Data analysis for nano-material's design by using diffraction pattern

Aiming to determine which planes provide a greater influence on the response of the magnetita due to preferential growth, four different mathematical procedures were used to corroborate and propose the synthesis of nanomaterials design: (1) non-parametric statistics, (2) topology of the crystalline structure planes, (3) discrete dynamical systems based on the octahedral Fe elements of the crystalline structure, and (4) unsupervised machine learning by using K-means algorithm. The obtained results of applying these methods serve to specify a synthesis design by knowing which plane has the greatest influence. Interestingly, we identified that the planes (4 2 2) and (3 1 1) seem to be very important for the response of the material and this is due to their heterogeneity and their shortest path. In all the analysis performed, these planes emerged as relevant in the different properties we evaluated. Furthermore, from the topological analysis, we identified the shortest path as a valuable variable for analysing magnetic material. The proposed methodology seems to be useful for nanomaterials design.