Resolving pseudosymmetry in tetragonal ZrO₂ using electron backscatter diffraction with a modified dictionary indexing approach

Abstract

Resolving pseudosymmetry has long presented a challenge for electron backscatter diffraction and has been notoriously challenging in the case of tetragonal ZrO2 in particular. In this work, a method is proposed to resolve pseudosymmetry by building upon the dictionary indexing method and augmenting it with the application of global optimization to fit accurate pattern centers, clustering of the Hough-indexed orientations to focus the dictionary in orientation space and interpolation to improve the accuracy of the indexed solution. The proposed method is demonstrated to resolve pseudosymmetry with 100% accuracy in simulated patterns of tetragonal ZrO2, even with high degrees of binning and noise. The method is then used to index an experimental data set, which confirms its ability to efficiently and accurately resolve pseudosymmetry in these materials. The present method can be applied to resolve pseudosymmetry in a wide range of materials, possibly even some more challenging than tetragonal ZrO2. Source code for this implementation is available online.

Crystal orientation and detector distance effects on resolving pseudosymmetry by electron backscatter diffraction

“…In our previous work, we revealed the effects of pixel resolution and image noise on the ability to resolve pseudosymmetry; as intuitively expected, smaller and noisier images hampered our ability to correctly resolve pseudosymmetry (Pang et al, 2020b). Yet, much is still unknown about what ISSN 1600-5767 # 2021 International Union of Crystallography other factors affect the ability of intensity-based indexing methods to distinguish between pseudosymmetry variants.…”

“…It makes sense that intensity-based indexing approaches would also be sensitive to crystal orientation, but this has yet to be studied in detail in any material. Recently, we tested our modified dictionary indexing method on a tetragonal zirconia (ZrO 2 ) material and found a distribution of confidence index (CI) values, here defined as the difference in normalized dot product (NDP) between the variants with the highest and second-highest NDP, over the 100 random orientations tested (Pang et al, 2020b). This observation suggested that pseudosymmetry was more easily resolved for certain crystal orientations, but this issue was not systematically investigated in that work.…”

“…The past few years have seen the development of a new family of intensity-based indexing approaches that perform full image comparisons with high-quality dynamically simulated patterns (Chen et al, 2015;Nolze et al, 2017;Foden et al, 2019). These intensity-based indexing approaches are more sensitive to subtle pattern differences and can thus more easily distinguish between pseudosymmetric crystal orientations compared with Hough-based indexing schemes (Nolze et al, 2016;Jackson et al, 2018;De Graef et al, 2019;Lenthe et al, 2019;Pang et al, 2020b).…”

Role of grain constraint on the martensitic transformation in ceria‐doped zirconia

“…Since crack formation is associated with the release of internal elastic stresses, we believe that in the absence of cracking, these stresses accumulate during the early stages of phase transformation and inhibit further martensite formation. At this stage, we note that monoclinic phase tends to form in self‐accommodating variant pairs in these materials 17,25,49 . In such microstructures, the deviatoric strain components of the variants point in opposite directions (and thus cancel in the long‐range), whereas the dilatational strain components point in the same direction normal to the habit plane.…”

“…At this stage, autocatalytic nucleation has largely been exhausted, and significant additional driving force is needed to advance the transformation and “fill in” the gaps of partitioned tetragonal phase by the thickening of existing martensite plates or nucleation of small martensite plates in these confined regions 12,54 . However, transformation in the 13.5Ce pellet ceased far before the “filling in” regime, at 46% transformation (see also micrographs from our previous publications 17,49 ). It is believed that mechanical constraint presented by reduced cracking (as discussed in Section 5.1) leads to the suppression of autocatalysis at lower volume fractions, thus limiting the overall extent of transformation.…”