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Lattice parameter determination using a curved position‐sensitive detector in reflection geometry and application to Sm x /2 Nd x /2 Ce 1– x O 2–δ ceramics
Author(s) -
Pramanick A.,
Omar S.,
Nino J. C.,
Jones J. L.
Publication year - 2009
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889809010085
Subject(s) - extrapolation , lattice constant , lattice (music) , diffraction , geometry , solid angle , detector , debye , total internal reflection , optics , physics , mathematics , condensed matter physics , mathematical analysis , acoustics
X‐ray diffractometers with curved position‐sensitive (CPS) detectors have become popular for their ability to perform fast data collection over a wide 2θ range, enabling kinetics studies of chemical reactions and measurement of other time‐resolved solid‐state phenomena. While the effect of sample displacement on hkl ‐specific apparent lattice parameters has been explored for a transmission‐mode Debye–Scherrer geometry, such effects for a reflection‐mode Debye–Scherrer geometry are not yet well understood. The reflection‐mode Debye–Scherrer geometry for CPS detectors is unique in the sense that the angle for the incident X‐ray beam is kept fixed with respect to the normal of a flat diffracting sample, while the diffracted beams are measured at multiple angles with respect to the sample normal. An efficient method for precise lattice parameter determination using linear extrapolation of apparent lattice parameters calculated from different hkl diffraction peaks is proposed for such geometries. The accuracy involved with this method is investigated for an Si powder standard. The extrapolation method is then applied to develop an empirical relationship between composition ( x ) and the lattice parameter ( a o ) of Sm x /2 Nd x /2 Ce 1− x O 2−δ ceramics for solid oxide fuel cell electrolytes. In this system, the empirical relationship between x and a o is compared with a previous theoretical prediction.