ARTICLE IN PRESS Physica B 404 (2009) 2178–2183
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Atomistic simulation of the point defects in B2-type MoTa alloy Jian-Min Zhang a,, Fang Wang a, Ke-Wei Xu b, Vincent Ji c a b c
College of Physics and Information Technology, Shaanxi Normal University, Xian 710062, Shaanxi, PR China State Key Laboratory for Mechanical Behavior of Materials, Xian Jiaotong University, Xian 710049, Shaanxi, PR China ICMMO/LEMHE UMR 8182, Universite´ Paris-Sud 11, 91405 Orsay Cedex, France
a r t i c l e in f o
a b s t r a c t
Article history: Received 7 January 2009 Received in revised form 3 March 2009 Accepted 6 April 2009
The formation and migration mechanisms of three different point defects (mono-vacancy, anti-site defect and interstitial atom) in B2-type MoTa alloy have been investigated by combining molecular dynamics (MD) simulation with modified analytic embedded-atom method (MAEAM). From minimization of the formation energy, we find that the anti-site defects MoTa and TaMo are easier to form than Mo and Ta mono-vacancies, while Mo and Ta interstitial atoms are difficult to form in the alloy. In six migration mechanisms of Mo and Ta mono-vacancies, one nearest-neighbor jump (1NNJ) is the most favorable due to its lowest activation and migration energies, but it will cause a disorder in the alloy. One next-nearest-neighbor jump (1NNNJ) and one third-nearest-neighbor jump (1TNNJ) can maintain the ordered property of the alloy but require higher activation and migration energies, so the 1NNNJ and 1TNNJ should be replaced by straight [1 0 0] six nearest-neighbor cyclic jumps (S[1 0 0]6NNCJ) or bent [1 0 0] six nearest-neighbor cyclic jumps (B[1 0 0]6NNCJ) and [11 0] six nearestneighbor cyclic jumps ([11 0]6NNCJ), respectively. Although the migrations of Mo and Ta interstitial atoms need much lower energy than Mo and Ta mono-vacancies, they are not main migration mechanisms due to difficult to form in the alloy. & 2009 Elsevier B.V. All rights reserved.
PACS: 61.66.Dk 61.72.Bb 67.80.Mg Keywords: MoTa Vacancy Anti-site defect Interstitial atom MAEAM
1. Introduction Molybdenum and Tantalum are widely used as high temperature technological materials in industry due to their excellent properties of high strength, high melting point and corrosion resistance [1], etc. Nevertheless, the poor fracture resistance at room temperature and creep resistance of the pure metal limit their applications. The MoTa [2–4] and other [5–8] alloys made of refractory metals display high melting temperature aerospace and nuclear application. As is well known that the point defects (vacancy, anti-site defect and interstitial atom) directly affect the kinetic and thermodynamic behaviors of the alloys and it is thus very important to get a good understanding of their formation and migration in the alloys. The first principles thermodynamic analysis shows that the Mo–Ta alloy is a B2-type ordered alloy of the CsCl-type [9]. In this paper, the formation and migration energies of three different point defects (mono-vacancy, anti-site defect and interstitial atom) in B2-type MoTa ordered alloy have been investigated by combining molecular dynamics (MD) simulation with modified analytic embedded-atom method (MAEAM) [10–12]. In our previous papers, the MAEAM has been
