Incommensurate Chirality Density Wave Transition in a Hybrid Molecular Framework

Using single-crystal x-ray diffraction we characterize the 235 K incommensurate phase transition in the hybrid molecular framework tetraethylammonium silver(I) dicyanoargentate, [NEt_{4}]Ag_{3}(CN)_{4}. We demonstrate the transition to involve spontaneous resolution of chiral [NEt_{4}]^{+} conformations, giving rise to a state in which molecular chirality is incommensurately modulated throughout the crystal lattice. We refer to this state as an incommensurate chirality density wave (XDW) phase, which represents a fundamentally new type of chiral symmetry breaking in the solid state. Drawing on parallels to the incommensurate ferroelectric transition of NaNO_{2}, we suggest the XDW state arises through coupling between acoustic (shear) and molecular rotoinversion modes. Such coupling is symmetry forbidden at the Brillouin zone center but symmetry allowed for small but finite modulation vectors q=[0,0,q_{z}]^{*}. The importance of long-wavelength chirality modulations in the physics of this hybrid framework may have implications for the generation of mesoscale chiral textures, as required for advanced photonic materials.