Orientation distribution-Lotgering factor relationship in a polycrystalline material-as an example of bismuth titanate prepared by a magnetic field

Abstract

This paper correlated a convenient orientation index, Lotgering factor (LF), with the orientation distribution of a crystal-orientated polycrystalline material, theoretically and experimentally. For particle-oriented bismuth titanate (Bi4Ti3O12) as a model, a Cauchy probability density function (CF) was valid for representing the orientation distribution of oriented material. The LF was calculated from XRD patterns which were derived from assumed orientation distribution. The standard deviation was used for the indicator of the LF with the orientation distribution. The non-linear relationship was found between them theoretically. This relationship was supported by the experimental data using particle-oriented bismuth titanate prepared by a magnetic field. The LF and orientation distribution of oriented bismuth titanate were obtained from the XRD patterns and the rocking curves, respectively. The result leads the LF to more convenient orientation index in relation to orientation distribution.