The fluorite-related anion-excess structure of CeN0.222O0.667F1.333: Ordering of defect clusters

This investigation presents the preparation of CeN_0.222O_0.667F_1.333 by a solid-state reaction from a mixture of CeN:CeF₃:CeO₂ = 1:2:1.5 and its structural investigation. The samples were annealed at 900°C in platinum tubes for different times. The basic structure found by powder neutron diffraction is anion-excess fluorite-related. The unit cell is an orthorhombic distortion of the cubic fluorite cell and has the space group Abm2. The lattice constants are a = 577.71(2) pm, B = 572.76(5) pm, and c = 573.32(6) pm. The structure refined by Rietveld analysis shows that [1:0:2]- defect clusters are present. In samples prepared by longer annealing times an ordering of these clusters to larger aggregates, i.e., toward the vernier phases, was observed. This was deduced from full profile analysis without refining a structural model by comparing the instrumental resolution curves of several models.     

An adaptive pruning algorithm for the discrete L-curve criterion

We describe a robust and adaptive implementation of the L-curve criterion. The algorithm locates the corner of a discrete L-curve which is a log–log plot of corresponding residual norms and solution norms of regularized solutions from a method with a discrete regularization parameter (such as truncated SVD or regularizing CG iterations). Our algorithm needs no predefined parameters, and in order to capture the global features of the curve in an adaptive fashion, we use a sequence of pruned L-curves that correspond to considering the curves at different scales. We compare our new algorithm to existing algorithms and demonstrate its robustness by numerical examples.