International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2006). Vol. D. ch. 3.4, pp. 486-489

Table 3.4.3.6 

V. Janoveca* and J. Přívratskáb

a Department of Physics, Technical University of Liberec, Hálkova 6, 461 17 Liberec 1, Czech Republic, and bDepartment of Mathematics and Didactics of Mathematics, Technical University of Liberec, Hálkova 6, 461 17 Liberec 1, Czech Republic
Correspondence e-mail:  janovec@fzu.cz

Table 3.4.3.6 | top | pdf |
Ferroelastic domain pairs and twins with compatible walls

[F_1:] symmetry of [{\bf S}_1]; [g_{1j}]: twinning operations; [K_{1j}]: twinning group; Axis: axis of domain pair; Equation: direction of the axis; [\varphi ]: disorientation angle; [{\sf \overline J}_{1j} ]: symmetry of the twin pair; [{\underline t}_{1j}^{\star}]: twinning operation; [{\sf \overline T}_{1j}]: symmetry of the twin and wall, twin law of the twin; Classification: see Table 3.4.4.3[link].

[F_1 ] [g_{1j} ] [K_{1j}] Axis Equation Wall normals [\varphi] [{\sf \overline J}_{1j}] [\underline t^{\star}_{1j} ] [{\sf\overline T}_{1j}] Classification
1 [2^{\star}_z] [2^{\star}_Z] [[B\bar{1}0]] (a)   [[001]] (1) [2^{\star}_z]   1 [{\rm AR}^{\star}]
  [[1B0]_e] [\underline2^{\star}_z] [\underline2^{\star}_z] [\underline2^{\star}_z] SI
1 [m^{\star}_z] [m^{\star}_z] [[B\bar{1}0] ] (a)   [[001]_e ] (1) [{\underline m}^{\star}_z ] [{\underline m}^{\star}_z ] [{\underline m}^{\star}_z ] SI
  [[1B0] ] [m^{\star}_z]   1 [{\rm AR}^{\star}]
[\bar{1}] [m^{\star}_z], [2^{\star}_z] [2^{\star}_z/m^{\star}_z ] [[B\bar{1}0]] (a)   [[001]] (1) [2_z^{\star}/\underline{m}^{\star}_z] [\underline{m}^{\star}_z ] [\underline{m}^{\star}_z ] SR
  [[1B0]] [\underline2^{\star}_z/m^{\star}_z] [\underline2^{\star}_z] [\underline2^{\star}_z] SR
[2_z] [2^{\star}_x], [2^{\star}_y] [2^{\star}_x2^{\star}_y2_z ] [[001]]     [[100] ] (2) [2^{\star}_x\underline2^{\star}_y\underline2_z ] [\underline2^{\star}_y] [\underline2^{\star}_y] SR
    [[010]] [\underline2^{\star}_x2^{\star}_y\underline2_z ] [\underline2^{\star}_x] [\underline2^{\star}_x] SR
[2_z] [m^{\star}_x], [m^{\star}_y] [m^{\star}_xm^{\star}_y2_z ] [[001]]     [[100] ] (2) [\underline{m}^{\star}_xm^{\star}_y\underline2_z ] [\underline{m}^{\star}_x ] [\underline{m}^{\star}_x ] SR
  [[010]] [m^{\star}_x\underline{m}^{\star}_y\underline2_z ] [\underline{m}^{\star}_y ] [\underline{m}^{\star}_y ] SR
[2_z] [4^{\star}_z], [4_z^{3 \star}] [4^{\star}_z] [[001]] (b) [\Bigl[] [[1B0]] (3) [\underline2_z]   1 [{\rm A}\underline {\rm R}]
[[B\bar{1}0] ] [\underline2_z ] 1 [{\rm A}\underline{\rm R}]
[2_z] [\bar4^{\star}_z ], [\bar4_z^{*3}] [\bar{4}^{\star}_z ] [[001]] (b) [\Bigl[] [[1B0]] (3) [\underline2_z ]   1 [{\rm A}\underline{\rm R} ]
[[B\bar{1}0] ] [\underline2_z]   1 [{\rm A}\underline{\rm R} ]
[2_z] [3_z], [6_z^5] [6_{z}] [[001]] (c)   [[1B0]] (4) [\underline2_z]   1 [{\rm A}\underline{\rm R}]
  [[B\bar{1}0]] [\underline2_z]   1 [{\rm A}\underline{\rm R}]
[3_z^2], [6_z] [6_z] [[001]] (c)   [[1B0] ] (4) [\underline2_z]   1 [{\rm A}\underline{\rm R}]
  [[B\bar{1}0] ] [\underline2_z]   1 [{\rm A}\underline{\rm R}]
[2_z ] [\bar3_z^5], [\bar6_z ] [6_{z}/m_z] [[001]] (c)   [[1B0] ] (4) [\underline2_z ]   1 [{\rm A}\underline{\rm R} ]
  [[B\bar{1}0]] [\underline2_z]   1 [{\rm A}\underline{\rm R}]
[\bar3_z], [\bar6_z^5] [6_z/m_z] [[001]] (c)   [[1B0]] (4) [\underline2_z]   1 [{\rm A}\underline{\rm R} ]
  [[B\bar{1}0] ] [\underline2_z]   1 [{\rm A}\underline{\rm R}]
