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Molecular dynamics simulation of dislocation intersections in aluminum
Materials Science and Engineering A363 (2003) 234–241
Molecular dynamics simulation of dislocation intersections in aluminum M. Li a , W.Y. Chu a,∗ , C.F. Qian b , K.W. Gao a , L.J. Qiao a b
a Department of Materials Physics, University of Science and Technology, Beijing 100083, China Department of Mechanical Engineering, Beijing University of Chemical Technology, Beijing 100029, China
Received 2 December 2002; received in revised form 14 July 2003
Abstract The molecular dynamics method is used to simulate dislocation intersection in aluminum containing 1.6 × 106 atoms using embedded atom method (EAM) potential. The results show that after intersection between two right-hand screw dislocations of opposite sign there are an extended jog corresponding to a row of 1/3 vacancies in the intersected dislocation, and a trail of vacancies behind the moving dislocation. After intersection between screw dislocations of same sign, there are an extended jog corresponding to a row of 1/3 interstitials in the intersected dislocation, and a trail of interstitials behind the moving dislocation. After intersection between screw and edge dislocations with different Burgers vector, there are a constriction corresponding to one 1/3 vacancy in the edge dislocation, and no point-defects behind the screw dislocation. When a moving screw dislocation intersects an edge dislocation with the same Burgers vector, the point of intersection will split into two constrictions corresponding to one 1/3 vacancy and 1/3 interstitial, respectively. The moving screw dislocation can pass the edge dislocation only after the two constrictions, which can move along the line of intersection of the two slip planes, meet and annihilate. © 2003 Elsevier B.V. All rights reserved. Keywords: Molecular dynamics simulation; Dislocation intersection; Extended jog; Constriction; Aluminum
1. Introduction Elasticity theory of dislocation has been proven successful in explaining a broad variety of dislocation behavior [1]. The core region of dislocation and their interactions where linear elasticity assumption fails, however, are still the subject of extensive research. There are a lot of works about atomistic simulations of dislocation core [2–7]. Molecular dynamics method is one kind of atomistic simulations and can simulate successfully various dislocation behaviors. For example, dislocation emission, crack propagation and healing can be simulated by a molecular dynamics method [8–10]. The intersection process between a screw dislocation and a 60◦ dislocation has been stimulated via molecular dynamics method [5]. The annihilation process of screw dislocations has been simulated and found dislocation do not split into partials if their separation is less than certain distance [6]. Molecular dynamics simulation of supersonic dislocation has been performed [7]. ∗ Corresponding author. Tel.: +86-10-6233-2345; fax: +86-10-6233-2345. E-mail address: [email protected] (W.Y. Chu).
0921-5093/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-5093(03)00644-0
In the present paper, a molecular dynamics method is used to simulate dislocation intersection and exhibit the detail of various extended jogs and constrictions formed after intersection in aluminum.
