Chiral Crystals in Light from Pasteur to the Present

Alan Mackay (1926-2025), an imaginative crystallographer (Birkbeck College, University of London), often spoke of the “tyranny of space groups” in the service of a generalization of organized structures in chemistry. Indeed, we know the vast majority of what we know about molecular structure from the scattering of X-rays from crystals. Diffraction works so well because crystals have long-range, triperiodic translational symmetry, they conform to one of the 230 classical space groups. The sharp edges and flat faces of polyhedral crystal, so unlike most everything else in Nature, “flash forth their symmetry”, according to Federov who enumerated the space groups in 1890. However, a large fraction of simple molecular crystals can be made to grow with helicoidal morphologies, structures with curvature that are decidedly not straight. This is a common though little-known fact about crystal form that is easy to observe. Indeed, such crystals could were prepared in the 19 th C. by von Liebig and Pasteur, but they failed to notice the pathological morphologies. Had they added twisted crystals to their catalogues of discovery, we might have been further along in Mackay’s program to generalize crystallography. Evidence supporting mechanisms of whole-body mechanical deformations of growing crystals is provided. The twisting of radially arrayed helicoidal crystallites in rhythmically banded spherulites leads to

spectacular spontaneous optical patterns in a great variety of materials form small molecules that grow when the crystallographic driving forces are high. Some of the optoelectronic properties of such films are described, including chiroptical polarization and enhanced electrical conductivity and photoconductivity. The coherence and loss of coherence of the rhythmic polycrystalline growth is investigated through simulation.