Isotope effect on anharmonic thermal atomic vibration and κ refinement of 12C and 3C diamond

Abstract

Isotope dependence of diamond structure of the mixed crystals of 13C x 12C(1−x), which were grown under high pressure, has been examined by diffraction study using synchrotron radiation. The lattice constant is expressed by: \eqalign{a(\AA) = 3.56712 (5) - [9.01 (5) \times 10^{-4}X]\cr + [3.65 (4) \times 10^{-4}X^{2}],} where X = [13C]/([12C] + [13C]). Anharmonic thermal vibration of natural (X = 0.020) and 13C diamond (X = 0.985) was clarified by applying the Gram–Charlier series expansion to the temperature factors. The anharmonicity of natural diamond was larger than that of 13C diamond. The isotope effect on the localized electron density has also been elucidated by application of the κ refinement. 13C diamond has a larger κ parameter, 0.993 (1), than natural diamond, 0.931 (7), which proves that the valence electron of natural diamond is more widely distributed than that of 13C diamond.