Mean inner potential of elemental crystals from density-functional theory calculations: Efficient computation and trends

Abstract

The mean inner potential (V0) of crystals plays an important role in electron microscopy. In a few cases, it has been measured experimentally, using mostly electron holography; however, it is not uncommon to find reports that disagree by a few volts regarding the mean inner potential of the same material. Different levels of theory have also been used to estimate its value, often by building the crystal as a superposition of isolated atoms or ions—an independent-atom approximation that does not take bonding into account. In a few cases, density-functional theory (DFT) calculations were done to capture such bonding, frequently using computer-intensive all-electron approaches. In this article, we describe in detail a faster implementation based on postprocessing files produced by a DFT code that relies on the projector-augmented wave method. We deployed this approach to compute values of V0 for 44 elemental solids, and we provide the first quantum-mechanical calculation of the mean inner potential beyond the independent-atom approximation for many of them. We also report instances in which different surface terminations for the same material led to differences in V0 of more than 3 V, highlighting the dependence of the mean inner potential on the boundary conditions of the sample. Finally, by comparing our values of V0 with other material properties, we show that it correlates mostly linearly with the mass density, that it can be used to compute a good approximation to the orbital diamagnetic contribution to the magnetic susceptibility, and that it provides a simple route to compute atomic scattering amplitudes for forward scattering of electrons.