In Situ Quantitative Plasmon Spectroscopic Determination and Imaging of Multiple Solid-State Properties at the Nanoscale
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In Situ Quantitative Plasmon Spectroscopic Determination and Imaging of Multiple SolidState Properties at the Nanoscale: a New Capability for Material Research
Vladimir P. Oleshko and James M. Howe University of Virginia, Department of Materials Science & Engineering, Charlottesville, VA 22904-4745, USA ABSTRACT Measuring material properties is critical to understanding the behavior of contemporary nanostructured materials. In this paper, we show that as a consequence of the universal binding energy relation (UBER), universal features and strong scaling correlations exist between the volume plasmon energy and cohesive energy, valence electron density, elastic constants and hardness of various materials with metallic and covalent bonding. Based on these relations, we propose novel techniques that allow direct measurement and imaging of material properties in situ using valence electron energy-loss spectroscopy combined with energy-filtering transmission electron microscopy. This is illustrated by evaluation of elastic and cohesive properties of individual metastable nanoprecipitates in structural alloys and hardness of diesel-engine soot particles. The results demonstrate that new plasmon spectro-microscopic techniques have the potential to determine quantitatively and image multiple solid-state properties at the nanoscale, establishing a new capability for material research. INTRODUCTION Complementary to comprehensive structural and chemical information accessible by highspatial resolution analytical electron microscopy in different imaging, diffraction and spectroscopic modes, valence electron energy-loss spectroscopy (VEELS) enables analyzing the spectrum of low-loss electron excitations (0-50 eV energy loss) that involve inter- and intraband transitions and collective excitations of bonding electrons responsible for many physical and chemical properties of solid materials. Due to an opportunity to probe electronic structures with high spatial (0.1-1.0 nm) and spectral (0.1-1.5 eV) resolution, VEELS and energy-filtering transmission electron microscopy (EFTEM) have been applied to determine dielectric and optical parameters and phase compositions of various classes of materials [1-3]. One of the 17 major inelastic scattering events in this range are quantized high-frequency (1016-10 Hz) volume and surface (interface) collective electron excitations, so called plasmons, generated by fast electrons passing through any solid that allows one to probe various states of matter [4]. Outer-shell electrons involved in such correlated longitudinal oscillations behave as a single quasi-particle with a characteristic angular resonance frequency and move coherently with a common frequency and wave-vector. The energy of volume plasmons is related to the valence electron density, n [4,5], as: 4 4 2 1/2 f 2 2 2 f 2 2 1/2 (1) Ep = ħωp = [(ħωp ) +3/5vf q + ħ q /4m +…] ≅ [(ħωp ) +Eg ] , 2 1/2 f where ωp =[ne /(ε0m)] is the free electron plasma frequency, e is the electron charge, ε0 is the permittivity of vacuum, m is the
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