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

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. D. ch. 3.3, pp. 409-410

Section 3.3.6.10. Variety of twinning in gibbsite, Al(OH)3

Th. Hahna* and H. Klapperb

a Institut 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

3.3.6.10. Variety of twinning in gibbsite, Al(OH)3

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Gibbsite (older name: hydrargillite) forms a pronounced layer structure with a perfect cleavage plane [(001)]. It is monoclinic with eigensymmetry [{\cal H} = 12/m1], but strongly pseudo-hexagonal with an axial ratio [b/a = \tan 30.4^\circ]. In contrast to most other pseudo-hexagonal crystals, the twofold eigensymmetry axis b is not parallel but normal to the pseudo-hexagonal c axis. The normal to the cleavage plane [(001)] is inclined by [\beta - 90^\circ = 4.5^\circ] against [001]. Owing to the pseudo-hexagonal metrics of the plane [(001)], the lattice planes [(110)] and [({\bar 1}10)], equivalent with respect to the eigensymmetry [{\cal H} = 2/m], form an angle of 60.8°.

The following four significant twin laws have been observed by Brögger (1890[link]):

  • (i) (001) reflection twin: the cleavage plane (001) acts both as twin mirror and composition plane. The pseudo-hexagonal axes [001] of both partners are inclined to each other by 9.0°. This twin law is quite common in natural and synthetic gibbsite.

  • (ii) (100) reflection twin: the twin mirror plane (100) is also the composition plane. The angle between the (001) planes of both partners is 9.0°, as in (i)[link]; the pseudo-hexagonal axes [001] of both partners are parallel. This twin law is not common.

  • (iii) (110) reflection twin: again, twin mirror plane and composition plane coincide. The two (001) planes span an angle of 4.6°. This twin law is very rare in nature, but is often observed in synthetic materials. A sixfold sector twin of synthetic gibbsite, formed by cyclic repetition of {110} twin reflection planes 60.8° apart, is shown in Fig. 3.3.6.10[link]. The pseudo-hexagonal axis [001] is common to all domains. Since the (001) plane is inclined towards this axis at 94.5°, the six (001) facets of the twinned crystal form a kind of `umbrella' with [001] as umbrella axis (Fig. 3.3.6.10[link]a). This (001) umbrella faceting was recently observed in twinned synthetic gibbsite crystals by Sweegers et al. (1999[link]).

    [Figure 3.3.6.10]

    Figure 3.3.6.10 | top | pdf |

    Sixfold reflection twin of gibbsite, Al(OH)3, with equivalent (110) and [({\bar 1}10]), both as twin mirror and composition planes. (a) Perspective view of a tabular sixfold sector twin with pseudo-hexagonal twin axis c. In each sector the monoclinic b axis is normal to the twin axis c, whereas the a axis slopes slightly down by about 4.5° ([\beta = 94.5^\circ]), leading to an umbrella-like shape of the twin. (b) Polarization micrograph of a sixfold twinned hexagon (six orientation states) of the shape shown in (a). Pairs of opposite twin components have the same optical extinction position. Courtesy of Ch. Sweegers, PhD thesis, University of Nijmegen, 2001.

    In contrast to orthorhombic aragonite with only three pseudo-hexagonal orientation states, these gibbsite twins exhibit six different orientation states. This is due to the absence of any eigensymmetry element along the pseudo-hexagonal axis [001]. The intersection symmetry of all orientation states is [\bar 1]. The reduced composite symmetry of a domain pair is [{\cal K}^*=12'/m'1], with [m'] the twin mirror plane (110).

  • (iv) `Median law': According to Brögger (1890[link]), this twin law implies exact parallelism of non-equivalent edges [[110]_{\rm I}] and [[010]_{\rm II}], and vice versa, of partners I and II. The twin element is an irrational twofold axis parallel to (001), bisecting exactly the angle between [110] and [010], or alternatively, an irrational twin reflection plane normal to this axis. This interesting orientation relation, which has been observed so far only for gibbsite, does not obey the minimum condition for twinning as set out in Section 3.3.2.2[link]. An alternative interpretation, treating these twins as rational [130] rotation twins, is given by Johnsen (1907[link]), cf. Tertsch (1936[link]), pp. 483–484. Interestingly, this strange `twin law' is the most abundant one among natural gibbsite twins.

References

First citation Brögger, W. C. (1890). Hydrargillit. Z. Kristallogr. 16, second part, pp. 16–43, especially pp. 24–43 and Plate 1.Google Scholar
 First citation Johnsen, A. (1907). Tschermak's Zwillingstheorie und das Gesetz der Glimmerzwillinge. Centralbl. Mineral. Geolog. Palaeontol. pp. 400–409, especially p. 407.Google Scholar
 First citation Sweegers, C., van Enckevort, W. J. P., Meekes, H., Bennema, P., Hiralal, I. D. K. & Rijkeboer, A. (1999). The impact of twinning on the morphology of γ-Al(OH)3 crystals. J. Cryst. Growth, 197, 244–253.Google Scholar
 First citation Tertsch, H. (1936). Bemerkungen zur Frage der Verbreitung und zur Geometrie der Zwillingsbildungen. Z. Kristallogr. 94, 461–490.Google Scholar








































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