[2_x] [2^{\star}_{xy} ], [4_z] [4_z2_x2_{xy} ] [[\bar{C}C2] ] (d)   [[110] ] (5) [2^{\star}_{xy}]   1 [{\rm AR}^{\star}]
  [[1\bar{1}C]_e] [\underline2^{\star}_{xy} ] [\underline2^{\star}_{xy} ] [\underline2^{\star}_{xy}] SI
[2_x] [m^{\star}_{xy} ], [\bar4_z] [\bar4_z2_xm_{xy} ] [[\bar{C}C2]] (d)   [[110]_e ] (5) [\underline{m}^{\star}_{xy} ] [\underline{m}^{\star}_{xy} ] [\underline{m}^{\star}_{xy}] SI
  [[1\bar{1}C] ] [m^{\star}_{xy}]   [1] [{\rm AR}^{\star}]
[2_x] [2^{\star}_{x{^\prime}} ], [3_z^2] [3_z2_x] [[\sqrt{3}C], C, [\bar4]] (e)   [[\bar1\sqrt{3}0]] (6) [2^{\star}_{x{^\prime}}]   1 [{\rm AR}^{\star}]
  [[\sqrt{3}1C]_e ] [\underline2^{\star}_{x{^\prime}}] [\underline2^{\star}_{x{^\prime}} ] [\underline2^{\star}_{x{^\prime}} ] SI
[2_x] [m^{\star}_{x{^\prime}} ], [\bar3_z^5] [\bar{3}_zm_x ] [[\sqrt{3}C], C, [\bar4]] (e)   [[\bar1\sqrt{3}0]_e ] (6) [\underline{m}^{\star}_{x{^\prime}} ] [\underline{m}^{\star}_{x{^\prime}} ] [\underline{m}^{\star}_{x{^\prime}} ] SI
  [[\sqrt{3}1C] ] [m^{\star}_{x{^\prime}} ]   1 [{\rm AR}^{\star}]
[2_x] [2^{\star}_{y{^\prime}} ], [6_z] [6_z2_x2_y] [[\bar{C}], [\sqrt{3}C], [\bar4]] (f)   [[\sqrt{3}10]] (7) [2^{\star}_{y{^\prime}}]   1 [{\rm AR}^{\star}]
  [[\bar1\sqrt{3}C]_e] [\underline2^{\star}_{y{^\prime}} ] [\underline2^{\star}_{y{^\prime}} ] [\underline2^{\star}_{y{^\prime}} ] SI
[2_x] [m^{\star}_{y{^\prime}} ], [\bar6_z] [\bar{6}_z2_xm_y ] [[\bar{C}], [\sqrt{3}C], [\bar4]] (f)   [[\sqrt{3}10]_e ] (7) [\underline{m}^{\star}_{y{^\prime}}] [\underline{m}^{\star}_{y{^\prime}} ] [\underline{m}^{\star}_{y{^\prime}} ] SI
  [[\bar1\sqrt{3}C] ] [m^{\star}_{y{^\prime}}]   1 [{\rm AR}^{\star}]
[2_{xy}] [m^{\star}_{x} ], [\bar4_z^{3}] [\bar4_zm_x2_{xy} ] [[0C\bar{1}] ] (g)   [[100]_e ] (8) [\underline{m}^{\star}_{x} ] [\underline{m}^{\star}_{x} ] [\underline{m}^{\star}_{x}] SI
  [[01C]] [m^{\star}_{x}]   1 [{\rm AR}^{\star}]
[m_z] [m^{\star}_x], [2^{\star}_y] [m^{\star}_x2^{\star}_ym_z ] [[001]]     [[100]_e] (2) [\underline{m}^{\star}_x\underline2^{\star}_ym_z ] [\underline{m}^{\star}_x ] [\underline{m}^{\star}_x\underline2^{\star}_ym_z ] SI
    [[010]] [m_x^{\star}2_y^{\star}m_z] [m_z] [{\rm AR}^{\star}]
[m_{z}] [4_z], [\bar4_z^3 ] [4_z/m_{z}] [[001]] (b)   [[1B0]_{e0}] (3) [m_z ]   [m_z ] AI
  [[B\bar{1}0]_{0e}] [m_z] [m_z] AI
[4_z^3], [\bar4_z] [4_z/m_z] [[001]] (b)   [[1B0]_{e0}] (3) [m_z]   [m_z] AI
  [[B\bar{1}0]_{0e}] [m_z] [m_z] AI
[m_z] [3_z], [\bar6^5_z ] [\bar6_{z}] [[001]] (c)   [[1B0]_{e0} ] (4) [m_z ]   [m_z] AI
  [[B\bar{1}0]_{0e} ] [m_z]   [m_z ] AI
[3^2_z], [\bar6_z] [\bar6_z] [[001]] (c)   [[1B0]_{e0} ] (4) [m_z]   [m_z] AI
  [[B\bar{1}0]_{0e} ] [m_z]   [m_z ] AI
[m_z] [\bar3_z], [6_z^5 ] [6_{z}/m_z] [[001]] (c)   [[1B0]_{e0}] (4) [m_z]   [m_z] AI
  [[B\bar{1}0]_{0e} ] [m_z]   [m_z] AI
[\bar3_z^5], [6_z] [6_z/m_z] [[001]] (c)   [[1B0]_{e0} ] (4) [m_z]   [m_z ] AI
  [[B\bar{1}0]_{0e} ] [m_z]   [m_z ] AI
[m_x] [m^{\star}_{xy} ], [4_z] [4_zm_xm_{xy} ] [[\bar{C}C2]] (d)   [[110]_e ] (5) [\underline{m}^{\star}_{xy}] [\underline{m}^{\star}_{xy}] [\underline{m}^{\star}_{xy}] SI
  [[1\bar{1}C]] [m^{\star}_{xy}]   1 [{\rm AR}^{\star}]
[m_x] [2^{\star}_{xy} ], [\bar4_z] [\bar{4}_zm_x2_{xy} ] [[\bar{C}C2]] (d)   [[110] ] (5) [2^{\star}_{xy}]   1 [{\rm AR}^{\star}]
  [[1\bar{1}C]_e] [\underline2^{\star}_{xy}] [\underline2^{\star}_{xy}] [\underline2^{\star}_{xy}] SI
[m_x] [m^{\star}_{x{^\prime}} ], [3_z^2] [3_zm_x] [[\sqrt{3}C], C, [\bar4]] (e)   [[\bar1\sqrt{3}0]_e ] (6) [\underline{m}^{\star}_{x{^\prime}}] [\underline{m}^{\star}_{x{^\prime}} ] [\underline{m}^{\star}_{x{^\prime}} ] SI
