PubliÃ© le 21/04/2022 par Constantin Doru

The regular packing of identical bodies is a fundamental problem (which fascinated natural scientists since Greek antiquity), but also has important applications to nanomaterials, which are often produced using building blocks whose shape controls their properties. Spindle-shaped nanoparticles (elongated and with sharp tips) are very promising in this respect, but their stacking had never been determined.

A collaboration between the ICS (CNRS/UniversitÃ© de Strasbourg), the LPS (CNRS/UniversitÃ© Paris-Saclay), the SOLEIL synchrotron and a Spanish team proved that pentagonal gold bipyramids form a triclinic lattice, the lowest possible symmetry. Moreover, the optical response of the assemblies depends on the orientation of the exposed facets, opening the perspective of applications to the detection of very dilute analytes. This work has just been published in the journal *Advanced Materials* and has been highlighted by the Institute of physics (INP) of the CNRS.

Figure 1: A) Tiling the plane with regular pentagons. B) Three-dimensional assembly of pentagonal bipyramids.

This surprising loss of symmetry can be understood through the analogy with a planar tiling using regular pentagons (Figure 1A): the individual objects have a fivefold rotation axis *C*_{5}, but to cover the plane they must pair up in order to recover an inversion center *I*. To do it, they must however reduce their rotation symmetry to order 2.

Similarly, the bipyramids associate in a triclinic structure, with two particles per unit cell (Figure 1B). This result was obtained by X-ray scattering and by electron microscopy. Numerical simulations reproduce the symmetry and packing fraction of the stacking, confirming that it is the most compact solutions.

Thus, the fruitful back-and-forth between synthesis, characterization and modelling allowed us to solve a problem of â€œpureâ€ mathematics, but also to obtain a material with unexpected properties.

**Reference**

Double-lattice packing of pentagonal gold bipyramids in supercrystals with triclinic symmetry

Jieli

Lyu, Wajdi Chaabani, Evgeny Modin, Andrey Chuvilin, Thomas Bizien,

Frank Smallenburg, Marianne ImpÃ©ror-Clerc, Doru Constantin, Cyrille

Hamon

Adv. Mater. (2022), sous presse.

DOI : 10.1002/adma.202200883

**Contact**

Frank Smallenburg, Marianne ImpÃ©ror-Clerc, Doru Constantin, Cyrille Hamon