Ab initio investigations on the stability of seven-fold approximants

Abstract

The stability of theoretical heptagonal approximants was investigated. No approximant phase has yet been confirmed consisting of all three heptagonal rhomb prototiles. To solve this problem, two new approximant structures were constructed from supertiles taken from the ThB₄ and YCrB₄ structure types. In order to compare structural stability, the total energy convex hulls were calculated for the ternary systems B–Cr–RE (RE = Dy, Er, Ho, Y), as well as B–Mn–Dy and B–Mn–Y, by means of ab initio calculations, using density functional theory. This included all known stable monary, binary and ternary phases. Additionally, several layered boride structure types, which are not stable in the respective ternary systems but show four-, five-, six- or seven-fold local environments, were included by chemical substitution. In all ternary systems, the theoretical approximants were found to be mechanically stable, but chemically unstable by an amount of energy larger than the margin of error. A tendency towards the stabilization of structures showing five- or 10-fold local environments was observed. This is consistent with the findings of decagonal approximants in the systems B–Ti–Ru and B–Mg–Ru.

Keywords:

• approximant
• heptagonal rhomb prototile
• ab initio calculation
• stability

Acknowledgements

The authors thank Marek Mihalkovic and Daniel Jung for their ideas and fruitful discussions and Sandro Bigler for his contributions to this work. Financial support by ETH Zurich is gratefully acknowledged.