Theoretical calculations of stabilities and properties of transition metal borocarbides TM3B3C and TM4B3C2 compound

Qian-Ku Hu; Yi-Ming Hou; Qing-Hua Wu; Shuang-Hong Qin; Li-Bo Wang; Ai-Guo Zhou

doi:10.7498/aps.68.20190158

Journals >Acta Physica Sinica >Volume 68 >Issue 9 >Page 096201-1 > Article

Acta Physica Sinica
Vol. 68, Issue 9, 096201-1 (2019)

Theoretical calculations of stabilities and properties of transition metal borocarbides TM₃B₃C and TM₄B₃C₂ compound

Qian-Ku Hu^1、2、*, Yi-Ming Hou¹, Qing-Hua Wu¹, Shuang-Hong Qin¹, Li-Bo Wang¹, and Ai-Guo Zhou¹

Author Affiliations

¹School of Materials Science and Engineering, Henan Key Laboratory of Materials on Deep-Earth Science and Technology, Henan Polytechnic University, Jiaozuo 454000, China

²State Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, China

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DOI: 10.7498/aps.68.20190158 Cite this Article

Qian-Ku Hu, Yi-Ming Hou, Qing-Hua Wu, Shuang-Hong Qin, Li-Bo Wang, Ai-Guo Zhou. Theoretical calculations of stabilities and properties of transition metal borocarbides TM₃B₃C and TM₄B₃C₂ compound [J]. Acta Physica Sinica, 2019, 68(9): 096201-1 Copy Citation Text

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Crystal structures of the (a), (b) Nb3B3C and (c), (d) Nb4B3C2. The light brown, blue and pink spheres represent Nb, B and C atoms, respectively. The Nb6B trigonal prisms and Nb6C octahedrons are painted green and dark brown.(a), (b) Nb3B3C和(c), (d) Nb4B3C2的晶体结构(棕球, Nb原子; 蓝球, B原子; 粉球, C原子; Nb6B三棱柱和Nb6C八面体分别用绿色和褐色表示)

Fig. 1. Crystal structures of the (a), (b) Nb₃B₃C and (c), (d) Nb₄B₃C₂. The light brown, blue and pink spheres represent Nb, B and C atoms, respectively. The Nb₆B trigonal prisms and Nb₆C octahedrons are painted green and dark brown. (a), (b) Nb₃B₃C和(c), (d) Nb₄B₃C₂的晶体结构(棕球, Nb原子; 蓝球, B原子; 粉球, C原子; Nb₆B三棱柱和Nb₆C八面体分别用绿色和褐色表示)

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Energy differences of Ta3B3C and Ta4B3C2 phases with respect to their most competing phases as a function of temperature.不同温度下Ta3B3C, Ta4B3C2相分别和其相应最稳定竞争组合相的自由能之差

Fig. 2. Energy differences of Ta₃B₃C and Ta₄B₃C₂ phases with respect to their most competing phases as a function of temperature. 不同温度下Ta₃B₃C, Ta₄B₃C₂相分别和其相应最稳定竞争组合相的自由能之差

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Fig. 3. Phonon dispersion curves of (a) Ta₃B₃C and (b) Ta₄B₃C₂ structures. (a) Ta₃B₃C和(b) Ta₄B₃C₂结构的声子色散曲线

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Fig. 4. Band structures and density of states of (a), (c) Ta₃B₃C and (b), (d) Ta₄B₃C₂ structures. (a), (c) Ta₃B₃C和(b), (d) Ta₄B₃C₂结构的能带结构和态密度图

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模型	晶系和空间群	晶格参数(Å, degree)	原子坐标
注: ^a文献[17]中的实验值.
Nb₃B₃C	Orthorhombic Cmcm	a = 3.284, 3.265^a, b = 28.877, 28.710^a, c = 3.144, 3.129^a, α = β = γ = 90	Nb1 (4c) (0, 0.2128, 0.25), Nb2 (4c) (0, 0.3620, 0.25), Nb3 (4c) (0, 0.4532, 0.25), B1 (4c) (0, 0.1120, 0.25), B2 (4c) (0, 0.0155, 0.25), B3 (4c) (0, 0.0790, 0.25), C (4c) (0, 0.2878, 0.25)
Nb₄B₃C₂	Orthorhombic Cmcm	a = 3.257, 3.229^a, b = 37.874, 37.544^a, c = 3.153, 3.133^a, α = β = γ = 90	Nb1 (4c) (0, 0.1621, 0.75), Nb2 (4c) (0, 0.2805, 0.75), Nb3 (4c) (0, 0.3946, 0.75), Nb4 (4c) (0, 0.4642, 0.25), B1 (4c) (0, 0.0854, 0.75), B2 (4c) (0, 0.0118, 0.25), B3 (4c) (0, 0.0602, 0.25), C1 (4c) (0, 0.2202, 0.75), C2 (4c) (0, 0.3383, 0.75)
Ta₃B₃C	Orthorhombic Cmcm	a = 3.267, b = 28.688, c = 3.133, α = β = γ = 90	Ta1 (4c) (0, 0.2121, 0.25), Ta2 (4c) (0, 0.3619, 0.25), Ta3 (4c) (0, 0.4531, 0.25), B1 (4c) (0, 0.1130, 0.25), B2 (4c) (0, 0.0155, 0.25), B3 (4c) (0, 0.0791, 0.25), C (4c) (0, 0.2874, 0.25)
Ta₄B₃C₂	Orthorhombic Cmcm	a = 3.243, b = 37.609, c = 3.141, α = β = γ = 90	Ta1 (4c) (0, 0.1615, 0.75), Nb2 (4c) (0, 0.2806, 0.75), Nb3 (4c) (0, 0.3945, 0.75), Nb4 (4c) (0, 0.4641, 0.25), B1 (4c) (0, 0.0861, 0.75), B2 (4c) (0, 0.0118, 0.25), B3 (4c) (0, 0.0602, 0.25), C1 (4c) (0, 0.2202, 0.75), C2 (4c) (0, 0.3380, 0.75)

