Modelling of the mechanical properties of α-cristobalite

Abstract

Auxetic materials exhibit the unexpected property of becoming fatter when stretched and thinner when compressed, in other words, they exhibit a negative Poisson's ratio. This counter-intuitive behaviour imparts many beneficial effects on the materials' macroscopic properties that make auxetics superior to conventional materials in many commercial applications. This unusual property has now been discovered, predicted or deliberately introduced in various classes of materials and structures such as foams, microporous polymers, silicates and zeolites. Recent research suggests that auxetic behavior results from a synergism between the material's internal structure (geometry setup) and the deformation mechanism it undergoes when submitted to a stress. The silicate a.-cristobalite is an auxetic material which has attracted a lot of attention in recent years. Negative Poisson's ratios in the (010) and (001) planes of single crystalline a.-cristobalite were independently discovered and reported in 1992 by Keskar and Chelikowsky (through ab initio modelling work) and by Yeganeh-Haeri and co-workers (experimentally using laser Brillouin spectroscopy). The experimental work suggests that Poisson's ratios in the (010) plane are mostly negative for loading close to the [101] and [101] directions whilst Poisson's ratios the in the (100) plane are mostly negative for loading close to the [011] and [011] directions. There have been various attempts to explain this unusual behaviour and several models based on dilation I relative rotation of the Si04 tetrahedral units have been proposed. However, these models do not make any reference to the fact that when one looks at the (010) and (100) planes of structure of a.-cristobalite, one may notice that the atomic positions form a geometric pattern which may be trivially described as the rectangles equivalent of the 'rotating squares' sttucture (a structure which is well known for its auxetic properties). This dissertation presents various molecular modelling experiments aimed to (i) correctly simulating the experimentally observed negative Poisson's ratio in a-cristobalite, and, (ii) understanding more clearly the mechanisms which result in the negative Poisson's ratio, and in particular, attempting to verify that the 'rotating rectangles' mechanism plays an important role in producing the auxetic effect. It will be shown that the CVFF 300 force-field within the molecular modelling package Cerius2 provides an adequate and practical description of the behaviour of a-cristobalite. An optimal methodology based on energy minimisation and NPT molecular dynamics techniques will be developed for examining the atomic displacements that occur when a-cristobalite is subjected to uniaxial loads. It will also be shown that the atomic displacements that occur when a-cristobalite is subjected to uniaxial loads are compatible with the 'rotating rectangles' model, hence confirming that this simple model may be used to explain the observed negative values of the Poisson's ratios. This is extremely significant as it allows us to understand how materials found in nature, achieve this unusual property of having negative Poisson's ratios and may help us design new man-made materials which mimic those occurring naturally.