2. Simulation procedure ¯ diThe length of aluminum crystal along the x = [1 1¯ 2] ¯ rection is 31.2 nm, the width along the y = [1 1 1] direction is 21 nm, and the height along the z = [1 1 0] direction is 25.8 nm. The number of atoms used here is about 1.6 × 106 . The inter-atomic potential used here is the embedded atom method (EAM) [11]. This potential is developed by fitting of the equilibrium lattice parameter, the cohesive energy, the elastic constants, the vacancy migration energy, the intrinsic stacking fault energy, the experimentally measured phonon-dispersion relations, the surface energy, and the equation of state (EOS). Therefore, it has a good accuracy and reliability. The inner atoms follow the Newton’s second law and a leapfrog algorithm is applied to calculate the positions and velocities of atoms [12]. The initial velocity is the Maxwell–Boltzmann distribution corresponding to
M. Li et al. / Materials Science and Engineering A363 (2003) 234–241
a given temperature, which is maintained at 30 K during simulations. The dislocations are implemented by displacing the position of each atom with displacement field according to linear elasticity theory of dislocation, and then relaxing for 1.0 ps. The potential energy of all lattice atoms distributes between −3.33 and −3.38 eV, and energy of the atoms around dislocation core distributes between −3.3 and −3.2 eV, which is higher than that of the lattice atoms. These atoms with various energy distributions are distinguished using various colors. Therefore, the positions of the dislocations at any instant can be determined. When temperature exceeds 200 K, however, the energy distribution of the lattice atoms widens greatly and overlays with that of dislocation core. In this case, the site of dislocation line cannot be determined according to energy distribution, i.e. the color of the atoms. Therefore, the system temperature in this simulation is maintained at 30 K by scaling the atom velocities during the sim-
235
ulation. Thompson tetrahedron notation [1] is used to mark Burgers vectors and slip planes. A right-hand screw dislocation EF is moving on the (1 1¯ 1) plane, and the intersected dislocation PQ is located on the (1 1 1) plane and its Burgers vector will change according to request, as shown in Fig. 1(a). In order to be intersected, the ends of the PQ dislocation must be fixed on the front and latter surfaces of the (1 1¯ 1) plane. Therefore, a fixed boundary condition is used for the front and back surfaces. For the other surfaces, free boundary condition is used. A shear stress τ on the (1 1¯ 1) plane is applied with a loading rate of 162 MPa/ps. This high deformation rate is used only to accelerate our calculation without altering the qualitative outcome of the simulation. The time step is 5 × 10−3 ps. When the stress increased to 650 MPa corresponding to a strain of 2.53%, it was kept constant. The force acted on the moving dislocation is F1 = τb and along the [1¯ 1 2] direction. The force acted on the intersected dislocation
Fig. 1. Intersection between two screw dislocations of opposite sign: (a) a right-hand screw dislocation moving on the (1 1¯ 1) plane and a left-hand screw dislocation pinned on the (1 1 1) plane; (b) intersecting of the two dislocation at R; (c) a trail of point defects SVW and an extended jog RS; (d) schematic drawing of the extended jog RS.
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is F2 = τb cos 70.5 = τb/3, which is perpendicular to the dislocation PQ and make it curve because of the fixed ends.
3. Results and discussion 3.1. Intersection between two screw dislocations with the opposite sign A right-hand screw dislocation EF with b1 = DC = [1 1 0]/2 is moving on the (1 1¯ 1) plane, and a left-hand screw dislocation PQ with b2 = BA = [1 1¯ 0]/2 is pinned on the (1 1 1) plane, as shown in Fig. 1(a). The moving dislocation EF intersects the pinned dislocation PQ at R, as shown in Fig. 1(b). After intersection, there are an extended jog RS in the intersected dislocation PQ, and a trail of point defects SVW behind the moving dislocation, as shown in Fig. 1(c). The schematic drawing of the extended jog RS is shown in Fig. 1(d). The partial Bδ dissociates into Bα + αδ at point R, and partial αA into δα + αA at point U, resulting in forming a stair-rod dipole δα–αδ [1]. The Burger vectors of the stair-rod dipole are ±[1 1 0]/6, the atom spacing along the dipole line is [1 1¯ 1]/2, and the normal distance between the step planes containing the dipole lines is [0 0 1]/2. Thus, the vacant volume per atom site is ((1/6) [1 1 0]a0 × (1/2)[1 1¯ 0]a0 ) (1/2)[0 0 1]a0 = a03 /12. The volume of an atom is a03 /4 so that the stair-rod dipole δr–rδ in the unit jog corresponds to a row of 1/3 vacancies. The atomic configuration around the trail of the point defects SVW on the (1 1¯ 1) plane is shown in Fig. 2(a), we can see that the trail of the point defects is a fold row of vacancies. The position of the jog in the moving dislocation EF can change during moving toward, therefore the trail of the vacancies becomes a fold. The atomic configuration around the extended jog RS on the (1 1 1) plane is shown in Fig. 2(b). In Fig. 2(b), SV is the part of the trail of the vacancies on the (1 1 1) plane, and the extended jog RS is a hollow tube, whose volume is about 1/3 of a row of vacancies. The simulation result is consistent with the calculated result. Therefore, the extended jog formed in the intersected dislocation is a row of 1/3 vacancies. 3.2. Intersection of two right-hand screw dislocations The intersection process between two right-hand dislocations is similar to Fig. 1. There is also an extended jog RS in the intersected dislocation PQ, and a trail of point defects SGH behind the moving dislocation EF after intersection, as shown in Fig. 3(a). The schematic drawing of the extended jog RS is shown in Fig. 3(b). A stair-rod dipole AB/δβ–δβ/AB forms, and the similar calculation shows that the interstitial volume per atom site in the dipole is also a03 /12 [1]. Therefore, the stair-rod
Fig. 2. The atomic configurations around the point defects SVW on the (1 1¯ 1) plane (a), and the extended jog RS on the (1 1 1) plane (b).
