# X-ray Diffraction Data Analysis by Machine Learning Methods--A Review
## 4 Applications of Machine Learning in XRD Data Analysis
### Lattice Analysis
[103] introduces a CNN-based ML model for space group and crystal dimensionality. The ML algorithms they tested used both experimental and computed XRD patterns, which were generated using a data augmentation process based on domain knowledge. As stated by the authors, physics-informed data augmentation is more robust (avoids overfitting), model independent, and offers higher interpretability compared with explicit regularization, while also being more robust than noise-based data augmentation. The reported accuracy for the dimensionality and space group classification was 93% and 89%, respectively, for a set of 115 thin film metal halides, when using data augmentation. Interestingly, the classification accuracy was reduced to approximately 84% and 80% (for dimensionality and space group, respectively) when using only simulated XRD patterns for training and keeping all of the experimental data for the testing phase, highlighting both the importance of data augmentation and some of its limitations for the data analysis applications of real XRD data. XRD patterns collected at several temperatures can explain structural transitions. In this regard, fluctuations in XRD patterns are an effect of the charge density waves that show the change in the size of the unit cell and of those that involve intra-unit cell distortions. [PERSON] et al. [104] developed an unsupervised and interpretable machine learning algorithm for the study of phase transitions in (Ca\({}_{x}\)Sr\({}_{1-x}\))\({}_{3}\)Rh\({}_{4}\)Sn\({}_{13}\) and Cd\({}_{2}\)Re\({}_{2}\)O\({}_{7}\) materials and plotted the phase diagram of the former; by applying the introduced model to the analysis of thousands of Brillouin zones, the authors demonstrate the potential application of their approach to the real-time analysis of temperature dependencies and automation of the inverse scattering problem [105]. The same model [104] was applied by [PERSON] et al. [106] to reveal the structural evolution of the kagome superconductors \(AV_{3}\)Sb\({}_{5}\) (\(A=\) K, Rb, and Cs) through the charge density wave order parameter. X-ray Laue microdiffraction scan analyses were indexed using a machine learning method based on clustering and labeling algorithms by [PERSON] et al. [107]. Their model was tested on four materials (CuAlMn, AuCuZn, and CuAlNi alloys and BaTiO\({}_{3}\) ceramics). To increase the computational efficiency of the approach and allow the model to be harnessed as part of real-time processing in a synchrotron pipeline, the original Laue patterns were processed with a CNN autoencoder for dimensionality reduction. Dropout layers were used as part of the CNN architecture to mitigate overfitting, and PCA was applied to the output of the CNN encoder to further reduce feature space dimensionality. The analysis of the phase transformations in Ni-Ti-Co thin films was performed by [PERSON] et al. [108] aided by unsupervised hierarchical clustering machine learning. The ML model describes phase mixtures belonging to multiple cubic structures (_Pm3m_, _Fm3m_, and _Im3m_), as well as orthorhombic and hexagonal structures. A total of 177 XRD patterns were analyzed and, ultimately, clustered into six groups based on composition. Together with the crystal structure, phase, and thermal hysteresis behavior, this study maps the material properties of Ni-Ti-Co alloys onto the chemical composition space. In another approach of unsupervised machine learning, a fuzzy c-means (FCM) clustering algorithm was used by [PERSON] et al. [109] to classify tantalum oxynitride thin film structures obtained by pulsed laser deposition. The unsupervised ML analysis grouped XRD patterns into four clusters, which corresponded to mixtures having similar chemical and phase composition. Their overall results showed that the proposed procedure (including experimental methods and ML data analysis) is efficient and could enable the identification of deposition parameters for obtaining a desired phase.