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used successfully to investigate the self-diffusion [13] and phonons [14] of BCC transition metals, and the properties of the alloys [15–18]. The following three contents have been concerned in this paper. Firstly, the lattice constant and formation energy of the B2-type MoTa alloy are calculated from the energy minimization. The results are in good agreement with the ab initio [9,19] and experimental [20] data. Second, the formation energies of the Mo and Ta mono-vacancies VMo and VTa, anti-site defects MoTa and TaMo that is Mo occupies Ta sublattice and Ta occupies Mo sublattice, and Mo and Ta interstitial atoms IMo and ITa at octahedral site have been calculated. Both anti-site defects MoTa (especially) and TaMo are favorable defects due to their lowest formation energies. Finally, the migration and activation energies have also been determined from energy–displacement curves for seven migration mechanisms: (a) one nearest-neighbor jump (1NNJ), (b) one next-nearest-neighbor jump (1NNNJ), (c) straight [1 0 0] six nearest-neighbor cyclic jumps (S[1 0 0]6NNCJ), (d) bent [1 0 0] six nearest-neighbor cyclic jumps (B[1 0 0]6NNCJ), (e) one third-nearest-neighbor jump (1TNNJ), (f) [11 0] six nearestneighbor cyclic jumps ([11 0]6NNCJ) for VMo and VTa, and (g) one jump of interstitial atom (1IAJ) for IMo and ITa. For Mo monovacancy three favorable migration mechanisms are [11 0]6NNCJ, B[1 0 0]6NNCJ and S[1 0 0]6NNCJ, successively. While for Ta monovacancy three favorable migration mechanisms are S[1 0 0]6NNCJ,
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Table 1 The input physical parameters of Mo and Ta [21–24]. Elements
a (nm)
Ec (eV)
Ef1v (eV)
C11 (eV/nm3)
C12 (eV/nm3)
C44 (eV/nm3)
Mo Ta
0.31468 0.33026
6.82 8.10
3.10 2.95
2870 1640
1050 970
690 520
Table 2 The MAEAM model parameters for Mo and Ta. Elements
fe
n
a
F0 (eV)
k0 (eV)
k1 (eV)
k2 (eV)
k3 (eV)
Mo Ta
0.4234 0.4718
0.5523 0.3611
0.0334 0.1694
3.72 5.15
1.8157 0.0166
4.1996 1.1950
1.8792 0.6498
0.0545 0.0945
B[1 0 0]6NNCJ and [11 0]6NNCJ successively. Although the migrations of Mo and Ta interstitial atoms need much lower energy than Mo and Ta mono-vacancies, they are not main migration mechanisms due to difficult to form in the alloy.
2. Computation methodology and procedure 2.1. MAEAM In MAEAM, the total energy Etotal of a crystal is expressed as [12] Etotal ¼
X
Fðri Þ þ
i
ri ¼
X
X 1X X fðrij Þ þ MðP i Þ; 2 i jðaiÞ i
f ðrij Þ;
(1)
Pi ¼
2.2. The configurations of the defects in B2-type MoTa ordered alloy 2
f ðr ij Þ;
(3)
jðaiÞ
where F(ri) is the energy to embed an atom in site i with electron density ri, which is given by a linear superposition of the spherical averaged atomic electron density of other atoms f(rij), rij is the separation distance of atom j from atom i, f(rij) is the pair potential between atoms i and j, and M(Pi) is the modified term, which describes the energy deviation from the linear superposition. Embedding function F(ri), pair potential f(rij), modified term M(Pi) and atomic electron density f(rij) take the following forms [10,12]: n ri ri , (4) Fðri Þ ¼ F 0 1 n ln
re
fðrij Þ ¼ k0 þ k1
r ij r 1e
2
þ k2
re
r ij r 1e
4
þ k3
" 2 2 # Pi Pi MðP i Þ ¼ a , 1 exp 1 Pe Pe
f ðrij Þ ¼ f e
6 r 1e , r ij
r 1e r ij
12
Ec Ef1v
O
(1) Mono-vacancy, Fig. 1(b), the absentation of a Mo or a Ta atom on Mo or Ta sublattice site forms a Mo mono-vacancy VMo or a Ta mono-vacancy VTa. (2) Anti-site defect, Fig. 1(c), a Mo atom replaces a Ta atom or a Ta atom replaces a Mo atom forms a Mo anti-site defect MoTa or a Ta anti-site defect TaMo. (3) Interstitial atom, Fig. 1(d), a Mo or a Ta atom occupies the high symmetrically octahedral site forms a Mo interstitial atom IMo or a Ta interstitial atom ITa.
2.3. Calculation procedure (6)
(7)
!35 ,
For the B2-type MoTa ordered alloy, as is shown in Fig. 1(a), the Mo atoms (gray balls) are located on the vertexes of a cube unit cell and the Ta atoms (black balls) are arranged on the center and vice versa. As is shown in Fig. 1(b–d), the following three possible configurations of the point defects are investigated:
(5)
where the subscript e denotes equilibrium state and r1e is the first nearest-neighbor distance at equilibrium. In this paper, the atomic electron density at equilibrium state fe is chosen as [12] fe ¼
where the superscripts Mo, Ta in the electron density function f(rij) and interaction potential f(rij) represent them for Mo and Ta, respectively.
