The prediction of the structure of members of the homologous series of the higher rare earth oxides

The structural principle supported by the determination of the structures of the anion-deficient, fluorite-related, homologous series of higher rare earth oxides, is reviewed. The principle is applied to predict the structure of the β(2) phase, one of the members of the homologous series, RnO2n−2m. Addition of the rule that during reaction or phase transformation, oxygen or vacant oxygen sites move in close-packed layers, allows the steps in the transformation of β(2) to its homologue β(3) to be shown. This transformation has been observed at atomic-resolution in the electron microscope and is interpreted in terms of intermediate forms that appear as modulated distortion waves sweeping the specimen.