School of Physics - Theses
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ItemAtomic resolution microscopy using electron energy-loss spectroscopy( 2008)This thesis explores the theory of electron energy-loss spectroscopy (EELS) in atomic resolution electron microscopy. The first unequivocal evidence of the effective nonlocal potential in momentum-transfer-resolved EELS is presented. For suitable geometries, the nonlocal potential can be well approximated by a local potential. In scanning transmission electron microscopy (STEM) the validity of this is mainly influenced by the detector size and, contrary to conventional wisdom, a thin annular detector does not allow direct image interpretation. It is found that the best way to ensure the potential is well approximated by a local potential is to use a detector with a large collection angle. To simplify computation and interpretation it is desirable to make the single-channelling approximation. In this approximation only the elastic scattering of the probe before the ionisation event is modelled. It is shown how this approximation breaks down for the small detectors used in momentum-transfer-resolved EELS and this is confirmed with experimental results. Double-channelling calculations, where the channelling of the probe both before and after the ionisation event are modelled, can also be simulated. An alternative approximation for small detectors that includes double channelling and is more applicable for momentum-transfer-resolved EELS is also presented. Beyond chemical information, the fine structure of an absorption edge gives bonding and electronic information. Incorporating fine structure into channelling theory allows the exploration of the effects of channelling on fine structure. The weighting of the two different spectra in graphite, as a function of incident probe tilt in momentum-transfer-resolved EELS, is calculated using double-channelling simulations. This is combined with experimental data and multivariate statistical analysis to extract the two physical spectra, greatly simplifying the analysis of a large data set. The effect of the nonlocal potential and channelling on site-specific electronic structure analysis by channelling EELS is examined. It is found that using a large on-axis detector can make the interaction effectively local, leading to a greater change in the spectra as a function of sample tilt. Alternatively offsetting the detector can achieve similar results but at the cost of greater statistical noise. Channelling calculations were combined with the program FEFF and the full energy differential cross section was calculated from first principles for the aluminium K edge as a function of sample tilt in nickel aluminate spinel. Qualitative agreement with experiment was found but quantitative agreement will require further investigation. The theory of fine structure in STEM was examined, using strontium titanate to see how the high spatial resolution of STEM can be used in conjunction with energy-loss near-edge spectroscopy measurements. The possibility of imaging unoccupied electron molecular orbitals using STEM was also examined.
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ItemTheoretical aspects of scanning transmission electron microscopy( 2005-08)This thesis explores the theory describing wavefunctions and images, both elastic and inelastic, formed in scanning transmission electron microscopy. A method is presented for calculating the elastic wavefunction based upon a new formulation of the boundary conditions which couples the probe to Bloch states within the crystal in a single step. Though this method is fundamentally equivalent to previous approaches based upon the superposition of wavefunctions corresponding to individual plane wave components in the incident probe, it provides new insight into the some of the dynamics, allows for efficient calculations, and proves useful for demonstrating well known results such as reciprocity relations. A formal inversion technique is also presented that uses a collection of diffraction plane data in scanning transmission electron microscopy to reconstruct the object potential, even in the presence of strong multiple scattering. The new form of the boundary conditions allows for a generalization of a crosssection expression for calculating inelastic images, making use of the theory of mixed dynamic form factors. This enables the simulation of images for a range of inelastic mechanisms, including thermal scattering, used to simulate high-angle annular dark field imaging, and inner-shell ionization, used to simulate electron energy loss spectroscopy images. A multislice form of this expression is given. Selection between the methods can thus be based on the sample of interest: the Bloch wave method is very efficient when the sample is crystalline; the multislice method is more appropriate if the sample lacks periodicity. The issue of cross-talk, where dynamical probe spreading may result in a signal containing contributions from several columns and therefore confound direct interpretation, is assessed for high-angle annular dark field imaging. Single atom images are simulated to provide an estimate of the localization of signal in electron energy loss spectroscopy, and confirm that the limitations of probe size generally outweigh those of the nature of the ionization interaction. The feasibility of column-by-column spectroscopic identification is demonstrated through a combination of experimental data and supporting calculations. Data demonstrating the location and spectroscopic identification of a single impurity atom in the bulk are supported by simulation and it is demonstrated that a quantitative comparison can offer further useful information: an estimate for the depth of the impurity. The contribution to electron energy loss spectroscopy images from electrons which have undergone thermal scattering prior to causing an inner-shell ionization event is assessed. It is concluded that this contribution is significant in strongly scattering specimens imaged using fine probes. It will be necessary to include this contribution if quantitative comparisons are to be made.