Applications of Machine Learning in Material Science & Chemical Engineering

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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:

  1. Mo dopant defects where (GMM class 1 & 3 extractions) were selected.
  2. A deep-learning-based “atom finder” was employed to extract the atom positions in thousands of noisy images.
  3. 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.
  4. 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.

Markov Process

Transition Dynamics

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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