Crystal structures of (Li0.925Eu3+0.025)TaO3, (Li0.968Eu3+0.032)(Ta0.81Ti0.19)O2.937, (Li0.967Sm3+0.033)(Ta0.89Ti0.11)O2.978, and (Li0.950Sm3+0.033Mg0.017)(Ta0.89Ti0.11)O2.987 were investigated by X-ray powder diffraction. The initial structural parameters, taken from those of the isomorphous compound (Li0.977Eu3+0.023)(Ta0.89Ti0.11)O2.968 (space group R3c and Z = 6), were refined by the Rietveld method. A pattern-fitting method based on the maximum-entropy method was subsequently used to determine the three-dimensional electron-density distributions (EDDs) that are free from the structural bias. We confirmed that the EDDs are in accord with the resulting structural models, each of which was composed of the [(Ta, Ti)O6] octahedron and [(Li, Eu, Sm, Mg)O12] polyhedron. We compared these polyhedra and found that the prominent difference among these compounds was the centroid-to-(Li, Eu, Sm, Mg) distance (eccentricity) of [(Li, Eu, Sm, Mg)O12]. The high correlation was demonstrated between the magnitude of eccentricity and photoluminescence intensity under near ultraviolet excitation.

The crystal structure of SiAl5O2N5 was characterized by laboratory X-ray powder diffraction (CuKα1). The title compound is hexagonal with space group P63/mmc (Z = 2). The unit-cell dimensions are a = 0.303153(3) nm, c = 3.28153(3) nm, and V = 0.261178(5)  nm3. The initial structural model was successfully derived by the direct methods and further refined by the Rietveld method. The final structural model showed the positional disordering of two of the four (Si,Al) sites. The maximum-entropy method-based pattern fitting (MPF) method was used to confirm the validity of the split-atom model, in which conventional structure bias caused by assuming intensity partitioning was minimized. The reliability indices calculated from the MPF were R wp = 5.00%, S (=R wp/R e) = 1.25, R p = 3.76%, R B = 1.26%, and R F  = 0.90%. The disordered crystal structure was successfully described by overlapping four types of domains with ordered atom arrangements. The distribution of atomic positions in each of the domains can be achieved in the space group P63 mc. Two of the four types of domains are related by a pseudo-symmetry inversion, and the two remaining domains also have each other the inversion pseudo-symmetry.

Crystal structure of Li2BaSiO4 was reinvestigated by laboratory X-ray powder diffraction. The title compound was hexagonal with space group P63cm, Z=6, unit-cell dimensions a=0.810 408(2) nm, c=1.060 829(4) nm, and V=0.603 370(3) nm3. The initial structural model was successfully derived by the direct methods and further refined by the Rietveld method, with the anisotropic atomic displacement parameters being assigned for all atoms. The reliability indices calculated from the Rietveld refinement were Rwp=6.72%, S=1.17, Rp=5.06%, RB=1.86%, and RF=0.98%. The maximum-entropy method-based pattern fitting (MPF) method was used to confirm the validity of the structural model, in which conventional structure bias caused by assuming intensity partitioning was minimized. The final reliability indices calculated from MPF were Rwp=6.74%, S=1.17, Rp=5.10%, RB=1.49%, and RF=0.69%. Atomic arrangements of the final structural model were in excellent agreement with the three-dimensional electron-density distributions determined by MPF.

Crystal structure of Li2SrSiO4 was reinvestigated by laboratory X-ray powder diffraction. The title compound was trigonal with space group P3121, Z=3, unit-cell dimensions a=0.502 281 (4) nm and c=1.245 520(8) nm, and V=0.272 129(3) nm3. The initial structural model was derived by the direct methods and further refined by the Rietveld method. The maximum-entropy method-based pattern fitting (MPF) method was used to confirm the validity of the structural model, in which conventional structure bias caused by assuming intensity partitioning was minimized. The final reliability indices calculated from MPF were Rwp=8.04%, S=1.22, Rp=6.01%, RB=1.50%, and RF=0.66%. Atomic arrangements of the final structural model were in excellent agreement with the three-dimensional electron-density distributions determined by MPF.