This section describes the class dislocationSystem.
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| Class Description |
| Edge Dislocations |
| Screw Dislocations |
| Slip Systems |
| Dominant Dislocation Systems |
| The Dislocation Tensor |
| Complete Function list |
Dislocation are microscopic displacements within the regular atom lattice of a crystaline material ussualy as a result of plastic deformation. Dislocations are described by a Burgers vector describing the direction of the atomic shift and a line vector describing the direction of the displacements within the material. One distinguishes two cases:
Here the directions of the atomic shifts are orthogonal to the direction the displacements spread within the material. In order to define a edge dislocation we proceed as follows
% define a crystal symmetry cs = crystalSymmetry('432'); % define a burgers vector in crystal coordinates b = Miller(1,1,0,cs,'uvw') % define a line vector in crystal coordinates l = Miller(1,-1,-2,cs,'uvw') % setup the dislocation system dS = dislocationSystem(b,l)
b = Miller
size: 1 x 1
symmetry: 432
u 1
v 1
w 0
l = Miller
size: 1 x 1
symmetry: 432
u 1
v -1
w -2
dS = dislocationSystem
symmetry: 432
edge dislocations : 1 x 1
Burgers vector line vector energy
[1 1 0] [1 -1 -2] 1
Screw dislocations are characterized by the fact that Burgers vector and line vector are perpendicular to each other.
% define a burgers vector in crystal coordinates b = Miller(1,1,0,cs,'uvw') % define a line vector in crystal coordinates l = Miller(1,1,0,cs,'uvw') % setup the dislocation system dS = dislocationSystem(b,l)
b = Miller
size: 1 x 1
symmetry: 432
u 1
v 1
w 0
l = Miller
size: 1 x 1
symmetry: 432
u 1
v 1
w 0
dS = dislocationSystem
symmetry: 432
screw dislocations: 1 x 1
Burgers vector energy
[1 1 0] 1
Dislocation systems are tightly related to slip systems. Given a set of slip systems the corresponding dislocation systems can be computed by
% dominant slip systems in cubic fcc material sS = symmetrise(slipSystem.fcc(cs)) % the corresponding dislocation systems dS = dislocationSystem(sS)
sS = slipSystem
symmetry: 432
size: 24 x 1
u v w | h k l CRSS
0 1 -1 1 1 1 1
-1 0 1 1 1 1 1
1 -1 0 1 1 1 1
0 -1 1 1 1 1 1
1 0 -1 1 1 1 1
-1 1 0 1 1 1 1
1 -1 0 1 1 -1 1
1 0 1 1 1 -1 1
0 1 1 1 1 -1 1
-1 0 -1 1 1 -1 1
0 -1 -1 1 1 -1 1
-1 1 0 1 1 -1 1
0 1 -1 -1 1 1 1
1 0 1 -1 1 1 1
1 1 0 -1 1 1 1
-1 0 -1 -1 1 1 1
-1 -1 0 -1 1 1 1
0 -1 1 -1 1 1 1
-1 0 1 1 -1 1 1
1 1 0 1 -1 1 1
0 1 1 1 -1 1 1
-1 -1 0 1 -1 1 1
0 -1 -1 1 -1 1 1
1 0 -1 1 -1 1 1
Warning: Miller indices are converted to hkl
dS = dislocationSystem
