Molecular dynamics study of six-dimensional hard hypersphere crystals

Six-dimensional hard hypersphere systems in the A₆, D₆, and E₆ crystalline phases have been studied using event-driven molecular dynamics simulations in periodic, skew cells that reflect the underlying lattices. In all the simulations, the systems had sufficient numbers of hyperspheres to capture the first coordination shells, and the larger simulations also included the complete second coordination shell. The equations of state, for densities spanning the fluid, metastable fluid, and solid regimes, were determined. Using molecular dynamics simulations with the hyperspheres tethered to lattice sites allowed the computation of the free energy for each of the crystal lattices relative to the fluid phase. From these free energies, the fluid-crystal coexistence region was determined for the E₆, D₆, and A₆ lattices. Pair correlation functions for all the examined states were computed. Interestingly, for all the states examined, the pair correlation functions displayed neither a split second peak nor a shoulder in the second peak. These behaviors have been previously used as a signature of the freezing of the fluid phase for hard hyperspheres in two to five dimensions.