A quantitative analysis of the volume fraction dependence of the resistivity of cermets using a general effective media equation

Abstract

The results analyzed, all from previous work, are for W-Al2O3 (as prepared and annealed; 300 K) and Ni-SiO2 (4.2 and 291 K). These results, in which the resistivity changes from 10−5 to 107 Ω cm as the metal volume fraction is varied, can all be quantitatively fitted to a general effective media (GEM) equation. The GEM equation was developed as an interpolation between Bruggeman’s symmetric and asymmetric media equations for ellipsoidal grains. It has four parameters. The conductivities of the low [σ(lo)] and high [σ(hi)] conductivity components, fc=(1−φc), where φc is the critical (percolation) volume fraction of the σ(hi) component and t is an exponent. f is the volume fraction of the dielectric or σ(lo) component. As, when σ(lo)=0 or σ(hi)=∞ the GEM equation reduces to the percolation equations, it can also be regarded an interpolation formula between these equations. The W-Al2O3 (as prepared; 300 K) and Ni-SiO2 (291 K) results need a five-parameter fit as ρ(hi) [1/σ(lo)] is modeled as an intergranular tunneling process with ρ(hi)=ρ(0)exp{C[(1−fc)/(1−f )]1/3−1}, ρ(0) and C being variable parameters. The log rms deviations for fits are W-Al2O3 (as prepared) 3.3%, W-Al2O3 (annealed) 0.66%, Ni-SiO (4.2 K) 2.3%, and Ni-SiO2 (291 K) 1.3%.