Determination of Mean Inner Potential and Inelastic Mean Free Path of ZnTe Using Off-Axis Electron Holography and Dynamical Effects Affecting Phase Determination

The Mean Inner Potential of Hematite α-Fe2O3 Across the Morin Transition

We measure the mean inner potential (MIP) of hematite, α-Fe2O3, using electron holography and transmission electron microscopy. Since the MIP is sensitive to valence electrons, we propose its use as a chemical bonding parameter for solids. Hematite can test the sensitivity of the MIP as a bonding parameter because of the Morin magnetic phase transition. Across this transition temperature, no change in the corundum crystal structure can be distinguished, while a change in hybridized Fe-3d and O-2p states was reported, affecting ionic bonding. For a given crystallographic phase, the change in the MIP with temperature is expected to be minor due to thermal expansion. Indeed, we measure the temperature dependence in corundum α-Al2O3(112¯0) between 95 and 295 K showing a constant MIP value of ∼16.8 V within the measurement accuracy of 0.45 V. Thus, our objectives are as follows: measure the MIP of hematite as a function of temperature and examine the sensitivity of the MIP as a bonding parameter for crystals. Measured MIPs of α-Fe2O3(112¯0) above the Morin transition are equal, 17.85 ± 0.50 V, 17.93 ± 0.50 V, at 295 K, 230 K, respectively. Below the Morin transition, at 95 K, a significant reduction of ∼1.3 V is measured to 16.56 ± 0.46 V. We show that this reduction follows charge redistribution resulting in increased ionic bonding.

Interpretation of mean free path values derived from off-axis electron holography amplitude measurements

In this work, we have explored the factors which govern mean free path values obtained from off-axis electron holography measurements. Firstly, we explore the topic from a theoretical perspective, and show that the mean amplitude reconstructed from off-axis holograms is due to the coherent portion of the direct, central object-transmitted beam only - it is not affected by the presence or absence of other scattered beams. Secondly, we present a detailed experimental study which compares mean free path values obtained from hologram sideband, centreband, EELS, and TEM measurements as a function of optical collection angle and energy-loss-filtering. These results confirm that the coherent portion of the direct beam defines the mean amplitude, and additionally show that the coherent portion corresponds to the conventional energy-filtered signal (with threshold 5 eV in this work). Finally, we present summary measurements from a selection of different materials, and compare the results against a simple electron scattering model. This study reinforces the claim that the mean amplitude is defined by the energy-filtered direct beam, and confirms that the contributions of elastic and inelastic scattering to the total mean free path are broadly in line with theoretical expectations for these different materials. These results in aggregate indicate that neither experimental collection angles nor enhanced sensitivity to low-loss phonon scattering affect the mean amplitude signal arising from off-axis holography reconstructions, nor the associated mean free path values which are derived from this mean amplitude.

Mean Inner Potential of Liquid Water

Improving our experimental and theoretical knowledge of electric potentials at liquid-solid boundaries is essential to achieve a deeper understanding of the driving forces behind interfacial processes. Electron holography has proved successful in probing solid-solid interfaces but requires knowledge of the materials' mean inner potential (MIP, V_{0}), which is a fundamental bulk material property. Combining off-axis electron holography with liquid phase transmission electron microscopy (LPTEM), we provide the first quantitative MIP determination of liquid water V_{0}=+4.48±0.19  V. This value is larger than most theoretical predictions, and to explain the disagreement we assess the dominant factors needed in quantum simulations of liquid water. A precise MIP lays the foundations for nanoscale holographic potential measurements in liquids, and provides a benchmark to improve quantum mechanical descriptions of aqueous systems and their interfaces in, e.g., electrochemistry, solvation processes, and spectroscopy.

Quantitative measurement of nanoscale electrostatic potentials and charges using off-axis electron holography: Developments and opportunities

Off-axis electron holography has evolved into a powerful electron-microscopy-based technique for characterizing electromagnetic fields with nanometer-scale resolution. In this paper, we present a review of the application of off-axis electron holography to the quantitative measurement of electrostatic potentials and charge density distributions. We begin with a short overview of the theoretical and experimental basis of the technique. Practical aspects of phase imaging, sample preparation and microscope operation are outlined briefly. Applications of off-axis electron holography to a wide range of materials are then described in more detail. Finally, challenges and future opportunities for electron holography investigations of electrostatic fields and charge density distributions are presented.