dipole AB/δβ–δβ/AB in the unit jog corresponds to a row of 1/3 interstitials. The atomic configuration around the trail of the point defects SGH on the (1 1¯ 1) plane is shown in Fig. 3(c). As viewed along the atomic row of abcd, we can see the arrangement of the atoms in the region of bc is closer together than that of ab and cd. Measurement indicates that the distance of eight atoms in the region of bc is equal to that of seven atoms in the region of ab. This means that there is an interstitial in the region of bc. The situation is the same in the whole zone of SGH. Therefore, the trail of the point defects after intersection between perpendicular pair of right-hand screw dislocations is a row of interstitials. The atomic
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Fig. 3. Intersection between two screw dislocations of same sign: (a) a trail of point defects SGH and an extended jog RS after intersection; (b) schematic drawing of the extended jog RS; (c) the atomic configuration around the point defects SGH on the (1 1¯ 1) plane; (d) the atomic configuration around RS on the (1 1 1) plane.
configuration around the extended jog RS on the (1 1 1) plane is shown in Fig. 3(d). As viewed along the atomic row of abcd, the arrangement of the atoms in the region of bc is closer together than that of ab or cd. The distance of four atoms between ab is equal to that of four 1/3 atoms between bc. Therefore, the extended jog formed in the intersected right-hand screw dislocation is a row of 1/3 interstitials.
3.3. Intersection between screw and edge dislocations with different Burgers vector After a moving dislocation with b1 = [1 1 0]/2 intersects an edge dislocation with b2 = [1¯ 0 1]/2 at R, an extended jog RS forms, as shown in Fig. 4(a). The atomic configuration around the extended jog RS on the (1 1 1) plane is shown in Fig. 4(b). Fig. 4(b) shows that the extended jog contains
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Fig. 4. Intersection between screw and edge dislocations with different Burgers vector: (a) a constriction R formed in the intersected edge dislocation; (b) the atomic configuration around the constriction R corresponding to one 1/3 vacancy on the (1 1 1) plane.
only one 1/3 vacancy, and is in fact a constriction. This is due to high fault energy of aluminum. There are no point defects behind the moving dislocation EF because there is a kink instead of jog in the dislocation EF after intersection, and it will disappear through slip on the (1 1¯ 1) plane. 3.4. Intersection between screw and edge dislocation with the same Burgers vector After the moving screw dislocation with b1 = [1¯ 0 1]/2 intersects the edge dislocation with b2 = b1 = [1¯ 0 1]/2 at R, a constriction R forms, as shown in Fig. 5(a). The two parts of
the moving dislocation EF, i.e. ER and RF, will move on the (1 1¯ 1) plane, and the two parts of the intersected dislocation PQ, i.e. PR and RQ, however, move on the (1 1 1) plane. The constriction R must be kept at the line of intersection of the two slip planes. The independent movement of the four parts of the dislocation converging on R cause the constriction to split into R and R , as shown in Fig. 5(b). The two constrictions of R and R can move along the line of intersection of the two slip planes through the independent movement of the four parts of the dislocation converging on the constrictions of R and R . The two constrictions can meet again, as shown in Fig. 5(c). The moving screw dislocation can pass the edge
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Fig. 5. Intersection between screw and edge dislocations with same Burgers vector: (a) intersecting of the two dislocation at R; (b) two constrictions of R and R moving along the line of intersection of the two slip planes; (c) meeting of the two constrictions; (d) the moving screw dislocation passing the edge dislocation after the two constrictions meeting and annihilating; (e) schematic drawing of the constriction R.
