Single Crystals of Vanadium Oxides as a Lens for Understanding Structural and Electronic Phase Transformations, Ion Transport, Chemo-Mechanical Coupling, and Electrothermal Neuronal Emulation

electron and spin localization and disorder couple strongly to structural preferences. The rich structural diversity manifests as a "rugged" free energy landscape with multiple interconvertible polymorphs. Such a landscape sets up structural, electronic, and magnetic transitions that underpin the promise of these materials as ion-insertion battery electrodes; compact primitives for brain-inspired computing, and heterogeneous catalysts. Here, we examine the structural and compositional diversity, electronic instabilities, defect dynamics, structure transformations, mechanical properties, and surface structure of vanadium oxides using single crystals as a distinctive lens. Single crystals enable the measurement of structure-function correlations without the ensemble and orientational averaging inevitable in polycrystalline materials. Their well-defined surfaces further enable examination of facet-dependent reactivity toward molecular adsorbates, ion fluxes, and lattice (mis)matched solids. We provide a comprehensive account of vanadium-oxide single-crystal studies, from delineation of common structural motifs to single-crystal growth techniques, topochemical modification strategies, mechanisms underpinning electronic instabilities, and implementation as electrothermal neurons and battery electrode materials.