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

Isotope dependence of diamond structure of the mixed crystals of 13 C x 12 C(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 = [ 13 C]/([ 12 C] + [ 13 C]). Anharmonic thermal vibration of natural ( X = 0.020) and 13 C 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 13 C diamond. The isotope effect on the localized electron density has also been elucidated by application of the κ refinement. 13 C 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 13 C diamond.