J. Mater. Sci. Technol. ›› 2019, Vol. 35 ›› Issue (11): 2714-2726.DOI: 10.1016/j.jmst.2019.05.052
• Research Article • Previous Articles Next Articles
Zhipeng Suna, Fuzhi Daib, Ben Xuac, Wenzheng Zhanga*()
Received:
2019-03-23
Revised:
2019-04-21
Accepted:
2019-05-20
Online:
2019-11-05
Published:
2019-11-23
Contact:
Zhang Wenzheng
Zhipeng Sun, Fuzhi Dai, Ben Xu, Wenzheng Zhang. Dislocation-mediated migration of nterphase boundaries[J]. J. Mater. Sci. Technol., 2019, 35(11): 2714-2726.
Fig. 1. Geometry of the simulation cell used in the present simulation. The orientation of the simulation cell: x: dislocation line direction; z: interface normal. Periodic boundary conditions were enforced in x and y directions. Vacuum regions are created above and below the entire system in order to allow free relaxation of the system in the z direction. a1 and a2 are the smallest lattice vectors along the x and y directions, respectively, after the addition of a small strain for meeting periodic boundary conditions.
IPBs | OR | b | p | ξ | n | d (?) | |
---|---|---|---|---|---|---|---|
δp | δd | ||||||
OIF1 | 0.91° | 2.94° | [[101]]f/2|[[111]]b/2 | (-111)f|(-101)b | [0.79 0.20 0.58]f | (-0.30,-0.70,0.65)f | 14.1 |
OIF2 | 0.53° | 0.53° | [[101]]f/2|[[111]]b/2 | (11-1)f|(10-1)b | [0.79,-0.20,0.58]f | (-0.53,-0.71,0.46)f | 10.2 |
OIF3 | 2.94° | 0.91° | [[011]]f/2|[-[111]]b/2 | (11-1)f|(10-1)b | [0.79,-0.20,0.58]f | (-0.55,0.18,0.81)f | 19.1 |
OIF4 | 1.33° | 0.62° | [ | (11-1)f|(10-1)b | [0.79,-0.20,0.58]f | (-0.62,-0.19,0.77)f | 23.2 |
OIF5 | 0.98° | 5.26° | [ | (20-2)f|(11-2)b | [-0.58,-0.57,-0.58]f | (-0.41,-0.41,0.81)f | 29.4 |
SIF1 | 0.91° | 2.94° | [[011]]f/2|[-[111]]b/2 [ | (-111)f|(-101)b | [0.79 0.20 0.58]f | (0.59,0.02,-0.81)f | 19.7 56.2 |
SIF2 | 2.94° | 0.91° | [[101]]f/2|[[111]]b/2 [ | (11-1)f|(10-1)b | [0.79,-0.20,0.58]f | (0.57,0.61,-0.55)f | 13.3 37.9 |
Table 1 Crystallographic features of different IPBs examined in this work.
IPBs | OR | b | p | ξ | n | d (?) | |
---|---|---|---|---|---|---|---|
δp | δd | ||||||
OIF1 | 0.91° | 2.94° | [[101]]f/2|[[111]]b/2 | (-111)f|(-101)b | [0.79 0.20 0.58]f | (-0.30,-0.70,0.65)f | 14.1 |
OIF2 | 0.53° | 0.53° | [[101]]f/2|[[111]]b/2 | (11-1)f|(10-1)b | [0.79,-0.20,0.58]f | (-0.53,-0.71,0.46)f | 10.2 |
OIF3 | 2.94° | 0.91° | [[011]]f/2|[-[111]]b/2 | (11-1)f|(10-1)b | [0.79,-0.20,0.58]f | (-0.55,0.18,0.81)f | 19.1 |
OIF4 | 1.33° | 0.62° | [ | (11-1)f|(10-1)b | [0.79,-0.20,0.58]f | (-0.62,-0.19,0.77)f | 23.2 |
OIF5 | 0.98° | 5.26° | [ | (20-2)f|(11-2)b | [-0.58,-0.57,-0.58]f | (-0.41,-0.41,0.81)f | 29.4 |
SIF1 | 0.91° | 2.94° | [[011]]f/2|[-[111]]b/2 [ | (-111)f|(-101)b | [0.79 0.20 0.58]f | (0.59,0.02,-0.81)f | 19.7 56.2 |
SIF2 | 2.94° | 0.91° | [[101]]f/2|[[111]]b/2 [ | (11-1)f|(10-1)b | [0.79,-0.20,0.58]f | (0.57,0.61,-0.55)f | 13.3 37.9 |
Fig. 3. Plots of system potential energy vs. time for (a) OIF1-OIF4 and (b) OIF5 and SIF1. The slopes of the curves are proportional to the migration rates of the interphase boundaries.