dislocation and move toward only after the two constrictions meet and annihilate, as shown in Fig. 5(d). The schematic drawing of the constriction R is shown in Fig. 5(f). At the line of intersection of the (1 1¯ 1) and (1 1 1) planes the moving screw dislocation CB = Cα + αB on the (1 1¯ 1) plane will react with the edge dislocation CB = Cδ + δB on the (1 1 1) plane, i.e. Cα + αB + αB + Cδ → Cα + αB/δB + C. αB/δB is a stair-rod dislocation.
The atomic configurations around the constrictions of R and R on the (1 1 1) plane are shown in Fig. 6(a) and (b), respectively. Fig. 6 indicates that the constriction R corresponds to 1/3 vacancy, and the constriction R corresponds to 1/3 interstitial. Therefore, the two constrictions corresponding to 1/3 vacancy and 1/3 interstitial, respectively, can annihilate after meeting.
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Fig. 6. The atomic configurations around the constrictions on the (1 1 1) plane: (a) R corresponding to 1/3 vacancy; (b) R corresponding to 1/3 interstitial.
4. Summary
Acknowledgements
After intersection between two screw dislocations, there are an extended jog in the intersected dislocation, which corresponds to a row of 1/3 vacancies for the dislocations of opposite sign or 1/3 interstitials for the dislocations of same sign, and a trail of vacancies or interstitials behind the moving dislocation. After intersection between screw and edge dislocation with different Burgers vector, a constriction corresponding to one 1/3 vacancy forms in the intersected edge dislocation. When a moving screw dislocation intersects an edge dislocation with the same Burgers vector, the point of intersection will split into two constrictions corresponding to 1/3 vacancy and 1/3 interstitial, respectively. The moving dislocation can pass the edge dislocation only after the two constriction, which can move along the line of intersection of the two slip planes, meet and annihilate.
The project was supported by the special Funds for the Major state Basic Research Projects (No. G19990650) and by the National Natural Science Foundation of China (310272020).
References [1] J.P. Hirth, J. Lothe, Theory of Dislocations, Wiley, New York, 1982. [2] L.H. Yang, P. Soderlind, J.A. Moriarty, Mater. Sci. Eng. A 309–310 (2001) 102. [3] G. Lu, N. Kioussis, U.V. Bulatov, E. Kaxiras, Mater. Sci. Eng. A 309–310 (2001) 142. [4] T. Veffe, Mater. Sci. Eng. A 309–310 (2001) 113. [5] S.J. Zhou, D.L. Preston, P.S. Lomdahl, D.M. Beazley, Science 279 (1998) 1417.
M. Li et al. / Materials Science and Engineering A363 (2003) 234–241 [6] S. Swaminarayan, R. LeSar, P. Lomdahl, D. Beazley, J. Mater. Res. 13 (1998) 3478. [7] P. Gumbsch, H. Gao, Science 283 (1999) 965. [8] S. Li, K.W. Gao, L.J. Qiao, F.X. Zhou, W.Y. Chu, Comput. Mater. Sci. 20 (2001) 143. [9] V. Bulator, F.F. Abraham, L. Kubin, B. Devincre, S. Yip, Nature 391 (1998) 669.
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[10] R.G. Hoagland, M.S. Daw, J.P. Hirth, J. Mater. Res. 6 (1991) 2565. [11] Y. Mishin, D. Farkas, M.J. Mehl, D.A. Papaconstantopoulos, Phys. Rev. B59 (1999) 3393. [12] D.C. Rapaport, The Art of Molecular Dynamics Simulation, Cambridge University Press, Cambridge, 1995.
