Small-angle X-ray powder diffraction analyses and high-resolution electron microscopy of allophane samples (SiO2/Al2O3 ratio, 1.12 to 1.68) showed that allophanes consist of nearly identical spherical particles with diameters of about 40 Å and retain their characteristic “hollow” spherical morphology at different ambient moisture and even after dehydroxylation by heating at 500° to 600°C. Unheated allophane samples gave another X-ray powder diffraction band whose maximum position varied from 12.3 to 14.5 A depending on their SiO2/Al2O3 ratio. The appearance of this band may denote some long-range ordering in the structure of allophane. Unlike the spherical particles of allophane, the tube unit of imogolite collapsed on dehydroxylation. This observation suggests that imogolite and allophane are different in their framework structures and that a Si- or Si(Al)-tetrahedral sheet rather than an Al-octahedral sheet constitutes the framework structure of allophane, irrespective of its SiO2/Al2O3 ratio.

Small angle scattering (SAS) is a widely used technique for characterizing structures of wide ranges of materials. For such wide ranges of applications of SAS, there exist a large number of ways to model the scattering data. While such analysis models are often available from various suites of SAS data analysis software packages, selecting the right model to start with poses a big challenge for beginners to SAS data analysis. Here, we present machine learning (ML) methods that can assist users by suggesting scattering models for data analysis. A series of one-dimensional scattering curves have been generated by using different models to train the algorithms. The performance of the ML method is studied for various types of ML algorithms, resolution of the dataset, and the number of the dataset. The degree of similarities among selected scattering models is presented in terms of the confusion matrix. The scattering model suggestions with prediction scores provide a list of scattering models that are likely to succeed. Therefore, if implemented with extensive libraries of scattering models, this method can speed up the data analysis workflow by reducing search spaces for appropriate scattering models.