(2)
jðaiÞ
X
3
where O ¼ a2 is the atomic volume for a metal with BCC structure. The seven parameters F0, n, k0, k1, k2, k3 and a in Eqs. (4)–(7) can be determined by fitting lattice constant a, the cohesion energy Ec, mono-vacancy formation energy Ef1v and elastic constants C11, C12 and C44. The physical parameters and the calculated model parameters for Mo and Ta are listed in Tables 1 and 2, respectively. For the B2-type MoTa ordered alloy, the Mo–Mo and Ta–Ta interaction potentials can be described by Eq. (5) in MAEAM, whereas for Mo–Ta interactions, we take Johnson’s formula [25] " Mo # Ta f ðr ij Þ Mo 1 f ðr ij Þ Ta fMoTa ðr ij Þ ¼ f ðr Þ þ f ðr Þ , (9) ij ij Mo 2 f Ta ðr ij Þ f ðr ij Þ
(8)
The molecular dynamics simulation is conducted in an 8a 8a 8a computational cell with 1024 atoms, where a is the lattice constant of the alloy. In order to check the effects of the computational cell size on the final results, the formation energies of three different defects have been calculated in cell sizes from 4a 4a 4a to 10a 10a 10a and the convergent results are obtained from 6a 6a 6a. Considering up to the third-nearestneighbor jump (1TNNJ) and different initial positions of the defects as shown in Fig. 1 need one more crystal unit cell, respectively, we have chosen an 8a 8a 8a cell. One of the point defects is created in the center of the cell and the total energy is
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ITa Ta
VTa
Mo
VMo
MoTa
TaMo
IMo
Fig. 1. Unit cell of MoTa ordered alloy with and without point defect: (a) perfect lattice, (b) mono-vacancy, (c) anti-site defect and (d) interstitial atom at octahedral site.
Mo
Ta 2 6 15
VMo
3
15
3
2 6 4
4
y
2
x
3
6
o 1 5
4
z
IMo
Fig. 2. The six migration mechanisms of Mo mono-vacancy: (a) 1NNJ, (b) 1NNNJ, (c) S[1 0 0]6NNCJ, (d) B[1 0 0]6NNCJ, (e) 1TNNJ and (f) [11 0]6NNCJ and one jump of interstitial atom (g) 1IAJ.
minimized with respect to local atomic displacements with a simultaneous volume relaxation. The formation energies of the mono-vacancy, anti-site defect, interstitial atom and the alloy are calculated by the following formulas, respectively: Ef1v ðAÞ ¼ Erel ðn 1Þ Eper ðnÞ þ Ec ðAÞ,
(10)
Efant ðAB Þ ¼ Erel ðnÞ Eper ðnÞ þ Ec ðBÞ Ec ðAÞ,
(11)
Efi ðAÞ ¼ Erel ðn þ 1Þ Eper ðnÞ Ec ðAÞ,
(12)
0
0
DEc ¼ Eper ðnÞ=n xEc ðMoÞ ð1 xÞEc ðTaÞ,
(13)
where the parameters A or B represents the element Mo or Ta in the alloy, x is the atomic proportion of the Mo elements in the alloy (here, x ¼ 0.5 for B2-type MoTa ordered alloy), Erel(n–s)(s ¼ 0, 71) and Eper(n) represent the total energy of the system with and without defect, respectively, Ec(A) or Ec(B) is the cohesion energy 0 0 of the element Mo or Ta in the alloy, and Ec ðMoÞ or Ec ðTaÞ is the cohesion energy of a pure Mo or Ta metal [2,26]. The atomic migration in MoTa alloy is also simulated with MD. All migration mechanisms considered here involve either monovacancy or interstitial atom. Taken a Mo vacancy or a Mo interstitial atom as examples, the migration paths are shown in Fig. 2(a) one nearest-neighbor jump, (b) one next-nearestneighbor jump, (c) straight [1 0 0] six nearest-neighbor cyclic jumps, (d) bent [1 0 0] six nearest-neighbor cyclic jumps, (e) one third-nearest-neighbor jump, (f) [11 0] six nearest-neighbor cyclic jumps of the mono-vacancy and (g) one jump of interstitial atom. The migration mechanisms (c) S[1 0 0]6NNCJ and (d) B[1 0 0]6NNCJ are considered here for comparing to the mechanism (b) 1NNNJ since they are all result in a vacancy to migrate to its next-nearest-neighbor site. A similar comparison is
