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 T-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 form σ ~ T-1/2 e-φb/kBT. In the opposite regime, as may be realized in compressed grains, the approach toward the monocrystal grain conductivity as a function of temperature and bias is also considered.