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Acta Metall Sin  2025, Vol. 61 Issue (5): 797-808    DOI: 10.11900/0412.1961.2024.00096
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First Principles Study on the Precipitation and Properties of Carbides in the Surface Carburized Layer of Tantalum Alloys
MENG Xianglong1, LIU Ruiliang1(), Li D. Y.2()
1 Key Laboratory of Superlight Material and Surface Technology of Ministry of Education, College of Materials Science and Chemical Engineering, Harbin Engineering University, Harbin 150001, China
2 Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, Canada T6G 1H9
Cite this article: 

MENG Xianglong, LIU Ruiliang, Li D. Y.. First Principles Study on the Precipitation and Properties of Carbides in the Surface Carburized Layer of Tantalum Alloys. Acta Metall Sin, 2025, 61(5): 797-808.

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Abstract  

Tantalum and its alloys have high melting points and good wear resistance, which are primarily used in fields such as the aerospace and nuclear energy industry. Surface modification techniques such as carburization can be used to obtain a modified layer containing tantalum carbide on the surface of tantalum and its alloys, thereby significantly improving their surface properties. However, the structure and properties of tantalum carbide precipitated on the surface of different tantalum alloys remain unclear. This study focuses on Ta-Mo and Ta-W alloys, and constructs fcc and hcp complex tantalum carbide (Ta, M)C (M = Mo, W) models with different alloying elements and their contents. The energy and mechanical properties of different complex tantalum carbide structures were calculated using the first principles method based on the density functional theory to explore the strengthening and toughening mechanisms of complex tantalum carbides. Calculation results indicate that when the content of Mo and W is less than 50%, fcc structured complex tantalum carbide can be easily formed, and the higher the concentration of Mo and W atoms, the lower the modulus and hardness of the complex tantalum carbide with an fcc structure, and the better the toughness. When the content of Mo and W exceeds 50%, tantalum carbides with an hcp structure are easy to form. As the concentration of Mo and W atoms increases, the modulus and hardness of complex tantalum carbides with an hcp structure increase, whereas the toughness decreases.

Key words:  tantalum alloy      complex tantalum carbide      first-principles calculation      crystal structure      stability      mechanical property     
Received:  27 March 2024     
ZTFLH:  TG146.4  
Fund: National Natural Science Foundation of China(52371060);Natural Science Foundation of Heilongjiang Province(LH2023E060);Fundamental Research Funds for the Central Universities(3072023WD010)
Corresponding Authors:  LIU Ruiliang, professor, Tel: (0451)82518731, E-mail: liuruiliang@hrbeu.edu.cn;
D. Y. Li, Tel: (0451)82518731, E-mail: dongyang.li@ualberta.ca

URL: 

https://www.ams.org.cn/EN/10.11900/0412.1961.2024.00096     OR     https://www.ams.org.cn/EN/Y2025/V61/I5/797

Fig.1  Super structural models of the special quasi-random structure (SQS) of complex tantalum carbides
(a) fcc (b) hcp
Crystal structureCarbide

Lattice constant

nm

Angle

(°)

Volume

nm3

Ef

eV·atom-1

Ec

eV·atom-1

fccTaC, this worka¯ = 0.44781α = β = γ = 90.000.71839-0.5962-8.5998
TaC[34]a = 0.447-0.59
Ta0.75Mo0.25Ca¯ = 0.44554α = 90.04, β = γ = 90.000.70753-0.4089-8.1705
Ta0.5Mo0.5Ca¯ = 0.44320α = β =89.78, γ = 90.220.69645-0.2246-7.7442
Ta0.25Mo0.75Ca¯ = 0.44061α = 89.79, β = γ = 90.000.68428-0.0432-7.6155
MoCa¯ = 0.43699α = β = γ = 90.000.667560.1400-6.8956
hcpTa2C

a = b = 0.31249,

c = 0.49593

α = β = 90.00,

γ = 120.00

0.33551-0.6163-8.6566
(P3¯m1, this work)
Ta2C (P3¯m1)[34]

a = b = 0.311,

c = 0.495

γ = 120.00-0.60
Ta0.75Mo0.25C

a = 0.45271,

b = 0.45256,

c = 0.43049

α = 90.05,

β = 89.96,

γ = 120.01

0.68590-0.1681-7.9208
Ta0.5Mo0.5C

a = 0.44703,

b = 0.44702,

c = 0.42883

α = 90.07,

β = 89.98,

γ = 120.01

0.59361-0.1616-7.6633
Ta0.25Mo0.75C

a = 0.44261,

b = 0.44227,

c = 0.42681

α = 89.99,

β = 90.01,

γ = 120.02

0.57870-0.1610-7.4476
MoC

a = b = 0.43761,

c = 0.42422

α = β = 90.00,

γ = 120.00

0.56283-0.1519-7.1876
Table 1  Crystallographic parameters, formation energy (Ef), and cohesive energy (Ec) of complex tantalum carbide with Mo
Fig.2  Ec (a) and Ef (b) of complex tantalum carbide containing Mo with different structures
Crystal structureCarbide

Lattice constant

nm

Angle

(°)

Volume

nm3

Ef

eV·atom-1

Ec

eV·atom-1

fccTaC, this worka¯ =0.44781α = β = γ = 90.000.71839-0.5962-8.5998
TaC[34]a = 0.447-0.59
Ta0.75W0.25Ca¯ = 0.44543