symmetry: 432
edge dislocations : 24 x 1
Burgers vector line vector energy
[0 1 -1] (2 -1 -1) 2
[-1 0 1] (-1 2 -1) 2
[1 -1 0] (-1 -1 2) 2
[0 -1 1] (-2 1 1) 2
[1 0 -1] (1 -2 1) 2
[-1 1 0] (1 1 -2) 2
[1 -1 0] (1 1 2) 2
[1 0 1] (-1 2 1) 2
[0 1 1] (-2 1 -1) 2
[-1 0 -1] (1 -2 -1) 2
[0 -1 -1] (2 -1 1) 2
[-1 1 0] (-1 -1 -2) 2
[0 1 -1] (2 1 1) 2
[1 0 1] (-1 -2 1) 2
[1 1 0] (1 -1 2) 2
[-1 0 -1] (1 2 -1) 2
[-1 -1 0] (-1 1 -2) 2
[0 -1 1] (-2 -1 -1) 2
[-1 0 1] (1 2 1) 2
[1 1 0] (1 -1 -2) 2
[0 1 1] (2 1 -1) 2
[-1 -1 0] (-1 1 2) 2
[0 -1 -1] (-2 -1 1) 2
[1 0 -1] (-1 -2 -1) 2
screw dislocations: 6 x 1
Burgers vector energy
(0 -1 -1) 1
(0 -1 1) 1
(-1 1 0) 1
(1 0 1) 1
(1 1 0) 1
(1 0 -1) 1
dS = dislocationSystem.bcc(cs)
Warning: Miller indices are converted to hkl
dS = dislocationSystem
symmetry: 432
edge dislocations : 48 x 1
Burgers vector line vector energy
[1 -1 1] (-2 -1 1) 2
[1 1 -1] (2 -1 1) 2
[1 1 -1] (1 -2 -1) 2
[-1 1 1] (1 2 -1) 2
[1 -1 1] (-1 1 2) 2
[-1 1 1] (-1 1 -2) 2
[1 -1 1] (1 2 1) 2
[1 1 1] (-1 2 -1) 2
[1 1 -1] (1 1 2) 2
[1 1 1] (-1 -1 2) 2
[-1 1 1] (2 1 1) 2
[1 1 1] (2 -1 -1) 2
[-1 1 1] (0 1 -1) 2
[1 -1 1] (-1 0 1) 2
[1 1 -1] (1 -1 0) 2
[-1 1 1] (-1 0 -1) 2
[1 -1 1] (-1 -1 0) 2
[1 1 -1] (0 -1 -1) 2
[1 1 -1] (1 0 1) 2
[-1 1 1] (1 1 0) 2
[1 -1 1] (0 1 1) 2
[-1 -1 -1] (0 -1 1) 2
[-1 -1 -1] (1 0 -1) 2
[-1 -1 -1] (-1 1 0) 2
[-1 1 1] (-1 4 -5) 2
[1 -1 1] (-5 -1 4) 2
[1 1 -1] (4 -5 -1) 2
[-1 1 1] (-4 1 -5) 2
[1 -1 1] (-5 -4 1) 2
[1 1 -1] (1 -5 -4) 2
[1 1 -1] (4 1 5) 2
[-1 1 1] (5 4 1) 2
[1 -1 1] (1 5 4) 2
[-1 -1 -1] (-1 -4 5) 2
[-1 -1 -1] (5 -1 -4) 2
[-1 -1 -1] (-4 5 -1) 2
[1 -1 1] (1 -4 -5) 2
[1 1 -1] (-5 1 -4) 2
[-1 1 1] (-4 -5 1) 2
[1 -1 1] (4 -1 -5) 2
[1 1 -1] (-5 4 -1) 2
[-1 1 1] (-1 -5 4) 2
[-1 -1 -1] (-4 -1 5) 2
[-1 -1 -1] (5 -4 -1) 2
[-1 -1 -1] (-1 5 -4) 2
[1 1 -1] (1 4 5) 2
[-1 1 1] (5 1 4) 2
[1 -1 1] (4 5 1) 2
screw dislocations: 4 x 1
Burgers vector energy
(-1 -1 -1) 1
(1 -1 1) 1
(-1 1 1) 1
(1 1 -1) 1
As each dislocation corresponds to an deformation of the atom lattice a dislocation can also be described by a deformation matrix. This matrix is the dyadic product between the Burgers vector and the line vector and can be computed by
dS.tensor
ans = dislocationDensityTensor size : 52 x 1 unit : au rank : 2 (3 x 3) mineral: 432
The unit of the deformation tensor is the unit of the burgers vector which is assumet to be au in MTEX.
| Syntax | |
| dS = dislocationSystem(b,l) | |
| dS = dislocationSystem(sS) | |
| Input | |
| b | @Miller Burgers vector |
| n | @Miller line vector |
| sS | @slipSystem |
| pr | poisson ratio |
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