IPBs | S1 | θ1 | S2 | θ2 | vIPB (m/s) |
---|---|---|---|---|---|
OIF1 | (-111)f|(-101)b | 71.4° | - | - | 64.5 |
OIF2 | (11-1)f|(01-1)b | 10.6° | - | - | 6.67 |
OIF3 | (11-1)f|(01-1)b | 46.7° | - | - | 107 |
OIF4 | (11-1)f|(01-1)b | 25.3° | (11-1)f|(01-1)b | 25.3° | 30.2 |
OIF5 | (10-1)f|(11-2)b | 29.8° | (0-11)f|(1-12)b | 29.3° | 12.0 |
SIF1 | (12-2)f|(-13-2)b | 41.9° | (-17-1)f|(-43-1)b | 87.0° | 47.9 |
SIF2 | (-1-11)f|(0-11)b | 2.7° | (-122)f|(-314)b | 82.0° | 0.0 |
Table 2 Migration rate and related parameters of different IPBs.
IPBs | S1 | θ1 | S2 | θ2 | vIPB (m/s) |
---|---|---|---|---|---|
OIF1 | (-111)f|(-101)b | 71.4° | - | - | 64.5 |
OIF2 | (11-1)f|(01-1)b | 10.6° | - | - | 6.67 |
OIF3 | (11-1)f|(01-1)b | 46.7° | - | - | 107 |
OIF4 | (11-1)f|(01-1)b | 25.3° | (11-1)f|(01-1)b | 25.3° | 30.2 |
OIF5 | (10-1)f|(11-2)b | 29.8° | (0-11)f|(1-12)b | 29.3° | 12.0 |
SIF1 | (12-2)f|(-13-2)b | 41.9° | (-17-1)f|(-43-1)b | 87.0° | 47.9 |
SIF2 | (-1-11)f|(0-11)b | 2.7° | (-122)f|(-314)b | 82.0° | 0.0 |
Fig. 4. MD snapshots of OIF3 interface migration. The core structure of interfacial dislocations extends to small stacking faults. The crystal structure of each atom is identified by the a-CNA (adaptive common neighbor analysis). Green: fcc atoms; Blue: bcc atoms; Red: HCP atoms; White: unknown structure.
Fig. 5. MD snapshots of interfacial dislocation behaviors corresponding to uniform interface migration process for (a) OIF1, (b) OIF2, (c) OIF3 and (d) OIF4, where the atoms near the dislocation cores with Burgers vectors 1/2[[101]]f|1/2[[111]]b and 1/2[[011]]f|1/2[$\bar{1}$11]b are colored orange and green, respectively. In this figure, the positions of the atoms near the interfacial dislocation core are depicted at different simulation times. The fcc and bcc atoms are not present here.
Fig. 6. MD snapshots showing shear-coupled interface migration of OIF1 O-line interface. Shear deformation can be clearly observed in the transformed region. Atoms in the small dashed box in the left-hand image will be selected as samples for calculation of the atomic displacement (described in the text). Green: fcc atoms; Blue: bcc atoms; White: unrecognized structure.
IPBs | Direction of shear | Magnitude of shear | ||||
---|---|---|---|---|---|---|
Present work | PTMC | Angular difference | Present work | PTMC | Discrepancy | |
OIF1 | [-0.12 -0.42 -0.90]f | [-0.13 -0.44 -0.89]f | 1.5° | 0.3009 | 0.2851 | 1.58% |
OIF2 | [0.78 -0.13 0.61]f | [0.79 -0.11 0.60]f | 1.5° | 0.9184 | 1.0954 | 17.70% |
OIF3 | [-0.71 0.19 -0.68]f | [-0.70 0.20 -0.69]f | 2.4° | 0.3815 | 0.4755 | 9.40% |
OIF4 | [-0.57 0.26 -0.78]f | [-0.60 0.27 -0.75]f | 1.6° | 0.2680 | 0.2851 | 1.71% |
Table 3 Comparison of the macroscopic shear characteristics determined from the present simulation and PTMC.
