Topological, geometric, and chemical order in materials: insights from solid-state NMR

Unlike the long-range order of ideal crystalline structures, local order is an intrinsic characteristic of real materials and often serves as the key to the tuning of their properties and their final applications. Although researchers can easily assess local ordering using two-dimensional imaging techniques with resolution that approaches the atomic level, the diagnosis, description, and qualification of local order in three dimensions is much more challenging. Solid-state nuclear magnetic resonance (NMR) and its panel of continually developing instruments and methods enable the local, atom-selective characterization of structures and assemblies ranging from the atomic to the nanometer length scales. By making use of the indirect J-coupling that distinguishes chemical bonds, researchers can use solid-state NMR to characterize a variety of materials, ranging from crystalline compounds to amorphous or glassy materials. In crystalline compounds showing some disorder, we describe and distinguish the contributions of topology, geometry, and local chemistry in ways that are consistent with X-ray diffraction and computational approaches. We give examples of materials featuring either chemical disorder in a topological order or topological disorder with local chemical order. For glasses, we show that we can separate geometric and chemical contributions to the local order by identifying structural motifs with a viewpoint that extends from the atomic scale up to the nanoscale. As identified by solid state NMR, the local structure of amorphous materials or glasses consists of well-identified structural entities up to at least the nanometer scale. Instead of speaking of disorder, we propose a new description for these structures as a continuous assembly of locally defined structures, an idea that draws on the concept of locally favored structures (LFS) introduced by Tanaka and coworkers. This idea provides a comprehensive picture of amorphous structures based on fluctuations of chemical composition and structure over different length scales. We hope that these local or molecular insights will allow researchers to consider key questions related to nucleation and crystallization, as well as chemically (spinodal decomposition) or density-driven (polyamorphism) phase separation, which could lead to future applications in a variety of materials.