Molecular dynamics simulation of dislocation intersections in aluminum M. Li a , W.Y. Chu a,∗ , C.F. Qian b , K.W. Gao a , L.J. Qiao a b
a Department of Materials Physics, University of Science and Technology, Beijing 100083, China Department of Mechanical Engineering, Beijing University of Chemical Technology, Beijing 100029, China
Received 2 December 2002; received in revised form 14 July 2003
Abstract The molecular dynamics method is used to simulate dislocation intersection in aluminum containing 1.6 × 106 atoms using embedded atom method (EAM) potential. The results show that after intersection between two right-hand screw dislocations of opposite sign there are an extended jog corresponding to a row of 1/3 vacancies in the intersected dislocation, and a trail of vacancies behind the moving dislocation. After intersection between screw dislocations of same sign, there are an extended jog corresponding to a row of 1/3 interstitials in the intersected dislocation, and a trail of interstitials behind the moving dislocation. After intersection between screw and edge dislocations with different Burgers vector, there are a constriction corresponding to one 1/3 vacancy in the edge dislocation, and no point-defects behind the screw dislocation. When a moving screw dislocation intersects an edge dislocation with the same Burgers vector, the point of intersection will split into two constrictions corresponding to one 1/3 vacancy and 1/3 interstitial, respectively. The moving screw dislocation can pass the edge dislocation only after the two constrictions, which can move along the line of intersection of the two slip planes, meet and annihilate. © 2003 Elsevier B.V. All rights reserved. Keywords: Molecular dynamics simulation; Dislocation intersection; Extended jog; Constriction; Aluminum
1. Introduction Elasticity theory of dislocation has been proven successful in explaining a broad variety of dislocation behavior [1]. The core region of dislocation and their interactions where linear elasticity assumption fails, however, are still the subject of extensive research. There are a lot of works about atomistic simulations of dislocation core [2–7]. Molecular dynamics method is one kind of atomistic simulations and can simulate successfully various dislocation behaviors. For example, dislocation emission, crack propagation and healing can be simulated by a molecular dynamics method [8–10]. The intersection process between a screw dislocation and a 60◦ dislocation has been stimulated via molecular dynamics method [5]. The annihilation process of screw dislocations has been simulated and found dislocation do not split into partials if their separation is less than certain distance [6]. Molecular dynamics simulation of supersonic dislocation has been performed [7]. ∗ Corresponding author. Tel.: +86-10-6233-2345; fax: +86-10-6233-2345. E-mail address: [email protected] (W.Y. Chu).
0921-5093/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-5093(03)00644-0
In the present paper, a molecular dynamics method is used to simulate dislocation intersection and exhibit the detail of various extended jogs and constrictions formed after intersection in aluminum.
2. Simulation procedure ¯ diThe length of aluminum crystal along the x = [1 1¯ 2] ¯ rection is 31.2 nm, the width along the y = [1 1 1] direction is 21 nm, and the height along the z = [1 1 0] direction is 25.8 nm. The number of atoms used here is about 1.6 × 106 . The inter-atomic potential used here is the embedded atom method (EAM) [11]. This potential is developed by fitting of the equilibrium lattice parameter, the cohesive energy, the elastic constants, the vacancy migration energy, the intrinsic stacking fault energy, the experimentally measured phonon-dispersion relations, the surface energy, and the equation of state (EOS). Therefore, it has a good accuracy and reliability. The inner atoms follow the Newton’s second law and a leapfrog algorithm is applied to calculate the positions and velocities of atoms [12]. The initial velocity is the Maxwell–Boltzmann distribution corresponding to
M. Li et al. / Materials Science and Engineering A363 (2003) 234–241
a given temperature, which is maintained at 30 K during simulations. The dislocations are implemented by displacing the position of each atom with displacement field according to linear elasticity theory of dislocation, and then relaxing for 1.0 ps. The potential energy of all lattice atoms distributes between −3.33 and −3.38 eV, and energy of the atoms around dislocation core distributes between −3.3 and −3.2 eV, which is higher than that of the lattice atoms. These atoms with various energy distributions are distinguished using various colors. Therefore, the positions of the dislocations at any instant can be determined. When temperature exceeds 200 K, however, the energy distribution of the lattice atoms widens greatly and overlays with that of dislocation core. In this case, the site of dislocation line cannot be determined according to energy distribution, i.e. the color of the atoms. Therefore, the system temperature in this simulation is maintained at 30 K by scaling the atom velocities during the sim-
