On the role of rotating tetrahedra for generating auxetic behavior in NAT and related systems

Systems with negative Poisson’s ratios (auxetic) exhibit the unexpected feature of expanding laterally when uniaxially stretched and becoming narrower when compressed. Here, we examine the role of the tetrahedra found in the frameworks of the predicted auxetic zeolites natrolite (NAT), thomsonite (THO) and edingtonite (EDI) for generating negative Poisson’s ratios in an attempt to relate the auxeticity in the (0 0 1) plane to rotations of the tetrahedra in the zeolite framework. The behavior of the tetrahedra is then examined in terms of their 2D projections in the (0 0 1) plane and we show that in the extreme scenario, where the three-dimensional tetrahedra in the zeolite framework are perfectly rigid and simply rotate relative to each other, then their 2D projected behavior in the (0 0 1) plane becomes equivalent to the idealized two-dimensional ‘rotating squares model’ with a Poisson’s ratio of −1.