Calculation of the structure factors and new expression of the order parameters for the quaternary alloy with spherical symmetry

From the extension of the concepts used in our three previous works (B. Grosdidier 2018, 2019, 2021), we investigate the structure and calculate the order parameters in the quaternary alloy. We show that the order may be described by two conceptualizations as for the ternary alloy. All structural quantities and the relationships between them are calculated. In the frame of our approach, we propose a new and more concise formula of the order parameters. We check the consistency of our approach on several “toys models” having specific behaviour of their atomic species. All order parameters are calculated in both conceptualizations. Some of them are plotted on tetrahedral quaternary phase diagrams. We retrieve our results by studying the atom exchanges in several kinds of iso - stoichiometric quaternary alloys. We describe several properties specific to the quaternary alloy that do not exist in binary or in ternary alloys.