also taken between (e) 1TNNJ and (f) [11 0]6NNCJ. For six nearestneighbor cyclic jumps (6NNCJ) mechanisms, a vacancy performs a cycle of six successive nearest-neighbor jumps (dotted lines with arrowhead) in such way that the initially perfect order is locally destroyed during the cycle but is totally restored upon its completion excepting the Mo vacancy migrates to its nextnearest-neighbor site along [1 0 0] direction for S[1 0 0]6NNCJ (Fig. 2(c)) and B[1 0 0]6NNCJ (Fig. 2(d)) or to its third-nearestneighbor site along [11 0] direction for [11 0]6NNCJ (Fig. 2(f)). The terms straight and bent used here mean that the migrations of associated a vacancy and three atoms are in one plane and out one plane, respectively. The migration energy is determined as following. The vector of each jump (solid line with arrowhead in Fig. 2) is defined to connect the initial and final equilibrium positions of the vacancy or interstitial atom. The atom exchanging with the vacancy is moved towards the vacancy along the negative jump vector, while the interstitial atom is moved along the jump vector. Each jump is achieved by a series small step. At each step the total energy of the simulation cell is minimized to the lowest value through full relaxation of the atoms. The maximum (saddle point) energy Q (that is activation energy of the diffusion) of the system minus initial energy Ef (that is the formation energy of the defect at initial position) of the system is defined as the migration energy Em of the defect. That is Em ¼ Q Ef
(14)
3. Results and discussions The variation of the average energy per atom in perfect MoTa alloy system with lattice constant is shown in Fig. 3. The abscissa
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10
Energy (eV/atom)
8 6 4 2 0 -2 -4 -6 -8 2.5
2.0
3.0
3.5 4.0 Lattice constant (Å)
4.5
5.0
5.5
Fig. 3. Variation of the average energy per atom in a perfect MoTa alloy with lattice constant. Table 3 Calculated lattice constant a, cohesion energy Ec, formation energy DEc of the MoTa alloy and the cohesion energy of Mo Ec(Mo) and Ta Ec(Ta) in MoTa alloy. Method
a (nm)
Ec (eV)
DEc (eV)
Ec (Mo)(eV)
Ec (Ta)(eV)
MAEAM Ab initio
0.3235 0.3214 [9] 0.3177 [19]
7.611
0.151 0.275 [9] 0.205 [19] 0.11470.026 [20]
6.821
8.400
Experiment
Table 4 Calculated formation energies Ef (eV) for three different point defects in MoTa alloy. Mono-vacancy VMo 3.233
Anti-site VTa 3.218
MoTa 0.062
Interstitial atom TaMo 0.485
IMo 7.263
ITa 7.759
and ordinate values at the vale point correspond to the equilibrium lattice constant a and cohesion energy Ec, respectively. Determined lattice constant a, cohesion energy Ec and formation energy DEc of the alloy, and cohesion energies of the Mo Ec(Mo) and Ta Ec(Ta) in the alloy are listed in Table 3 together with available values of the experimental [20] and the ab initio calculations [9,19] for comparing. The determined lattice constant a of 0.3235 nm and the formation energy DEc of 0.151 eV for the alloy are in good agreement with the ab initio calculations of a ¼ 0.3214 nm [9] and DEc ¼ 0.205 eV [19] as well as the experimental value of DEc ¼ 0.11470.026 eV [20]. The calculated formation energies of mono-vacancy Ef1v, anti-site defect Efant and interstitial atom Efi are listed in Table 4. It can be seen that the formation energies of -0.062 and 0.485 eV for Mo and Ta anti-site defects are much lower than that of 3.233 and 3.218 eV for Mo and Ta mono-vacancy and that of 7.263 and 7.759 eV for Mo and Ta interstitial atom. So we conclude that the anti-site defects are more favorable. This means that while the Mo component is slightly rich in MoTa alloy, the abundant Mo atoms will occupy Ta sublattices to form the Mo anti-site defects neither to form the Ta mono-vacancies nor Mo interstitial atoms. On the contrary, when the Ta component is slightly rich in the MoTa alloy, the abundant Ta atoms will occupy Mo sublattices to form the Ta anti-site defects neither to form the Mo mono-vacancies nor Ta interstitial atoms. In MoTa alloy, the much lower formation energies of anti-sites and nearly close to the formation energies of the mono-vacancy (comparing with Table 1) and interstitial atom [27] in pure Mo or Ta metal may be
2181
