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The solid‐state synthesis of perovskite BiFeO₃has been a topic of interest for decades. Many studies have reported challenges in the synthesis of BiFeO₃from starting oxides of Bi₂O₃and Fe₂O₃, mainly associated with the development of persistent secondary phases such as Bi₂₅FeO₃₉(sillenite) and Bi₂Fe₄O₉(mullite). These secondary phases are thought to be a consequence of unreacted Fe‐rich and Bi‐rich regions, that is, incomplete interdiffusion. In the present work, in situ high‐temperature X‐ray diffraction is used to demonstrate that Bi₂O₃first reacts with Fe₂O₃to form sillenite Bi₂₅FeO₃₉, which then reacts with the remaining Fe₂O₃to form BiFeO₃. Therefore, the synthesis of perovskite BiFeO₃is shown to occur via a two‐step reaction sequence with Bi₂₅FeO₃₉as an intermediate compound. Because Bi₂₅FeO₃₉and the γ‐Bi₂O₃phase are isostructural, it is difficult to discriminate them solely from X‐ray diffraction. Evidence is presented for the existence of the intermediate sillenite Bi₂₅FeO₃₉using quenching experiments, comparisons between Bi₂O₃behavior by itself and in the presence of Fe₂O₃, and crystal structure examination. With this new information, a proposed reaction pathway from the starting oxides to the product is presented.

 

In this work, we measure DC and AC conductivity and Hall voltage to determine the origin of electrical insulating properties of Fe-doped β-Ga2O3 single crystals, which are measured perpendicular to the 2¯01 crystallographic plane. We find that electrical conduction is predominantly controlled by free electrons in the temperature range 230–800 °C with the mutual compensation of the impurity donor (Si) and acceptor dopant (Fe), explaining the low concentration of free electrons and Fermi level pinning over a wide range of temperatures. Furthermore, the negative temperature-dependence of the carrier mobility indicates that it is limited by optical phonon scattering. Importantly, we find electrical conductivity to be largely independent of oxygen partial pressure (pO2) from air to 10−4 atm at 600 °C, but it becomes slightly dependent on pO2 at 800 °C, as intrinsic non-stoichiometric point defects begin to influence the charge balance. 

Scientists use imaging to identify objects of interest and infer properties of these objects. The locations of these objects are often measured with error, which when ignored leads to biased parameter estimates and inflated variance. Current measurement error methods require an estimate or knowledge of the measurement error variance to correct these estimates, which may not be available. Instead, we create a spatial Bayesian hierarchical model that treats the locations as parameters, using the image itself to incorporate positional uncertainty. We lower the computational burden by approximating the likelihood using a noncontiguous block design around the object locations. We use this model to quantify the relationship between the intensity and displacement of hundreds of atom columns in crystal structures directly imaged via scanning transmission electron microscopy (STEM). Atomic displacements are related to important phenomena such as piezoelectricity, a property useful for engineering applications like ultrasound. Quantifying the sign and magnitude of this relationship will help materials scientists more precisely design materials with improved piezoelectricity. A simulation study confirms our method corrects bias in the estimate of the parameter of interest and drastically improves coverage in high noise scenarios compared to non-measurement error models.