Mean inner potential of graphite measured by electron holography: Probing charge distribution and orbital diamagnetic susceptibility

The mean-inner-potential (MIP) of a crystal is the average electrostatic Coulomb potential within a crystal with respect to vacuum. We conducted off-axis electron holography experiments on highly-oriented-pyrolytic-graphite (HOPG) in a transmission-electron-microscope to measure the MIP from nanometer-scale volumes of Bernal graphite oriented with respect to the electron beam, along the principal-axis or directions in the basal plane. These MIP were related to mean orbital electron radii and diamagnetic susceptibilities in perpendicular planes. These measurements are interesting compared to magneto-transport measurements, which report large anisotropy. Along the principal-axis, the susceptibility is highest amongst diamagnetic materials. However, those measurements vary significantly depending on type, size, and thickness of samples, indicating that the signal is significantly extrinsic due to defect induced interfaces. Indeed, structural examination of HOPG show stacking-faults and planar rotations around the principal-axis, such that measuring intrinsic properties requires probing a volume of ∼10² × 10² × 10² nm³. Experiments on such individual graphite crystals with (0001) basal, or (1–100), (2-1-10) prismatic planes, resulted in MIP of 10.16 ± 0.40V, 11.37 ± 0.35V, 12.66 ± 0.41V, respectively. First-principles calculations confirm these anisotropic measurements with 11.72V, 13.65V, 14.56 V, respectively. These measured MIP enable to determine projected mean-radii of electron orbitals and volume susceptibilities at 0.704 ± 0.015 Å, (−1.99 ± 0.08) × 10⁻⁵; 0.744 ± 0.015 Å, (−2.23 ± 0.07) × 10⁻⁵; 0.785 ± 0.015 Å, (−2.48 ± 0.08) × 10⁻⁵.