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Single crystals of five (Al,Ge)-mullites incorporating Pb, and four of which also incorporating foreign cations (Fe,Cr,Nd,Sm) were grown by flux techniques in a PbO-MoO3 flux. They were characterized by scanning electron microscopy, electron microprobe analyses, single-crystal X-ray diffraction. In addition, the refractive indices of mullite containing Nd were determined by spindle-stage optical investigations. Careful inspection of the single-crystal X-ray diffraction data revealed that weak superstructure reflections observed in all doped crystals violating the reflection conditions can be attributed to λ/2 contributions in the primary X-ray beam. Consequently, all crystal structures were refined in space group Pbam, thus avoiding a symmetry lowering to a noncentrosymmetric subgroup as done in earlier work on a (Al,Ge)-mullite doped with Pb and Nd (Saalfeld & Klaska, Z. Kristallogr. 1985, 172, 129–133). The following phases with chemical compositions used in the refinements were obtained: undoped mullite (Al4.50Ge1.50O9.75; a = 7.6559(4) Å, b = 7.7763(4) Å, c = 2.9233(2) Å, V = 174.04(2) Å3); (Pb,Fe)-doped mullite (Pb0.02Fe0.68Al3.95Ge1.37O9.70; a = 7.7125(7) Å, b = 7.8527(7) Å, c = 2.9528(2) Å, V = 178.83(3) Å3); (Pb,Cr)-doped mullite (Pb0.01Cr0.63Al3.90Ge1.47O9.75; a = 7.6917(6) Å, b = 7.8168(6) Å, c = 2.9522(2) Å, V = 177.50(2) Å3); (Pb,Nd)-doped mullite (Pb0.06Nd0.02Al4.82Ge1.18O9.69; a = 7.6585(7) Å, b = 7.7666(7) Å, c = 2.9164(3) Å, V = 173.47(3) Å3); (Pb,Sm)-doped mullite (Pb0.06Sm0.02Al4.55Ge1.45O9.79; a = 7.6563(3) Å, b = 7.7873(3) Å, c = 2.9236(1) Å, V = 174.31(1) Å3); Pb is only incorporated into the crystal structure when a co-dopant element is present. Then it resides together with Nd or Sm in the oxygen-vacancy sites created by the formation of triclusters of AlO4 and GeO4 tetrahedra. In the case of (Pb,Fe)-doped mullite, Fe shares the same position as Al and Ge. In contrast to the (Al,Si)-mullites, Ge is located in both tetrahedral sites T and T*. The occupancies follow a substitution scheme according to Pb q (Nd,Sm) r (Cr,Fe) z Al4+2v−z Ge2−2v O10−v+q+3/2r . With v = number of vacancies, such a mullite can be understood as a “stuffed mullite” derived from a related “open mullite” (no vacancies filled with large cations) of composition (Cr,Fe) z Al4+2v−z Ge2−2v O10−v and then “stuffed” with qPb2+ + r(Nd3+,Sm3+) formula units where concurrently the number of available O3-vacancies is reduced by q + 3/2r units of extra oxygen. Thus, charge compensation upon incorporation of Pb2+ and (Nd,Sm)3+ is achieved by adding the amount of oxygen corresponding to the oxidation state of divalent Pb2+ and trivalent rare-earth elements. Based on this description, the maximum number of large cations which can be stuffed into the mullite structure can directly be calculated from the v-value of the related “open mullite”. In contrast, the smaller cations Fe3+ and Cr3+ are directly substituting Al3+. In the stuffed mullites, Pb and (Nd,Sm) could not be distinguished and were refined with a mixed occupancy on the same site. In addition to structure analysis, refractive indices of (Pb,Nd)-mullite were determined by immersion methods using a micro-refractometer spindle stage yielding n x = 1.697(3), n y = 1.708(3), and n z = 1.710(3) and 2V z = 122(4)°. The mean refractive index corresponds closely to the corresponding parameter calculated from the chemical composition whereas it would be significantly off if the extra cations were ignored, thus representing an independent evidence for the incorporation of Pb and Nd into the crystal structure.

Single crystals of ABW-type CsAlTiO4 (CAT), CsFeTiO4 (CFT), CsGaTiO4 (CGT), and ANA-type CsTi1.1Si1.9O6.5 (CST) were grown and characterized by electron microprobe analyses, single-crystal X-ray diffraction, thermal analyses, and spindle-stage optical investigations to determine the electronic polarizability of 4-coordinated Ti4+, α([4]Ti4+). The crystal structure of CAT was confirmed to crystallize in the highest possible topological symmetry Imma (a = 8.9677(2) Å, b = 5.7322(1) Å, c = 9.9612(3) Å) with tetrahedrally coordinated Al and Ti equally distributed on Wyckoff position 8i. Twinning by reticular merohedry with a twin index of 2 was observed for most of the crystals resulting in a hexagonal twin lattice (a = 11.487(3) Å, c = 8.968(2) Å) with Laue symmetry 6/mmm. Refractive indices measured by immersion methods on an untwinned specimen are n x = 1.716(5), n y = 1.725(2), and n z = 1.727(1) with 2V z = 127.1(6)°. The diffraction patterns of CFT and CGT clearly showed superstructure reflections causing a symmetry lowering of index 4 with a transformation according to 2a, b, c from Imma to Pmab with a = 18.3054(7) Å, b = 5.8083(2) Å, c = 9.9938(4) Å for CFT, and a = 18.2921(6) Å, b = 5.7636(2) Å, c = 9.9210(3) Å for CGT. Refractive indices for CGT are n x = 1.750(3), n y = 1.772(3), and n z = 1.776(2) with 2V z = 132(1)°. The crystal structure of the ANA-type CsTi1.1Si1.9O6.5 was confirmed to crystallize in space group Ia 3 ¯ $\overline{3}$ d (a = 13.8333(4) Å). The extra 0.5 O atoms are needed for charge compensation and to allow the sum of electronic polarizabilities to give a total electronic polarizability calculated from the refractive index n = 1.718(4). The electronic polarizability of [4]Ti4+ was calculated from the difference between the observed total polarizabilities (derived from the mean refractive indices of CAT and CGT) and the sum of electronic polarizabilities of cations and anions omitting the polarizability of Ti resulting in α([4]Ti4+) = 5.15(5) Å3.