A series of glass ceramics have been synthesized to produce bulk materials with nanometer-sized barium titanate (BaTiO 3 ) crystals grown in a residue glass matrix. Structureproperty relations have been made to determine the size distribution and the dielectric temperature dependence of the ceramics. Through dielectric and density mixing laws, it has been inferred that depolarization fields limit the dielectric polarizability of the particles and influence the transition temperature. The transition temperature, dielectric anomaly broadening, and peak dielectric constant all scale systematically with the mean size of the BaTiO 3 crystals, which is consistent with an intrinsic size effect. In addition, scaling the transition temperature with the Ishikawa relation predicts a critical size of 17 nm, for which BaTiO 3 cannot support a ferroelectric transition. These results are discussed in relation to other size studies on ferroelectric materials.

Barium titanate (BaTiO 3 ) base-metal electrode multilayer ceramic capacitors of an X7R-formulation, sintered at 12001C under low oxygen partial pressures (of pO 2 % 10 À9 and 10 À11 atm, respectively), followed by annealing at 10001C in an atmosphere containing a higher oxygen partial pressure (of pO 2 % 10 À5-10 À6 atm), have been analyzed for crystalline phases using X-ray diffractometry, for microstructure using transmission electron microscopy, and for microchemistry using energy-dispersive X-ray spectroscopy and electron energy loss spectroscopy. The classical core-shell structure characterized by a core consisting of tetragonal ferroelectric {011) domains and featureless shell (designated type I) was observed only in sample A sintered in pO 2 % 10 À9 atm. For sample B sintered in pO 2 % 10 À11 atm, the core-shell structure is predominantly type II, consisting of a featureless shell similar to type I, but a core of modulated domains. The core of type II contained incommensurately modulated {111} superlattice domains along /111S. The superlattice can be described by a displacive modulation with incommensurate wave vectors k 1 5 0.58a à , k 2 5 0.58b à , and k 3 5 0.58c à . It is due to the ordering of defect associates ðTi atm, but became ordered along /111S and gave rise to structural modulation.

The f1 11g twins frequently observed in pressureless-sintered BaTiO 3 ceramics have been analyzed by the X-ray diffractometry, scanning and transmission electron microscopy. Both the single twins and double lamellar twins are growth (or annealing) twins. The twins lying in the f1 11g mirror planes, which is not one of the symmetry elements of the (basic) crystal lattice's but that of the superlattice's, are therefore superlattice twins. The f1 11g twins, particularly the double twins, were found more frequently from samples sintered in an Ar atmosphere of lower oxygen partial pressure (pO 2 ). Further decreasing of pO 2 using the Ar-5% H 2 mixture has rendered the sintered samples entirely of hexagonal BaTiO 3 , the 6H-polytype. The formation of such twins is attributed to changing of the corner-sharing TiO 6 octahedra to Ti 2 O 9 face-sharing octahedra, which accommodates for local oxygen deficiency in tetragonal BaTiO 3 . The stacking sequence alters accordingly from c-layer (constituting the 3C-polytype, treating tetragonal pseudo-cubic) to h-layer (as in (chc) 1 (chc) 2 of 6H). J ournal