Volume 102, Number 6, June 2013
|Number of page(s)||6|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||03 July 2013|
Symmetry detection of auxetic behaviour in 2D frameworks
1 Theoretische Physik I, Friedrich-Alexander Universität Erlangen-Nürnberg - Staudtstr. 7, 91058 Erlangen, Germany
2 Department of Chemistry, University of Sheffield - Sheffield S3 7HF, UK
3 Department of Engineering, University of Cambridge - Trumpington Street, Cambridge CB2 1PZ, UK
Received: 24 May 2013
Accepted: 17 June 2013
A symmetry-extended Maxwell treatment of the net mobility of periodic bar-and-joint frameworks is used to derive a sufficient condition for auxetic behaviour of a 2D material. The type of auxetic behaviour that can be detected by symmetry has Poisson's ratio −1, with equal expansion/contraction in all directions, and is here termed equiauxetic. A framework may have a symmetry-detectable equiauxetic mechanism if it belongs to a plane group that includes rotational axes of order n = 6, 4, or 3. If the reducible representation for the net mobility contains mechanisms that preserve full rotational symmetry (A modes), these are equiauxetic. In addition, for n = 6, mechanisms that halve rotational symmetry (B modes) are also equiauxetic.
PACS: 62.20.dj – Poisson's ratio
© EPLA, 2013
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