On the utilization of B$ouml$ttcher's formula for correct correlation of dielectric constant of powder and bulk

Abstract

Investigations have been made to determine the behaviour of Böttcher's equation for different dielectric constants and packing fractions. Two packing fractions δ (one being δ=1) give the correct values of the dielectric constant for the bulk. The graphs of δ against ϵp/δ (where ϵp is the dielectric constant of the powder at packing fraction δ) yield minima the δ and ϵp of which, when applied to Böttcher's equation, yield the correct values of the dielectric constant for bulk up to the highest value of dielectric constant, 114, investigated.

Tuning Ferroelectric, Dielectric, and Magnetic Properties of BiFeO3 Ceramics by Ca and Pb Co‐Doping

“…The increase of the dielectric constants with increasing Ca/Pb concentration in the higher frequency ranges may be attributed to the reduction of defects (V O 2+ and V Bi 3− ) during heat treatment, which may promote the formation of intrinsic 6s 2 lone electrons of the Bi ions . In addition, the contraction of unit cell volume with the increase in doping content x leads to an increase in the packing fraction as described by Böttcher's formula, which may be correlated with the increase of the dielectric constants . Meanwhile, as revealed in Figure a–d, the densification of the BFO ceramics after Ca/Pb co‐doping is one direct evidence of the increased packing fraction for the increased dielectric constants.…”