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.
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.
Fund: National Natural Science Foundation of China(52371060);Natural Science Foundation of Heilongjiang Province(LH2023E060);Fundamental Research Funds for the Central Universities(3072023WD010)
Fig.1 Super structural models of the special quasi-random structure (SQS) of complex tantalum carbides (a) fcc (b) hcp
Crystal structure
Carbide
Lattice constant
nm
Angle
(°)
Volume
nm3
Ef
eV·atom-1
Ec
eV·atom-1
fcc
TaC, this work
= 0.44781
α = β = γ = 90.00
0.71839
-0.5962
-8.5998
TaC[34]
a = 0.447
-0.59
Ta0.75Mo0.25C
= 0.44554
α = 90.04, β = γ = 90.00
0.70753
-0.4089
-8.1705
Ta0.5Mo0.5C
= 0.44320
α = β =89.78, γ = 90.22
0.69645
-0.2246
-7.7442
Ta0.25Mo0.75C
= 0.44061
α = 89.79, β = γ = 90.00
0.68428
-0.0432
-7.6155
MoC
= 0.43699
α = β = γ = 90.00
0.66756
0.1400
-6.8956
hcp
Ta2C
a = b = 0.31249,
c = 0.49593
α = β = 90.00,
γ = 120.00
0.33551
-0.6163
-8.6566
(Pm1, this work)
Ta2C (Pm1)[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 structure
Carbide
Lattice constant
nm
Angle
(°)
Volume
nm3
Ef
eV·atom-1
Ec
eV·atom-1
fcc
TaC, this work
=0.44781
α = β = γ = 90.00
0.71839
-0.5962
-8.5998
TaC[34]
a = 0.447
-0.59
Ta0.75W0.25C
= 0.44543
α = 90.00,
β = 89.99,
γ = 90.00
0.70699
-0.3759
-8.6364
Ta0.5W0.5C
= 0.44339
α = 89.79,
β = 90.19,
γ = 90.06
0.69731
-0.1566
-8.2123
Ta0.25W0.75C
= 0.44096
α = β = 90.00,
γ = 90.06
0.68590
0.0565
-8.3138
WC
= 0.43821
α = β = γ = 90.00
0.67320
0.2909
-7.8169
hcp
Ta2C
a = b = 0.31249,
c = 0.49593
α = β = 90.00,
γ = 120.00
0.33551
-0.6163
-8.6566
(Pm1, this work)
Ta2C (Pm1)[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 (11)
GPa
C12 (12)
GPa
C44 (44)
GPa
G
GPa
B
GPa
E
GPa
HV
GPa
G / B
TaC, this work
720
134
154
200
330
500
21.8
0.607
0.25
TaC[34]
737
141
175
216.90
339.67
24.53
Ta0.75Mo0.25C
668
138
152
167
302
423
20.9
0.605
0.25
Ta0.5Mo0.5C
576
165
146
151
310
389
17.0
0.554
0.27
Ta0.25Mo0.75C
581
174
123
122
339
327
13.2
0.486
0.29
MoC
684
166
70
200
331
499
7.0
0.360
0.34
Ta0.75W0.25C
715
139
156
179
310
450
21.5
0.603
0.25
Ta0.5W0.5C
630
150
147
156
341
407
18.8
0.577
0.26
Ta0.25W0.75C
611
207
132
129
370
346
12.4
0.458
0.30
WC
769
170
67
200
330
500
7.0
0.348
0.34
Table 3 Elastic constants and mechanical properties of complex tantalum carbides with fcc structure
Carbide (hcp)
C11
C12
C13
C33
C44
Ta2C (Pm1, this work)
480
143
138
498
120
Ta2C (Pm1)[34]
479
164
149
504
133
Ta0.75Mo0.25C
511
194
138
764
120
Ta0.5Mo0.5C
532
203
151
783
157
Ta0.25Mo0.75C
568
206
159
811
203
MoC
618
213
159
854
263
Ta0.75W0.25C
537
197
138
787
130
Ta0.5W0.5C
581
209
154
823
181
Ta0.25W0.75C
621
224
164
878
235
WC
699
232
167
953
302
Table 4 Elastic constants of complex tantalum carbides with hcp structure
Carbide
(hcp)
G
GPa
B
GPa
E
GPa
Hv
GPa
G / B
GPa
Ta2C (Pm1, this work)
149
255
374
16.9
0.583
0.26
Ta2C (Pm1)[34]
148.08
264.66
15.87
Ta0.75Mo0.25C
160
300
407
15.6
0.532
0.27
Ta0.5Mo0.5C
180
315
454
18.8
0.573
0.26
Ta0.25Mo0.75C
209
330
517
23.6
0.632
0.24
MoC
246
348
597
30.3
0.706
0.21
Ta0.75W0.25C
171
310
433
17.2
0.552
0.27
Ta0.5W0.5C
203
333
507
22.1
0.609
0.25
Ta0.25W0.75C
234
356
576
26.8
0.658
0.23
WC
282
385
681
34.7
0.732
0.21
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 structure
Carbide
C
Ta
Mo
W
fcc
TaC
1.7981
-1.7982
Ta0.75Mo0.25C
1.6594
-1.8032
-1.2279
Ta0.5Mo0.5C
1.5107
-1.7975
-1.2240
Ta0.25Mo0.75C
1.4359
-1.8233
-1.3068
MoC
1.3520
-1.3520
Ta0.75W0.25C
1.6932
-1.7852
-1.4175
Ta0.5W0.5C
1.5430
-1.5437
Ta0.25W0.75C
1.5538
-1.8413
-1.4579
WC
1.5449
-1.5449
hcp
Ta2C
1.8033
-0.9016
Ta0.75Mo0.25C
1.4781
-1.6082
-1.1061
Ta0.5Mo0.5C
1.3812
-1.6431
-1.1380
Ta0.25Mo0.75C
1.3137
-1.6530
-1.1950
MoC
1.1998
-1.1998
Ta0.75W0.25C
1.5063
-1.6027
-1.2308
Ta0.5W0.5C
1.4430
-1.6329
-1.2666
Ta0.25W0.75C
1.4100
-1.6492
-1.3263
WC
1.3852
-1.3852
Table 6 Average Bader charge of each atom in complex tantalum carbide with different structures
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