Truchet-tile structure of a topologically aperiodic metal-organic framework

TL;DR

This paper demonstrates that a specific metal-organic framework exhibits a topologically aperiodic structure analogous to Truchet tilings, revealing new insights into complex 3D tiling patterns at the atomic scale.

Contribution

It introduces a novel atomic-scale realization of a topologically aperiodic Truchet tiling within a metal-organic framework, linking geometric frustration to its structure.

Findings

The framework is a 3D topologically aperiodic tiling.

The structure is formed by zinc clusters with disordered connections.

The aperiodic structure arises from geometric frustration.

Abstract

Periodic tilings can store information if individual tiles are decorated to lower their symmetry. Truchet tilings - the broad family of space-filling arrangements of such tiles - offer an efficient mechanism of visual data storage related to that used in barcodes and QR codes. Here, we show that the crystalline metal-organic framework [OZn$_4$][1,3-benzenedicarboxylate]$_3$ (TRUMOF-1) is an atomic-scale realisation of a complex three-dimensional Truchet tiling. Its crystal structure consists of a periodically-arranged assembly of identical zinc-containing clusters connected uniformly in a well-defined but disordered fashion to give a topologically aperiodic microporous network. We suggest that this unusual structure emerges as a consequence of geometric frustration in the chemical building units from which it is assembled.