Geminography: the crystallography of twins

Abstract:We review the available information on crystal twinning at high pressures and analyze the effect of hydrostatic pressure on the pseudosymmetry of selected compounds. Twinning by merohedry, type I and II, as well as pseuomerohedral twinning at high pressures has been described. For twinning by merohedry type I (inversion twinning) a reliable characterization of the twin domains and volume fractions is difficult and largely depends on the experimental conditions, i.e. the number of measured Friedel pairs and the chosen wavelength. For twinning by merohedry, type II, and for twinning by pseuodmerohedry twin volume fractions could be reliably determined for several cases. In none of these a significant influence of hydrostatic pressure on the volume fractions of the individuals was observed. Pressure-induced twinning has been observed for compounds which undergo first-order phase transitions. The twinning operation in the described cases is related to the loss of rotational symmetry elements of the higher symmetrical polymorph although the high and low pressure phases are not in group-subgroup relationship. The analysis of pseudosymmetry of several compounds as a function of pressure suggests that this parameter can be used to predict the (in)stability of compounds. In particular, a decrease in pseudosymmetry seems to be strongly correlated with the occurrence of first-order phase transitions in which the crystal breaks or amorphizes. The effect of hydrostatic and chemical pressure on the pseudosymmetry of the crystal structures can lead to different or even opposite trends, suggesting that the increase or decrease of pseudosymmetry cannot be understood as a pure volume effect.

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“…For further reading on twinning the reader is referred to the review articles available in the literature e.g. [4][5][6][7].…”

Section: Twinningmentioning

confidence: 99%

Twinning and pseudosymmetry under high pressure

Friese

Grzechnik

2014

Zeitschrift Für Kristallographie – Crystalline Materials

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“…(Hahn et al, 1999;. Some crystallographers interested in grain boundaries are following the work of Pond & Vlachavas (1983) and are trying to integrate the CSL rotations in that synthesis (Grimmer & Nespolo, 2006).…”

Section: A Brief Overview On Simple Twinningmentioning

confidence: 99%

Multiple twinning in cubic crystals: geometric/algebraic study and its application for the identification of the Σ3ⁿgrain boundaries

Cayron

2006

Acta Crystallogr A Found Crystallogr

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Multiple twinning in cubic crystals is represented geometrically by a threedimensional fractal and algebraically by a groupoid. In this groupoid, the variant crystals are the objects, the misorientations between the variants are the operations, and the AE3 n operators are the different types of operations (expressed by sets of equivalent operations). A general formula gives the number of variants and the number of AE3 n operators for any twinning order. Different substructures of this groupoid (free group, semigroup) can be equivalently introduced to encode the operations with strings. For any coding substructure, the operators are expressed by sets of equivalent strings. The composition of two operators is determined without any matrix calculation by string concatenations. It is multivalued due to the groupoid structure. The composition table of the operators is used to identify the AE3 n grain boundaries and to reconstruct the twin related domains in the electron back-scattered diffraction maps.

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“…The subject is extremely wide and some recent reviews have been published (see e.g. Klapper, 2003 andGrimmer &). Here we give just a brief summary of the aspects that from the viewpoint of mathematical crystallography are more directly related to the above problems.…”

Section: Reticular Theory Of Twinningmentioning

confidence: 99%

Does mathematical crystallography still have a role in the XXI century?

Nespolo

2007

Acta Cryst Sect A

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Mathematical crystallography is the branch of crystallography dealing specifically with the fundamental properties of symmetry and periodicity of crystals, topological properties of crystal structures, twins, modular and modulated structures, polytypes and OD structures, as well as the symmetry aspects of phase transitions and physical properties of crystals. Mathematical crystallography has had its most evident success with the development of the theory of space groups at the end of the XIX century; since then, it has greatly enlarged its applications, but crystallographers are not always familiar with the developments that followed, partly because the applications sometimes require some additional background that the structural crystallographer does not always possess (as is the case, for example, in graph theory). The knowledge offered by mathematical crystallography is at present only partly mirrored in International Tables for Crystallography and is sometimes still enshrined in more specialist texts and publications. To cover this communication gap is one of the tasks of the IUCr Commission on Mathematical and Theoretical Crystallography (MaThCryst).

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Geminography: the crystallography of twins

Cited by 48 publications

References 38 publications

Twinning and pseudosymmetry under high pressure

Twinning and pseudosymmetry under high pressure

Multiple twinning in cubic crystals: geometric/algebraic study and its application for the identification of the Σ3ⁿgrain boundaries

Does mathematical crystallography still have a role in the XXI century?

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Geminography: the crystallography of twins

Cited by 48 publications

References 38 publications

Twinning and pseudosymmetry under high pressure

Twinning and pseudosymmetry under high pressure

Multiple twinning in cubic crystals: geometric/algebraic study and its application for the identification of the Σ3ngrain boundaries

Does mathematical crystallography still have a role in the XXI century?

Contact Info

Product

Resources

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Multiple twinning in cubic crystals: geometric/algebraic study and its application for the identification of the Σ3ⁿgrain boundaries