Energetics and dynamics of caged Zn₄ in i-ScZn

Abstract

In i-ScZn, like other quasicrystals of the i-CaCd class, the innermost shell of the icosahedral cluster is a Zn₄ tetrahedron, which thus breaks the symmetry of the outer cluster shells. We investigate theoretically the dynamics of individual tetrahedra, using interatomic pair potentials, fitted from an ab initio database, and molecular dynamics (MD). This includes the formulation of an effective Hamiltonian written in terms of a rigid-body rotation representing the state of each tetrahedron. We characterize the minimum-energy orientations of a tetrahedron, as well as the paths of the transitions between minima (reorientations). The velocity autocorrelations were evaluated for the tetrahedral atoms in the MD dynamics; the corresponding spectral density S(ω) is fairly well fitted by a simplified model in which each atom hops in a double well.

Keywords:

• molecular dynamics
• effective Hamiltonian
• tetrahedron cluster
• Sc-Zn
• vibrational density of states

Acknowledgements

This work was supported by US Department of Energy Grant DE-FG02-89ER-45405 (CLH) and by Slovak VEGA 2/0157/08. CLH thanks the Slovak Academy of Sciences for hospitality and the Slovak National Scholarship Program for a visitor's fellowship.

Notes

Note

1. One suspects this large motion of Zn (or Cd in Ca-Cd compounds) is related to the extremely anomalous c/a ratios of elemental Zn and Cd; it is surprising that pair potentials capture such effects.