A synchrotron X-ray diffraction study of a small congruent LiNbO₃crystal: A compatible approach to powder diffraction

Abstract

Single-crystal synchrotron X-ray diffraction (XRD) data were collected and refined for congruent lithium niobate crystals 8 and 6 μm in diameter, sizes that are comparable to the size of the powder particles used in powder diffraction. The motivation for using such small crystals is to minimize problems such as extinction, which decrease with crystal size. The R/wR factors were 0.011/0.014 and 0.019/0.018, for the 8 and 6 μm data, respectively, and the goodness of fit factors were 2.3(1) and 1.63(8), which compare favorably with values obtained from previous powder and single-crystal diffraction studies. Results from single-crystal XRD using crystals less than 10 μm in size may rival those obtained from powder diffraction.

X-ray diffraction using focused-ion-beam-prepared single crystals

“…Abrahams & Marsh, 1986). Furthermore, our reconstructed difference ED is comparable to those reported by Etschmann & Ishizawa (2001) and Hsu et al (1997), although our data are characterized by fewer artifacts and less blurring. This could, however, mainly be due to the applied MEM approach, which better estimates non-measured reflections (structure factors) with their statistically most likely values (Coppens, 1997).…”

“…We compare the refined structure parameters and reconstructed EDs of three differently prepared crystals, of which two were prepared by FIB and one was a manually cut crystal. We discuss the results with respect to reference data from spherical crystals and synchrotron data that have already been published (Etschmann & Ishizawa, 2001;Abrahams & Marsh, 1986;Hsu et al, 1997;Iyi et al, 1992).…”

“…Commonly, small crystals with irregular shape, as grown or as cut from larger crystals, are used for SC-XRD (Hsu et al, 1997). Regularly shaped crystals are usually prepared by grinding of single-domain crystals into spheres (Massa, 2011;Abrahams, Reddy & Bernstein, 1966;Iyi et al, 1992;Etschmann & Ishizawa, 2001;Abrahams & Marsh, 1986). Alternatively, a focused-ion-beam (FIB) preparation, which allows nano-fabrication of samples with defined size and shape, could be utilized.…”

“…For our study we used already commercially available high-quality LiNbO 3 crystals grown by the Czochralski method (Volk & Wö hlecke, 2008). Furthermore, the crystal structure of LiNbO 3 is well known and has already been analyzed extensively (Abrahams, Reddy & Bernstein, 1966;Abrahams, Levinstein & Reddy 1966;Hamzaoui et al, 2006;Hsu et al, 1997;Etschmann & Ishizawa, 2001;Iyi et al, 1992;Abrahams & Marsh, 1986).…”