This paper correlated a convenient orientation index, Lotgering factor (LF), with the orientation distribution of a crystalorientated polycrystalline material, theoretically and experimentally. For particle-oriented bismuth titanate (Bi 4 Ti 3 O 12 ) 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.

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The fracture toughness of silicon nitride (Si3N4) ceramics was evaluated directly from their microstructures via deep learning using convolutional neural network models. Totally 156 data sets containing microstructural images and relative densities were prepared from 45 types of Si3N4 samples as input feature quantities (IFQs) and were correlated to the fracture toughness as an objective variable. The data sets were divided into two groups. One was used for training, resulting in the creation of regression models for two kinds of IFQs: the microstructures only and a combination of the microstructures and the relative densities. The other group was used for testing the validity of the created models. As a result, the determination coefficient was approximately 0.8 even when using only the microstructures as the IFQs and was further improved when adding the relative densities. It was revealed that the fracture toughness of Si3N4 ceramics was well evaluated from their microstructures.

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