  [[\sqrt{3}1C] ] [m^{\star}_{x{^\prime}}]   [1] [{\rm AR}^{\star}]
[m_x] [2^{\star}_{x{^\prime}} ], [\bar3_z^5] [\bar3_zm_x] [[\sqrt{3}C], C, [\bar4]] (e)   [[\bar1\sqrt{3}0] ] (6) [2^{\star}_{x{^\prime}}]   [1] [{\rm AR}^{\star}]
  [[\sqrt{3}1C]_e] [\underline2^{\star}_{x{^\prime}}] [\underline2^{\star}_{x{^\prime}}] [\underline2^{\star}_{x{^\prime}}] SI
[m_x] [m^{\star}_{y{^\prime}} ], [6_z] [6_zm_xm_y] [[\bar{C}], [\sqrt{3}C], [\bar4]] (f)   [[\sqrt{3}10]_e] (7) [\underline{m}^{\star}_{y{^\prime}} ] [\underline{m}^{\star}_{y{^\prime}} ] [\underline{m}^{\star}_{y{^\prime}} ] SI
  [[\bar1\sqrt{3}C] ] [m^{\star}_{y{^\prime}}]   [1] [{\rm AR}^{\star}]
[m_x] [2^{\star}_{y{^\prime}} ], [\bar6_z] [\bar{6}_zm_x2_y ] [[\bar{C}], [\sqrt{3}C], [\bar4]] (f)   [[\sqrt{3}10] ] (7) [2^{\star}_{y{^\prime}}]   [1] [{\rm AR}^{\star}]
  [[\bar1\sqrt{3}C]_e ] [\underline2^{\star}_{y{^\prime}} ] [\underline2^{\star}_{y{^\prime}}] [\underline2^{\star}_{y{^\prime}} ] SI
[m_{xy}] [2^{\star}_{x} ], [\bar4^3_z] [\bar{4}_z2_xm_{xy} ] [[0C\bar{1}]] (g)   [[100]] (8) [2^{\star}_{x}]   [1] [{\rm AR}^{\star}]
  [[01C]_e] [\underline2^{\star}_{xy}] [\underline2^{\star}_{x}] [\underline2^{\star}_{x}] SI
[2_z/m_z] [m^{\star}_x], [m^{\star}_y] [m^{\star}_xm^{\star}_ym_z ] [[001] ]     [[100]] (2) [\underline{m}^{\star}_xm^{\star}_ym_z ] [\underline{m}^{\star}_x] [\underline{m}^{\star}_x\underline2^{\star}_ym_z ] SR
    [[010]] [m^{\star}_x\underline{m}^{\star}_ym_z ] [\underline{m}^{\star}_y] [\underline2^{\star}_x\underline{m}^{\star}_ym_z ] SR
[2_z/m_z] [4^{\star}_z], [4^{3 \star}_z] [4^{\star}_z/m_z ] [[001]] (b) [\Bigl[] [[1B0]] (3) [\underline2_z/m_z]   [m_z] [{\rm A}\underline {\rm R}]
[[B\bar{1}0]] [\underline2_z/m_z] [m_z] [{\rm A}\underline {\rm R}]
[2_z/m_z] [3_z], [6_z^5] [6_{z}/m_z] [[001]] (c)   [[1B0]] (4) [\underline2_z/m_z]   [m_z ] [{\rm A}\underline {\rm R}]
  [[B\bar{1}0] ] [\underline2_z/m_z]   [m_z] [{\rm A}\underline {\rm R}]
[3_z^2], [6_z] [6_z/m_z ] [[001]] (c)   [[1B0] ] (4) [\underline2_z/m_z]   [m_z] [{\rm A}\underline {\rm R}]
  [[B\bar{1}0] ] [\underline2_z/m_z]   [m_z] [{\rm A}\underline {\rm R}]
[2_x/m_x] [m^{\star}_{xy} ], [4_z] [4_z/m_zm_xm_{xy} ] [[\bar{C}C2]] (d)   [[110]] (5) [2^{\star}_{xy}/\underline{m}^{\star}_{xy} ] [\underline{m}^{\star}_{xy}] [\underline{m}^{\star}_{xy}] SR
  [[1\bar{1}C]] [\underline2^{\star}_{xy}/m^{\star}_{xy} ] [\underline2^{\star}_{xy}] [\underline2^{\star}_{xy}] SR
[2_x/m_x] [m^{\star}_{x{^\prime}} ], [3_z^2] [\bar{3}_zm_x ] [[\sqrt{3}CC\bar4] ] (e)   [[\bar1\sqrt{3}0]] (6) [2^{\star}_{x{^\prime}}/\underline{m}^{\star}_{x{^\prime}} ] [\underline{m}^{\star}_{x{^\prime}}] [\underline{m}^{\star}_{x{^\prime}}] SR
  [[\sqrt{3}1C]] [\underline2^{\star}_{x{^\prime}}/m^{\star}_{x{^\prime}} ] [\underline2^{\star}_{x{^\prime}} ] [\underline2^{\star}_{x{^\prime}} ] SR
[2_x/m_x] [m^{\star}_{y{^\prime}} ], [6_z] [6_z/m_zm_xm_y ] [[\bar{C}], [\sqrt{3}C], [\bar4]] (f)   [[\sqrt{3}10] ] (7) [2^{\star}_{y{^\prime}}/\underline{m}^{\star}_{y{^\prime}} ] [\underline{m}^{\star}_{y{^\prime}}] [\underline{m}^{\star}_{y{^\prime}}] SR
  [[\bar1\sqrt{3}C]] [\underline2^{\star}_{y{^\prime}}/m^{\star}_{y{^\prime}} ] [\underline2^{\star}_{y{^\prime}} ] [\underline2^{\star}_{y{^\prime}} ] SR
[2_x2_y2_z] [2^{\star}_{x\bar{y}} ], [2^{\star}_{xy}] [4^{\star}_z2_x2^{\star}_{xy} ] [[001]]   [\Bigl[] [[110]] (10) [2^{\star}_{xy}\underline2^{\star}_{x\bar{y}}\underline2_z ] [\underline2^{\star}_{x\bar{y}}] [\underline2^{\star}_{x\bar{y}}] SR
