delocalization

"Delocalization" means a phenomenon by which local information cannot be obtained in image observation or EELS using a small probe. This phenomenon is caused by (1) lens aberrations and (2) inelastic scattering. (1) When a high-resolution TEM image is observed, lattice fringes smaller than the point resolution of a TEM sometimes appear at a location different from its true position due to objective-lens aberrations (mainly spherical aberration). For example, when a crystal grain boundary is observed, lattice fringes appear across the boundary. This phenomenon is called the delocalization due to lens aberrations. (2) Incident electrons can be inelastically scattered even when they do not hit the specimen but travel near the edge of a specimen. This phenomenon is called delocalization due to inelastic scattering. This delocalization appears conspicuously in EELS. As an energy loss in inelastic scattering is smaller, delocalization is larger. For instance, surface plasmon excitation can occur even when an electron beam travels a few nm apart from the specimen. In core excitations, delocalization can be larger than the inter-atomic distance when the energy loss is small. As a result, when a specimen is scanned by a probe smaller than an atomic distance, the atom position may not be identified. Electrons inelastically scattered at small scattering angles produce lattice fringes and diffraction contrast similar to elastically scattered electrons (contrast is preserved). Such a behavior (the wave nature of inelastically scattered electrons is similar to that of elastically scattered electrons) is termed "nonlocality."