Thermoelectricity offers solutions for the low-carbon economy through the development of energy-efficient technology. Modest improvement in thermoelectric performance would allow, for example, waste heat in car exhausts to be converted into useful power, and hot spots on computer chips to be cooled using solid state refrigerators. However, most thermoelectric materials have complicated structures with scarce or harmful elements. Zinc oxide and its alloys are attractive candidates because of their simplicity, high thermal stability, corrosion resistance, non-toxicity and low cost. The electronic transport of zinc oxide is ideal for thermoelectric applications, but its thermal conductivity is too high. However, nanostructuring reduces the thermal conductivity by an order of magnitude. We aim to understand this phenomenon by measuring lattice vibrations using inelastic neutron scattering.