  [[1\bar10]] [\underline2^{\star}_{xy}2^{\star}_{x\bar{y}}\underline2_z ] [\underline2^{\star}_{xy}] [\underline2^{\star}_{xy}] SR
[2_x2_y2_z] [m^{\star}_{x\bar{y}} ], [m^{\star}_{xy}] [\bar{4}^{\star}_z2_xm^{\star}_{xy} ] [[001]]   [\Bigl[] [[110]] (10) [\underline{m}^{\star}_{xy}m^{\star}_{x\bar{y}}\underline2_z ] [\underline{m}^{\star}_{xy} ] [\underline{m}^{\star}_{xy}] SR
  [[1\bar10]] [m^{\star}_{xy}\underline{m}^{\star}_{x\bar{y}}\underline2_z ] [\underline{m}^{\star}_{x\bar{y}} ] [\underline{m}^{\star}_{x\bar{y}} ] SR
[2_x2_y2_z] [2^{\star}_{x{^\prime}} ], [2^{\star}_{y{^\prime}}] [6_z2_x2_y] [[001]]     [[\bar1\sqrt{3}0] ] (9) [2^{\star}_{x{^\prime}}\underline2^{\star}_{y{^\prime}}\underline2_z ] [\underline2^{\star}_{y{^\prime}}] [\underline2^{\star}_{y{^\prime}} ] SR
    [[\sqrt{3}10]] [\underline2^{\star}_{x{^\prime}}2^{\star}_{y{^\prime}}\underline2_z ] [\underline2^{\star}_{x{^\prime}}] [\underline2^{\star}_{x{^\prime}} ] SR
[2_x2_y2_z] [m^{\star}_{x{^\prime}} ], [m^{\star}_{y{^\prime}}] [6_z/m_zm_xm_y ] [[001]]     [[\bar1\sqrt{3}0]] (9) [\underline{m}^{\star}_{x{^\prime}}m^{\star}_{y{^\prime}}\underline2_z ] [\underline{m}^{\star}_{x{^\prime}} ] [\underline{m}^{\star}_{x{^\prime}}] SR
    [[\sqrt{3}10]] [{m}^{\star}_{x{^\prime}}\underline{m}^{\star}_{y{^\prime}}\underline2_z ] [\underline{m}^{\star}_{y{^\prime}} ] [\underline{m}^{\star}_{y{^\prime}}] SR
[2_{x\bar{y}}2_{xy}2_z ] [m^{\star}_{x} ], [m^{\star}_{y}] [{\bar 4}_z^\star m_x^\star 2_{xy} ] [[001]]   [\Bigl[] [[100]] (12) [\underline{m}^{\star}_{x}m^{\star}_{y}\underline2_z ] [\underline{m}^{\star}_{x} ] [\underline{m}^{\star}_{x}] SR
  [[010]] [m^{\star}_{x}\underline{m}^{\star}_{y}\underline2_z ] [\underline{m}^{\star}_{y} ] [\underline{m}^{\star}_{y}] SR
[2_{x\bar{y}}2_{xy}2_z ] [2^{\star}_{xz} ], [4_y] [4_z3_{p}2_{xy} ] [[B2\bar{B}]] (h)   [[101]] (11) [2^{\star}_{xz}]   1 [{\rm AR}^{\star}]
  [[\bar{1}B1]] [\underline2^{\star}_{xz}] [\underline2^{\star}_{xz}] [\underline2^{\star}_{xz}] SI
[2_{x\bar{y}}2_{xy}2_z ] [m_{xz}^{\star} ], [\bar4_y] [m_z\bar{3}_{p}m_{xy} ] [[B2\bar{B}]] (h)   [[101]] (11) [\underline{m}_{xz}^{\star}] [\underline{m}_{xz}^{\star}] [\underline{m}_{xz}^{\star}] SI
  [[\bar{1}B1] ] [m_{xz}^{\star}]   1 [{\rm AR}^{\star}]
[m_xm_y2_z] [m^{\star}_{x\bar{y}} ], [m^{\star}_{xy}] [4^{\star}_zm_xm^{\star}_{xy} ] [[001]]   [\Bigl[] [[110]] (10) [m^{\star}_{x\bar{y}}\underline{m}^{\star}_{xy}\underline2_z ] [\underline{m}^{\star}_{xy} ] [\underline{m}^{\star}_{xy}] SR
  [[1\bar10]] [\underline{m}^{\star}_{x\bar{y}}{m}^{\star}_{xy}\underline2_z ] [\underline{m}^{\star}_{x\bar{y}} ] [\underline{m}^{\star}_{x\bar{y}} ] SR
[m_xm_y2_z] [2^{\star}_{x\bar{y}} ], [2^{\star}_{xy}] [\bar{4}^{\star}_zm_x2^{\star}_{xy} ] [[001]]   [\Bigl[] [{[110]}] (10) [2^{\star}_{xy}\underline2^{\star}_{x\bar{y}}\underline2_z ] [\underline2^{\star}_{x\bar{y}} ] [\underline2^{\star}_{x\bar{y}} ] SR
  [[1\bar10]] [\underline2^{\star}_{xy}2^{\star}_{x\bar{y}}\underline2_z ] [\underline2^{\star}_{xy}] [\underline2^{\star}_{xy} ] SR
[m_xm_y2_z] [m^{\star}_{x{^\prime}} ], [m^{\star}_{y{^\prime}}] [6_zm_xm_y] [[001]]     [[\bar1\sqrt{3}0] ] (9) [\underline{m}^{\star}_{x{^\prime}}m^{\star}_{y{^\prime}}\underline2_z ] [\underline{m}^{\star}_{x{^\prime}} ] [\underline{m}^{\star}_{x{^\prime}} ] SR
