Accounting for the resistivity contribution of grain boundaries in metals: critical analysis of reported experimental and theoretical data for Ni and Cu

In the present paper, reported literature data on the grain-size dependence of resistivity of Ni and Cu are critically evaluated by two conceptually different methods. One is the phenomenological approach of Andrews (Phys. Lett. 19: 558, 1965) according to which in a polycrystalline metal there is a resistivity contribution inversely proportional to the average grain diameter, the proportionality constant defined as the Andrews parameter A. The other method is the customary Mayadas-Shatzkes (MS) model (Phys Rev B 1: 1382, 1970) yielding a grain-boundary reflection coefficient R. During the analysis, special care was taken to rely only on data for which the surface scattering resistivity contribution was definitely negligibly small and the grain size was determined by direct microscopy imaging. By sorting out with this analysis the most reliable grain-size-dependent resistivity data for polycrystalline Ni and Cu metals with random grain boundaries, we have then derived the current best room-temperature values of the Andrews parameter A, the specific grain-boundary resistivity and the reflection coefficient R. We have also found a fairly good relation between the parameters A and R and compared the experimental values with their theoretical estimates reported in the literature. Then, the conceptual differences between the two approaches are discussed and the deficiencies of the MS model, especially in connection with the validity of Matthiessen's rule, are highlighted. A major conclusion is that by the Andrews method one can derive a model-independent reliable parameter characterizing the grain-boundary contribution to the resistivity of metals.