Various methods for determining the critical metallic volume fraction phi _c at the metal-insulator transition

The metal-insulator transition in composite Al-Ge films has been extensively studied experimentally. Using the superconducting properties of clusters composed of aluminium grains in the presence of a magnetic field, the critical metallic volume fraction phi _c^gp has been determined for the case of grain percolation (gp). Because the films investigated are composed of extremely small grains of Al partially coated with amorphous Ge, the critical volume fraction phi _c takes on a comparably large value. Typically about 56 at.% Al. The low-temperature electrical conductivity data are examined using a number of criteria for phi _c. Most of these criteria yield values phi _c to within 1% of phi _c^gp. However, one widely used criterion involving the fitting of the low-temperature conductivity data to a T^1/2 dependence, as suggested by the electron-electron interaction theory, was found to yield a significantly smaller value for phi _c. Methods based on room-temperature data are also evaluated. These criteria yield phi _c values that are within +or-1% of phi _c^gp.