    [[\sqrt{3}10] ] [{m}^{\star}_{x{^\prime}}\underline{m}^{\star}_{y{^\prime}}\underline2_z ] [\underline{m}^{\star}_{y{^\prime}} ] [\underline{m}^{\star}_{y{^\prime}} ] SR
[m_xm_y2_z] [2^{\star}_{x{^\prime}} ], [2^{\star}_{y{^\prime}}] [6_z/m_zm_xm_y ] [[001]]     [[\bar1\sqrt{3}0] ] (9) [2^{\star}_{x{^\prime}}\underline2^{\star}_{y{^\prime}}\underline2_z ] [\underline2^{\star}_{y{^\prime}} ] [\underline2^{\star}_{y{^\prime}}] SR
    [[\sqrt{3}10] ] [\underline2^{\star}_{x{^\prime}}2^{\star}_{y{^\prime}}\underline2_z ] [\underline2^{\star}_{x{^\prime}} ] [\underline2^{\star}_{x{^\prime}} ] SR
[m_x2_ym_z] [m^{\star}_{x{^\prime}} ], [2^{\star}_{y{^\prime}}] [\bar{6}_zm_x2_y ] [[001]]     [[\bar1\sqrt{3}0]_e ] (9) [\underline{m}^{\star}_{x{^\prime}}\underline2^{\star}_{y{^\prime}}m_z ] [\underline{m}^{\star}_{x{^\prime}} ] [\underline{m}^{\star}_{x{^\prime}}\underline2^{\star}_{y{^\prime}}m_z ] SI
    [[\sqrt{3}10] ] [{m}^{\star}_{x{^\prime}}2^{\star}_{y{^\prime}}m_z ]   [m_z] [{\rm AR}^{\star}]
[2_xm_ym_z] [m^{\star}_{x\bar{y}} ], [2^{\star}_{xy}] [4_z/m_zm_xm_{xy} ] [[001]]     [[110] ] (10) [2^{\star}_{xy}m^{\star}_{x\bar{y}}m_z ]   [m_z] [{\rm AR}^{\star}]
  [[1\bar10]_e] [\underline2^{\star}_{xy}\underline{m}^{\star}_{x\bar{y}}m_z ] [\underline{m}^{\star}_{x\bar{y}} ] [\underline2^{\star}_{xy}\underline{m}^{\star}_{x\bar{y}}m_z ] SI
[2_xm_ym_z] [m^{\star}_{y{^\prime}} ], [2^{\star}_{x{^\prime}}] [\bar{6}_z2_xm_y ] [[001]]     [[\bar1\sqrt{3}0] ] (9) [2^{\star}_{x{^\prime}}m^{\star}_{y{^\prime}}m_z ]   [m_z] [{\rm AR}^{\star}]
    [[\sqrt{3}10]_e ]   [\underline{2}^{\star}_{x{^\prime}}\underline{m}^{\star}_{y{^\prime}}m_z ] [\underline{m}_{y{^\prime}} ] [\underline{2}^{\star}_{x{^\prime}}\underline{m}^{\star}_{y{^\prime}}m_z ] SI
[2_xm_ym_z] [m^{\star}_{x{^\prime}} ], [2^{\star}_{y{^\prime}}] [6_z/m_zm_xm_y ] [[001]]     [[\bar1\sqrt{3}0]_e] (9) [\underline{m}^{\star}_{x{^\prime}}\underline2^{\star}_{y{^\prime}}m_z ] [\underline{m}^{\star}_{x{^\prime}} ] [\underline{m}^{\star}_{x{^\prime}}\underline2^{\star}_{y{^\prime}}m_z ] SI
    [[\sqrt{3}10] ] [m^{\star}_{x{^\prime}}2^{\star}_{y{^\prime}}m_z ]   [m_z] [{\rm AR}^{\star}]
[m_{x\bar{y}}m_{xy}2_z] [2^{\star}_{x}], [2^{\star}_{y} ] [\bar{4}^{\star}_z2^{\star}_xm_{xy}] [[001]]   [\Bigl[] [[100] ] (12) [2^{\star}_{x}\underline2^{\star}_{y}\underline2_z ] [\underline2^{\star}_{y}] [\underline2^{\star}_{y}] SR
          [[010]]   [\underline2^{\star}_{x}2^{\star}_{y}\underline2_z ] [\underline2^{\star}_{x} ] [\underline2^{\star}_{x}] SR
[m_{x\bar{y}}m_{xy}2_z ] [m^{\star}_{xz} ], [\bar4_y] [\bar{4}_z3_{p}m_{xy} ] [[B2\bar{B}]] (h)   [[101]_e] (11) [\underline{m}^{\star}_{xz}] [\underline{m}^{\star}_{xz}] [\underline{m}^{\star}_{xz}] SI
  [[\bar{1}B1] ]   [m^{\star}_{xz}]   1 [{\rm AR}^{\star}]
[m_{x\bar{y}}m_{xy}2_z ] [2^{\star}_{xz} ], [4_y] [m_z\bar{3}_{p}m_{xy} ] [[B2\bar{B}]] (h)   [[101] ] (11) [2^{\star}_{xz}]   1 [{\rm AR}^{\star}]
  [[\bar{1}B1]_e] [\underline2^{\star}_{xz}] [\underline2^{\star}_{xz}] [\underline2^{\star}_{xz} ] SI
[m_{x\bar{y}}2_{xy}m_z ] [m^{\star}_{xz} ], [4_y] [m_z\bar{3}_{p}m_{xy}(m^{\star}_{xz}) ] [[B2\bar{B}]] (h)   [[101]_e] (11) [\underline{m}^{\star}_{xz}] [\underline{m}^{\star}_{xz}] [\underline{m}^{\star}_{xz}] SI
  [[\bar{1}B1] ] [m^{\star}_{xz}]   [1] [{\rm AR}^{\star}]
[m_{x\bar{y}}2_{xy}m_z ] [2^{\star}_{xz} ], [\bar4_y] [m_z\bar{3}_{p}m_{xy}(2^{\star}_{xz}) ] [[B2\bar{B}]] (h)   [[101]] (11) [2^{\star}_{xz}]   1 [{\rm AR}^{\star}]
