In principle Vadim is perfectly right, annealing will promote grain growth, depending on annealing time and temperature grain growth will differ. In case of tetragonal ziconia grain growth is relatively slow compared to other ceramics. However close to application temperature (surface temperature something between 1200-1400°C) of a TBC coating grain growth will be considerable and grain size and pore structure will be affected changing the thermal conductivity.
Does the nanostructured TBC produced by suspension plasma spraying? if so, there are much wider band of porosity levels. although the high porosity levels lead to a decrease of thermal conductivity, it increase at the first hours of annealing, meanwhile the modulus increase. It may cause higher stress in TBC. there are many publications related to SPS TBCs.