Bm = (1/12p)rws-3Ecohη2 = (m/4e2ħ2Nve)Ecohη2(Ep2-Eg2).
Here rws is the Wigner-Seitz (WS) atomic radius, η is the anharmonicity parameter, Nve is the number of valence electrons per atom and Vwse is the WS volume. The universality and scaling reflect the nature of electron - atom nuclei (ion) interactions and an essentially exponential decay of the electron density with interatomic distance, thus indicating that Ep is an invaluable parameter to characterize physical properties of engineering EES materials.
First principle calculations of elastic properties for Li, Si and Li-Si alloys 2 as well as experimental and theoretical analyses of VEEL spectra of Li-Si phases 3 indicate strong correlations between Ep, n, Li content and elastic moduli (Fig. 1a). For monitoring physico-chemical changes during cycling of Si anodes with VEELS/STEM spectroscopic imaging, one can therefore use these correlations to determine and map both elastic properties and compositions of the Li-Si phases.
Nanophase carbons (soot particles (fullerenes), nanotubes, graphene, mesoporous carbons) are widely used as a conductive structure-holding matrix for electrodes, current collectors and separators in various types of batteries and supercapacitors. 4 Due to mixed sp2/sp3 bonding and subsequently different short-range and long-range atomic ordering, carbons exhibit a broad variety of physico-mechanical properties regarding hardness and elasticity. Assuming each carbon atom supplies 4 valence electrons to the solid, the mass density, r, is related to n and Ep as
ρ = nMC/4NA = εom*MCEp2/4NAħ2e2 = (m*/m) Ep2/276.79,
where MC is the carbon atomic weight, NA is the Avogadro number, m* is the renormalized electron mass, and the ratio m*/m = 0.87. Several forms of carbons (diamond, graphite, diamond-like, hydrogenated and amorphous films) exhibit strong correlations between the energy of the mixed σ+π volume plasmon peak, Epmax, ρ, amount of sp2/sp3 bonding ratio and Hm. (Fig. 1b). The estimated microhardness of individual 20-60 nm carbon nanoonions, Hm (C65) = 1286 kgmm-2 is typical for carbon soot (800-1760 kgmm-2). 1 The value reported for elemental sulfur, Hm(S8) = 25-32 kgmm-2, can be assigned to weak intermolecular bonding in the solid as compared to intramolecular covalent bonding within molecular S8 units. 5 The large modulus mismatch and poor cohesion between hard carbons and soft sulfur microparticles may explain the propensity for cracking along sulfur-carbon interfaces, which often occurs upon drying of S8-carbon cathodes. The variations in Hm between the components in poly(S-random-1,3-diisopropenylbenzene) copolymer-carbon cathodes appear to be significantly less, hence the enhanced fracture toughness leads to a crack-free morphology. 4 Utilizing Ep - elastic moduli (Hm) – composition (density) correlations, one can employ VEELS-S/TEM to determine quantitatively and image physico-mechanical properties of nanophase electrode materials in situ providing further insights into the structure - property relations in prospective EES systems and design of intentionally modified high-performance electrode materials.
 V.P. Oleshko, J. Nanosci. Nanotechnol. 12 (2012), 8580.
 V.B. Shenoy, et al., J. Power Sources 195 (2010) 6825.
 J. Danet, et al., Phys. Chem. Chem. Phys., 12 (2010) 220.
 V.P. Oleshko, et al., Microsc. Microanal. 22 (2016) 1198.
 H. Li, Y.H. Han, R.C. Bradt, J. Mater. Sci. 29 (1994) 5641.