  Transparent oxide materials, such as $CuAlO_{2}$, a p-type transparent
conducting oxide (TCO), have recently been studied for high temperature
thermoelectric power generators and coolers for waste heat. TCO materials are
generally low cost and non-toxic. The potential to engineer them through strain
and nano-structuring are two promising avenues toward continuously tuning the
electronic and thermal properties to achieve high zT values and low cost/kW-hr
devices. In this work, the strain-dependent lattice thermal conductivity of 2H
$CuAlO_{2}$ is computed by solving the phonon Boltzmann transport equation with
interatomic force constants extracted from first-principles calculations. While
the average bulk thermal conductivity is around 32 W/(K-m) at room temperature,
it drops to between 5-15 W/(K-m) for typical experimental grain sizes from 3nm
to 30nm at room temperature. We find that strain can offer both an increase as
well as a decrease in the thermal conductivity as expected, however the overall
inclusion of small grain sizes dictates the potential for low thermal
conductivity in this material.
