First-principles calculations of stabilities and physical properties of ternary niobium borocarbides and tantalum borocarbides

Qian-Ku Hu; Shuang-Hong Qin; Qing-Hua Wu; Dan-Dan Li; Bin Zhang; Wen-Feng Yuan; Li-Bo Wang; Ai-Guo Zhou

doi:10.7498/aps.69.20200234

Journals >Acta Physica Sinica >Volume 69 >Issue 11 >Page 116201-1 > Article

Acta Physica Sinica
Vol. 69, Issue 11, 116201-1 (2020)

First-principles calculations of stabilities and physical properties of ternary niobium borocarbides and tantalum borocarbides

Qian-Ku Hu, Shuang-Hong Qin, Qing-Hua Wu, Dan-Dan Li, Bin Zhang, Wen-Feng Yuan, Li-Bo Wang, and Ai-Guo Zhou^*

Author Affiliations

Henan Key Laboratory of Materials on Deep-Earth Engineering, School of Materials Science and Engineering, Henan Polytechnic University, Jiaozuo 454000, China

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DOI: 10.7498/aps.69.20200234 Cite this Article

Qian-Ku Hu, Shuang-Hong Qin, Qing-Hua Wu, Dan-Dan Li, Bin Zhang, Wen-Feng Yuan, Li-Bo Wang, Ai-Guo Zhou. First-principles calculations of stabilities and physical properties of ternary niobium borocarbides and tantalum borocarbides[J]. Acta Physica Sinica, 2020, 69(11): 116201-1 Copy Citation Text

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The crystal structures of (a), (b) Ta3B3C; (c) Ta4B3C2; (d) Ta3BC2; (e) Ta6B4C3; (f) Ta7B4C4; (g) Ta7B6C3. The light brown, blue and pink spheres represent Ta, B, and C atoms, respectively. The Ta6B triangular prisms and Ta6C octahedrons are painted green and dark brown.

Fig. 1. The crystal structures of (a), (b) Ta₃B₃C; (c) Ta₄B₃C₂; (d) Ta₃BC₂; (e) Ta₆B₄C₃; (f) Ta₇B₄C₄; (g) Ta₇B₆C₃. The light brown, blue and pink spheres represent Ta, B, and C atoms, respectively. The Ta₆B triangular prisms and Ta₆C octahedrons are painted green and dark brown.

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Fig. 2. Ternary phase diagrams of (a) Nb-B-C and (b) Ta-B-C. Red, stable; blue, metastable; green, unstable.

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Fig. 3. Energy differences of (a) Nb-B-C and (b) Ta-B-C ternary phases with respect to their most competing phases as a function of temperature.

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Fig. 4. Phonon dispersion curves of Nb-B-C and Ta-B-C ternary phases.

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Fig. 5. Density of states of Nb-B-C and Ta-B-C ternary phases.

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m	n	空间群	模型	晶格参数/Å			模型	晶格参数/Å
m	n	空间群	模型	a	b	c	模型	a	b	c
0	1	Cmmm	Nb₃B₂C	3.254	13.808	3.141	Ta₃B₂C	3.240	13.697	3.127
0	2	Cmcm	Nb₂BC	3.235	18.330	3.153	Ta₂BC	3.220	18.165	3.140
0	3	Cmmm	Nb₅B₂C₃	3.225	22.903	3.153	Ta₅B₂C₃	3.199	22.659	3.138
0	4	Cmcm	Nb₃BC₂	3.214	27.376	3.156	Ta₃BC₂	3.198	27.132	3.150
1	1	Pmmm	Nb₄B₄C	3.290	18.994	3.145	Ta₄B₄C	3.277	18.878	3.127
1	2	Immm	Nb₅B₄C₂	3.267	23.600	3.150	Ta₅B₄C₂	3.248	23.377	3.138
1	3	Pmmm	Nb₆B₄C₃	3.243	28.028	3.154	Ta₆B₄C₃	3.225	27.872	3.141
1	4	Immm	Nb₇B₄C₄	3.242	32.545	3.158	Ta₇B₄C₄	3.224	32.315	3.147
2	1	Cmmm	Nb₅B₆C	3.302	24.414	3.134	Ta₅B₆C	3.289	24.208	3.122
2	2	Cmcm	Nb₃B₃C	3.284	28.877	3.144	Ta₃B₃C	3.267	28.688	3.133
2	3	Cmmm	Nb₇B₆C₃	3.264	33.364	3.148	Ta₇B₆C₃	3.246	33.164	3.136
2	4	Cmcm	Nb₄B₃C₂	3.257	37.874	3.153	Ta₄B₃C₂	3.243	37.609	3.141
3	1	Pmmm	Nb₆B₈C	3.309	14.889	3.137	Ta₆B₈C	3.298	14.788	3.122
3	2	Immm	Nb₇B₈C₂	3.290	34.247	3.144	Ta₇B₈C₂	3.276	34.007	3.131
3	3	Pmmm	Nb₈B₈C₃	3.276	19.350	3.148	Ta₈B₈C₃	3.258	19.235	3.135
3	4	Immm	Nb₉B₈C₄	3.268	43.255	3.151	Ta₉B₈C₄	3.252	42.977	3.138
4	1	Cmmm	Nb₇B₁₀C	3.312	35.192	3.131	Ta₇B₁₀C	3.299	34.990	3.116
4	2	Cmcm	Nb₄B₅C	3.296	39.694	3.139	Ta₄B₅C	3.280	39.441	3.125
4	3	Cmmm	Nb₉B₁₀C₃	3.281	44.206	3.142	Ta₉B₁₀C₃	3.263	43.924	3.130
4	4	Cmcm	Nb₅B₅C₂	3.273	48.729	3.145	Ta₅B₅C₂	3.257	48.400	3.134

Table 1.

