Beyond the Classical Approach

The thermopower strongly depends on the shape of the density of states (DOS) as shown by the Mott formula  

Another way to enhance ZT is by decoupling the electronic and thermal properties to design PGEC , i.e. a Phonon Glass and Electrical 

Crystal as proposed by Slack. The material should have lattice thermal conductivities close to those of amorphous materials, but electronic properties associated with crystalline materials. As the characteristic length scales for phonon and electron diffusion can be different, it could in principle be possible to independently optimise these two properties. Some clathrates indeed show a glass-like thermal conductivity. Also, in the case of skutterudites, it has been proposed that rattling by introducing one heavy atom in vacant sites could reduce the thermal conductivity. Thermal conductivity is indeed reduced, even if the rattling mechanism is not at the origin of this phenomenon as shown recently by inelastic neutron diffraction. 

Extensions of the Heikes formula have been proposed taking into account the other possible origins of entropy which are linked to the spins and orbitals. First, by considering a system containing mixed-valent cations ]V[( )+/M( +i)+ with spin values S and S +i, an extra entropy term coming from spins can be added and  

More recently, such a calculation has been performed for the Na,cCo02 case, taking into account the orbital and spin degeneracy term. In these layered cobaltites, Co and Co are supposed to be in low spin states, i.e. only with t2g orbitals. S would then be equal to 

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Beyond the classical approach, one has to consider the concept of octupolar nonlinearity in order to optimize the NLO response. Thus, it is sometimes convenient to decompose the P tensor into irreducible spherical multipolar components [27, 28]. When Kleinman symmetry applies i.e. under off-resonant conditions, the decomposition for p is as follows. 

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