Deformation mechanisms leading to auxetic behaviour in the α-cristobalite and α-quartz structures of both silica and germania

Abstract

Analytical expressions have been developed in which the elastic behaviour of the α-quartz and α-cristobalite molecular tetrahedral frameworks of both silica and germania are modelled by rotation, or dilation or concurrent rotation and dilation of the tetrahedra. Rotation and dilation of the tetrahedra both produce negative Poisson’s ratios (auxetic behaviour), whereas both positive and negative values are possible when these mechanisms act concurrently. Concurrent rotation and dilation of the tetrahedra reproduces with remarkable accuracy both the positive and negative ν31 Poisson’s ratios observed for silica α-quartz and α-cristobalite, respectively, when loaded in the x3 direction. A parametric fit of the concurrent model to the germania α-quartz experimental ν31 Poisson’s ratio is used to predict ν31 for germania α-cristobalite, for which no experimental value exists. This is predicted to be +0.007. Strain-dependent ν31 trends, due to concurrent rotation and dilation in the silica structures, are in broad agreement with those predicted from pair-potential calculations, although significant differences do occur in the absolute values. With the model of concurrent dilation and rotation of the tetrahedra we predict that an alternative uniaxial stress (σ3)-induced phase exists for both silica, α-quartz and α-cristobalite, and germania, α-cristobalite, having geometries in reasonable agreement with β-quartz and idealized β-cristobalite, respectively.

Three-dimensional cellular structures with negative Poisson's ratio and negative compressibility properties

“…However, it is well known that the Poisson's ratio need not be a positive quantity, and materials having a negative Poisson's ratio, commonly known as auxetics , do exist. In fact, in recent years, there have been several important developments in this field, which led to the prediction, discovery and/or development of several types of auxetic materials (Lakes 1987;Wojciechowski 1989;Evans et al 1991;Alderson et al 2002;Scarpa et al 2005) and structures/models (Gibson et al 1982;Rothenburg et al 1991;Evans et al 1994;Wojciechowski & Branka 1994;Scarpa et al 2004;Grima et al 2005;Alderson & Evans 2009). These include nano-scale materials such as zeolites Sanchez-Valle et al 2005), silicates (Yeganeh-Haeri et al 1992;Alderson & Evans 2009), cubic materials (Baughman et al 1998a;Norris 2006) and liquid crystalline polymers (He et al 1998(He et al , 2005; micro-scale materials such as foams (Lakes 1987;Chan & Evans 1997;Alderson et al 2006;Grima et al 2009;Alderson & Alderson 2010;Bianchi et al 2011) and micro-porous polymers (Caddock & Evans 1989;Alderson & Evans 1992;Alderson et al 2002;Ravirala et al 2005); biological systems such as cancellous bone (Williams & Lewis 1982) and macro-scale models based on re-entrant geometries (Gibson et al 1982;Evans et al 1994Evans et al , 1995Choi & Lakes 1995;Masters & Evans 1996), chiral ...…”

Temperature dependence of Young׳s modulus of silica refractories

“…It is also evident that the Poisson ratio is predicted to be negative. Of course, this is no surprise, because cristobalite is known to be an auxetic material [7,[16][17][18].…”

Molecular modelling of structure and deformation mechanisms of auxetic behaviour in the α-quartz structures

“…The CTM allows the possibility of both positive and negative Poisson's ratios to be realised when rotation and dilation of a tetrahedron act in an opposite sense to each other (i.e. one expands the structure whereas the other contracts the structure) [12].…”

“…He believed deformation mechanisms can occur in at least three different ways: first, a cooperative, "rigid" rotation of the linked tetrahedra analogous to the mechanism for [12] reported fully analytical models for α-cristobalite and α-quartz to explain how auxetic and non-auxetic behaviour can be produced in both cases. The analytical models show both auxetic and non-auxetic behaviour for the α-cristobalite and α-quartz frameworks can arise when the deformation mechanism comprises of concurrent rotation and dilation of the tetrahedra (the Concurrent Tetrahedra Model-CTM).…”