Discussion of an auxetic model possessing a complete bandgap at
Auxetics 2007 @ Malta, Mon 24 - Wed 26 September 200

A.C. Sparavigna

J.N. Grima

English

J. N. Grima

SPARAVIGNA, Amelia Carolina

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

04 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEPhonons in a two-dimensional auxetic lattice / J.N. Grima; A.C. Sparavigna. - (2007). ((Intervento presentato alconvegno Auxetics 2077, 4th International Workshop on Auxetics and Related Systems tenutosi a Malta nel Settembre,24-26.OriginalPhonons in a two-dimensional auxetic latticePublisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2507912 since: 1 Auxetics 2007 @ Malta, Mon 24 - Wed 26 September 2007  Phonons in a two-dimensional auxetic lattice J.N. Grima1 and A. Sparavigna2,*  1 Department of Chemistry, University of Malta, Msida MSD 2080, Malta 2 Dipartimento di Fisica, Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy. E-mail: amelia.sparavigna@polito.it  PACS:  62.20, 63.20 Auxetics are materials and structures displaying a negative Poisson's ratio, meaning that they exhibit a lateral extension, instead of shrinking, when they are stretched. Although in the past two decades there has been considerable developments on systems exhibiting auxetic behaviour, the studies of the modes of vibrations in auxetic structures is still in its infancy. Here we aim starting a discussion on models of two-dimensional lattices, in which the lattice is represented by a planar network where sites are connected by strings and rigid rods, in order to obtain an auxetic structure.  In particular, we discuss a model based on the recently proposed ‘rotating squares’ structure [1-3], see Fig. 1(a). We show that since the proposed lattice has a basis, translational and rotational mode dispersions are observed displaying a complete bandgap when the ratio of masses in the lattice basis is different from one (Fig.1(b),(c)). In analogy with the behaviour of crystalline lattices, the acoustic mode velocity is strongly reduced when the mass ratio increases.   References:  [1] J.N. Grima, A. Alderson and K.E. Evans, Zeolites with negative Poisson's ratios, Paper presented at the 4th Materials Chemistry conference, Dublin (Ireland), July 1999 (P81).  [2] J.N. Grima and K.E. Evans, J. Mat. Sci. Lett., 19 (2000) p.1563-1565.  [3] Y. Ishisbashi and M. Iwata, J. Phys. Soc. Jap., 69 (2000) 2702.  (*) Author for correspondence  2 Auxetics 2007 @ Malta, Mon 24 - Wed 26 September 2007  (a)  (b) (c)  Fig. 1(a): The lattice discussed here where masses are connected with strings; (b) the reduced mode frequencies as a function of wavenumbers along directions X,Y and D, when the units of the lattice basis have the same mass, and (c) the reduced mode frequencies as a function of  wavenumbers, when the units of the lattice have different masses (M1=4Mo). Note the complete bandgap between translational and rotational modes and the lower group velocity of translational (acoustic) modes. 

Phonons in a two-dimensional auxetic lattice

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Phonons in a two-dimensional auxetic lattice

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