D1 Electron Microscopy (TEM/SEM)

Topic

Transmission electron microscopy (TEM)—the experimental method described by this model—illuminates the sample with a beam of accelerated electrons rather than visible light; the resolution limit of the microscope is determined by the de Broglie wavelength of these accelerated electrons, adjusted for relativistic effects given how closely their speed approaches the speed of light. The shorter this de Broglie wavelength, the finer the detail the electron microscope can resolve. Increasing the electron acceleration voltage results in a shorter de Broglie wavelength—according to the relativistically corrected relationship—thereby improving the microscope's resolution limit.

In a well-designed transmission electron microscope, the accelerated electron's de Broglie wavelength is much shorter than the interatomic spacing within the sample; this enables the microscope, when operating in high-resolution mode, to achieve atomic resolution—the ability to distinguish individual atomic planes within the sample's crystal structure in the resulting image. Operating in this high-resolution mode allows the transmission electron microscope to reveal not only the size and shape of each nanoparticle in the sample but also its internal crystal structure, resolved plane by atomic plane.

Consequently, this model—based on electron microscopy and its resolution limit—allows the average particle size of the entire sample to be determined by counting a sufficient number of individual particle images captured by the microscope: the more individual particles counted across this set of images, the more representative the calculated average size becomes of the actual size distribution present in the sample as a whole. The fact that this electron microscopy—thanks to the electron's short de Broglie wavelength—achieves a resolution far below the limit imposed by the wavelength of visible light means that this electron microscope can resolve individual nanoparticles (in terms of both size and shape) that the other optical method can no longer distinguish from one another.

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