Energy of twin boundaries in potassium lithium sulfate (KLiSO4)

What is it about?

For several decades crystals of potassium lithium sulfate were grown in Aachen from aqueous solutions and investigated experimentally by Professor Theo Hahn and his collaborators. They found that all crystals were twinned, and determined the twin laws and twin boundaries. All observed twin operations leave the lattice formed by the symmetry translations of KLiSO4 invariant, so-called merohedric twinning. The KLiSO4 phase stable at ambient temperature and pressure has point group 6, its lattice is hexagonal with point group 6/mmm. It follows that there exist three merohedric twin laws giving rise to reflection, inversion and translation twins, respectively. After the death of Theo Hahn, his colleague, Prof. Helmut Klapper approached us with the wish of calculating the energy of the twin boundaries observed in KLiSO4 as a tribute to Hahn. We gladly agreed and used the code DMol3, which had been developed by Bernard Delley based on density functional theory. We found that the twin boundaries observed most frequently [reflection twin with boundary plane (0 0 01)] have very low energy, inversion twins with boundary plane (1 0 -1 0) have medium energy and are frequent in Cr-doped crystals, whereas reflection and rotation twins with boundary plane (1 0 -1 0) have the highest energy, the first of which was observed only rarely, the second not at all. The situation is different after heating the crystals above 708 K (435C), where they become orthorhombic and cooling them afterwards back to room temperature: the inversion twins have disappeared, reflection twins with boundary plane (1 0 -1 0) have become more frequent despite their higher energy. Earlier work of the authors on Brazil and Esterel twin boundaries in -quartz led to similar results: Brazil twins with boundary (1 0 -1 1) have the lowest energy, the energy is ten times higher for boundary plane (0 1 -1 1) and about forty times higher for Esterel twins with boundary plane (1 0 -1 1). In -quartz precipitated from hot hydrothermal veins, so called low quartz, the frequency of occurrence decreases with increasing energy. In high quartz, which transformed from the -quartz of solidified magma to -quartz at room temperature, Esterel twins are the most common twins although their energy is high whereas Brazil twins do not occur.

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Why is it important?

Our results show that not only for KLiSO4 but also for quartz, the energy of twins and the frequency of their occurrence are closely related for crystals grown from aqueous solutions, whereas for the formation of transformation twins the availability of twin nuclei plays a major role.