2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/20543We propose a microscopic method for modeling atomic ordering effects in multi-component solid solutions, which is based on minimizing the number of unfavorable interatomic bonds in the system. Atomic ordering effects are studied in the solid solutions Si{6-x}AlxOxN{8-x} (beta-SiAlONs) and hypothetical Si{6-x}BexO{2x}N{8-2x} in the beta-Si3N4-Be-O system. It is established that in beta-SiAlONs, Al,O atoms form separate quasi-one-dimensional ``channels''. On the contrary, in Si{6-x}BexO{2x}N{8-2x}, Be and O atoms constitute a whole cluster. This means that homogeneous solid solutions cannot be formed in the beta-Si3N4-Be-O system under equilibrium conditions.5 pages, 4 figures. RevTeX4Materials Sciencetext