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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. 

Zinc oxide densification mechanisms occurring during the cold sintering process (CSP) are examined by investigating specifically the effects of ion concentration in solution, temperature, pressure, and die sealing. The experiments suggest that mass transport through solution is a primary densification mechanism and that either a pre‐loaded solution or grain dissolution can supply migrating ions. Additionally, results indicate cold sintering zinc oxide requires a critical pressure value, above which densification is relatively pressure independent under the majority of process conditions. This critical pressure is related to thermal expansion of the liquid and determines the uniaxial pressure threshold for densification. The data supports a three‐stage interpretation of cold sintering, which includes quick compaction, grain rearrangement, and dissolution‐reprecipitation events. Further, it is observed that under the lowest temperature conditions a net decrease in particle size can occur during the cold sintering process.

 

Lead‐based relaxor ferroelectrics are characterized by outstanding piezoelectric and dielectric properties, making them useful in a wide range of applications. Despite the numerous models proposed to describe the relation between their nanoscale polar structure and the large properties, the multiple contributions to these properties are not yet revealed. Here, by combining atomistic and mesoscopic‐scale structural analyses with macroscopic piezoelectric and dielectric measurements across the (100–x)Pb(Mg_1/3Nb_2/3)O₃–xPbTiO₃(PMN–xPT) phase diagram, a direct link is established between the multiscale structure and the large nonlinear macroscopic response observed in the monoclinic PMN‐xPT compositions. The approach reveals a previously unrecognized softening effect, which is common to Pb‐based relaxor ferroelectrics and arises from the displacements of low‐angle nanodomain walls, facilitated by the nanoscale polar character and lattice strain disorder. This comprehensive comparative study points to the multiple, distinct mechanisms that are responsible for the large piezoelectric response in relaxor ferroelectrics.