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Competing ordered structures formed by particles with a regular tetrahedral patch decoration

We study the ordered equilibrium structures of patchy particles where the patches are located on the surface of the colloid such that they form a regular tetrahedron. Using optimization techniques based on ideas of evolutionary algorithms we identify possible candidate structures. We retain not only the energetically most favourable lattices but also include a few energetically less favourable particle arrangements (i.e., local minima on the enthalpy landscape). Using suitably developed Monte Carlo based simulations techniques in an NPT ensemble we evaluate the thermodynamic properties of these candidate structures along selected isobars and isotherms and identify thereby the respective ranges of stability. We demonstrate on a quantitative level that the equilibrium structures at a given state point result from a delicate compromise between entropy, energy (i.e., the lattice sum) and packing.