Assessing free lattice and structure parameters from the atomic level

Paufler, P.

doi:10.1002/crat.201500273

Cited by 1 publication

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“…If symmetry descends, more and more free lattice and structure parameters dominate the arrangement of distances for the equilibrium structure. The assessment of these relaxational degrees of freedom has been in the focus of crystallography for many decades, since the first structures have been determined up to recent attempts from the atomic level [31], and even with mathematical schemes to generate complexity like cellular automatons [32]. The presented considerations may give rise to optimization of pair potentials beyond the scope of the Standard Morse Potential, which is widely used, e.g., in Molecular Dynamic Simulations [33] and Bond Valence Methods [34].…”

Section: Stability Of Unary Structuresmentioning

confidence: 99%

Harmonic Principles of Elemental Crystals—From Atomic Interaction to Fundamental Symmetry

et al. 2018

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The formation of crystals and symmetry on the atomic scale has persistently attracted scientists through the ages. The structure itself and its subtle dependence on boundary conditions is a reflection of three principles: atomic attraction, repulsion, and the limitations in 3D space. This involves a competition between simplicity and high symmetry on the one hand and necessary structural complexity on the other. This work presents a simple atomistic crystal growth model derived for equivalent atoms and a pair potential. It highlights fundamental concepts, most prominently provided by a maximum number of equilibrium distances in the atom's local vicinity, to obtain high symmetric structural motifs, among them the Platonic Solids. In this respect, the harmonically balanced interaction during the atomistic nucleation process may be regarded as origin of symmetry. The minimization of total energy is generalized for 3D periodic structures constituting these motifs. In dependence on the pair potential's short-and long-range characteristics the, by symmetry, rigid lattices relax isotropically within the potential well. The first few coordination shells with lattice-specific fixed distances do not necessarily determine which equilibrium symmetry prevails. A phase diagram calculated on the basis of these few assumptions summarizes stable regions of close-packed fcc and hcp, next to bcc symmetry for predominantly soft short-range and hard long-range interaction. This lattice symmetry, which is evident for alkali metals as well as transition metals of the vanadium and chromium group, cannot be obtained from classical Morse or Lennard-Jones type potentials, but needs the range flexibility within the pair potential.

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