Decorating emulsion droplets by particles stabilizes foodstuff and pharmaceuticals. Interfacial particles also influence aerosol

formation, thus impacting atmospheric CO₂ exchange. While particles at disordered droplet interfaces were extensively

investigated, those at the ubiquitous ordered interfaces have never been studied.

We have recently demonstrated that a two-dimensional hexagonally-packed crystalline monolayer of oil and surfactant

molecules forms at the surface of common oil emulsion droplets, surfactant-stabilized in water, at a temperature T=T_s.

The incompatibility of the hexagonal structure of this monolayer with a curved geometry implies that defects must be

present in its structure even at the ground state. While the elastic properties of two-dimensional crystals have been widely

studied in the past, the properties of freely-deforming curved two-dimensional crystals have never been studied.

We study the properties of curved two-dimensional crystals by following the dynamics of tracer colloidal particles incorporated

into the crystalline structure. We demonstrate the particles to be spontaneously dragged to particular surface locations. We

identify these particles "attractors" with topological defects within the crystalline structure. At T=T_d < T_s, the droplets undergo

a sphere-icosahedron shape transformation, with the attractors self-positioning onto their vertices and fixing there the positions

of the surface-adsorbed particles. At an even lower temperature, the particles are spontaneously expelled from the droplets.

These phenomena allow functional liquid “atoms” to be designed, with their “valency” fixed by precise temperature-tuned

positioning, and type, of the interfacial ligands, enabling self-assembly into supra-“atomic” structures. Our observations also

impact upon the understanding of protein positioning on cell membranes, controlling essential biological functions.