  Medium and high entropy ceramics, with their distinctive disordered
structures, exhibit ultra-low thermal conductivity and high temperature
stability. These properties make them strong contenders for next generation
thermal barrier coating (TBC) materials. However, predicting their thermal
conductivity has been challenging, primarily due to their unique phonon
scattering mechanisms. Apart from the conventional phonon-phonon scattering
mechanism, the phonon-disorder scattering, comprising both mass and force
constant disorder, are also expected to make significant contribution in
determining the thermal conductivity of medium and high entropy ceramics.
However, it remains challenging to quantify the phonon-disorder contribution,
particular in the aspect of force constant disorder. Here we demonstrated a
relationship between the lattice disorder, a quantity more readily calculable,
with force constant disorder, rendering it possible to substitute the force
constant disorder by lattice disorder. Based on this relationship and drawing
inspiration from Klement's equation of static imperfection, we have developed a
model that quantitatively assesses the connection between disorder and thermal
conductivity. Applying our model to the medium/high entropy rocksalt and
pyrochlore oxides as representatives, we found good alignment between the
theoretical predictions and experimental measurements of thermal
conductivities, confirming the validity of our model. The model developed
offers a critical predictive tool for rapid screening of TBC materials based on
medium and high entropy ceramics.
