The triboelectric effect, charge transfer during sliding, is well established but the thermodynamic driver is not well understood. We hypothesize here that flexoelectric potential differences induced by inhomogeneous strains at nanoscale asperities drive tribocharge separation. Modelling single asperity elastic contacts suggests that nanoscale flexoelectric potential differences of ±1-10 V or larger arise during indentation and pull-off. This hypothesis agrees with several experimental observations, including bipolar charging during stick-slip, inhomogeneous tribocharge patterns, charging between similar materials, and surface charge density measurements.
There is a growing interest in the flexoelectric effect, since at the nanoscale it is predicted to be very large. However, there have been no direct observations of flexoelectric bending consistent with current theoretical work that implies strains comparable to or exceeding the yield strains of typical materials. Here we show a direct observation of extraordinarily large, two-dimensional reversible bending at the nanoscale in dysprosium scandate due to the converse flexoelectric effect, with similar results for terbium and gadolinium scandate. Within a transmission electron microscope, thin features bend up to 90° with radii of curvature of about 1 μm, corresponding to very large nominal strains. Analysis including independent experimental determination of the flexoelectric coefficient is semiquantitatively consistent with interpreting the results as due to flexoelectricity. These results experimentally demonstrate large flexoelectric bending at the nanoscale.
X-ray photoelectron spectroscopy, ultraviolet photoelectron spectroscopy and density functional theory calculations were used to study the electronic structure of three lanthanide scandates: GdScO 3 , TbScO 3 , and DyScO 3 . X-ray photoelectron spectra simulated from first principles calculations using a combination of on-site hybrid and GGA+U methods were found to be in good agreement with experimental x-ray photoelectron spectra. The hybrid method was used to model the ground state electronic structure and the GGA+U method accounted for the shift of valence state energies due to photoelectron emission via a Slater-Janak transition state approach. From these results, the lanthanide scandate valence bands were determined to be composed of Ln4f, O2p, and Sc3d states, in agreement with previous work. However, contrary to previous work the minority Ln4f states were found to be located closer to, and in some cases at, the valence band maximum. This suggests that minority Ln4f electrons may play a larger role in lanthanide scandate properties than previously thought.
We develop the relationship between the strain derivative of the mean-inner potential and surface contributions to flexoelectricity, identifying the true surface-specific component of the flexoelectric response of finite samples. Density functional theory calculations on a range of experimentally observed, low energy SrTiO3, MgO, and Si surfaces demonstrate that the mean-inner potential and its contributions to flexoelectricity are sensitive to small differences in surface structure, chemistry, and adsorbates. We also introduce a method to estimate mean-inner potential contributions to flexoelectricity using electron scattering factors and use this approximation to predict total flexoelectric responses for a variety of insulators. Strategies to experimentally disentangle bulk and surface flexoelectric terms are also discussed.
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