  [[\bar{1}B1]_e ] [\underline2^{\star}_{xz}] [\underline2^{\star}_{xz}] [\underline2^{\star}_{xz}] SI
[m_xm_ym_z] [m^{\star}_{xy} ], [m^{\star}_{x\bar{y}}] [4^{\star}_z/m_zm_xm^{\star}_{xy} ] [[001]]   [\Bigl[] [[110]] (10) [m^{\star}_{x\bar{y}}\underline{m}^{\star}_{xy}m_z ] [\underline{m}^{\star}_{xy} ] [\underline2^{\star}_{x\bar{y}}\underline{m}^{\star}_{xy}m_z ] SR
  [[1\bar10]] [\underline{m}^{\star}_{x\bar{y}}{m}^{\star}_{xy}m_z ] [\underline{m}^{\star}_{x\bar{y}} ] [\underline{m}^{\star}_{x\bar{y}}\underline{2}^{\star}_{xy}m_z ] SR
[m_xm_ym_z] [m^{\star}_{x{^\prime}} ], [m^{\star}_{y{^\prime}}] [6_z/m_zm_xm_y ] [[001]]     [[\bar1\sqrt{3}0] ] (9) [\underline{m}^{\star}_{x{^\prime}}m^{\star}_{y{^\prime}}m_z ] [\underline{m}^{\star}_{x{^\prime}}] [\underline{m}^{\star}_{x{^\prime}}\underline2^{\star}_{y{^\prime}}m_z ] SR
    [[\sqrt{3}10] ] [m^{\star}_{x'}\underline{m}^{\star}_{y'}m_z ] [\underline{m}^{\star}_{y'}] [\underline{2}^{\star}_{x'}\underline{m}^{\star}_{y'}m_z ] SR
[m_{xy}m_{\bar{x}y}m_z ] [m^{\star}_{xz} ], [4_y] [m_z\bar{3}_{p}m_{xy} ] [[B2\bar{B}]] (h)   [[101]] (11) [2^{\star}_{xz}/\underline{m}^{\star}_{xz} ] [\underline{m}^{\star}_{xz}] [\underline{m}^{\star}_{xz}] SR
  [[\bar{1}B1]] [\underline2^{\star}_{xz}/m^{\star}_{xz} ] [\underline2^{\star}_{xz}] [\underline2^{\star}_{xz} ] SR
[4_z] [2^{\star}_{xz} ], [4_y] [4_z3_{p}2_{xy} ] [[010]]     [[101]] (13) [2^{\star}_{xz}]   1 [{\rm AR}^{\star}]
    [[\bar101]_e ] [\underline2^{\star}_{xz}] [\underline2^{\star}_{xz}] [\underline2^{\star}_{xz}] SI
[4_z] [m^{\star}_{xz} ], [\bar{4}_y] [m_z\bar{3}_{p}m_{xy} ] [[010]]     [[101]_e] (13) [\underline{m}^{\star}_{xz}] [\underline{m}^{\star}_{xz}] [\underline{m}^{\star}_{xz}] SI
    [[\bar101]] [m^{\star}_{xz}]   [1] [{\rm AR}^{\star}]
[\bar{4}_z] [m^{\star}_{xz} ], [\bar4_y] [\bar{4}_z3_{p}m_{xy} ] [[010]]     [[101]] (13) [\underline{m}^{\star}_{xz}] [\underline{m}^{\star}_{xz}] [\underline{m}^{\star}_{xz}] SI
    [[\bar101]] [m^{\star}_{xz}]   [1] [{\rm AR}^{\star}]
[\bar{4}_z] [2^{\star}_{xz} ], [4_y] [m_z\bar{3}_{p}m_{xy} ] [[010]]     [[101] ] (13) [2^{\star}_{xz}]   [1] [{\rm AR}^{\star}]
    [[\bar101]_e ] [\underline2_{xz}^{\star}] [\underline2_{xz}^{\star}] [\underline2_{xz}^{\star}] SI
[4_z/m_z] [m^{\star}_{xz} ], [4_y] [m_z\bar{3}_{p}m_{xy} ] [[010]]     [[101]] (13) [2^{\star}_{xz}/\underline{m}^{\star}_{xz} ] [\underline{m}^{\star}_{xz}] [\underline{m}^{\star}_{xz}] SR
    [[\bar101]] [\underline2^{\star}_{xz}/m^{\star}_{xz} ] [\underline2^{\star}_{xz}] [\underline2^{\star}_{xz}] SR
[4_z2_x2_{xy} ] [2^{\star}_{xz} ], [2^{\star}_{x\bar{z}}] [4_z3_{p}2_{xy} ] [[010]]   [\Bigl[] [[101]] (13) [2^{\star}_{xz}\underline2^{\star}_{x\bar{z}}\underline2_{y} ] [\underline2^{\star}_{\bar{x}z} ] [\underline2^{\star}_{\bar{x}z} ] SR
  [[\bar101]] [\underline2^{\star}_{xz}2^{\star}_{x\bar{z}}\underline2_y ] [\underline2^{\star}_{xz} ] [\underline2^{\star}_{xz} ] SR
[4_z2_x2_{xy} ] [m^{\star}_{xz} ], [m^{\star}_{x\bar{z}}] [m_z\bar{3}_{p}m_{xy} ] [[010]]   [\Bigl[] [[101] ] (13) [\underline{m}^{\star}_{xz}m^{\star}_{x\bar{z}}\underline2_y ] [\underline{m}^{\star}_{xz}] [\underline{m}^{\star}_{xz}] SR
  [[\bar101]] [m^{\star}_{xz}\underline{m}^{\star}_{x\bar{z}}\underline2_y ] [\underline{m}^{\star}_{x\bar{z}}] [\underline{m}^{\star}_{x\bar{z}}] SR
[4_zm_xm_{xy} ] [m^{\star}_{x\bar{z}} ], [2^{\star}_{xz}] [m_z\bar{3}_{p}m_{xy} ] [[010]]     [[101]] (13) [2^{\star}_{xz}m^{\star}_{x\bar{z}}m_y ]   [m_y ] [{\rm AR}^{\star}]
