Having established a mathematical understanding of triply periodic minimal surfaces (TPMS), the subsequent step involves exploring their connections to crystals. Inspired by the derivation of zero equipotential surfaces, density functional theory (DFT) is utilised to calculate surfaces of a given charge density. It was observed that as the charge density approaches zero, these surfaces converge to the TPMS that align with the symmetry of the corresponding crystal. Following an introduction to DFT, which helps in the understanding of the computational method used for calculating surfaces of a given charge density, examples of Na, Cu, Al, Zr, and NiTi, which have different crystal lattices are presented.

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Visualisation of Minimal Surfaces Corresponding to Crystals

  • Mengdi Yin

摘要

Having established a mathematical understanding of triply periodic minimal surfaces (TPMS), the subsequent step involves exploring their connections to crystals. Inspired by the derivation of zero equipotential surfaces, density functional theory (DFT) is utilised to calculate surfaces of a given charge density. It was observed that as the charge density approaches zero, these surfaces converge to the TPMS that align with the symmetry of the corresponding crystal. Following an introduction to DFT, which helps in the understanding of the computational method used for calculating surfaces of a given charge density, examples of Na, Cu, Al, Zr, and NiTi, which have different crystal lattices are presented.