Abstract
Grain boundary (GB) energy is an essential parameter in determining the microstructure of metallic and other materials, and tremendous effort has gone into determining the structure, energy and properties of GB’s. Presently, GB energies are most often calculated because it is difficult and/or tedious to determine them experimentally. Grain boundary modelling studies have revealed correlations between GB energy and: i) a change in electron density due an atom deficit at the GB, and ii) a rigid body translation normal to the GB, or the so-called normal volume expansion, which may also be associated with an atom deficit. In this work, valence electron energy loss spectroscopy (VEELS) and extended energy-loss fine structure (EXELFS) analysis in a scanning/transmission (S/TEM) electron microscope were used to examine fundamental GB properties such as the electron density and volume expansion, respectively.
In VEELS, plasmon peaks are generated due to collective oscillations of the valence electrons in the solid due to the interaction with the incident high-energy electron beam. Based on the Drude model, the plasmon energy is proportional to the valence electron density. Four well-characterized GB’s with different GB energies were examined in this work. Plasmon energy profiles obtained from line scans across the GB’s revealed that the plasmon energy is lower at the GB than the bulk due to a lower valence electron density, and that the energy decreased with increasing GB energy. The decrease in valence electron density was also found to extend further into the matrix on either side of the GB’s with increasing GB energy. Moreover, plasmon damping at the GB’s increased with increasing GB energy, presumably because additional scattering of the plasmon occurs with increasing disregistry at the GB. The intensity of the GB response function, obtained by Fourier deconvolution, showed an increase in intensity with GB energy, revealing the effects of different plasmon frequencies and dielectric constants at the GB. Localization of the VEELS signal was found to depend on the orientation of the sample, while sample thickness was found to have a negligible effect on the plasmon peak energy at the GB.
The volume expansion in a GB can be experimentally determined using EXELFS in a S/TEM, where the electron beam can be focused to form a sub-nanometer probe, allowing one to determine changes in nearest neighbor (n.n.) distances at a GB with nanometer-scale spatial resolution. In this investigation, EXELFS performed on three GB’s showed that the average n.n. distances at the GB’s increased with increasing GB energy. Fourier filtering also revealed an increase in static disorder with increasing GB energy. The total volume expansion at the GB calculated according to the plasmon energy profile showed excellent agreement with volume expansions measured using other experimental techniques. Thus, EXELFS provides complementary information to VEELS on the volume expansion at the GB. Taken together, the results of this investigation experimentally and conclusively demonstrate that the GB energy increases proportional to the decrease in electron density and concomitant increase in specific volume expansion at a GB.
