Body-Centered Cubic (cI)#
Stiffness Matrix#
Atom Arrangement#
Figure 1: Body-centered cubic lattice structure
Slip Systems#
index |
slip direction |
plane normal |
|---|---|---|
1 |
\([ 1 \bar 1 1]\) |
\(( 0 1 1)\) |
2 |
\([ 1 \bar 1 1]\) |
\(( 1 0 \bar 1)\) |
3 |
\([ 1 \bar 1 1]\) |
\((\bar 1 \bar 1 0)\) |
4 |
\([\bar 1 \bar 1 1]\) |
\(( 0 \bar 1 \bar 1)\) |
5 |
\([\bar 1 \bar 1 1]\) |
\(( 1 0 1)\) |
6 |
\([\bar 1 \bar 1 1]\) |
\((\bar 1 1 0)\) |
7 |
\([ 1 1 1]\) |
\(( 0 1 \bar 1)\) |
8 |
\([ 1 1 1]\) |
\((\bar 1 0 1)\) |
9 |
\([ 1 1 1]\) |
\(( 1 \bar 1 0)\) |
10 |
\([\bar 1 1 1]\) |
\(( 0 \bar 1 1)\) |
11 |
\([\bar 1 1 1]\) |
\((\bar 1 0 \bar 1)\) |
12 |
\([\bar 1 1 1]\) |
\(( 1 1 0)\) |
Figure 2: \(\{1 1 0\}\) slip system
index |
slip direction |
plane normal |
|---|---|---|
13 |
\([ 1 \bar 1 1]\) |
\(( 2 1 \bar 1)\) |
14 |
\([ 1 \bar 1 1]\) |
\((\bar 1 1 2)\) |
15 |
\([ 1 \bar 1 1]\) |
\(( 1 2 1)\) |
16 |
\([\bar 1 \bar 1 1]\) |
\(( 2 \bar 1 1)\) |
17 |
\([\bar 1 \bar 1 1]\) |
\(( 1 1 2)\) |
18 |
\([\bar 1 \bar 1 1]\) |
\((\bar 1 2 1)\) |
19 |
\([ 1 1 1]\) |
\(( 1 1 \bar 2)\) |
20 |
\([ 1 1 1]\) |
\(( 1 \bar 2 1)\) |
21 |
\([ 1 1 1]\) |
\((\bar 2 1 1)\) |
22 |
\([\bar 1 1 1]\) |
\(( 1 \bar 1 2)\) |
23 |
\([\bar 1 1 1]\) |
\(( 1 2 \bar 1)\) |
24 |
\([\bar 1 1 1]\) |
\(( 2 1 1)\) |
Figure 3: \(\{1 1 2\}\) slip system
index |
slip direction |
plane normal |
|---|---|---|
25 |
\([ 1 \bar 1 1]\) |
\((\bar 1 2 3)\) |
26 |
\([ 1 \bar 1 1]\) |
\(( 1 3 2)\) |
27 |
\([ 1 \bar 1 1]\) |
\((\bar 2 1 3)\) |
28 |
\([ 1 \bar 1 1]\) |
\(( 2 3 1)\) |
29 |
\([ 1 \bar 1 1]\) |
\(( 3 1 \bar 2)\) |
30 |
\([ 1 \bar 1 1]\) |
\(( 3 2 \bar 1)\) |
31 |
\([\bar 1 \bar 1 1]\) |
\(( 1 2 3)\) |
32 |
\([\bar 1 \bar 1 1]\) |
\((\bar 1 3 2)\) |
33 |
\([\bar 1 \bar 1 1]\) |
\(( 2 1 3)\) |
34 |
\([\bar 1 \bar 1 1]\) |
\((\bar 2 3 1)\) |
35 |
\([\bar 1 \bar 1 1]\) |
\(( 3 \bar 1 2)\) |
36 |
\([\bar 1 \bar 1 1]\) |
\(( 3 \bar 2 1)\) |
37 |
\([ 1 1 1]\) |
\(( 1 2 \bar 3)\) |
38 |
\([ 1 1 1]\) |
\(( 1 \bar 3 2)\) |
39 |
\([ 1 1 1]\) |
\(( 2 1 \bar 3)\) |
40 |
\([ 1 1 1]\) |
\(( 2 \bar 3 1)\) |
41 |
\([ 1 1 1]\) |
\((\bar 3 1 2)\) |
42 |
\([ 1 1 1]\) |
\((\bar 3 2 1)\) |
43 |
\([\bar 1 1 1]\) |
\(( 1 \bar 2 3)\) |
44 |
\([\bar 1 1 1]\) |
