Crystallographic–Morphological Paradoxes in Metal–Organic Frameworks

30 May 2022, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


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.


Crystal engineering
Metal-organic framework
Concave morphology
Single crystals
Merohedral twinning
Miller index
Laue class statistics
Concave facets
Concave polyhedron


Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.