Mean inner potential of graphite measured by electron holography: Probing charge distribution and orbital diamagnetic susceptibility. (July 2021) - Auslender, Avi; Levi, George; Ezersky, Vladimir; Gorfman, Semën; Diéguez, Oswaldo; Kohn, Amit
Abstract: 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 ∼10 2 × 10 2 × 10 2 nm 3 . 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 . Graphical abstract: Image 1 Highlights: The Mean Inner Potential was measured for Bernal graphite crystals with basal and prismatic surfaces. The MIP measurements are from individual nanometer-scale crystals, enabled by off-axis electron holography in a transmission electron microscope. These measurements are in accordance with our first-principles calculations. We extracted the electron orbital radii and diamagnetic orbital susceptibility in specified crystallographic planes. Our reported orbital diamagnetic susceptibilities represent an intrinsic property compared to magnetometry, which is influenced by extrinsic defects.