We study a small system of spherically confined hard spheres using the Widom particle insertion method as an indicator for the ordering transition. By Monte Carlo simulations we determine the insertion probability as a function of the number of particles and the box size. We find an increase of the insertion probability upon increasing density, which becomes more pronounced as the box size decreases. The increase of the insertion probability corresponds to an increase of the order, which is confirmed by a local bond-order analysis and the simulation snapshots. The ordered structures can be described as defective solids.
Materials by design for sustainable solutions in the energy, medical, transport, and engineering sectors
