Negative Hydration Expansion in ZrW2O8: Microscopic Mechanism, Spaghetti Dynamics, and Negative Thermal Expansion

We use a combination of X-ray diffraction, total scattering and quantum mechanical calculations to determine the mechanism responsible for hydration-driven contraction in ZrW$_2$O$_8$. Inclusion of H$_2$O molecules within the ZrW$_2$O$_8$ network drives the concerted formation of new W--O bonds to give one-dimensional (--W--O--)$_n$ strings. The topology of the ZrW$_2$O$_8$ network is such that there is no unique choice for the string trajectories: the same local changes in coordination can propagate with a large number of different periodicities. Consequently, ZrW$_2$O$_8$ is heavily disordered, with each configuration of strings forming a dense aperiodic `spaghetti'. This new connectivity contracts the unit cell \emph{via} large shifts in the Zr and W atom positions. Fluctuations of the undistorted parent structure towards this spaghetti phase emerge as the key NTE phonon modes in ZrW$_2$O$_8$ itself. The large relative density of NTE phonon modes in ZrW$_2$O$_8$ actually reflect the degeneracy of volume-contracting spaghetti excitations, itself a function of the particular topology of this remarkable material.