Diffusion and transport coefficients in synthetic opals

Opals are structures composed of close-packed spheres in the size range of nano to micrometers. They are sintered to create small necks at the points of contact. We have solved the diffusion problem in such structures. The relation between the diffusion coefficient and the thermal and electrical conductivity is used to estimate the transport coefficients of opal structures as a function of the neck size and the mean free path of the carriers. The theory presented is also applicable to the diffusion problem in other periodic structures.