If you have a modulated DSC available you can measure your materials Cp's directly after calibraing with something that is known (water, for example).Some years ago we examined coatings of MWCNTs and found Cp's in the range of 0.68 to 0.8 J/g/K; I think most graphtic and graphenic carbons are in this approximate range. AlN will probably be clsoe to its bulk value,