MTE5881 Chap.6 Convergent-Beam Electron Diffraction
Convergent-Beam Electron Diffraction
A convergent electron probe turns diffraction spots into discs whose internal intensity acts as a two-dimensional rocking curve. Finite specimen thickness elongates reciprocal points into relrods, and the nearly flat electron Ewald surface can intersect several conditions. Because electrons interact strongly with matter, intensity transfers among beams and must be described dynamically.
Useful patterns are selected for symmetry integrity, clean oscillations and controlled geometry before quantitative fitting. Disc radius and disc-centre separation encode different aspects of the experiment: convergence controls sampled incident directions, while reciprocal geometry controls where reflections are centred.
The internal intensity cannot be converted directly to a structure factor by a kinematic square root because thickness, beam energy, excitation error, absorption and coupling reflections all influence it. Quantitative work instead fits spatially resolved patterns with a dynamical calculation and uses regions with complementary parameter sensitivity.
What this chapter covers
- 01
Relrods
- 02
CBED discs
- 03
Rocking curves
- 04
Dynamical coupling
- 05
Bloch-wave method
- 06
Multislice method
Worked example · free
Repair a kinematic CBED interpretation
- +2Identify strong electron interaction and intensity transfer among beams.
- +1Name thickness, beam energy, excitation and coupling as additional dependencies.
- +2Require corrected two-dimensional pattern matching with a full dynamical simulation.
Key terms
- Dynamical scattering
- Multiple-beam intensity transfer inside a specimen that couples diffraction amplitudes.
- Rocking curve
- Intensity variation with incident orientation, recorded across a CBED disc in two dimensions.
- Multislice
- A dynamical method that alternates projected-potential interaction and Fourier propagation through slices.
- Relrod
- An elongated reciprocal feature produced by limited specimen thickness along the beam direction.
- Excitation error
- A measure of how far a reciprocal condition lies from its exact diffraction setting.
- Bloch wave
- A dynamical formalism representing coupled electron propagation through eigenstates of the periodic crystal potential.
- Sensitivity mask
- A selected pattern region designed to retain reliable pixels with useful and distinguishable parameter response.
- Disc centre
- The reciprocal-geometry position of a convergent-beam reflection, distinct from intensity variations inside that disc.
- Beam coupling
- Dynamical exchange of electron intensity among simultaneously excited diffracted beams while traversing the specimen.
Convergent-Beam Electron Diffraction FAQ
Why does convergence create discs?
A convergent cone contains many incident directions. Each direction shifts the diffraction condition slightly, so every reflection spreads into a disc whose internal intensity records an angular field rather than a single point.
Why is single scattering inadequate?
Electrons interact strongly with crystal potential and can scatter among several beams before leaving the specimen. The recorded intensity therefore depends on coupling, thickness, energy and geometry as well as the target structure factor.
What makes a pattern suitable for fitting?
Expected symmetry should be intact, thickness should be reasonably uniform, discs should not be clipped or saturated, oscillations should be informative and detector state should be characterised. Visual brightness alone is not a quantitative criterion.
Exam move
Sketch the transition from spots to discs and explain what varies inside a disc. Pair every CBED noun with its role: relrod for finite thickness, nearly flat Ewald surface for simultaneous conditions, rocking curve for angular intensity and dynamical simulation for beam coupling. Practise rejecting the square-root shortcut by naming the missing parameters.
When selecting a pattern, state quality criteria before looking at the fit. Compare Bloch-wave and multislice at the method level without claiming one is universally superior. End by connecting the chosen geometry to the parameter sensitivity needed later in QCBED. Redraw the pattern twice, once with a smaller convergence angle and once with changed specimen thickness.
Predict which visual scale or oscillation behaviour should respond and which reciprocal indexing remains fixed. Build a counterexample in which thickness changes while structure is constant; use it to explain why integrated brightness cannot identify an amplitude alone.
Mark near-Bragg regions, farther regions, overlap, saturation and damaged pixels on a practice disc field, then state which parameters each retained region helps constrain. For Bloch-wave and multislice, describe the computational idea and common purpose rather than presenting them as rival labels.
Finish with a pattern-selection checklist covering symmetry, thickness uniformity, clean oscillations, unclipped discs, detector state and reproducible geometry. A quantitative conclusion should survive a second region or sensitivity mask. Add a geometry audit that measures disc radius separately from centre spacing and predicts the consequence of excessive or insufficient convergence.
Label the transmitted beam and two indexed diffracted discs before interpreting their internal contrast. For every candidate parameter, write a second parameter that could mimic part of its effect, then identify the spatial pattern region that helps distinguish them. Compare total-count matching with full-field matching and explain which information the former discards.
Reject a visually attractive pattern if symmetry is broken, edges are clipped or thickness varies across the probe. Preserve rejected regions as negative controls and record the criterion applied before fitting. This practice turns image selection into an auditable experimental decision.
