Various two terminal electrode geometry configurations are commonly employed to probe the electrical properties of materials with the key consideration being how current flows through the sample. Here, finite element modeling is used to simulate the dc electrical response of an electrically homogeneous sample (based on single crystal SrTiO3) using two terminal electrode geometries based on full surface, top‐bottom macro‐contacts as is commonly used when characterizing bulk ceramics or large single crystals and top‐bottom and top‐top micro‐contacts that are used to characterize thin films and local intra‐ and inter‐granular regions in ceramics. Well‐known equations for macro‐ and micro‐contacts are used to calculate the conductivity of the sample and are compared to the intrinsic values to determine their accuracy. A geometric factor returns accurate bulk conductivity values when there is homogeneous current flow whereas the spreading resistance equation gives the most accurate conductivity values for heterogeneous current flow. When micro‐contacts are used, the response is dominated by a small region of high current density in the vicinity of the contact, providing local electrical properties. Interference can occur when regions of high current density overlap, providing a less resistive route for current flow, thus reducing the applicability of the spreading resistance equation. For top‐top micro‐contacts at small separations, the conductivity is overestimated. The accuracy of the spreading resistance equation increases as the contact separation increases and is within 10% error when they are separated by eight times the micro‐contact radius. Convergence of the error to values lower than 10% becomes increasingly difficult and requires excessively large (and experimentally challenging) separation distances. For example, to obtain a result with an error below 5% requires separations in excess of 28 times the micro‐contact radius. Confinement occurs when the sample size limits the ability of the current to spread out from a micro‐contact, thus increasing the resistance. As the sample shape and dimensions can limit current flow, a geometric factor can sometimes be used to determine accurate conductivity values. In some cases, interference can counter‐balance confinement to yield fortuitously accurate conductivity values.

An NMR crystallographic approach, involving the combination of 119Sn NMR spectroscopy, XRD, and DFT calculations, is demonstrated for the characterization of La2Sn2–xTixO7 ceramics. A phase change from pyrochlore (La2Sn2O7) to a layered perovskite phase (La2Ti2O7) is predicted (by radius ratio rules) to occur when x ≈ 0.95. However, the sensitivity of NMR spectroscopy to the local environment is able to reveal a significant two-phase region is present, extending from x = 1.8 to ∼0.2, with limited solid solution at the two extremes, in broad agreement with powder XRD measurements. DFT calculations reveal that there is preferential site substitution of Sn in La2Ti2O7, with calculated shifts for Sn substitution onto Ti1 and Ti2 sites (in the “bulk” perovskite layers) in better agreement with experiment than those for Ti3 and Ti4 (“edge” sites). Substitution onto these two sites also produces structural models with lower relative enthalpy. As the Sn content decreases, there is a further preference for substitution onto Sn2. In contrast, the relative intensities of the spectral resonances suggest that Ti substitution into the pyrochlore phase is random, although only a limited solid solution is observed (up to ∼7% Ti). DFT calculations predict very similar 119Sn shifts for Sn substitution into the two proposed models of La2Ti2O7 (monoclinic (P21) and orthorhombic (Pna21)), indicating it is not possible to distinguish between them. However, the relative energy of the Sn-substituted orthorhombic phase was higher than that of substituted monoclinic cells, suggesting that the latter is the more likely structure.

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Micro-contact impedance spectroscopy (MCIS) is potentially a powerful tool for the exploration of resistive surface layers on top of a conductive bulk or substrate material. MCIS employs micro-contacts in contrast to conventional IS where macroscopic electrodes are used. To extract the conductivity of each region accurately using MCIS requires the data to be corrected for geometry. Using finite element modeling on a system where the resistivity of the surface layer is at least a factor of ten greater than the bulk/substrate, we show how current flows through the two layers using two typical micro-contact configurations. This allows us to establish if and what is the most accurate and reliable method for extracting conductivity values for both regions. For a top circular micro-contact and a full bottom counter electrode, the surface layer conductivity (σ s ) can be accurately extracted using a spreading resistance equation if the thickness is ~10 times the micro-contact radius; however, bulk conductivity (σ b ) values can not be accurately determined. If the contact radius is 10 times the thickness of the resistive surface, a geometrical factor using the microcontact area provides accurate σ s values. In this case, a spreading resistance equation also provides a good approximation for σ b . For two top circular micro-contacts on thin resistive surface layers, the MCIS response from the surface layer is independent of the contact separation; however, the bulk response is dependent on the contact separation and at small separations contact interference occurs. As a consequence,