Calculation of the total structure factor and of the layers with their three order parameters for a ternary alloy with spherical symmetry from its invariance under the symmetry group S3 of exchanges of its components

Abstract

We investigate the decomposition of the structure factor of a ternary alloy with spherical symmetry into the largest number of linearly independent and invariant quantities under the group of symmetries S3, which acts on the alloy's components. This decomposition reveals three physical quantities with different invariance properties. The first is related to the numbers of particles irrespectively of their chemical species. The second is associated with the ratios of the number of atoms of one species with respect to the other two. The third is associated to the nature of the order of one species with respect to the other two. We calculate all total and partial structure factors, which exactly match the results for binary alloys in the formalism of Bhatia-Thornton when two of the three species are identical. Our approach enables to exactly determine the radii of the layers and their three order parameters for a ternary alloy.