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Density-based cluster was then applied to estimate the variance of each distribution & a diffusion coefficient within a framework of a random walk model in 2-dimensions.
Principal Components Analysis (PCA)
Local Crystallography Analysis
The analysis was taken further, conducting local crystallography analysis on classes 1 & 3. This was done by:
- Mo dopant defects where (GMM class 1 & 3 extractions) were selected.
- A deep-learning-based “atom finder” was employed to extract the atom positions in thousands of noisy images.
- These atom configurations were then aggregated to produced an image of the average defect configuration. The averaged images provide the central Mo atom and six W neighbor atoms for each defect class.
- PCA was then applied to exact the first 2 eigenmodes of the averaged images — extracting vectors of maximum variation.
It appears plausible that there is significant variation in the relative position of the central Mo atom with respect to neighbouring W atoms. This may be attributed to the presence of S vacancies next to Mo dopant.
The PCA analysis & lattice symmetry was then used to split the 2 classes (class 1 and 3) into 4 subclasses. These subclasses represent:
- MOw: undistorted
- (MOw + Vs): 3 MOw + Vs complexes.
Defect State-Transition Analysis
As represented in figure 6a, each “flow” describes a defect moving between states. As a consequence we can analyze the transition between states as a Markov process.
Figure 6.c and 6.d provide the transition dynamic schemata & matrix respectively (describing the probability of moving between defect states).
From a physics/chemistry theoretical perspective, it can be argued that transitions between states correspond to the lower diffusion barrier of an S vacancy (single atom vacancy). It appears that these chemical structures are short-lived & unstable (which may in-itself be a notable contribution).
Finally, the data suggests that variation in supply of S vacancies from different lattice directions can explain defect state transition probabilities.
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