Table 1.

Structural parameters of the Nb₃B₃C, Nb₄B₃C₂, Ta₃B₃C and Ta₄B₃C₂ configurations.

Nb₃B₃C, Nb₄B₃C₂, Ta₃B₃C和Ta₄B₃C₂晶体的结构参数

TM	TM₃B₃C			TM₄B₃C₂
TM	$\Delta {H_{{\rm{elements}}}}$	$\Delta {H_{{\rm{comp}}}}$	最稳定竞争组合	$\Delta {H_{{\rm{elements}}}}$	$\Delta {H_{{\rm{comp}}}}$	最稳定竞争组合
Sc	–0.637	0.071	6ScB₂ + Sc₄C₃ + Sc₂C = 4Sc₃B₃C	–0.520	0.144	10ScB₂ + 4Sc₄C₃ + Sc₂BC₂ = 7Sc₄B₃C₂
Ti	–0.896	0.019	9TiB₂ + TiC + Ti₈C₅ = 6Ti₃B₃C	–0.863	0.018	9TiB₂ + 7TiC + Ti₈C₅ = 6Ti₄B₃C₂
V	–0.687	0.101	3VB + C = V₃B₃C	–0.628	0.092	18VB + 7C + V₆C₅ = 6V₄B₃C₂
Cr	–0.294	0.159	3CrB + C = Cr₃B₃C	–0.194	0.178	9CrB + 4C + Cr₃C₂ = 3Cr₄B₃C₂
Mn	–0.100	0.195	3MnB + C = Mn₃B₃C	0.024
Fe	0.002			0.139
Co	0.094			0.255
Ni	0.296			0.456
Cu	0.738			0.959
Zn	0.713			0.929
Y	–0.385	0.089	9YB₂ + 5Y₂C + Y₂B₃C₂ = 7Y₃B₃C	–0.283	0.160	6YB₂ + 8Y₂C + 3Y₂B₃C₂ = 7Y₄B₃C₂
Zr	–0.851	0.019	3ZrB₂ + 2ZrC + Zr = 2Zr₃B₃C	–0.838	0.020	3ZrB₂ + 4ZrC + Zr = 2Zr₄B₃C₂
Nb	–0.698	–0.023	3NbB + C = Nb₃B₃C	–0.661	–0.002	C + 6Nb₃B₃C + Nb₆C₅ = 6Nb₄B₃C₂
Mo	–0.257	0.175	3MoB + C = Mo₃B₃C	–0.155	0.202	3MoB + C + MoC = Mo₄B₃C₂
Tc	–0.005	0.326	12TcB₂ + 11C + 3Tc₇B₃ = 11Tc₃B₃C	0.138
Ru	0.211			–0.369
Rh	0.230			–0.406
Pd	0.552			0.744
Ag	1.027			1.295
Cd	0.846			1.112
Hf	–0.920	0.016	3HfB₂ + 2HfC + Hf = 2Hf₃B₃C	–0.922	0.018	3HfB₂ + 4HfC + Hf = 2Hf₄B₃C₂
Ta	–0.704	0.003	3Ta₃B₄ + C + 3TaC = 4Ta₃B₃C	–0.691	–0.010	3Ta₃B₄ + C + 7TaC = 4Ta₄B₃C₂
W	–0.094	0.227	3WB + C = W₃B₃C	–0.007	0.273	3WB + C + WC = W₄B₃C₂
Re	0.281			0.425
Os	0.590			0.755
Ir	0.604			0.758
Pt	0.708			0.855
Au	1.096			1.310
Hg	1.186			1.333

Table 2.

Calculated formation enthalpies of different TM₃B₃C and TM₄B₃C₂ phases (eV/atom).

不同成分TM₃B₃C和TM₄B₃C₂的形成焓(eV/atom)

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.
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
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
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.

Calculated elastic constants C_ij, bulk modulus B, shear modulus G, Vickers hardness H_V of Ta₃B₃C and Ta₄B₃C₂ configurations (GPa).

Ta₃B₃C, Ta₄B₃C₂结构的弹性常数、体弹模量、剪切模量和维氏硬度 (GPa)

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