Spatial variability of electronic transport in BiFeO3-CoFe2O4 (BFO-CFO) self-assembled heterostructures is explored using spatially resolved first-order reversal curve (FORC) current voltage (IV) mapping. Multivariate statistical analysis of FORC-IV data classifies statistically significant behaviors and maps characteristic responses spatially. In particular, regions of grain, matrix, and grain boundary responses are clearly identified. k-Means and Bayesian demixing analysis suggest the characteristic response be separated into four components, with hysteretic-type behavior localized at the BFO-CFO tubular interfaces. The conditions under which Bayesian components allow direct physical interpretation are explored, and transport mechanisms at the grain boundaries and individual phases are analyzed. This approach conjoins multivariate statistical analysis with physics-based interpretation, actualizing a robust, universal, data-driven approach to problem solving, which can be applied to exploration of local transport and other functional phenomena in other spatially inhomogeneous systems.

Scanning probe microscopy has emerged as a primary tool for exploring and controlling the nanoworld. A critical part of scanning probe measurements is the information transfer from the tip-surface junction to the measurement system. This process reduces responses at multiple degrees of freedom of the probe to relatively few parameters recorded as images. Similarly, details of dynamic cantilever response at sub-microsecond time scales, higher-order eigenmodes and harmonics are lost by transitioning to the millisecond time scale of pixel acquisition. Hence, information accessible to the operator is severely limited, and its selection is biased by data processing methods. Here we report a fundamentally new approach for dynamic Atomic Force Microscopy imaging based on information-theory analysis of the data stream from the detector. This approach allows full exploration of complex tip-surface interactions, spatial mapping of multidimensional variability of material's properties and their mutual interactions, and imaging at the information channel capacity limit.

In recent decades, catalysis research has transformed from the predominantly empirical field to one where it is possible to control the catalytic properties via characterization and modification of the atomic-scale active centers. Many phenomena in catalysis, such as synergistic effect, however, transcend the atomic scale and also require the knowledge and control of the mesoscale structure of the specimen to harness. In this paper, we use our discovery of atomic-scale epitaxial interfaces in molybdenum-vanadium based complex oxide catalysts systems (i.e., Mo-V-M-O, M = Ta, Te, Sb, Nb, etc.) to achieve control of the mesoscale structure of this complex mixture of very different active phases. We can now achieve true epitaxial intergrowth between the catalytically critical M1 and M2 phases in the system that are hypothesized to have synergistic interactions, and demonstrate that the resulting catalyst has improved selectivity in the initial studies. Finally, we highlight the crucial role atomic scale characterization and mesoscale structure control play in uncovering the complex underpinnings of the synergistic effect in catalysis.