A frustrated planar XY model for niobia–zirconia ceramic alloys

Beam statistics and diffraction from materials in the critical state

It is shown that room-temperature diffraction pattern spots and diffuse scatter can appear to change their size and appearance relative to reciprocal-space sublattice reflections when the scattering material corresponds in structure to a critical phase. Under such a condition, the material is considered to be continually on the verge of a phase transition and the diffraction spot will have no definite width, its apparent size in reciprocal space dependent on the strength of the scattering into the diffracted beam. It is thought that the materials described in the experiments--niobia-zirconia ceramic alloys--are capable of entering such a critical phase because of their recently suggested planar XY spin character. After first describing how the seemingly crystalline ceramic alloy can display XY-like behavior, we analyze the intensity dependence of the critical scattering from the alloys oxygen superlattice using information-theoretic methods.