An interactive computer simulation of global microstructures in polycrystalline ceramics

Abstract

Microstructure is the single most important structural characteristic of a ferroelectric ceramic in determining its useful properties, such as dielectric constant, piezoelectric constant, remnant polarization, electrical resistance, thermal expansion, thermal conductivity, electric resistance, light scattering, magnetic permeability, toughness, fracture strength, thermal expansion, etc. Key features of the three dimensional (3D) microstructure are the grain size distribution and the distribution of grain boundaries and grain shapes. By using stereological methods to interpret two dimensional (2D) cross sections, the experimentalist can obtain at best mean values of these properties, but little or no information on the width of the distributions or their extreme values. One of the most important parameters, the mean 3D grain size, can only be obtained from 2D cross sections by making restrictive assumptions about the grain shapes (spherical) leading to errors greater than 20%. A key point which is little appreciated is that it is the extreme values of the microstructural parameters in 3D such as minimum or maximum grain size or pore size or number of neighboring grains which plays a key role in determining such properties as fracture strength. In the words of DeHoff,* the father of modern stereology, “It appears essential to seek more sophisticated measures of the microstructural state that yield more direct information about extreme values of interest.”