3. Crystallographic considerations: single crystals, nanoparticles, aggregates

3.1 Ideal nanoparticles, Platonic solids, and Archimedean solids

As a first approximation, the construction of a crystal made up of gold atoms, or at least understanding its structure, is similar to examining the stacking of its atoms as hard spheres that organize themselves in the most compact way possible (model proposed by M.V. Goldschmidt in 1928). A display of oranges stacked neatly in a shop is a good example of compact stacking.

This type of stacking of hard spheres accurately describes reality, insofar as the chemical bonds between atoms are not very directional in the case of a metal such as gold, due to the spherical symmetry of its 6s orbitals mentioned above. Compact stacking, when limited to a small number of atoms, as in the case of metal nanoparticles,...