Intergrain scattering in polycrystals

Transport through grain boundaries in polycrystals is described from first principles using quantum scattering theory, explicitly including Feshbach resonances to account for intermittently trapped electronic surface states. An effective<i>T</i>-matrix is derived then used to calculate the electrical conductivity which exhibits breakdown, a sharp increase at a critical intergrain bias. Under typical conditions where the electron thermal energy,kBT, is much less than the intergrain barrier height,φb, the electrical conductivity has the formσ∼T-1/2e-φb/kBT. Temperature dependence of the conductivity is also considered for thermal energies much larger than the applied bias, as may be realized in tightly-compressed grains.