235
ulation. Thompson tetrahedron notation [1] is used to mark Burgers vectors and slip planes. A right-hand screw dislocation EF is moving on the (1 1¯ 1) plane, and the intersected dislocation PQ is located on the (1 1 1) plane and its Burgers vector will change according to request, as shown in Fig. 1(a). In order to be intersected, the ends of the PQ dislocation must be fixed on the front and latter surfaces of the (1 1¯ 1) plane. Therefore, a fixed boundary condition is used for the front and back surfaces. For the other surfaces, free boundary condition is used. A shear stress τ on the (1 1¯ 1) plane is applied with a loading rate of 162 MPa/ps. This high deformation rate is used only to accelerate our calculation without altering the qualitative outcome of the simulation. The time step is 5 × 10−3 ps. When the stress increased to 650 MPa corresponding to a strain of 2.53%, it was kept constant. The force acted on the moving dislocation is F1 = τb and along the [1¯ 1 2] direction. The force acted on the intersected dislocation
Fig. 1. Intersection between two screw dislocations of opposite sign: (a) a right-hand screw dislocation moving on the (1 1¯ 1) plane and a left-hand screw dislocation pinned on the (1 1 1) plane; (b) intersecting of the two dislocation at R; (c) a trail of point defects SVW and an extended jog RS; (d) schematic drawing of the extended jog RS.
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is F2 = τb cos 70.5 = τb/3, which is perpendicular to the dislocation PQ and make it curve because of the fixed ends.
3. Results and discussion 3.1. Intersection between two screw dislocations with the opposite sign A right-hand screw dislocation EF with b1 = DC = [1 1 0]/2 is moving on the (1 1¯ 1) plane, and a left-hand screw dislocation PQ with b2 = BA = [1 1¯ 0]/2 is pinned on the (1 1 1) plane, as shown in Fig. 1(a). The moving dislocation EF intersects the pinned dislocation PQ at R, as shown in Fig. 1(b). After intersection, there are an extended jog RS in the intersected dislocation PQ, and a trail of point defects SVW behind the moving dislocation, as shown in Fig. 1(c). The schematic drawing of the extended jog RS is shown in Fig. 1(d). The partial Bδ dissociates into Bα + αδ at point R, and partial αA into δα + αA at point U, resulting in forming a stair-rod dipole δα–αδ [1]. The Burger vectors of the stair-rod dipole are ±[1 1 0]/6, the atom spacing along the dipole line is [1 1¯ 1]/2, and the normal distance between the step planes containing the dipole lines is [0 0 1]/2. Thus, the vacant volume per atom site is ((1/6) [1 1 0]a0 × (1/2)[1 1¯ 0]a0 ) (1/2)[0 0 1]a0 = a03 /12. The volume of an atom is a03 /4 so that the stair-rod dipole δr–rδ in the unit jog corresponds to a row of 1/3 vacancies. The atomic configuration around the trail of the point defects SVW on the (1 1¯ 1) plane is shown in Fig. 2(a), we can see that the trail of the point defects is a fold row of vacancies. The position of the jog in the moving dislocation EF can change during moving toward, therefore the trail of the vacancies becomes a fold. The atomic configuration around the extended jog RS on the (1 1 1) plane is shown in Fig. 2(b). In Fig. 2(b), SV is the part of the trail of the vacancies on the (1 1 1) plane, and the extended jog RS is a hollow tube, whose volume is about 1/3 of a row of vacancies. The simulation result is consistent with the calculated result. Therefore, the extended jog formed in the intersected dislocation is a row of 1/3 vacancies. 3.2. Intersection of two right-hand screw dislocations The intersection process between two right-hand dislocations is similar to Fig. 1. There is also an extended jog RS in the intersected dislocation PQ, and a trail of point defects SGH behind the moving dislocation EF after intersection, as shown in Fig. 3(a). The schematic drawing of the extended jog RS is shown in Fig. 3(b). A stair-rod dipole AB/δβ–δβ/AB forms, and the similar calculation shows that the interstitial volume per atom site in the dipole is also a03 /12 [1]. Therefore, the stair-rod
Fig. 2. The atomic configurations around the point defects SVW on the (1 1¯ 1) plane (a), and the extended jog RS on the (1 1 1) plane (b).
