Dynamics of Underconstraint: Relevance to Negative Thermal Expansion in ZrW2O8

Minimal models are developed to examine the origin of large negative thermal expansion (NTE) in under-constrained systems, such as ZrW2O8. The dynamics of these models reveals how underconstraint can organize a thermodynamically extensive manifold of low energy modes that drives NTE and extend across the entire Brillioun zone. Mixing of twist and translation in the eigenvectors for rigid unit motion, for which in ZrW2O8 there is evidence from infrared and neutron scattering measurements, emerges naturally in our model as a signature of underconstraint.