    [[\bar101]_e ] [\underline2^{\star}_{xz}\underline{m}^{\star}_{x\bar{z}}m_y ] [\underline2^{\star}_{xz}] [\underline2^{\star}_{xz}\underline{m}^{\star}_{x\bar{z}}m_y ] SI
[\bar{4}_z2_xm_{xy} ] [m^{\star}_{xz} ], [m^{\star}_{x\bar{z}}] [\bar{4}_z3_{p}m_{xy} ] [[010]]   [\Bigl[] [[101]] (13) [\underline{m}^{\star}_{xz}m^{\star}_{x\bar{z}}\underline2_y ] [\underline{m}^{\star}_{xz}] [\underline{m}^{\star}_{xz}] SR
  [[\bar101]] [m^{\star}_{xz}\underline{m}^{\star}_{x\bar{z}}\underline2_y ] [\underline{m}^{\star}_{x\bar{z}} ] [\underline{m}^{\star}_{x\bar{z}} ] SR
[\bar{4}_zm_x2_{xy} ] [m_{x\bar{z}}^{\star} ], [2_{xz}^{\star}] [m_z\bar{3}_{p}m_{xy} ] [[010]]     [[101]] (13) [2^{\star}_{xz}m^{\star}_{x\bar{z}}m_y ]   [m_y] [{\rm AR}^{\star}]
    [[\bar101]] [\underline2^{\star}_{xz}\underline{m}^{\star}_{x\bar{z}}m_y ] [\underline{m}^{\star}_{x\bar{z}}] [\underline2^{\star}_{xz}\underline{m}^{\star}_{x\bar{z}}m_y ] SR
[\bar{4}_z2_xm_{xy} ] [2^{\star}_{xz} ], [2^{\star}_{x\bar{z}}] [m_z\bar{3}_{p}m_{xy} ] [[010]]     [[101]] (13) [2^{\star}_{xz}2^{\star}_{x\bar{z}}2_y ] [\underline2^{\star}_{x\bar{z}}] [\underline2^{\star}_{x\bar{z}}] SR
    [[\bar101] ] [\underline2^{\star}_{xz}\underline{2}^{\star}_{x\bar{z}}2_y ] [\underline{2}^{\star}_{x\bar{z}} ] [\underline2^{\star}_{xz}\underline{2}^{\star}_{x\bar{z}}2_y ] SI
[4_z/m_zm_xm_{xy} ] [m^{\star}_{xz} ], [m^{\star}_{\bar{x}z}] [m_z\bar{3}_{p}m_{xy} ] [[010]]   [\Bigl[] [[101]] (13) [\underline{m}^{\star}_{xz}m^{\star}_{\bar{x}z}m_y ] [\underline{m}^{\star}_{xz} ] [\underline{m}^{\star}_{xz}\underline{2}^{\star}_{\bar{x}z}m_y ] SR
  [[\bar101]] [m^{\star}_{xz}\underline{m}^{\star}_{x\bar{z}}m_y ] [\underline{m}^{\star}_{x\bar{z}} ] [\underline2^{\star}_{xz}\underline{m}^{\star}_{x\bar{z}}m_y ] SR
[3_{p}] [2^{\star}_{x} ], [3_r] [2_z 3_{p}] [[01\bar1]]     [[100]] (14) [2^{\star}_x]   [1] [{\rm AR}^{\star}]
    [[011]_e] [\underline2^{\star}_x] [\underline2^{\star}_x] [\underline2^{\star}_x] SI
[3_{p}] [m^{\star}_{x} ], [\bar3_r] [m_z \bar3_{p} ] [[01\bar1]]     [[100]_e] (14) [\underline{m}^{\star}_x ] [\underline{m}^{\star}_x ] [\underline{m}^{\star}_x ] SI
    [[011] ] [m^{\star}_x ]   [1] [{\rm AR}^{\star}]
[3_{p}] [2^{\star}_{xy} ], [4_y] [4_z 3_{p} 2_{xy} ] [[1\bar10]]     [[001]_e] (14) [\underline2^{\star}_{xy}] [\underline2^{\star}_{xy}] [\underline2^{\star}_{xy}] SI
    [[110]] [2^{\star}_{xy}]   [1] [{\rm AR}^{\star}]
[3_{p}] [m^{\star}_{xy} ], [\bar4_y] [\bar4_z3_{p}m_{xy} ] [[1\bar10]]     [[001]] (14) [m^{\star}_{xy}]   [1] [{\rm AR}^{\star}]
    [[110]_e] [\underline{m}^{\star}_{xy}] [\underline{m}^{\star}_{xy}] [\underline{m}^{\star}_{xy}] SI
[\bar3_{p}] [m^{\star}_{x} ], [3_r] [m_z\bar3_{p} ] [[01\bar1]]     [[100]] (14) [2^{\star}_x/\underline{m}^{\star}_x ] [\underline{m}^{\star}_x ] [\underline{m}^{\star}_x ] SR
    [[011]] [\underline2^{\star}_x/m^{\star}_x] [\underline2^{\star}_x ] [\underline2^{\star}_x] SR
[\bar3_{p}] [m^{\star}_{xy} ], [4_y] [m_z\bar3_{p}m_{xy} ] [[1\bar10]]     [[001]] (14) [\underline2^{\star}_{xy}/m^{\star}_{xy} ] [\underline2^{\star}_{xy}] [\underline2^{\star}_{xy}] SR
    [[110]] [2^{\star}_{xy}/\underline{m}^{\star}_{xy} ] [\underline{m}^{\star}_{xy}] [\underline{m}^{\star}_{xy}] SR
[3_{p} 2_{x\bar{y}} ] [2^{\star}_{x} ], [2^{\star}_{yz}] [4_z3_{p} 2_{xy} ] [[01\bar1]]     [[100]] (14) [2^{\star}_x\underline2^{\star}_{yz}\underline2_{y\bar{z}} ] [\underline2^{\star}_{yz} ] [\underline2^{\star}_{yz} ] SR
