USE OF IN-SITU XRD TO DEVELOP CONDUCTING CERAMICS WITH THE AURIVILLIUS CRYSTAL STRUCTURE
In-situ X-ray diffraction was used to study structural transformations in several n=3 Aurivilliustype phases: Bi4Ti3O12, Bi2La2Ti3O12, Bi2Sr2Nb2TiO12, Bi2Sr2Nb2AlO11.5 and Bi2Sr2Nb2GaO11.5. Order-disorder transformations have been linked to transitions to fast ion conduction in certain oxygen-deficient phases, such as Bi 2Sr2Nb2AlO11.5 and Bi2Sr2Nb2GaO11.5. Bi2La2Ti3O12 and Bi2Sr2Nb2TiO12 were synthesized and indexed as body-centered tetragonal with 4/mmm Laue symmetry. At room temperature, Bi4Ti3O12 has an orthorhombic unit cell with space group symmetry B2ab. As previously documented, it transforms to tetragonal above its Curie temperature of 675 �C. Indexing of XRD data collected for this study indicates the high temperature phase is body-centered tetragonal with 4/mmm Laue symmetry, similar to the structures of Bi2La2Ti3O12 and Bi2Sr2Nb2TiO12. None of these phases undergo additional phase transformations up to 1100 �C. Both Bi 2Sr2Nb2AlO11.5 and Bi2Sr2Nb2GaO11.5 have oxygendeficient perovskite-layers, with either primitive tetragonal or orthorhombic unit cells at room temperature. Both materials undergo multiple phase transformations. Above 875 �C, the unit cells are similar to those of the non-oxygen deficient n=3 Aurivillius-type phases, being bodycentered tetragonal with 4/mmm Laue symmetry. This behavior agrees with the expectations for oxygen-vacancy order-disorder transformations. The intermediate phases are not yet fully understood: they may be associated with partial disordering of oxygen vacancies or with a ferroelectric transition.
Recent developments in oxide ion conductors: Aurivillius phases
Recent advances in the study of Aurivillius phases (Bi2An-1BnO3n+3, n = 1−5) as oxide ion conductors are presented. The structures of modified Aurivillius phases containing extrinsic oxygen vacancies as well as Aurivillius phases containing intrinsic oxygen vacancies are surveyed. A detailed discussion of the conductivity behavior of these Aurivillius phases is given.
Corrections for x-ray absorption by a crystal of arbitrary shape
Auszug Ein direktes Verfahren zur Berechnung der Absorptionskorrektur mittels Rechenanlagen wird für die Weissenberg-equi-inclination-Methode, für die Euler-Wiege und die Präzessionsmethode beschrieben. Das Verfahren ist auf Kristalle mit einspringenden Winkeln anwendbar. Es ist jedoch auf solche Objektformen beschränkt, die sich durch Kombinationen analytisch ausdrückbarer Funktionen beschreiben lassen. Das Kristallvolumen wird in Volumenelemente unterteilt; diese werden durch eine Menge von Punkten eines räumlichen Rasters vertreten. Die Rasterpunkte sind in Bruchteilen der maximalen Kristallabmessungen festgelegt; diejenigen, die außerhalb des Kristallvolumens liegen, werden ausgeschlossen. Für Kristalle zentrosymmetrischer Gestalt braucht nur die Hälfte der im Kristall enthaltenen Rasterpunkte betrachtet zu werden. Auf den Kristall bezogene Einheitsvektoren für den einfallenden und den gebeugten Strahl werden für jede Interferenz eingeführt. Diese Vektoren sind in Gitterkonstanten der reziproken Zelle ausgedrückt und in einer Form dargestellt, die für die Auswertung mit Hilfe von Rechenanlagen geeignet ist. Die Abstände von jedem Rasterpunkt bis zur Kristalloberfläche sind bestimmt als Vielfache der Vektoren; ihre Summierung ergibt den Durchlässigkeitsfaktor. Hat der Kristall einspringende Winkel, so sind die Wegstrecken daraufhin zu prüfen, wieweit sie außerhalb des Kristalls verlaufen. Über die Anwendung des Verfahrens durch ein FORTRAN-Programm und über die Geschwindigkeit und Genauigkeit der Rechnung wird in einer späteren Mitteilung berichtet. Abstract A direct procedure, designed for application in high-speed computation, is described for the determination of x-ray absorption corrections in the equiinclination Weissenberg, Eulerian orienter, and precession geometries. Crystal shapes with re-entrant angles may be treated. The main restriction on the specimen shape is that it be representable by a combination of functions which may be expressed analytically. The crystal volume is subdivided into volume elements which are represented by a collection of grid points. The grid points are established as submultiples of the maximum dimensions of the crystal and are tested to reject those which lie outside the crystal volume. Only half of the grid points which are contained within the crystal need be considered explicitly when the crystal has a centrosymmetric shape. Unit vectors are established, relative to the crystal, in the directions of both the incident and diffracted beams for each reflection. These vectors are expressed in terms of reciprocal-cell dimensions in a form which may be evaluated by a computer. Distances from each grid point to the surface of the crystal are determined as multiples of these vectors and are summed to evaluate the transmission factor. If the crystal has re-entrant angles, the path lengths are tested to take account of portions of the beam paths which lie outside the crystal. Application of the procedure in a program written in FORTRAN and the speed and accuracy of the program will be evaluated in a later paper.