Percolation exponents and thresholds obtained from the nearly ideal continuum percolation system graphite-boron nitride

TLDR: In this paper, the volume fraction of graphite was measured as a function of the volume of the graphite disks, and the results for the exponents were compared with theoretical predictions and previous experiments and the reasons for the nonuniversality of $t$ are clarified.

Abstract: Compressed disks made from graphite and, its mechanical but not electrical isomorph, boron nitride as well as graphite-boron nitride powders, undergoing compression, are nearly ideal continuum percolation systems, as the ratio of their conductivities is nearly ${10}^{\ensuremath{-}18}$ and the scatter of the experimental points near the critical volume fraction ${\ensuremath{\varphi}}_{c}$ is very small. The following measurements, with the characteristic exponent(s) in brackets, are made on some or all of the samples in (axial) and at right angles (radial) to the direction of compression, as a function of the volume fraction of graphite (\ensuremath{\varphi}); dc conductivity ($s$ and $t$), dielectric constant ($s$), magnetoresistivity ${(t}_{\ensuremath{\perp}}),$ and noise power $(K).$ The noise power is also measured as function of resistance $(w)$ and volume ${(b}^{\ensuremath{'}}).$ The ${\ensuremath{\varphi}}_{c}$'s obtained for all measurements are consistent and explicable. The results for the exponents are less well understood but, where possible, these results are compared with theoretical predictions and previous experiments. The reasons for the nonuniversality of $t$ are clarified.