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  1. The effect of small changes in the specimen-to-detector distance on the unit-cell parameters is examined for synchrotron powder diffraction in Debye–Scherrer (transmission) geometry with a flat area detector. An analytical correction equation is proposed to fix the shift in 2θ values due to specimen capillary displacement. This equation does not require the use of an internal reference material, is applied during the Rietveld refinement step, and is analogous to the specimen-displacement correction equations for Bragg–Brentano and curved-detector Debye–Scherrer geometry experiments, but has a different functional form. The 2θ correction equation is compared with another specimen-displacement correction based on the use of an internal reference material in which new integration and calibration parameters of area-detector images are determined. Example data sets showing the effect of a 3.3 mm specimen displacement on the unit-cell parameters for 25°C CeO 2 , including both types of displacement correction, are described. These experiments were performed at powder X-ray diffraction beamlines at the National Synchrotron Light Source II at Brookhaven National Laboratory and the Advanced Photon Source at Argonne National Laboratory. 
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  2. Characterization of the thermal expansion in the rare earth di-titanates is important for their use in high-temperature structural and dielectric applications. Powder samples of the rare earth di-titanates R 2 Ti 2 O 7 (or R 2 O 3 ·2TiO 2 ), where R = La, Pr, Nd, Sm, Gd, Dy, Er, Yb, Y, which crystallize in either the monoclinic or cubic phases, were synthesized for the first time by the solution-based steric entrapment method. The three-dimensional thermal expansions of these polycrystalline powder samples were measured by in situ synchrotron powder diffraction from 25°C to 1600°C in air, nearly 600°C higher than other in situ thermal expansion studies. The high temperatures in synchrotron experiments were achieved with a quadrupole lamp furnace. Neutron powder diffraction measured the monoclinic phases from 25°C to 1150°C. The La 2 Ti 2 O 7 member of the rare earth di-titanates undergoes a monoclinic to orthorhombic displacive transition on heating, as shown by synchrotron diffraction in air at 885°C (864°C–904°C) and neutron diffraction at 874°C (841°C–894°C). 
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