Structural parameters of Nb_{(m + n + 2)}B_{(2m + 2)}C_n and Ta_{(m + n + 2)}B_{(2m + 2)}C_n crystals.

不同成分Nb_{(m + n + 2)}B_{(2m + 2)}C_n和Ta_{(m + n + 2)}B_{(2m + 2)}C_n晶体的结构参数

Phases	$ \Delta{H}_{\rm{elements}} $	$ \Delta{H}_{\rm{comp}} $	最稳定竞争组合	Phases	$ \Delta{H}_{\rm{elements}} $	$ \Delta{H}_{\rm{comp}} $	最稳定竞争组合
Nb₃B₂C	–0.620	0.070	Nb₃B₄ + 6NbB + Nb₆C₅ = 5Nb₃B₂C	Ta₃B₂C	–0.651	0.086	Ta₃BC₂ + 3TaB = 2Ta₃B₂C
Nb₂BC	–0.619	0.029	Nb₃B₄ + NbB + Nb₆C₅ = 5Nb₂BC	Ta₂BC	–0.664	0.035	Ta₃BC₂ + TaB = 2Ta₂BC
Nb₅B₂C₃	–0.586	0.036	3Nb₃B₄ + Nb₇B₄C₄ + 4Nb₆C₅ = 8Nb₅B₂C₃	Ta₅B₂C₃	–0.655	0.021	3Ta₃BC₂ + TaB = 2Ta₅B₂C₃
Nb₃BC₂	–0.586	0.019	Nb₃B₄ + 3Nb₇B₄C₄ + 4Nb₆C₅ = 16Nb₃BC₂	Ta₃BC₂	–0.660	–0.002	TaB + 2TaC = Ta₃BC₂
Nb₄B₄C	–0.679	0.030	3Nb₃B₄ + Nb₇B₄C₄ = 4Nb₄B₄C	Ta₄B₄C	–0.691	0.044	Ta₇B₄C₄ + 3Ta₃B₄ = 4Ta₄B₄C
Nb₅B₄C₂	–0.668	0.006	Nb₃B₄ + Nb₇B₄C₄ = 2Nb₅B₄C₂	Ta₅B₄C₂	–0.694	0.019	Ta₇B₄C₄ + Ta₃B₄ = 2Ta₅B₄C₂
Nb₆B₄C₃	–0.645	0.005	Nb₃B₄ + 3Nb₇B₄C₄ = 4Nb₆B₄C₃	Ta₆B₄C₃	–0.693	0.004	3Ta₇B₄C₄ + Ta₃B₄ = 4Ta₆B₄C₃
Nb₇B₄C₄	–0.632	–0.006	3Nb₃B₄ + 2C + 2Nb₆C₅ = 3Nb₇B₄C₄	Ta₇B₄C₄	–0.685	–0.017	3Ta₃B₄ + 4TaC = Ta₇B₄C₄
Nb₅B₆C	–0.697	0.015	3Nb₃B₄ + C + 2Nb₃B₃C = 3Nb₅B₆C	Ta₅B₆C	–0.697	0.024	C + Ta₅B₆ = Ta₅B₆C
Nb₃B₃C	–0.685	–0.001	3Nb₃B₄ + C + 3Nb₄B₃C₂ = 7Nb₃B₃C	Ta₃B₃C	–0.699	0.010	3Ta₇B₄C₄ + 9Ta₃B₄ + 4C = 16Ta₃B₃C
Nb₇B₆C₃	–0.664	0.0005	Nb₃B₃C + Nb₄B₃C₂ = Nb₇B₆C₃	Ta₇B₆C₃	–0.695	0.0008	5Ta₇B₄C₄ + 7Ta₃B₄ + 4C = 8Ta₇B₆C₃
Nb₄B₃C₂	–0.648	–0.001	5Nb₃B₄ + 4C + 7Nb₇B₄C₄ = 16Nb₄B₃C₂	Ta₄B₃C₂	–0.684	0.002	7Ta₇B₄C₄ + 5Ta₃B₄ + 4C = 16Ta₄B₃C₂
Nb₆B₈C	–0.695	0.019	2Nb₃B₄ + C = Nb₆B₈C	Ta₆B₈C	–0.685	0.034	2Ta₃B₄ + C = Ta₆B₈C
Nb₇B₈C₂	–0.683	0.008	3Nb₃B₄ + 2C + 4Nb₃B₃C = 3Nb₇B₈C₂	Ta₇B₈C₂	–0.686	0.020	Ta₇B₄C₄ + 7Ta₃B₄ + 4C = 4Ta₇B₈C₂
Nb₈B₈C₃	–0.665	0.008	C + 8Nb₃B₃C = 3Nb₈B₈C₃	Ta₈B₈C₃	–0.684	0.012	Ta₇B₄C₄ + 3Ta₃B₄ + 2C = 2Ta₈B₈C₃
Nb₉B₈C₄	–0.651	0.008	C + 5Nb₃B₃C + 3Nb₄B₃C₂ = 3Nb₉B₈C₄	Ta₉B₈C₄	–0.675	0.013	3Ta₇B₄C₄ + 5Ta₃B₄ + 4C = 4Ta₉B₈C₄
Nb₇B₁₀C	–0.693	0.021	C + 2Nb₂B₃ + Nb₃B₄ = Nb₇B₁₀C	Ta₇B₁₀C	–0.677	0.030	TaB₂ + 2Ta₃B₄ + C = Ta₇B₁₀C
Nb₄B₅C	–0.684	0.011	2C + Nb₃B₃C + 3Nb₃B₄ = 3Nb₄B₅C	Ta₄B₅C	–0.679	0.026	Ta₇B₄C₄ + 19Ta₃B₄ + 12C = 16Ta₄B₅C
Nb₉B₁₀C₃	–0.668	0.012	C + 2Nb₃B₃C + Nb₃B₄ = Nb₉B₁₀C₃	Ta₉B₁₀C₃	–0.677	0.019	3Ta₇B₄C₄ + 17Ta₃B₄ + 12C = 8Ta₉B₁₀C₃
Nb₅B₅C₂	–0.655	0.011	C + 5Nb₃B₃C = 3Nb₅B₅C₂	Ta₅B₅C₂	–0.670	0.018	5Ta₇B₄C₄ + 15Ta₃B₄ + 12C = 16Ta₅B₅C₂

