) and coordination number (CN) of Hf or Ta for ternary (Hf, Ta)C_1-_x vacancy ordered structures

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Table 1. Space groups, lattice constants, enthalpy above the convex-hull, formation enthalpy (ΔH_f), concentration of vacancy (x) and coordination number (CN) of Hf or Ta for ternary (Hf, Ta)C_1-_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 (C_ij) and mechanical properties-bulk modulus (B), shear modulus (G/), elastic modulus (E), Poisson’s ratio (μ), Vickers hardness (H_v) and Pugh’s ratio (G/B) of (Hf, Ta)C_1-_x vacancy ordered structures

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Table 2. Calculated elastic constants (C_ij) and mechanical properties-bulk modulus (B), shear modulus (G/), elastic modulus (E), Poisson’s ratio (μ), Vickers hardness (H_v) and Pugh’s ratio (G/B) of (Hf, Ta)C_1-_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

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Junhui PENG, Evgenii TIKHONOV. 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

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Paper Information

Category: EDITORIAL

Received: Mar. 20, 2021

Accepted: --

Published Online: Sep. 23, 2022

The Author Email: Junhui PENG (pjh1989@yeah.net)

DOI:10.15541/jim20210179

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

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

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

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

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

Table 1. Space groups, lattice constants, enthalpy above the convex-hull, formation enthalpy (ΔH_f), concentration of vacancy (x) and coordination number (CN) of Hf or Ta for ternary (Hf, Ta)C_1-_x vacancy ordered structures

Table 1. Space groups, lattice constants, enthalpy above the convex-hull, formation enthalpy (ΔH_f), concentration of vacancy (x) and coordination number (CN) of Hf or Ta for ternary (Hf, Ta)C_1-_x vacancy ordered structures

Table 2. Calculated elastic constants (C_ij) and mechanical properties-bulk modulus (B), shear modulus (G/), elastic modulus (E), Poisson’s ratio (μ), Vickers hardness (H_v) and Pugh’s ratio (G/B) of (Hf, Ta)C_1-_x vacancy ordered structures

Table 2. Calculated elastic constants (C_ij) and mechanical properties-bulk modulus (B), shear modulus (G/), elastic modulus (E), Poisson’s ratio (μ), Vickers hardness (H_v) and Pugh’s ratio (G/B) of (Hf, Ta)C_1-_x vacancy ordered structures