.. _crystal:

Crystal Structures
==================

.. _slip_systems:

Slip Systems
------------

:data:`bcc`-type :math:`\left\{1 1 0\right\}\left<1 1 1\right>` slip systems:
  :math:`(0 1 \bar 1)[1 1 1],\,(1 0 \bar 1)[1 1 1],\,(1 \bar 1 0)[1 1 1],\,(0 1 1)[1 1 \bar 1],\,(1 0 1)[1 1 \bar 1],\,(1 \bar 1 0)[1 1 \bar 1],` :math:`(0 1 1)[1 \bar 1 1],\,(1 0 \bar 1)[1 \bar 1 1],\,(1 1 0)[1 \bar 1 1],\,(0 1 \bar 1)[1 \bar 1 \bar 1],\,(1 0 1)[1 \bar 1 \bar 1],\,(1 1 0)[1 \bar 1 \bar 1]`.

:data:`fcc`-type, :math:`\left\{1 1 1\right\}\left<1 1 0\right>` slip systems:
  :math:`(1 1 1)[0 1 \bar 1],\,(1 1 1)[1 0 \bar 1],\,(1 1 1)[1 \bar 1 0],\,(1 1 \bar 1)[0 1 1],\,(1 1 \bar 1)[1 0 1],\,(1 1 \bar 1)[1 \bar 1 0],\,` :math:`(1 \bar 1 1)[0 1 1],\,(1 \bar 1 1)[1 0 \bar 1],\,(1 \bar 1 1)[1 1 0],\,(1 \bar 1 \bar 1)[0 1 \bar 1],\,(1 \bar 1 \bar 1)[1 0 1],\,(1 \bar 1 \bar 1)[1 1 0]`.

:data:`hcp`-type slip families:
  basal, prismatic, pyramidal.

:data:`hcp`-type slip systems (in the order basal, prismatic, pyramidal):
  :math:`(0 0 0 1)[2 \bar 1 \bar 1 0],\,(0 0 0 1)[\bar 1 2 \bar 1 0],\,(0 0 0 1)[\bar 1 \bar 1 2 0],\,(0 1 \bar 1 0)[2 \bar 1 \bar 1 0],\,(\bar 1 0 1 0)[\bar 1 2 \bar 1 0],\,(1 \bar 1 0 0)[\bar 1 \bar 1 2 0],\,` :math:`(1 0 \bar 1 1)[\bar 2 1 1 3],\,(1 0 \bar 1 1)[\bar 1 \bar 1 2 3],\,(0 1 \bar 1 1)[\bar 1 \bar 1 2 3],\,(0 1 \bar 1 1)[1 \bar 2 1 3],\,(\bar 1 1 0 1)[1 \bar 2 1 3],\,(\bar 1 1 0 1)[2 \bar 1 \bar 1 3],\,` :math:`(\bar 1 0 1 1)[2 \bar 1 \bar 1 3],\,(\bar 1 0 1 1)[1 1 \bar 2 3],\,(0 \bar 1 1 1)[1 1 \bar 2 3],\,(0 \bar 1 1 1)[\bar 1 2 \bar 1 3],\,(1 \bar 1 0 1)[\bar 1 2 \bar 1 3],\,(1 \bar 1 0 1)[\bar 2 1 1 3]`.

:data:`bct`-type slip families:
  :math:`\left\{100\right)\left<001\right]`, :math:`\left\{110\right)\left<001\right]`, :math:`\left\{100\right)\left<010\right]`, :math:`\left\{110\right)\left<1 \bar 11\right]`, :math:`\left\{110\right)\left<1 \bar10\right]`, :math:`\left\{100\right)\left<011\right]`, :math:`\left\{001\right)\left<010\right]`, :math:`\left\{001\right)\left<110\right]`, :math:`\left\{011\right)\left<01 \bar 1\right]` and :math:`\left\{211\right)\left<01 \bar 1\right]`.

:data:`bct`-type slip systems:
  :math:`(1 0 0)[0 0 1],\,(0 1 0)[0 0 1],\,(1 1 0)[0 0 1],\,(1 \bar 1 0)[0 0 1],\,(1 0 0)[0 1 0],\,(0 1 0)[1 0 0],` :math:`(1 1 0)[1 \bar 1 1],\,(1 1 0)[\bar 1 1 1],\,(1 \bar 1 0)[1 1 1],\,(1 \bar 1 0)[\bar 1 \bar 1 1],\,(1 1 0)[\bar 1 1 0],\,(1 \bar 1 0)[1 1 0],` :math:`(1 0 0)[0 1 1],\,(1 0 0)[0 1 \bar 1],\,(0 1 0)[1 0 1],\,(0 1 0)[1 0 \bar 1],\,(0 0 1)[1 1 0],\,(0 0 1)[1 \bar 1 0],` :math:`(0 0 1)[1 1 0],\,(0 0 1)[1 \bar 1 0],\,(1 0 1)[1 0 \bar 1],\,(1 0 \bar 1)[1 0 1],\,(0 1 1)[0 1 \bar 1],\,(0 1 \bar 1)[0 1 1],` :math:`(1 2 1)[\bar 1 0 1],\,(\bar 1 2 1)[1 0 1],\,(\bar 1 \bar 2 1)[1 0 1],\,(1 \bar 2 1)[\bar 1 0 1],\,(2 1 1)[0 \bar 1 1],\,(\bar 2 1 1)[0 \bar 1 1],` :math:`(\bar 2 \bar 1 1)[0 1 1],\,(2 \bar 1 1)[0 1 1].`