Consideration on the potential-composition relationships observed with amorphous intercalation systems such as LixWO3

Most amorphous compounds like LixWO3 show a steep potential-composition (phi-x) curve even in the middle range of x, the slopes (\df/dx\) of which are much larger than those of usual crystalline intercalation systems. To discuss such a phenomenon, we have calculated the rigorous solution of the phi-x relationship for a one-dimensional lattice of intercalation sites using a new statistic technique. According to that, the phi-x curve comes to show an unusual convex to concave inflection at the middle part, if the repulsive interaction between inserted ions exceeds a value as small as 3 kT. This excludes, therefore, the possibility that a steep fall of the potential arises from a large value of the repulsion energy, because no observed curves exhibit such an inflection. It has been, instead, found that the phi-x dependencies of those compounds can be accounted for, if we assume a relatively wide distribution of the site energy.