dipole AB/δβ–δβ/AB in the unit jog corresponds to a row of 1/3 interstitials. The atomic configuration around the trail of the point defects SGH on the (1 1¯ 1) plane is shown in Fig. 3(c). As viewed along the atomic row of abcd, we can see the arrangement of the atoms in the region of bc is closer together than that of ab and cd. Measurement indicates that the distance of eight atoms in the region of bc is equal to that of seven atoms in the region of ab. This means that there is an interstitial in the region of bc. The situation is the same in the whole zone of SGH. Therefore, the trail of the point defects after intersection between perpendicular pair of right-hand screw dislocations is a row of interstitials. The atomic
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Fig. 3. Intersection between two screw dislocations of same sign: (a) a trail of point defects SGH and an extended jog RS after intersection; (b) schematic drawing of the extended jog RS; (c) the atomic configuration around the point defects SGH on the (1 1¯ 1) plane; (d) the atomic configuration around RS on the (1 1 1) plane.
configuration around the extended jog RS on the (1 1 1) plane is shown in Fig. 3(d). As viewed along the atomic row of abcd, the arrangement of the atoms in the region of bc is closer together than that of ab or cd. The distance of four atoms between ab is equal to that of four 1/3 atoms between bc. Therefore, the extended jog formed in the intersected right-hand screw dislocation is a row of 1/3 interstitials.
3.3. Intersection between screw and edge dislocations with different Burgers vector After a moving dislocation with b1 = [1 1 0]/2 intersects an edge dislocation with b2 = [1¯ 0 1]/2 at R, an extended jog RS forms, as shown in Fig. 4(a). The atomic configuration around the extended jog RS on the (1 1 1) plane is shown in Fig. 4(b). Fig. 4(b) shows that the extended jog contains
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Fig. 4. Intersection between screw and edge dislocations with different Burgers vector: (a) a constriction R formed in the intersected edge dislocation; (b) the atomic configuration around the constriction R corresponding to one 1/3 vacancy on the (1 1 1) plane.
only one 1/3 vacancy, and is in fact a constriction. This is due to high fault energy of aluminum. There are no point defects behind the moving dislocation EF because there is a kink instead of jog in the dislocation EF after intersection, and it will disappear through slip on the (1 1¯ 1) plane. 3.4. Intersection between screw and edge dislocation with the same Burgers vector After the moving screw dislocation with b1 = [1¯ 0 1]/2 intersects the edge dislocation with b2 = b1 = [1¯ 0 1]/2 at R, a constriction R forms, as shown in Fig. 5(a). The two parts of
the moving dislocation EF, i.e. ER and RF, will move on the (1 1¯ 1) plane, and the two parts of the intersected dislocation PQ, i.e. PR and RQ, however, move on the (1 1 1) plane. The constriction R must be kept at the line of intersection of the two slip planes. The independent movement of the four parts of the dislocation converging on R cause the constriction to split into R and R , as shown in Fig. 5(b). The two constrictions of R and R can move along the line of intersection of the two slip planes through the independent movement of the four parts of the dislocation converging on the constrictions of R and R . The two constrictions can meet again, as shown in Fig. 5(c). The moving screw dislocation can pass the edge
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Fig. 5. Intersection between screw and edge dislocations with same Burgers vector: (a) intersecting of the two dislocation at R; (b) two constrictions of R and R moving along the line of intersection of the two slip planes; (c) meeting of the two constrictions; (d) the moving screw dislocation passing the edge dislocation after the two constrictions meeting and annihilating; (e) schematic drawing of the constriction R.
