The σ σ σ , S S S and κ κ κ el are 3 × 3 tensors and the three diagonal elements correspond to transport along the principal x, y and z directions. Since practical thermoelectric devices tend to be based around thin films or pressed pellets composed of randomlyoriented crystal grains, we focus mainly on the scalar averages (xx + yy + zz)/3, which we denote σ , S and κ el to distinguish them from the tensor quantities.