# X-ray Diffraction Data Analysis by Machine Learning Methods--A Review
## 4 Applications of Machine Learning in XRD Data Analysis
### Quantitative Phase Analysis  
Phase identification and phase-fraction determination of multiphase inorganic compounds were performed by [PERSON] et al. [98] for the Li-La-Zr-O compositional system using a data-driven approach. The authors prepared a training dataset starting from a total of 218 known inorganic compounds from the Li-La-Zr-O quaternary compositional system, which comprised 21 independent structures. In the simulation process, lattice parameters variation and randomly chosen peak profile parameters, as well as mixing parameters, were considered. Two training datasets containing 89,943 (D1) and 180,056 (D2) synthetic patterns were generated for the phase identification algorithms. For phase-fraction prediction a total of 13,930,000 (D3) XRD patterns were prepared. Moreover, a real-world dataset was obtained by acquiring XRD patterns of conventionally prepared inorganic powders. The prepared samples were synthesized from Li\({}_{2}\)O, La\({}_{2}\)O\({}_{3}\), and ZrO\({}_{2}\) powders by mixing and subsequent firing at 1000 \({}^{\circ}\)C.  
Phase identification was performed using the CNN, KNN, RF, and SVM algorithms. A comparison of the highest test accuracy values obtained in each case are presented in Table 4, which shows the superior performance of the CNN algorithm over other ML methods included in the study. \begin{table}
\begin{tabular}{c c} \hline
**Mineral Group** & **Mineral** \\ \hline Clay Minerals & Smectite, chlorite, sercite, and kaolinite \\ Zeolite Minerals & Laumontite and wairakite \\ Silica Minerals & Tridymite and cristobalite \\ Silicate Minerals & Clinopyroxene, epidote, prehnite, antrophyllite, and biotite, \\  & cordierite, and tal \\ Oxide Minerals & Magnetic, ilmenite, hematite, anatase, and rutile \\  & Marcasite \\ Sulfate Minerals & Anhydrite and alunite \\  & Calcite \\ \hline \end{tabular}
\end{table} 
Table 3: List of minerals identified from XRD data for the rock cuttings. Data from reference [96]. In what concerns the phase-fraction determination, the authors used an artificial neural network with a fixed architecture. This algorithm was also compared in terms of test errors by assessing the mean square error and R-square values of the phase-fraction regressions (Table 5). From the presented values, one can assess the KNN and SVM algorithms as best performing at the phase-fraction regression tasks. Quantification of the mineral composition of gas hydrate-bearing sediments was performed by [PERSON] et al. [99] using various algorithms including CNN, recurrent neural network (RNN), multilayer perceptron (MLP), RF, and long-short term memory (LSTM). A total of 488 materials with complex compositions, including 12 minerals (quartz, albite, opal-A, calcite, muscovite, dolomite, chlorite, kaolinite, illite, pyrite, NaCl, and K-feldspar) were quantified using the mentioned algorithms. The algorithms showed promising results for predicting mineral composition even for those which showed an amorphous broad peak. On the other hand, for samples with low opal-A content, compared to the others in the dataset, all algorithms had high errors compared to the traditional indexing method. This might have occurred because the training dataset contained only hundreds of patterns, and, because of this fact, the RF algorithm showed the highest possibility among the studied ones to predict mineral compositions. The ML methods used for the quantitative phase analysis offer automation and adaptability advantages, while the conventional methods are established but time consuming. The ML algorithms showed good results for the identification of composition and limited accuracy in terms of phase fraction determination. To the best of our knowledge, to date there is no available database containing experimental patterns with complex compositions and different phase fractions, which may contribute to the limited success of these ML models.