Wavevector Star Channel and Symmetry Group


The respected Comrade Kim Jong Un said:

"It is important to speed up technological development in major fields such as mechanical, metal, thermal and materials engineering, and to apply the achievements proactively in different economic sectors."

Researchers in Faculty of Chemistry of Kim Il Sung University have presented some new concepts of wavevector star channel and wavevector star channel group, which allow the effective study of phase transitions considering directly the translational symmetry breaking in crystals.

Spontaneous symmetry breaking, especially translational symmetry-breaking phenomena in ferroics and multiferroics such as ferromagnetics, ferroelectrics, ferroelastics,ferromagneto-ferroelectrics, ferroelectric ferroelastics etc. are currently of great significance in the field of condensed matter physics. Not only the formation of superstructures in crystals but also the occurrence of low-dimensional crystalline materials with translational periodicities in one or two directions such as polymers, liquid crystals, semiconductor superlattices, nano-tubes, nano-bands, thin films etc. are all the result of translational symmetry breaking.

The researchers studied the substars and substar groups of Lifschitz stars which actually contribute to the translational symmetry breaking of crystals and obtained the following results.

First, a method to find the wavevector star channel was proposed, where a new order parameter space on which the representation of the translation group acts was introduced, and based on this, the wavevector star channel actually taking part in the phase transition was found by the set of invariant vectors given by an image of the translational group representation, i.e. the translational L-group.

Second, the wavevector star channel groups that can be effectively used in studying the phase transitions accompanying translational symmetry breaking were found for the 80 Lifschitz stars of the 230 crystallographic space groups.

Finally, the study of a new five component reducible order parameter model which explains the symmetry changes observed in the pyroelectric PCT crystal showed that the symmetry and phenomenology of phase transitions can be effectively studied on the basis of the theory of the wavevector star channel group and its representation, rather than that of the full irreducible representation of the crystallographic space group.

The above results were published under the title of "Wavevector Star Channel and Symmetry Group" (https://doi.org/10.1107/S2053273321006318) of "Acta Crystallographica A-Foundation and Advances" (2021, 77, 572–592).