Thermoelectric tensor and figure of merit for a composite medium: some exact bounds

Thermoelectric transport in a macroscopically heterogeneous or composite medium is considered for the most general case of n anisotropic components mixed together with an arbitrary microstructure (i.e., not necessarily disordered or isotropic or cubic, so that the macroscopic behavior can be anisotropic too). A figure-of-merit-tensor (FMT) is defined that generalizes the usual scalar figure of merit. Some general bounds are derived for the bulk effective electrical conductivity and heat conductivity tensors, and also for the FMT. In particular, it is proven that the figure of merit of any composite can never be greater than the largest figure of merit of any of its components