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Interpretation of meV Resolution Phonon EELS Data

With the introduction of the Nion Co. Hermes high resolution monochromator, sub-10 meV resolution EELS has become a reality for electron microscopy.[1] This has enabled an IRlike spectroscopy in aloof scattering,[2] and mapping of bulk and surface phonon modes in a single MgO nanocube.[3] Theoretical work has also begun.[4] However, below about 50 meV, where the phonon systems must be treated with a scattering theory at finite temperature our understanding is still developing.[5] There, we expect Boson occupation statistics to affect the observed EELS results, giving both energy gain, and modification of energy loss results. There turn out to be three kinds of scattering events: 1) spontaneous emission of a collective phonon by the probe, an energy loss process, 2) an induced emission by occupied phonon modes, also an energy loss process, and 3) an induced absorption, or electron energy gain. We begin by writing the scattering probability for EELS in the familiar dielectric form, or equivalently, using the Dynamical Form factor, S(q, ω) [5]