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Based on the Lorentz model, the interband bulk plasmon peak energy of the ith oscillator is given by,
 [2313a]
where,
ħω_{i}  The plasmon excitation energy;
γ_{i}  The dumping factor;
n_{i}  The density of the valence electrons contributing to the plasmon excitation;
e  The electron charge;
ε_{0}  The dielectric constant in the vacuum.
However, perovskite type ferroelectric and highk dielectric materials, such as BaTiO_{3} and SrTiO_{3}, normally show only one interband plasmon peak [1–4].
The interpretation of the features of lowloss regions in EELS from freeelectron metals is fairly straightforward because the signals arise mainly from bulk and surface plasmon excitations and the energies of the peaks from bulk (E_{bulk}) and surface (E_{surface}) plasmon excitations have the simple relationship given by,
E_{bulk} = √2E_{surface}  [2313b]
On the other hand, the interpretation of the features of the lowloss regions from transition metals is more difficult because of some factors. In transition metals, both plasmon losses and interband transitions induce energy loss and the plamon losses generally do not occur at the energies theoretically predicted by freeelectron model. Different from the case presented in Equation 2313b for freeelectron metals, there is no simple relationship between the bulk and surface plasmon loss energies for a transition metal due to too much dependence on the band structure. Moreover, some electrons in certain dbands may not be able to participate in collective plamon oscillations.
The contribution of bulk loss to single scattering distribution (SSD) is given by,
I_{b}(E,t) = t•[I_{p}(E) + I_{int}(E)+I_{Ch}(E)]  [2313c]
where,
I_{p}  The bulk plasmonloss spectrum unit thickness.
I_{int}  The interband transition spectrum unit thickness (the region of 0 to 10 eV).
I_{Ch}  The Cherenkov radiation in unit thickness (the region of 0 to 10 eV).
An optical absorption method can directly provide the imaginary part of the dielectric function, ε_{2}, associated with a single electron excitation of an interband transition, while EELS cannot directly give ε_{2}. Therefore, based on the discussion in page4360, the real (ε_{1}) and the imaginary (ε_{2}) parts of the dielectric function can be extracted by a KramersKronig analysis.
[1] K.S. Katti, M. Qian, F. Dogan, M. Sarikaya, J. Am. Ceram. Soc. 85 (2002)
2236–2243.
[2] K. van Benthem, C. Elsasser, R.H. French, J. Appl. Phys. 90 (2001) 6156–6164.
[3] S. Schamm, G. Zanchi, Ultramicroscopy 88 (2001) 211–217.
[4] J. Zhang, A. Visinoiu, F. Heyroth, F. Syrowatka, M. Alexe, D. Hesse, H.S. Leipner,
Phys. Rev. B 71 (2005) 064108.