resulted from that the Mo and Ta atoms have similar valence electron structures and atomic radii (4d5ds1 and 2.01 A˚ for Mo, 5d36s2 and 2.09 A˚ for Ta). Variation of the system energy with the displacement of atom moving along migration paths are shown in Fig. 4 for monovacancy migration mechanisms of (a) 1NNJ, (b) 1NNNJ, (c) S[1 0 0]6NNCJ, (d) B[1 0 0]6NNCJ, (e) 1TNNJ and (f) [11 0]6NNCJ, and (g) interstitial atom migration mechanism of 1IAJ. The solid lines with closed rhombus and dashed lines with open circles correspond to Mo and Ta defects, respectively. The atom displacements pffiffiffi.at each jump are normalized to jump vector length of ð 3 2Þa for 1NNJ, S[1 0 0]6NNCJ, B[1 0 0]6NNCJ, and [11 0]6NNCJpin ffiffiffi Fig. 4(a, c, d and f), a for 1NNNJ and 1IAJ in Fig. 4(b and g), and 2a for 1TNNJ in Fig. 4(e). We can see that, except (b) 1NNNJ and (e) 1TNNJ of the vacancy and (g) 1IAJ of interstitial atom, the energy–displacement curve is not symmetry about the midpoint of each jump and the saddle point deviates from the midpoint towards either the initial or final position of the migrating atom. This is because, while the migrating atom is assumed to be removed, the crystal structures constructed by the remaining atoms are not symmetry about the midpoint of the jump vector. Even for three symmetry one-jumps, different from (b) 1NNNJ and (e) 1TNNJ of the mono-vacancy, the energy–displacement curves of interstitial atom (g) 1IAJ exhibit a wide (within a scope of 0.15a–0.30a and symmetrical 0.70a–0.85a) and shallow (change in energy not more than 0.06 eV) vale. This implies that the interstitial atom at octahedral site is unstable and will spontaneously migrate to nearly tetrahedron site (corresponding to the energy vale) as well as the thermally vibrate at where with large amplitude even at low temperatures. A similar phenomenon was also noted for Mo self-interstitial atom [28]. From Fig. 4, one can determine the activation energy Q (the maximum energy throughout all migration process) and migration energy Em by using Eq. (14). The results are listed in Table 5 and compared in Fig. 5. We can see that, in six migration mechanisms of the Mo (or Ta) mono-vacancy, the 1NNJ is the most favorable due to its lowest activation and migration energies. But such a migration, as can been seen in Fig. 2(a), will result in a disorder in the ordered alloy (one anti-site plus one mono-vacancy). In order to maintain the ordered property of the alloy and require lower migration energy, the 1NNNJ or 1TNNJ can be achieved by six successive 1NNJ. As discussed in this paper, for next-nearest-neighbor migration of Mo mono-vacancy, the S[1 0 0]6NNCJ and B[1 0 0]6NNCJ (especially) are preferred over the 1NNNJ, as well as for next-nearest-neighbor migration of Ta mono-vacancy, the S[1 0 0]6NNCJ (especially) and B[1 0 0]6NNCJ are preferred over the 1NNNJ. Similarly, for the third-nearestneighbor migration of Mo or Ta mono-vacancy, the [11 0]6NNCJ is preferred over the 1TNNJ. For each migration mechanism of the mono-vacancy except 1TNNJ, the migration of the Ta vacancy is easier than that of the Mo vacancy. From minimization of the activation and migration energies, we can conclude that, except 1NNJ with the lowest activation and migration energies but will lead to a disorder in the ordered alloy, for Mo vacancy three favorable migration mechanisms are [11 0]6NNCJ, B[1 0 0]6NNCJ and S[1 0 0]6NNCJ successively, while for Ta vacancy three favorable migration mechanisms are S[1 0 0]6NNCJ, B[1 0 0] 6NNCJ and [11 0]6NNCJ successively. In spite of the migration energy of a Mo or Ta interstitial atom is much lower than that of a Mo or Ta mono-vacancy, the much higher formation energy (more than twice to that of the mono-vacancy) leads to the Mo or Ta interstitial atom is difficult to form even nearly tetrahedron site (corresponding to the energy vale). Therefore the migration of a Mo or Ta interstitial atom is not a main migration mechanism in MoTa alloy.
