Negative Thermal Expansion in ${\mathrm{ZrW}}_2{\mathrm{O}}_8$: Mechanisms, Rigid Unit Modes, and Neutron Total Scattering

The local structure of the low-temperature ordered phase of the negative thermal expansion (NTE) material ${\mathrm{ZrW}}_2{\mathrm{O}}_8$ has been investigated by reverse Monte Carlo (RMC) modeling of neutron total scattering data. We obtain, for the first time, quantitative measurements of the extent to which the ${\mathrm{WO}}_4$ and ${\mathrm{ZrO}}_6$ polyhedra move as rigid units, and we show that these values are consistent with the predictions of rigid unit mode theory. We suggest that rigid unit modes are associated with the NTE. Our results do not support a recent interpretation of x-ray-absorption fine structure spectroscopy data in terms of a larger rigid structural component involving the Zr-O-W linkage.

Figure 1

Schematic diagram of the structure of the low-temperature $\alpha$ phase of ${\mathrm{ZrW}}_2{\mathrm{O}}_8$. (a) The arrangement of ${\mathrm{ZrO}}_6$ octahedra and ${\mathrm{WO}}_4$ tetrahedra. (b) Further detail of the environment around the unconnected ${\mathrm{WO}}_4$ pairs and definition of a labeling scheme consistent with 3.

Figure 2

Pair distribution function, $D(r)$, of ${\mathrm{ZrW}}_2{\mathrm{O}}_8$, obtained by direct Fourier transform of the total scattering data and from the RMC simulations. Principal contributions to the low-$r$ features are labeled.

Figure 3

Temperature dependence of the widths of various peaks in the pair distribution functions obtained from the RMC analysis.

Figure 4

Temperature dependence of the mean-square amplitudes of the rotational, translational, and distortive motions of the ${\mathrm{ZrO}}_6$ octahedra and ${\mathrm{WO}}_4$ tetrahedra obtained using our GA algorithms.