    [[011]] [\underline2^{\star}_x2^{\star}_{yz}\underline2_{y\bar{z}} ] [\underline2^{\star}_x] [\underline2^{\star}_x] SR
[3_{p} 2_{x\bar{y}} ] [m^{\star}_{x} ], [m^{\star}_{yz}] [m_z\bar3_{p}m_{xy} ] [[01\bar1]]     [[100]] (14) [\underline{m}^{\star}_xm_{yz}^{\star}\underline2_{y\bar{z}} ] [\underline{m}^{\star}_x ] [\underline{m}^{\star}_x ] SR
    [[011]] [m^{\star}_x\underline{m}^{\star}_{yz}\underline2_{y\bar{z}} ] [\underline{m}^{\star}_{yz}] [\underline{m}^{\star}_{yz}] SR
[3_{p} m_{x\bar{y}} ] [2^{\star}_{x} ], [m^{\star}_{yz}] [\bar4_z3_{p}m_{xy} ] [[01\bar1]]     [[100] ] (14) [m^{\star}_{yz}m_{y\bar{z}}2^{\star}_x ]   [m_{y\bar{z}}] [{\rm AR}^{\star}]
    [[011]_e] [\underline{m}_{yz}m_{y\bar{z}}\underline2^{\star}_x ] [\underline{m}_{yz} ] [\underline{m}_{yz}m_{y\bar{z}}\underline2^{\star}_x ] SI
[3_{p} m_{x\bar{y}} ] [m^{\star}_x], [2^{\star}_{yz}] [m_z\bar3_{p}m_{xy} ] [[01\bar1]]     [[100]_e] (14) [\underline{m}^{\star}_x\underline2^{\star}_{yz}m_{y\bar{z}} ] [\underline{m}^{\star}_x ] [\underline{m}^{\star}_x\underline2^{\star}_{yz}m_{y\bar{z}} ] SI
    [[011]] [m^{\star}_x2^{\star}_{yz}m_{y\bar{z}} ]   [m_{y\bar{z}}] [{\rm AR}^{\star}]
[\bar3_{p}m_{x\bar{y}}] [m^{\star}_x], [m^{\star}_{yz} ] [m_z \bar3_{p}m_{xy}] [[01\bar1]]     [[100]] (14) [\underline{m}^{\star}_xm^{\star}_{yz}m_{y\bar{z}} ] [\underline{m}^{\star}_x] [\underline{m}^{\star}_x\underline2^{\star}_{yz}m_{y\bar{z}} ] SR
    [[011]] [m^{\star}_x\underline{m}^{\star}_{yz}m_{y\bar{z}} ] [\underline{m}^{\star}_{yz}] [\underline2^{\star}_x\underline{m}^{\star}_{yz}m_{y\bar{z}} ] SR
Equations for directions of axes and shear angle [\varphi]:[\matrix{\pmatrix{a &f &e \cr f &b &d \cr e &d &c \cr}\quad\quad\quad\quad\quad\quad\quad\quad\quad\hfill& \pmatrix{a & d & 0 \cr d & b & 0 \cr 0 & 0 & c \cr}\hfill& \pmatrix{a & 0 & 0 \cr 0 & b & d \cr 0 & d & c \cr}\hfill\cr (a)\quad [001]\quad[1 {{\displaystyle d}\over{\displaystyle e}} 0]\hfill & (b)\quad [\bar1 \alpha 0]\quad [\alpha10]\hfill & (d)\quad[110] \quad [1\bar1 {{\displaystyle 2d}\over{\displaystyle a-b}}]\hfill\cr &\alpha={{\displaystyle 2d+\sqrt{(a-b)^2+4d^2}}\over{\displaystyle a-b}}\hfill& (e)\quad[\bar1\sqrt30]\quad [\sqrt31{{\displaystyle 4d}\over{\displaystyle b-a}}]\hfill\cr & (c)\quad[\bar1 \beta 0] \quad [\beta 10]\hfill& (f)\quad[\sqrt310]\quad [\bar1\sqrt3{{\displaystyle 4\sqrt3}\over{\displaystyle 3(a-b)}}]\hfill\cr & \beta={{\displaystyle(a-b)+2\sqrt{3}d+4\sqrt{(a-b)^2+4d^2}}\over{\displaystyle \sqrt3(a-b)-2d}}\hfill &\cr&&&\cr(1)\quad 2 \sqrt{d^2+e^2}\hfill & (2)\quad 2|d|\hfill & (5)\quad \sqrt{(a-b)^2+2d^2}\hfill\cr &(3)\quad {{1}\over{2}}\sqrt{(a-b)^2+4d^2}\hfill &(6)\quad {{\sqrt3}\over{2}}\sqrt{(a-b)^2+4d^2}\hfill\cr &(4)\quad {{\sqrt3}\over{2}}\sqrt{(a-b)^2+4d^2}\hfill & (7)\quad 2|d|\hfill\cr &&&\cr &&&\cr\pmatrix{a & b & -d \cr b & a & d \cr -d & d & c \cr}\hfill & \pmatrix{a & 0 & 0 \cr 0 & b & 0 \cr 0 & 0 & c \cr}\hfill & \pmatrix{a & d & 0 \cr d & a & 0 \cr 0 & 0 & c \cr}\hfill\cr (g)\quad[100]\quad[0\bar1 {{\displaystyle d}\over{\displaystyle b}}]\hfill & &(h)\quad[101]\quad[\bar1 {{\displaystyle 2d}\over{\displaystyle c-d}}1]\hfill\cr &&&\cr (8)\quad 2\sqrt{a^2+b^2}\hfill & (9)\quad {{\sqrt3}\over{2}} |a-b|\hfill & (11)\quad \sqrt{(a-c)^2+2d^2}\hfill\cr &(10)\quad|a-b|\hfill &(12)\quad 2|d|\hfill\cr &&&\cr &&&\cr\pmatrix{a & 0 & 0 \cr 0 & a & 0 \cr 0 & 0 & c \cr}\hfill&\pmatrix{a & d & d \cr d & a & d \cr d & d & a \cr}\hfill &\cr(13)\quad |a-c|\hfill & (14)\quad 2\sqrt2 |d|\hfill &\cr} ]