Table 2. Calculated formation enthalpies of different Nb-B-C and Ta-B-C phases (in eV/atom).

represents the elements as the reactants, and

indicates the most stable composite as the reactants.

结构	弹性常数									力学性能^a			硬度
结构	C₁₁	C₂₂	C₃₃	C₄₄	C₅₅	C₆₆	C₁₂	C₁₃	C₂₃	B	G	B/G	H_Chen	H_Tian
注: ^a二元相力学性能数据来自Materials Project网站.
Nb₃B₃C	544.3	479.8	522.8	181.5	171.9	245.3	170.9	132.9	162.2	275.3	189.7	1.45	24.8	24.7
Nb₄B₃C₂	551.5	499.2	548.5	184.0	175.1	257.1	183.2	132.7	157.8	282.9	195.8	1.44	25.5	25.4
Nb₆B₄C₃	533.3	493.8	548.1	174.9	161.3	255.2	175.4	138.9	151.7	278.5	189.5	1.47	24.4	24.3
Nb₇B₄C₄	535.9	505.9	526.4	172.2	161.3	259.1	184.0	142.8	152.6	280.6	188.3	1.49	23.9	23.8
Nb₇B₆C₃	553.1	494.5	563.2	188.7	179.6	255.6	176.4	132.1	157.7	282.5	198.9	1.42	26.3	26.2
Ta₃B₃C	569.6	514.4	563.5	194.1	180.0	261.8	187.1	147.3	173.9	295.9	200.8	1.47	25.3	25.3
Ta₄B₃C₂	581.1	535.3	602.1	197.3	185.1	275.8	200.3	146.0	170.2	305.7	209.0	1.46	26.2	26.2
Ta₃BC₂	550.0	547.7	550.0	159.8	159.5	292.1	216.7	160.0	149.2	299.6	191.8	1.56	22.7	22.9
Ta₆B₄C₃	584.7	539.6	614.2	203.0	189.9	279.9	195.5	168.0	144.1	305.9	213.9	1.43	27.4	27.3
Ta₇B₄C₄	563.1	547.5	571.5	183.6	170.4	281.4	200.2	162.0	164.3	303.9	200.8	1.51	24.4	24.5
Ta₇B₆C₃	584.7	540.0	614.2	203.0	190.0	280.0	195.5	168.0	144.1	305.9	213.9	1.43	27.4	27.3
TaB₂										302	200	1.51	24.4	24.5
NbB₂										287	195	1.47	24.8	24.8
TaC										324	215	1.51	25.6	25.9
NbC										239	161	1.48	21.6	21.4
SiC										213	187	1.14	33.6	32.2
Al₂O₃										232	147	1.58	18.7	18.7
TiN										259	180	1.44	24.3	24.0

Table 3.

Elastic constants C_ij, bulk modulus B, shear modulus G, Vickers hardness H_v of Nb-B-C and Ta-B-C ternary phases (in GPa).

Nb-B-C和Ta-B-C三元相的弹性常数C_ij、体模量B、剪切模量 G和维氏硬度H_v (单位: GPa)

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