  A first-principles informed approach to the calculation of Lorenz numbers for
complex thermoelectric materials is presented and discussed. Example
calculations illustrate the importance of using accurate band structures and
energy-dependent scattering times. Results obtained by assuming that the
scattering rate follows the density-of-states show that in the non-degenerate
limit, Lorenz numbers below the commonly assumed lower limit of 2(kB/q)^2 can
occur. The physical cause of low Lorenz numbers is explained by the shape of
the transport distribution. The numerical and physical issues that need to be
addressed in order to produce accurate calculations of the Lorenz number are
identified. The results of this study provide a general method that should
contribute to the interpretation of measurements of total thermal conductivity
and to the search for materials with low Lorenz numbers, which may provide
improved thermoelectric figures of merit, zT.
