Crystallographic–Morphological Paradoxes in Metal–Organic Frameworks

The symmetry of a crystal’s morphology usually reflects the symmetry of the crystallographic packing. For single-crystals, the space and point groups allow only a limited number of mathematical descriptions of the morphology (forms), all of which are convex polyhedrons. In contrast, concave polyhedrons are a hallmark of twinning and polycrystallinity and are inconsistent with single crystallinity. Here we report unique metallo-organic crystals that exhibit, on the one hand, single crystallinity and, on the other hand, a concave, multidomain appearance and a rare space group (P622). Despite these contradictions, it is puzzling that the symmetry of these crystals is linked at different hierarchies, from the molecular to the microscopic levels. They exhibit a deceptive combination of the three characteristics that define a crystal at different length scales: the unit cell, the organization of these unit cells, and morphology. The structural properties of this system are intrinsic, as no other materials (additives) were used to shape the facets. The unusual concave morphology of the crystals can be a direct consequence of the open molecular packing often found in metal-organic frameworks. This fact has not been recognized before in these and other porous materials. Such crystals offer new opportunities for the formation of 3D objects where the physical properties can be designed and predicted based on the point group symmetry.