Grain boundary curvatures in polycrystalline SrTiO₃: Dependence on grain size, topology, and crystallography

Abstract

By mapping grain orientations on parallel serial sections of a SrTiO3 ceramic, it was possible to reconstruct three‐dimensional orientation maps containing more than 3000 grains. The grain boundaries were approximated by a continuous mesh of triangles and mean curvatures were determined for each triangle. The integral mean curvatures of grain faces were determined for all grains. Small grains with fewer than 16 neighbors mostly have positive mean curvatures while larger grains with more than 16 neighbors mostly have negative mean curvatures. It is also possible to correlate the mean curvature of individual triangles with the crystallographic characteristics of the grain boundary. The mean curvature is lowest for grain boundaries with (100) orientations and highest for grain boundaries with (111) orientations. This trend is inversely correlated to the relative areas of grain boundaries and directly correlated to the relative grain boundary energy. The direct correlation between the energy and curvature is consistent with the expected behavior of grain boundaries made up of singular orientations. Furthermore, because both the relative energy and curvature of grain boundaries with (100) orientations are minima in the distributions, these boundaries also have the lowest driving force for migration.

Grain boundary energies in yttria‐stabilized zirconia

“…Here, grain boundary planes with the (100) orientation are low energy, as was found for rock salt structured MgO 22 and perovskite structured SrTiO 3 . 23 The observation of low energy [100] twist boundaries is consistent with the idea that the (100) orientation represents a minimum in the energy. Also consistent with the previous studies, there is an inverse correlation between the energy and relative areas of grain boundaries (Figure 6).…”

“…The method requires the characterization of many (>10 4 ) triple junctions, so three-dimensional (3D) orientation maps of polycrystals are required. The method has been applied to a number of materials, [20][21][22][23] and, in one instance when the results were compared to simulation, 24 there was considerable agreement between the simulated and measured energies. The Morawiec method has recently been improved, mainly by eliminating the need to discretize the fiveparameter space of grain boundary types, and this new method will be applied here to YSZ.…”

Nondestructive evaluation of 3D microstructure evolution in strontium titanate

“…Surface grooving pins grain boundaries at their location on the surface. The consequences of this pinning might actually reach deeper than the one layer of surface grains that has been excluded from the analysis here (Zhong et al, 2019). To exclude more grains deeper below the surface without introducing statistical bias towards larger grains (see Section 3.1) would require the exclusion of a layer of thickness at least the diameter of the largest grains in the specimen.…”

“…Even on large bulk specimens, amenable only to 2D analysis, statistical errors on the order of a factor of two are often reported (Ba ¨urer, Weygand et al, 2009). Other approaches to capture grain growth include studies that look at curvature (Rowenhorst et al, 2006) via morphological phase evolution, but do not capture crystallographic effects, and those that carefully investigate grain boundary character distributions (Zhong et al, 2019(Zhong et al, , 2017, but do not have time evolution. Ideally crystallographic, boundary curvature and grain boundary character distributions will all be captured for detailed graingrowth studies.…”

Real‐Time Capturing of Microscale Events Controlling the Sintering of Lead‐Free Piezoelectric Potassium‐Sodium Niobate

“…At present, the average grain-boundary to surface energies ratio γ gb /γ s is 1.18 and 1.11 for samples A and B, respectively. For comparison with the literature, SnO 2 , SrTiO 3 , Ni and Fe show a relative γ gb /γ s of 1.20, 0.96-1.04, 0.87-1.02, 0.96-1.26 [55][56][57][58]. Besides, these values of γ gb /γ s for both KNN ceramics shed light on the origin of the stagnant grain growth probably related to the pore drag effect as the pores are bound to the boundary.…”