Melting and Structural Transitions of Interacting Particle Arrays on Soft Shells.*

We report on a numerical study of the finite-temperature phase diagram of discrete particles with orientation-dependent interactions whose groundstate is a closed shell. According to continuum theory, a closed shell can undergo a buckling transition between a spherical and an icosahedral state as a function of the ratio of the stretching and bending moduli (the Föppl-von-Kármán (FvK) number). This buckling transition is reproduced by the discrete particle model. However, we find that at low temperatures the icosahedral structure is stable only at large FvK numbers. For low FvK numbers, it narrowly competes with a variety of different ordered structures, in particular when the pair-potential has a narrow width. When the temperature is increased, the various low FvK structures melt easily into a fluid state. If the temperature is raised further then the liquid state shell collapses into a 3D structure. On the other hand, the more stable high FvK icosahedral states never melt before they collapse. Our simulations emphasize the extraordinary stability of an icosahedral shell at large FvK numbers.