Comparisons of atomic thermal motions for graphite at 300 K based on X-ray, neutron, and phonon-spectrum data

Abstract

The mean-square amplitudes of vibration in graphite based on an X-ray charge-density analysis are 0.0032 (2) and 0.0140 (3) Å2 parallel to and perpendicular to the basal plane, respectively. Values for the parallel vibrations of 0.0031 (6) and 0.0032 Å2 were derived from temperature-dependent neutron measurements and a calculated phonon spectrum. The neutron measurements and the phonon spectrum both predict lower values [0.0090 (20) and 0.0098 Å2] for the out-of-plane vibrations. This small discrepancy may be caused by small changes in the core atomic scattering factors from the free-atom values or by a deficiency in the phonon-spectrum model.