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9
5.0
1NNJ
4.5 4.0
Mo Ta
3.5
6.0
0.2
0.4 0.6 Displacement
0.8
5
1.0
0.0
6.0
S [100]6NNCJ
5.5
Energy (eV)
Energy (eV)
6
3 0.0
5.0 4.5 4.0
0.2
0.4 0.6 Displacement
0.8
1.0
B [100] 6NNCJ
5.5 5.0 4.5 4.0 3.5
3.5
3.0
3.0 0
1
2 3 4 Displacement
5
6
0
1
2 3 4 Displacement
5
6
5
6
6.0
15 1TNNJ Energy (eV)
Energy (eV)
7
4
3.0
13
1NNNJ
8 Energy (eV)
Energy (eV)
5.5
11 9 7 5
[110] 6NNCJ
5.5 5.0 4.5 4.0 3.5
3
3.0 0.0
0.2
0.4 0.6 Displacement
0.8
1.0
0
1
2 3 4 Displacement
Energy (eV)
8.4 8.0
1IAJ
7.6 7.2 6.8 6.4 0.0
0.2
0.4 0.6 Displacement
0.8
1.0
Fig. 4. Energy–displacement curves for (a) 1NNJ, (b) 1NNNJ, (c) S[1 0 0]6NNCJ, (d) B[1 0 0]6NNCJ, (e) 1TNNJ and (f) [11 0]6NNCJ of Mo or Ta mono-vacancy, and (g) 1IAJ of Mo or Ta interstitial atom. The solid lines with closed rhombus and dashed lines with open circles correspond to Mo and Ta defects, respectively.
4. Conclusions Combining molecular dynamics (MD) simulation with modified analytic embedded-atom method (MAEAM), the formation and migration behaviors of three different point defects (vacancy, anti-site defect and interstitial atom) in B2-type MoTa ordered alloy have been investigated. The following conclusions are obtained: 1. Calculated lattice constant and formation energy of 0.3235 nm and 0.151 eV are in good agreement with the experimental and ab initio data. The cohesion energies of the alloy, Mo and Ta components are 7.611, 6.821 and 8.400 eV, respectively. 2. The anti-site defects MoTa (especially) and TaMo are easier to form than Mo and Ta mono-vacancies, while Mo and Ta
interstitial atoms are difficult to form. In other words, when the Mo (Ta) component is slightly rich in MoTa alloy, the abundant Mo (Ta) atoms will occupy Ta (Mo) sublattices to form the MoTa (TaMo) anti-site defects instead of Ta (Mo) mono-vacancies or Mo (Ta) interstitial atoms. 3. In six migration mechanisms of the Mo or Ta mono-vacancy, the 1NNJ is the most favorable one due to its lowest activation and migration energies, but it will result in a disorder in the ordered alloy. 4. In order to maintain the ordered property of the alloy as well as require lower migration energy, the 1NNNJ, and 1TNNJ of a Mo or Ta mono-vacancy can be achieved by S[1 0 0]6NNCJ or B[1 0 0]6NNCJ, and [11 0]6NNCJ. Furthermore, they are favorable in order of [11 0]6NNCJ, B[1 0 0]6NNCJ and S[1 0 0]6NNCJ for Mo vacancy, while in order of S[1 0 0]6NNCJ, B[1 0 0]6NNCJ and [11 0]6NNCJ for Ta vacancy.
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Table 5 The activation energy Q and migration energy Em for 1NNJ, 1NNNJ, S[1 0 0]6NNCJ, B[1 0 0]6NNCJ, 1TNNJ and [11 0]6NNCJ of Mo or Ta mono-vacancy, and 1IAJ of Mo or Ta interstitial atom in MoTa alloy. Element
Energy (eV)
1NNJ
1NNNJ
S[1 0 0]6NNCJ
B[1 0 0]6NNCJ
1TNNJ
[11 0]6NNCJ
1IAJ
Mo
Q Em Q Em
5.149 1.916 5.106 1.888
8.204 4.971 6.653 3.435
5.591 2.358 5.307 2.089
5.555 2.322 5.394 2.176
12.085 8.852 12.961 9.743
5.464 2.231 5.442 2.224
7.851 0.588 8.321 0.562
Ta
14 12
Q (Mo) Q (Ta)
Em (Mo) Em (Ta)
Energy (eV)
10 8 6 4 2 0 1NNJ
1NNNJ
S [100]6NNCJ B [100]6NNCJ
1TNNJ
[110] 6NNCJ
1IAJ
Mechanisms Fig. 5. The activation energy Q and migration energy Em for 1NNJ, 1NNNJ, S[1 0 0]6NNCJ, B[1 0 0]6NNCJ, 1TNNJ and [11 0]6NNCJ of Mo or Ta mono-vacancy, and 1IAJ of Mo or Ta interstitial atom migration in MoTa alloy.
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