  Rare-earth niobates and tantalates possess low thermal conductivities, which
can be further reduced in high-entropy compositions. Here, a large number of 40
compositions are synthesized to investigate the origin of low thermal
conductivity. Amongst, 29 possess single (nominally cubic) fluorite phases and
most of them are new compositionally complex (medium- or high-entropy)
compositions. One new finding is that doping 2 % of light element cations can
further reduce thermal conductivity. This large data set enables the discovery
of a negative correlation between the thermal conductivity and averaged radius
ratio of the 3+/5+ cations. While this ratio is still below the threshold for
forming long-range ordered weberite phases, this correlation suggests the
reduced thermal conductivity is related to short-range weberite order, which is
indeed revealed by diffuse scattering in X-ray and neutron diffraction.
Specifically, neutron diffraction is used characterize five selected specimens.
A better fit to a weberite structure is found at nanoscale (~1 nm). The
characteristic length (domain size) is smaller but with stronger short-range
ordering in more insulative materials. As it approaches the Ioffe-Regel limit,
the phonon limit breaks down and "diffusons" give rise to the observed
amorphous-like thermal conductivity. Disordered oxygen sublattices are also
confirmed by neutron diffraction.
