Twinning of crystals as a result of differences between symmetrical and energetical most favourable structure arrangements

Abstract

It is thought that the building units of crystal structures always tend to the highest possible symmetrical arrangements. These arrangements have not to correspond in every case to the energetical most favourable structure. Structures that show this distinct misfit tend to twinning. The examination of pentaerythrite and 1,2,4,5-tetrabromobenzene, two substances usually existing as twins, leads to the finding of structures -by lattice-energy calculations -with a better energy balance, but are not known yet as autonomous phases. Both cases showed arrangements with lower symmetry explaining the transition between the twin individuals. Following this theory the development of crystal twins is based on a structural instability caused by the conflict between the more favourable energetical arrangement and the highest available symmetry.Es wird davon ausgegangen, daR die Bausteine in den Kristahtrukturen stets eine hochstmogliche symmetrische Anordnung anstreben. Diese Anordnung muR nicht immer mit der energetisch gunstigsten Struktur iibereinstimmen. Strukturen, bei denen diese Diskrepanz ausgeprdgt ist, neigen zur Verzwillingung. Anhand von Pentaerythrit und 1,2,4,5-Tetrabrombenzol, die praktisch nur als Zwillinge bekannt sind, wurden durch Gitterenergieberechnungen Strukturen gefunden, die energetisch gunstiger sind, aber als eigenstandige Phasen bisher nicht bekannt sind. In beiden Fallen ergaben sich Anordnungcn geringerer Symmetrie. Mit Hilfe dieser Strukturen ist der Ubergang zwischen den Zwillingsindividuen erkllrbar. Nach dieser Theorie beruht die Bildung von Kristallzwillingen auf struktureller Instabilitat hervorgerufen durch den Konflikt zwischen energetisch giinstigster Anordnung und hochstmoglicher Symmetrie.

Br···Br and Br···H Interactions in Action: Polymorphism, Hopping, and Twinning in 1,2,4,5-Tetrabromobenzene

“…A twin interface in the β structure was visualized using CERIUS molecular modeling software . Two portions of crystal were created related by reflection through the twin plane (110): one portion was moved by 1 / 2 lattice repeats along c and [1̄10] directions, and the two parts were docked by hand while close contacts were monitored.…”

“…In addition to polymorphism, Gafner and Herbstein 7,8 reported that crystals of both structures of TBB form twinned crystals in which the components are related by the (110) mirror plane. Recent lattice energy calculations, carried out by Krafczyk et al for the β structure predict the two halves of this twin to be displaced relative to one another by [1̄10]/2 and c /2 and to have a lattice energy 2.8% lower than that of a single crystal.…”

Mapping the polymorphic transformation gateway vibration in crystalline 1,2,4,5-tetrabromobenzene

“…17 and 18), crystalline TBB naturally exists in its β polymorph, with the γ polymorph forming at higher temperatures. Single crystals of TBB are often twinned,19,20 and the crystals jump or split upon polymorph transformation, propelling themselves several centimeters. The jumping distances are largely dependent on the crystal size and resting face of the crystal, with large crystals having more pronounced jumping 10…”

Molecular Configuration at the Solid−Solid Interface: Twinning in Saccharin Crystals

“…A twinned crystal comprises two (or more in the case of multiple twinning) individual single crystals joined as a single particle such that the component parts are related by a symmetry element that does not exist in the single crystal. Such elements are typically mirror planes, rotation axes, or centers of inversion, and much phenomenological work has been reported in which such systems have been characterized by appropriate crystallographic and energetic relationships. − Saccharin has been chosen as a model system for this study and the work comprised three strategic elements: first the identification of the twin operation in saccharin crystals, second modification of the molecular mechanics based program HABIT to enable the energy of a twin to be calculated as a function of the juxtaposition of molecules about the twin plane, and finally the transformation of these energetic considerations into a visualization of the most likely interfacial molecular configuration.…”