IPBs | Direction of shear | Magnitude of shear | ||||
---|---|---|---|---|---|---|
Present work | PTMC | Angular difference | Present work | PTMC | Discrepancy | |
OIF1 | [-0.12 -0.42 -0.90]f | [-0.13 -0.44 -0.89]f | 1.5° | 0.3009 | 0.2851 | 1.58% |
OIF2 | [0.78 -0.13 0.61]f | [0.79 -0.11 0.60]f | 1.5° | 0.9184 | 1.0954 | 17.70% |
OIF3 | [-0.71 0.19 -0.68]f | [-0.70 0.20 -0.69]f | 2.4° | 0.3815 | 0.4755 | 9.40% |
OIF4 | [-0.57 0.26 -0.78]f | [-0.60 0.27 -0.75]f | 1.6° | 0.2680 | 0.2851 | 1.71% |
Fig. 7. Illustration of displacement of atoms in dashed box in Fig. 5 during interface migration: (a) real atomic displacements (di) during the migration of the OIF1 O-line interface (black arrow); (b) distribution of Txi-di for the OIF1 O-line interface (blue arrow). The two solid boxes show the relationship between the correlated Burgers vectors and correlated planes, respectively; (c) schematic plot of the atomic displacement distribution during the migration of the OIF1 O-line interface, where p=Δgu’xi/Δgu’bb and gbu’xi/gbu’$x^{O}_{\perp}$=n+k.
Fig. 8. MD images of interfacial dislocation behavior corresponding to “stick-slip” interface migration for (a, b) OIF5 and (c, d) SIF1. (b) illustrates the detailed dislocation reactions during the migration of OIF5. (d) shows the interface morphology of SIF1 at 300 ps. Dark yellow atoms: dislocations with Burgers vector 1/2[101]f|1/2[111]b; green atoms: dislocations with Burgers vector 1/2[011]f|1/2[$\bar{1}$11]b; violet atoms: dislocations with Burgers vector 1/2[1$\bar{1}$0]f|[100]b; black atoms: dislocations with Burgers vector 1/2[10$\bar{1}$]f|1/2[11$\bar{1}$]b; pink atoms: bcc atoms.
Fig. 9. Illustration of the atomic displacements during SIF1 migration: (a) schematic plot of the atomic displacements distribution during interface migration; (b) distribution of Txi-di (arrow in blue color).
IPBs | Cell size(nm3) | Number of atoms |
---|---|---|
OIF1 | 12.7*19.8*12.0 | 243808 |
OIF2 | 12.7*13.8*12.0 | 169517 |
OIF3 | 12.7*12.3*12.0 | 151160 |
OIF4 | 12.7*15.0*12.0 | 184371 |
OIF5 | 19.6*15.7*12.0 | 299823 |
SIF1 | 12.7*31.7*12.0 | 388350 |
SIF2 | 12.7*35.8*12.0 | 440833 |
Table A1. Simulation cell size and number of atoms for each IPB.
IPBs | Cell size(nm3) | Number of atoms |
---|---|---|
OIF1 | 12.7*19.8*12.0 | 243808 |
OIF2 | 12.7*13.8*12.0 | 169517 |
OIF3 | 12.7*12.3*12.0 | 151160 |
OIF4 | 12.7*15.0*12.0 | 184371 |
OIF5 | 19.6*15.7*12.0 | 299823 |
SIF1 | 12.7*31.7*12.0 | 388350 |
SIF2 | 12.7*35.8*12.0 | 440833 |
Fig. B1. Snapshots of the OIF1 O-line interface during relaxation at various temperatures: (a) 900 K. (b) 1100 K. (c) 1300 K. Green: fcc; Blue: bcc; White: cannot be identified, usually refers to the atoms around defects or severely off-site due to thermal vibration.
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