Atomic ordering effects and bond indices in quaternary systems Si-(Be,Al)-O-N

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We 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 Si6-xAlxOxN8-x (beta-SiAlONs) and hypothetical Si6-xBexO2xN8-2x 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 Si6-xBexO2xN8-2x, 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.