Simple Mathematical Model for the Electrical Conductivity of Highly Porous Ceramics

A novel approach has been proposed to describe the relationship between the conductivity and relative density of highly porous materials. As a first approximation, porous material was represented by a uniaxial string of spheres along the direction of the potential gradient. Then, a string of spheres was remodeled into a rotating body of sine‐wave functions, f ( x ) = (1 + r 0 )/2 + [(1 – r 0 )/2] sin (π x / c ) for 0 ≤ x < c and f (π x ) = (1 + r 0 )/2 + [(1 – r 0 )/2] sin {π( x + 1 − 2 c )/(l − c )} for c ≤ x < 1, where the former represents the shape of a sphere, the latter that of the bottleneck between neighboring spheres, and r 0 denotes the ratio of the minimum diameter at the bottleneck to the maximum diameter of the rotating body. It was shown that the calculated relationships reproduced the reported experimental results for the relationship between the porosity and conductivity of La 0.5 Sr 0.5 CoO 3 , BaF 2 , and (ZrO 2 ) 0.9 (Y 2 O 3 ) 0.1 . The relative conductivity to the bulk material was close to zero at 45–60% relative density, which is the density of green wares. It steeply increased with an increase in the relative density and then gradually approached that of the bulk material.