Body-centered cubic (cI)#

Atom arrangement#

Figure 1: Body-centered cubic lattice structure.

Slip systems#

index
slip direction
plane normal
\(1\)\([ 1 \bar 1 1]\)\(( 0 1 1)\)
\(2\)\([\bar 1 \bar 1 1]\)\(( 0 1 1)\)
\(3\)\([ 1 1 1]\)\(( 0 \bar 1 1)\)
\(4\)\([\bar 1 1 1]\)\(( 0 \bar 1 1)\)
\(5\)\([\bar 1 1 1]\)\(( 1 0 1)\)
\(6\)\([\bar 1 \bar 1 1]\)\(( 1 0 1)\)
\(7\)\([ 1 1 1]\)\((\bar 1 0 1)\)
\(8\)\([ 1 \bar 1 1]\)\((\bar 1 0 1)\)
\(9\)\([\bar 1 1 1]\)\(( 1 1 0)\)
\(10\)\([\bar 1 1 \bar 1]\)\(( 1 1 0)\)
\(11\)\([ 1 1 1]\)\((\bar 1 1 0)\)
\(12\)\([ 1 1 \bar 1]\)\((\bar 1 1 0)\)
../../_images/cI_slip_system_(110).svg

Figure 2: \(\{1 1 0\}\) slip system#

index
slip direction
plane normal
\(13\)\([\bar 1 1 1]\)\(( 2 1 1)\)
\(14\)\([ 1 1 1]\)\((\bar 2 1 1)\)
\(15\)\([ 1 1 \bar 1]\)\(( 2 \bar 1 1)\)
\(16\)\([ 1 \bar 1 1]\)\(( 2 1 \bar 1)\)
\(17\)\([ 1 \bar 1 1]\)\(( 1 2 1)\)
\(18\)\([ 1 1 \bar 1]\)\((\bar 1 2 1)\)
\(19\)\([ 1 1 1]\)\(( 1 \bar 2 1)\)
\(20\)\([\bar 1 1 1]\)\(( 1 2 \bar 1)\)
\(21\)\([ 1 1 \bar 1]\)\(( 1 1 2)\)
\(22\)\([ 1 \bar 1 1]\)\((\bar 1 1 2)\)
\(23\)\([\bar 1 1 1]\)\(( 1 \bar 1 2)\)
\(24\)\([ 1 1 1]\)\(( 1 1 \bar 2)\)
../../_images/cI_slip_system_(112).svg

Figure 3: \(\{1 1 2\}\) slip system#

index
slip direction
plane normal
\(25\)\([ 1 1 \bar 1]\)\(( 1 2 3)\)
\(26\)\([ 1 \bar 1 1]\)\((\bar 1 2 3)\)
\(27\)\([\bar 1 1 1]\)\(( 1 \bar 2 3)\)
\(28\)\([ 1 1 1]\)\(( 1 2 \bar 3)\)
\(29\)\([ 1 \bar 1 1]\)\(( 1 3 2)\)
\(30\)\([ 1 1 \bar 1]\)\((\bar 1 3 2)\)
\(31\)\([ 1 1 1]\)\(( 1 \bar 3 2)\)
\(32\)\([\bar 1 1 1]\)\(( 1 3 \bar 2)\)
\(33\)\([ 1 1 \bar 1]\)\(( 2 1 3)\)
\(34\)\([ 1 \bar 1 1]\)\((\bar 2 1 3)\)
\(35\)\([\bar 1 1 1]\)\(( 2 \bar 1 3)\)
\(36\)\([ 1 1 1]\)\(( 2 1 \bar 3)\)
\(37\)\([ 1 \bar 1 1]\)\(( 2 3 1)\)
\(38\)\([ 1 1 \bar 1]\)\((\bar 2 3 1)\)
\(39\)\([ 1 1 1]\)\(( 2 \bar 3 1)\)
\(40\)\([\bar 1 1 1]\)\(( 2 3 \bar 1)\)
\(41\)\([\bar 1 1 1]\)\(( 3 1 2)\)
\(42\)\([ 1 1 1]\)\((\bar 3 1 2)\)
\(43\)\([ 1 1 \bar 1]\)\(( 3 \bar 1 2)\)
\(44\)\([ 1 \bar 1 1]\)\(( 3 1 \bar 2)\)
\(45\)\([\bar 1 1 1]\)\(( 3 2 1)\)
\(46\)\([ 1 1 1]\)\((\bar 3 2 1)\)
\(47\)\([ 1 1 \bar 1]\)\(( 3 \bar 2 1)\)
\(48\)\([ 1 \bar 1 1]\)\(( 3 2 \bar 1)\)

Twin systems#

index
slip direction
plane normal
\(1\)\([\bar 1 1 1]\)\((2 1 1)\)
\(2\)\([1 1 1]\)\((\bar 2 1 1)\)
\(3\)\([1 1 \bar 1]\)\((2 \bar 1 1)\)
\(4\)\([1 \bar 1 1]\)\((2 1 \bar 1)\)
\(5\)\([1 \bar 1 1]\)\((1 2 1)\)
\(6\)\([1 1 \bar 1]\)\((\bar 1 2 1)\)
\(7\)\([1 1 1]\)\((1 \bar 2 1)\)
\(8\)\([\bar 1 1 1]\)\((1 2 \bar 1)\)
\(9\)\([1 1 \bar 1]\)\((1 1 2)\)
\(10\)\([1 \bar 1 1]\)\((\bar 1 1 2)\)
\(11\)\([\bar 1 1 1]\)\((1 \bar 1 2)\)
\(12\)\([1 1 1]\)\((1 1 \bar 2)\)

Interaction Matrices#

Slip-Slip#

index
label
description
\(1\)\(\alpha_0^\prime\)self interaction
\(2\)\(\alpha_1\)coli\(_{90^\circ}\)
\(3\)\(\alpha_2\)coplanar
\(4\)\(\alpha_3\)\(\)
\(5\)\(\alpha_3^\ast\)\(\)
\(6\)\(\alpha_4\)\(\)
\(7\)\(\alpha_5\)\(\)
\(8\)\(\alpha_6\)coli\(_{60^\circ}\)
\(9\)\(\alpha_7\)coli\(_{30^\circ}\)
\(10\)\(\alpha_8\)\(\)
\(11\)\(\alpha_8^\ast\)\(\)
\(12\)\(\alpha_9\)\(\)
\(13\)\(\alpha_9^\ast\)\(\)
\(14\)\(\alpha_{10}\)\(\)
\(15\)\(\alpha_{10}^\ast\)\(\)
\(16\)\(\alpha_{11}\)\(\)
\(17\)\(\alpha_{11}^\ast\)\(\)
\(18\)\(\alpha_{12}\)\(\)
\(19\)\(\alpha_{12}^\ast\)\(\)
\(20\)\(\alpha_{13}\)\(\)
\(21\)\(\alpha_{14}\)\(\)
\(22\)\(\alpha_{14}^\ast\)\(\)
\(23\)\(\alpha_{15}\)\(\)
\(24\)\(\alpha_{16}\)\(\)
\(25\)\(-\)\(\)
\(26\)\(-\)\(\)
\(27\)\(-\)\(\)
\(28\)\(-\)\(\)
  • 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.