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. 405-406

Section 3.3.6.4. Twinning of high-temperature quartz (β-quartz)

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

3.3.6.4. Twinning of high-temperature quartz (β-quartz)

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Upon heating quartz into the hexagonal high-temperature phase (point group 622) above 846 K, the Dauphiné twinning disappears, because the composite symmetry [{\cal K}] of the twinned low-temperature phase now becomes the eigensymmetry [{\cal H}] of the high-temperature phase. For Brazil twins, however, their nature as reflection or inversion twins is preserved during the transformation.

The eigensymmetry of high-temperature quartz is 622 (order 12). Hence, the coset of the Brazil twin law contains 12 twin operations, as follows:

  • (i) the six twin operations of a Brazil twin in low-temperature quartz, as listed above in Example 3.3.6.3.2[link];

  • (ii) three further reflections across planes [\{10{\bar 1}0\}], which bisect the three Brazil twin planes [\{11{\bar 2}0\}] of low-temperature quartz;

  • (iii) three further rotoinversions around [001]: [{\bar 6}{^1}], [{\bar 6}{^3} = m_z], [{\bar 6}{^5} = {\bar 6}{^{-1}}].

The composite symmetry is [ {\cal K} = {6\over m'}{2\over m'}{2\over m'}({\bar 1}{^\prime}),]a supergroup of index [2] of the eigensymmetry 622.

In high-temperature quartz, the combined Dauphiné–Brazil twins (Leydolt twins) are identical with Brazil twins, because the Dauphiné twin operation has become part of the eigensymmetry 622. Accordingly, both kinds of twins of low-temperature quartz merge into one upon heating above 846 K. We recommend that these twins are called `Brazil twins', independent of their type of twinning in the low-temperature phase. Upon cooling below 846 K, transformation Dauphiné twin domains may appear in both Brazil growth domains, leading to four orientation states as shown in Fig. 3.3.6.2[link]. Among these four orientation states, two Leydolt pairs occur. Such Leydolt domains, however, are not necessarily in contact (cf. Example 3.3.6.3.3[link] above).

In addition to these twins with `parallel axes' (merohedral twins), several kinds of growth twins with `inclined axes' occur in high-temperature quartz. They are not treated here, but additional information is provided by Frondel (1962[link]).

References

First citation Frondel, C. (1962). The system of mineralogy, 7th edition, Vol. III. Silica minerals, especially pp. 75–99. New York: Wiley.Google Scholar








































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