Structural resonance through harmonic and anharmonic interactions: the characterisation of local and overall chirality in TMACuCl3

The complicated structure of one of the phases of tetramethylammonium trichlorocuprate (TMACuCl3) is discussed. The observed deformations with respect to the high-symmetry space group have been decomposed into irreducible representations of this group (P63/mmc). The representations that induce the deformations are tau 5 (k=2 pi (0,0,1/5c)) and tau 6 (k=2 pi (0,0,2/5c)) (Kovalev notation). Structural resonance occurs between these two waves through anharmonic energy contributions. This resonance is such that in the resulting structure two building blocks are discernible, one block showing all characteristics of CsCuCl3 and one some of RbCuCl3. The elements of the gyration tensor have been calculated using single-crystal diffraction data. The chiral functions from which the tensor elements are calculated form fourth-order invariants when squared. This concept can be demonstrated on both the Jahn-Teller octahedra and the successive Cu and Cl layers of this compound. Furthermore, an explanation is given for the fact that some of the TMA groups are disordered, thus contributing to the free energy by an entropy term, and some are not. The superposition of the two waves is such that the E(X) in Jahn-Teller effect of the individual octahedra fits in precisely.