Soft manifold dynamics behind negative thermal expansion.

Minimal models are developed to examine the origin of large negative thermal expansion in underconstrained systems. The dynamics of these models reveals how underconstraint can organize a thermodynamically extensive manifold of low-energy modes which not only drives negative thermal expansion but extends across the Brillioun zone. Mixing of twist and translation in the eigenvectors of these modes, for which in ZrW2O8 there is evidence from infrared and neutron scattering measurements, emerges naturally in our model as a signature of the dynamics of underconstraint.