Modelling the states of minimum and maximum disorder in B4C ceramics: Which one is expected in spark plasma sintered boron carbide?

Boron carbide (B4C) ceramics, and especially the modern B4C ones fabricated by spark plasma sintering, are promising structural materials. The crystal structure of B4C is formed by boron-carbon icosahedra linked by boron-carbon chains. The atomic occupancies of both atomic chains and icosahedra are vital pieces of infor-mation for the understanding of the B4C ceramics' physical properties. This information is inferred by performing a Rietveld refinement of the corresponding X-ray diffraction pattern. To do this correctly, this study develops a model to rigorously determinate the crystallographic occupancies in B4C ceramics. The model formulates the applicable mathematical constraints among the different crystallographic occupancies and the restraints to be imposed. These mathematical conditions have physical implications, and they are vital for correctly using the Rietveld method avoiding the convergence into solutions with no physical meaning. The model was subsequently used to compute the maximum and minimum states of disorder in stoichiometric B4C, and was applied to a spark plasma sintered B4C demonstrating that its crystal structure is closer to the maximum disorder state. The model is potentially generalisable to other ceramics with similar problems and complex systems such as high-entropy alloys.