Dielectric-constant measurements in a system of NbC grains near the percolation threshold

Measurements of the complex dielectric constant (ε′ + iε″) on a series on NbC-KCl composites in a wide range of concentrations are performed as a function of φ (the volume fraction of the 1–3 μm NbC grains) at frequencies of 102, 103, 104 and 105 Hz. Frequency scaling of ε = ε′ + iε″ at the metal-insulator transition is different from one which follows from the scaling theory of an ideal percolation system. We observe two different values of the critical volume fraction of metal. The first critical concentration, φc1, is a cross-over point where the dielectric-constant frequency dependence changes and the loss factor is on the order of unity. The temperature behavior of the complex dielectric constant below the superconducting transition temperature Tc reveals a transformation of a system of isolated NbC grains into a system of weakly coupled tunneling junctions at φc1. The expected divergence of ε′ is observed as the second critical volume concentration φc2 > φc1 is approached. At this concentration a cross-over from the capacitive tunneling junction medium to a truly metallic state occurs. At φ > φc2, ε′ decreases rapidly as a function of φ and becomes negative at φ − φc2∼0.01, due to the negative effective real dielectric constant of the percolation metallic cluster which spans the system.