Quantum beam diffraction measurement and topological analysis of tetrahedrally coordinated non-crystalline materials

The construction of large quantum beam facilities such as the synchrotron radiation facility SPring-8 and the high-intensity proton accelerator facility J-PARC has provided access to high-intensity, high-energy quantum beams that are essential for structural analyses of non-crystalline materials via diffraction measurements in Japan. The developments of quantum beam diffraction techniques led to significant advancements in the research field. By the complementary use of X-rays, which are sensitive to heavy elements, and neutrons, which are sensitive to light elements, along with the advances in computer simulations and topological analysis techniques, we have achieved a deep understanding of disordered structures with intermediate-range ordering. In this article, we review the recent results obtained by the complementary use of quantum beam diffraction and topological analyses of silica polymorphs, covering silica crystals and densified silica glasses. The comparison between the persistent homology analysis data and the ring size distribution has led to the classification of a series of densified silica glasses and crystals in terms of ring persistency (ring shape) and ring entropy (topological order–disorder). This is a new concept to understand the nature of order–disorder observed in a series of silica polymorphs without using diffraction data. We also discuss the differences among disordered materials, which comprises an AA4 (A = Si) tetrahedral network (amorphous silicon), an AX4 (A = Si, X = O) tetrahedral network (glassy silica), and a non-tetrahedral network due to isolated AX4 (A = C, X = Cl) tetrahedra (liquid carbon tetrachloride) in terms of the origin of a three-peak structure, FSDP (Q1), PP (Q2), and Q3.