\(( 1 3 \bar 2)\) |
45 |
\([\bar 1 1 1]\) |
\(( 2 \bar 1 3)\) |
46 |
\([\bar 1 1 1]\) |
\(( 2 3 \bar 1)\) |
47 |
\([\bar 1 1 1]\) |
\(( 3 1 2)\) |
48 |
\([\bar 1 1 1]\) |
\(( 3 2 1)\) |
Twin systems#
index |
slip direction |
plane normal |
|---|---|---|
1 |
\([ 1 \bar 1 1]\) |
\(( 2 1 \bar 1)\) |
2 |
\([ 1 \bar 1 1]\) |
\((\bar 1 1 2)\) |
3 |
\([ 1 \bar 1 1]\) |
\(( 1 2 1)\) |
4 |
\([\bar 1 \bar 1 1]\) |
\(( 2 \bar 1 1)\) |
5 |
\([\bar 1 \bar 1 1]\) |
\(( 1 1 2)\) |
6 |
\([\bar 1 \bar 1 1]\) |
\((\bar 1 2 1)\) |
7 |
\([ 1 1 1]\) |
\(( 1 1 \bar 2)\) |
8 |
\([ 1 1 1]\) |
\(( 1 \bar 2 1)\) |
9 |
\([ 1 1 1]\) |
\((\bar 2 1 1)\) |
10 |
\([\bar 1 1 1]\) |
\(( 1 \bar 1 2)\) |
11 |
\([\bar 1 1 1]\) |
\(( 1 2 \bar 1)\) |
12 |
\([\bar 1 1 1]\) |
\(( 2 1 1)\) |
Cleavage Systems#
index |
slip direction |
plane normal |
|---|---|---|
1 |
\([010]\) |
\((100)\) |
2 |
\([001]\) |
\((010)\) |
3 |
\([100]\) |
\((001)\) |
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Figure 4: \(\{1 0 0\}\) cleavage system
Interaction Matrices#
Slip-Slip#
index |
label |
description |
|---|---|---|
1 |
\(h_0^\prime\) |
\(\text{self interaction}\) |
2 |
\(h_1\) |
\(\text{coli}_{60^\circ}\) |
3 |
\(h_2\) |
\(\text{coplanar}\) |
4 |
\(h_3\) |
|
5 |
\(h_3^\ast\) |
\(\text{J}_{1}\) |
6 |
\(h_4\) |
\(\text{J}_{2}\) |
7 |
\(h_5\) |
\(\text{J}_{3}\) |
8 |
\(h_6\) |
\(\text{coli}_{90^\circ}\) |
9 |
\(h_7\) |
\(\text{coli}_{30^\circ}\) |
10 |
\(h_8\) |
|
11 |
\(h_8^\ast\) |
\(\text{J}_{4}\) |
12 |
\(h_9\) |
|
13 |
\(h_9^\ast\) |
\(\text{J}_{5}\) |
14 |
\(h_{10}\) |
|
15 |
\(h_{10}^\ast\) |
\(\text{J}_{6}\) |
16 |
\(h_{11}\) |
|
17 |
\(h_{11}^\ast\) |
\(\text{J}_{7}\) |
18 |
\(h_{12}\) |
|
19 |
\(h_{12}^\ast\) |
\(\text{J}_{8}\) |
20 |
\(h_{13}\) |
\(\text{J}_{9}\) |
21 |
\(h_{14}\) |
|
22 |
\(h_{14}^\ast\) |
\(\text{J}_{10}\) |
23 |
\(h_{15}\) |
\(\text{J}_{11}\) |
24 |
\(h_{16}\) |
\(\text{J}_{12}\) |
25 |
\(-\) |
\(\{1 1 0\}\) - \(\{1 1 2\}\) collinear |
26 |
\(-\) |
\(\{1 1 2\}\) - \(\{1 2 3\}\) collinear |
27 |
\(-\) |
\(\{1 2 3\}\) - \(\{1 2 3\}\) collinear |
28 |
\(-\) |
R. Madec and L.P. Kubin. Dislocation strengthening in FCC metals and in BCC metals at high temperatures Acta Materialia, 126:166-173, 2017. doi:10.1016/j.actamat.2016.12.040.