Applications of Convergent Beam Electron Diffraction (CBED)
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CBED patterns are very useful, partially because they contain many quantitative information, much of which cannot be obtained by any other techniques. However, it is also important to point out that the value of the CBED techniques can be enhanced dramatically if quantitative simulations of the patterns are involved.

The CBED technique has become a well-established technique and is widely used for determination of structure, symmetry details and atom positions in a crystal as small as 20 Å in size. In general, any breaking of symmetry will affect the CBED patterns so that the convergent-beam diffraction can be applied to:
       i) Determination of crystal strain (invaluable for semiconductors and other multilayer nanostructures).
       ii) Direct observation of the reciprocal lattice.
       iii) Measurement of local variation of lattice parameter.
              For instance, CBED can be used to measure small (0.1%) changes in lattice parameter arising from compositional gradients.
       iv) Crystallographic data such as the unit cell and its corresponding lattice parameters, the Bravais lattice, crystal system, and identification of the full 3-D (three-dimensional) crystal symmetry (point group and space group). To obtain those 3-D parameters, crystals thicker than ~0.1 µm are needed. (see page2694)
       v) Identification of phases.
       vi) Characterizing line and planar defects such as dislocations, stacking faults, and grain boundaries.
       vii) TEM thickness determination.
       viii) Observation of higher order Laue zones (HOLZ) lines. In order to obtain the HOLZ rings in intensity, the magnification of the diffraction pattern should be small enough and the convergence angle should be large enough. These rings state that diffraction has occurred from other layers of the reciprocal lattice.
       ix) Determination of the atomic coordinates.
       x) Determination of the bonding charge density, valence-electron distribution, structure factors, and chemical bonding.
       xi) Enantiomorphism and polarity.

Note that many of those analyses require that the microscopists have a very good understanding of crystallography and/or chemistry. Both the learning and the doing can be time-consuming processes, depending on their established knowledge and experience.

At the high voltages used in transmission electron microscopy (TEM), the wavelength of the electrons is much smaller than typical lattice spacings, so that the Bragg angles are very small, on the order of a degree. The interaction of electrons with solids is so strong that the diffraction is almost always strongly dynamical, and the rocking curves are very broad, on the order of a degree for low-index reflections.

However, there are still some limitations in CBED applications:
         i) Need a single, through-thickness phase of the thin specimen. In practice, we need to grow the phase sufficiently large (in three dimension) so that its size is greater than the TEM film thickness. Therefore, it is normally not applicable to very small particles or grains.
         ii) Not applicable to the crystals which have high density of defects, e.g. stacking faults, twins and dislocations in silicon. The defects make CBED analysis difficult because they can alter the symmetry or contribute to the intensities of certain reflections in the CBED patterns.
         iii) Some CBED phenomena only appears in thick TEM specimens, e.g. sample thickness determination.


 

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