The mean inner potential (MIP) of a material is the volume averaged electrostatic (Coulomb) potential between the bulk and vacuum. Thus, the MIP is a fundamental material property, which depends on both composition and structure. Knowledge of MIP values also has significant implications for electron microscopy.[1]
However, measurements of the MIP are lacking for a wide range of materials due to the experimental complexity. One such materialis α-Al2O3 sapphire, which is also of scientific and technological importance. Here, for the first time, we report the MIP value of sapphire, measured using a novel sample preparation methodology and off-axis electron holography.
We prepared a TEM sample of a polished α-Al2O3(0001) wedge specimen at an angle of approximately 45°. The wedge sample enabled to improve the accuracy of the determined MIP by measuring the gradient of the phase variation of the reconstructed electron wave. The angle of the wedge was measured to an accuracy of better than 1° by both confocal optical microscopy and by subsequent perpendicular sectioning of the TEM sample in a focused ion beam. The validity of the proposed methodology was first verified on a Si(001) sample resulting in a MIP value of 13.16±0.45V in agreement with previous reports.
Our preliminary measurements, accounting for dynamical contributions, determined that the MIP of sapphire is 16.7±0.2V. We have also performed density-functional theory calculation of the MIP of Al2O3 slabs cut along (0001) and (1-100) planes, obtaining 15.7V and 16.7V, respectively. This measured MIP of sapphire depends on the degree of ionicity, which lies between theoretical calculations of charged ionic and neutral covalent bonding based on Dirac-Fock and Radi methods.[2] Since sapphire is predominantly an ionic material [3], our measured MIP indeed tends toward the ionic value.
References
- M. Gajdardziska-Josifovska, M.R. McCartney, W.J. de Ruijter, David J. Smith, J.K.
Weiss, J.M. Zuo, Accurate measurements of mean inner potential of crystal wedges using
digital electron holograms, Ultramicroscopy. 50 (1993) 285-299.
- Edgar Volkl, Lawrence F.Allard , David C.Joy, Introduction to electron holography,
Kluwer Academic. (1998) ISBN 0-306-44920-X.
- W.E. Lee, K.P.D. Lagerlof, Structural and Electron Diffraction Data for Sapphire (α-
Al2O3), Journal of electron microscopy technique. 2 (1985) 247-258.
