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

International Tables for Crystallography (2006). Vol. D, ch. 3.3, p. 421

Table 3.3.8.2 

Th. Hahna* and H. Klapperb

aInstitut für Kristallographie, Rheinisch–Westfälische Technische Hochschule, D-52056 Aachen, Germany, and bMineralogisch-Petrologisches Institut, Universität Bonn, D-53113 Bonn, Germany
Correspondence e-mail:  hahn@xtal.rwth-aachen.de

Table 3.3.8.2| top | pdf |
Examples of calculated obliquities [\omega] and lattice indices [j] for selected (hkl)[/][uvw] combinations and their relation to twinning

Calculations were performed with the program OBLIQUE written by Le Page (1999[link], 2002[link]).

Crystal(hkl)Pseudo-normal [uvw]Obliquity [[^\circ]] Lattice index [j]Remark
Gypsum
[A2/a]
[a = 6.51], [b = 15.15], [c = 6.28] Å
[\beta = 127.5^\circ]
(100) [302] 2.47 3 Dovetail twin (very frequent)
  [805] 0.42 4
(001) [203] 5.92 3 Montmartre twin (less frequent)
  [305] 0.95 5
(101) [101] 2.60 2 No twin
[(11{\bar 1})] [[31{\bar 4}]] 1.35 4 No twin
Rutile
[P4_2/mnm]
[a = 4.5933], [c = 2.9592] Å
(101) [102] 5.02 3 Frequent twin
  [307] 0.84 5
(301) [101] 5.43 2 Rare twin
(201) [304] 2.85 5 No twin
(210) or (130) [210] or [130] 0 5 No twin
Quartz
[P3_121]
[a = 4.9031], [c = 5.3967] Å
[(11{\bar 2}2)] [111] 5.49 2 Japanese twin (La Gardette) (rare)
[(10{\bar 1}1)] [211] 5.76 3 Esterel twin (rare)
[(10{\bar 1}2)] [212] 5.76 3 Sardinia twin (very rare)
[(21{\bar 3}0)] or [(14{\bar 5}0)] [540] or [230] 0 7 No twin
Staurolite
[C2/m]
[a = 7.781], [b = 16.620], [c = 5.656] Å
[\beta = 90.00^\circ]
(031) [013] 1.19 6 90° twin (rare)
(231) [313] 0.90 12 60° twin (frequent)
(201) [101] 0.87 3 No twin
(101) [102] 0.87 3 No twin
Calcite
[R{\bar 3}c]
[a = 4.989], [c = 17.062] Å
[hexagonal axes, structural
X-ray cell; cf. Section 3.3.10.2.2[link],
Example (5)[link]]
[(01{\bar 1}2)] [[5_\prime10_\prime1]] 5.31 2 No twin
  [[7_\prime14_\prime2]] 2.57 3  
  [481] 0.59 5  
[(10{\bar 1}4)] [421] 0.74 4 Rare deformation twin (r-twin)
[(01{\bar 1}8)] [121] 0.59 5 Frequent deformation twin (e-twin)
[(10{\bar 1}1)] [14.7.1] 1.54 5 No twin