dislocation and move toward only after the two constrictions meet and annihilate, as shown in Fig. 5(d). The schematic drawing of the constriction R is shown in Fig. 5(f). At the line of intersection of the (1 1¯ 1) and (1 1 1) planes the moving screw dislocation CB = Cα + αB on the (1 1¯ 1) plane will react with the edge dislocation CB = Cδ + δB on the (1 1 1) plane, i.e. Cα + αB + αB + Cδ → Cα + αB/δB + C. αB/δB is a stair-rod dislocation.
The atomic configurations around the constrictions of R and R on the (1 1 1) plane are shown in Fig. 6(a) and (b), respectively. Fig. 6 indicates that the constriction R corresponds to 1/3 vacancy, and the constriction R corresponds to 1/3 interstitial. Therefore, the two constrictions corresponding to 1/3 vacancy and 1/3 interstitial, respectively, can annihilate after meeting.
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Fig. 6. The atomic configurations around the constrictions on the (1 1 1) plane: (a) R corresponding to 1/3 vacancy; (b) R corresponding to 1/3 interstitial.
4. Summary
Acknowledgements
After intersection between two screw dislocations, there are an extended jog in the intersected dislocation, which corresponds to a row of 1/3 vacancies for the dislocations of opposite sign or 1/3 interstitials for the dislocations of same sign, and a trail of vacancies or interstitials behind the moving dislocation. After intersection between screw and edge dislocation with different Burgers vector, a constriction corresponding to one 1/3 vacancy forms in the intersected edge dislocation. When a moving screw dislocation intersects an edge dislocation with the same Burgers vector, the point of intersection will split into two constrictions corresponding to 1/3 vacancy and 1/3 interstitial, respectively. The moving dislocation can pass the edge dislocation only after the two constriction, which can move along the line of intersection of the two slip planes, meet and annihilate.
The project was supported by the special Funds for the Major state Basic Research Projects (No. G19990650) and by the National Natural Science Foundation of China (310272020).
References [1] J.P. Hirth, J. Lothe, Theory of Dislocations, Wiley, New York, 1982. [2] L.H. Yang, P. Soderlind, J.A. Moriarty, Mater. Sci. Eng. A 309–310 (2001) 102. [3] G. Lu, N. Kioussis, U.V. Bulatov, E. Kaxiras, Mater. Sci. Eng. A 309–310 (2001) 142. [4] T. Veffe, Mater. Sci. Eng. A 309–310 (2001) 113. [5] S.J. Zhou, D.L. Preston, P.S. Lomdahl, D.M. Beazley, Science 279 (1998) 1417.
M. Li et al. / Materials Science and Engineering A363 (2003) 234–241 [6] S. Swaminarayan, R. LeSar, P. Lomdahl, D. Beazley, J. Mater. Res. 13 (1998) 3478. [7] P. Gumbsch, H. Gao, Science 283 (1999) 965. [8] S. Li, K.W. Gao, L.J. Qiao, F.X. Zhou, W.Y. Chu, Comput. Mater. Sci. 20 (2001) 143. [9] V. Bulator, F.F. Abraham, L. Kubin, B. Devincre, S. Yip, Nature 391 (1998) 669.
241
[10] R.G. Hoagland, M.S. Daw, J.P. Hirth, J. Mater. Res. 6 (1991) 2565. [11] Y. Mishin, D. Farkas, M.J. Mehl, D.A. Papaconstantopoulos, Phys. Rev. B59 (1999) 3393. [12] D.C. Rapaport, The Art of Molecular Dynamics Simulation, Cambridge University Press, Cambridge, 1995.