Grain-boundary resistivity versus grain size distribution in three-dimensional polycrystals

We have studied the accuracy of the bricklayer model in the evaluation of the grain-boundary resistivity associated to a real three-dimensional (3D) polycrystal. An impedance network electrically equivalent to the 3D structure has been solved by direct calculation. In order to examine the progressive evolution from the bricklayer model to a completely disordered system, the ideal polycrystal was modified in a controlled way, according to a Voronoï diagram approach. From this, the grain-boundary resistivity of a polycrystal, as deduced from the 3D bricklayer model, is lower than the real value. The upper limit of the error made is around 15% in relation to the real one.