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Expressions for the electron energy-loss probability are obtained for electrons travelling parallel to, firstly, one and, secondly, two coaxial cylindrical interfaces between different media. These expressions have been evaluated for Al-vacuum interfaces confirming that the cylindrical modes behave in the manner expected. Experimental spectra are presented for electrons travelling through holes drilled in thin films of amorphous AIF3 (a-A1F3) in a scanning transmission electron microscope. Comparison of these spectra with calculated spectra indicates a discrepancy in the shape which is attributed to a modification of the a-A1F3 surrounding the drilled hole. The presence of a 6 eV peak in some spectra is attributed to the excitation of a surface mode on spheres of aluminium in the a-A1F3 film.
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Caroline Walsh (1989) studied this question.
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