Evolution of Symmetry in Elemental Crystals
In a recent paper in the scientific journal Symmetry, the harmonic evolution of structural symmetry was illustrated on the basis of three principles: atomic attraction, repulsion and 3D space limitations. In order to obtain high symmetrical structural motifs, including the Platonic Solids, a simple bottom-up atomistic crystal growth model derived for equivalent atoms and a pair potential involving a maximum number of equilibrium distances in the local area of the atoms was defined, as well as a phase diagram summarizing stable regions of close-packed fcc and hcp, next to bcc symmetry. Depending on the short- and long-range properties of the pair potentials, rigid lattices relax isotropically within the well potential through symmetry. The first few coordination shells with fixed distances unique to the lattice do not necessarily decide which symmetry of equilibrium prevails. The present chapter recaptures the evolution of structural symmetry in crystals followed by the basic concepts described above and the underlying weights, in order to stress the applicability of the model to empirical cases in solid state physics. In other areas, such as music and art, this leads us to a holistic view of similarities to structural characteristics. Goldschmidt’s work on basic rational series in science offers an impetus, reflecting the capacity of mathematical series as a fundamental instrument for more quantitative insights.
Dr. Matthias Zschornak
Institute of Experimental Physics, TU Bergakademie Freiberg, Leipziger Str. 23, Freiberg, Germany and Institute of Physics, TU Chemnitz, Reichenhainer Str. 70, Chemnitz, Germany.
Prof. Dirk C. Meyer
Institute of Experimental Physics, TU Bergakademie Freiberg, Leipziger Str. 23, Freiberg, Germany.
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