α = 90.00,

β = 89.99,

γ = 90.00

0.70699-0.3759-8.6364
Ta0.5W0.5Ca¯ = 0.44339

α = 89.79,

β = 90.19,

γ = 90.06

0.69731-0.1566-8.2123
Ta0.25W0.75Ca¯ = 0.44096

α = β = 90.00,

γ = 90.06

0.685900.0565-8.3138
WCa¯ = 0.43821α = β = γ = 90.000.673200.2909-7.8169
hcpTa2C

a = b = 0.31249,

c = 0.49593

α = β = 90.00,

γ = 120.00

0.33551-0.6163-8.6566
(P3¯m1, this work)
Ta2C (P3¯m1)[34]

a = b = 0.311,

c = 0.495

γ = 120-0.60
Ta0.75W0.25C

a = 0.45263,

b = 0.45262,

c = 0.43127

α = 89.94,

β =90.08,

γ = 120.00

0.61212-0.1640-8.1946
Ta0.5W0.5C

a = 0.44731,

b = 0.44718,

c = 0.43034

α = 89.93,

β = 89.98,

γ = 120.00

0.59638-0.1561-8.2137
Ta0.25W0.75C

a = 0.44306,

b = 0.44305,

c = 0.42889

α = 90.00,

β = 89.99,

γ = 119.99

0.58335-0.1573-8.2381
WC

a = b =0.43868,

c = 0.42730

α = β = 90.00,

γ = 120.00

0.56968-0.1543-8.2621
Table 2  Lattice parameters, Ef, and Ec of complex tantalum carbide with W
Fig.3  Energy of complex tantalum carbides containing W with different structures
(a) Ec (b) Ef
Carbide (fcc)

C11 (C¯11)

GPa

C12 (C¯12)

GPa

C44 (C¯44)

GPa

G

GPa

B

GPa

E

GPa

HV

GPa

G / Bν
TaC, this work72013415420033050021.80.6070.25
TaC[34]737141175216.90339.6724.53
Ta0.75Mo0.25C66813815216730242320.90.6050.25
Ta0.5Mo0.5C57616514615131038917.00.5540.27
Ta0.25Mo0.75C58117412312233932713.20.4860.29
MoC684166702003314997.00.3600.34
Ta0.75W0.25C71513915617931045021.50.6030.25
Ta0.5W0.5C63015014715634140718.80.5770.26
Ta0.25W0.75C61120713212937034612.40.4580.30
WC769170672003305007.00.3480.34
Table 3  Elastic constants and mechanical properties of complex tantalum carbides with fcc structure
Carbide (hcp)C11C12C13C33C44
Ta2C (P3¯m1, this work)480143138498120
Ta2C (P3¯m1)[34]479164149504133
Ta0.75Mo0.25C511194138764120
Ta0.5Mo0.5C532203151783157
Ta0.25Mo0.75C568206159811203
MoC618213159854263
Ta0.75W0.25C537197138787130
Ta0.5W0.5C581209154823181
Ta0.25W0.75C621224164878235
WC699232167953302
Table 4  Elastic constants of complex tantalum carbides with hcp structure

Carbide

(hcp)

G

GPa

B

GPa

E

GPa

Hv

GPa

G / B

GPa

ν
Ta2C (P3¯m1, this work)14925537416.90.5830.26
Ta2C (P3¯m1)[34]148.08264.6615.87
Ta0.75Mo0.25C16030040715.60.5320.27
Ta0.5Mo0.5C18031545418.80.5730.26
Ta0.25Mo0.75C20933051723.60.6320.24
MoC24634859730.30.7060.21
Ta0.75W0.25C17131043317.20.5520.27
Ta0.5W0.5C20333350722.10.6090.25
Ta0.25W0.75C23435657626.80.6580.23
WC28238568134.70.7320.21
Table 5  Mechanical properties of complex tantalum carbides with hcp structure
Fig.4  Mechanical properties of complex tantalum carbide containing Mo with different structures
(a) modulus
(b) Vickers hardness
(c) G / Bvs Poisson's ratio
Fig.5  Mechanical properties of complex tantalum carbide containing W with different structures
(a) modulus
(b) Vickers hardness
(c) G / Bvs Poisson's ratio
Fig.6  Total and projected density of states (DOS) of the same component in multi-component carbides in different crystal structures (The dashed lines indicate the Fermi energy levels; TDOS—total density of states)
(a) Ta0.5Mo0.5C (fcc) (b) Ta0.5Mo0.5C (hcp) (c) Ta0.5W0.5C (fcc) (d) Ta0.5W0.5C (hcp)
Fig.7  fm values of complex tantalum carbide containing Mo (a) and W (b) with different structures (fm is an indicator of metal bonding strength)
Crystal structureCarbideCTaMoW
fccTaC1.7981-1.7982
Ta0.75Mo0.25C1.6594-1.8032-1.2279
Ta0.5Mo0.5C1.5107-1.7975-1.2240
Ta0.25Mo0.75C1.4359-1.8233-1.3068
MoC1.3520-1.3520
Ta0.75W0.25C1.6932-1.7852-1.4175
Ta0.5W0.5C1.5430-1.5437
Ta0.25W0.75C1.5538-1.8413-1.4579
WC1.5449-1.5449
hcpTa2C1.8033-0.9016
Ta0.75Mo0.25C1.4781-1.6082-1.1061
Ta0.5Mo0.5C1.3812-1.6431-1.1380
Ta0.25Mo0.75C1.3137-1.6530-1.1950
MoC1.1998-1.1998
Ta0.75W0.25C1.5063-1.6027-1.2308
Ta0.5W0.5C1.4430-1.6329-1.2666
Ta0.25W0.75C1.4100-1.6492-1.3263
WC1.3852-1.3852
Table 6  Average Bader charge of each atom in complex tantalum carbide with different structures
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