9.1 Principles of electron diffraction

Electron diffraction harnesses the wave-like nature of electrons to probe crystal structures. It offers higher resolution and sensitivity to lighter elements than X-rays, thanks to shorter wavelengths and stronger interactions with matter.

This technique exploits electrons' charged nature, allowing precise beam control through electromagnetic lenses. It's particularly useful for studying thin films and nanostructures due to its surface sensitivity and ability to provide detailed structural information.

Electron Diffraction Fundamentals

Wave Nature and Wavelength

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• Electron diffraction based on wave-like nature of electrons described by de Broglie equation relating electron wavelength to momentum
• Electron wavelength typically much shorter than X-rays allowing for higher spatial resolution and sensitivity to lighter elements
• Shorter wavelength results in larger Ewald sphere in reciprocal space compared to X-ray diffraction
• De Broglie wavelength for 100 keV electrons approximately 0.037 Å

Interaction Strength and Scattering

• Electrons interact more strongly with matter compared to X-rays resulting in multiple scattering events and dynamical diffraction effects
• Strong interaction leads to higher probability of inelastic scattering processes (plasmon excitations, core-level ionizations)
• Atomic scattering factor for electrons decreases more slowly with increasing scattering angle compared to X-rays
  • Allows observation of higher-order reflections
  • Provides more structural information at high scattering angles

Charged Particle Nature

• Electrons are charged particles easily focused and manipulated using electromagnetic lenses
• Enables various diffraction techniques and imaging modes (selected area diffraction, convergent beam electron diffraction)
• Allows for precise control of beam characteristics (energy, convergence angle, spot size)

Electron-Crystal Interactions

Electrostatic Potential Interaction

• Electrons primarily interact with electrostatic potential of atoms in crystal lattice
• Differs from X-ray diffraction where interaction occurs with electron clouds
• Strong Coulombic interaction between electrons and atomic nuclei leads to higher probability of multiple scattering events
• Complicates interpretation of diffraction intensities due to dynamical effects

Inelastic Scattering Processes

• Inelastic scattering contributes to background in electron diffraction patterns
• Provides additional information about sample composition and electronic structure
• Examples of inelastic processes include:
  • Plasmon excitations (collective oscillations of valence electrons)
  • Core-level ionizations (used in electron energy loss spectroscopy)
• Energy filtered diffraction techniques can separate elastic and inelastic contributions

Surface Sensitivity and Penetration Depth

• Penetration depth of electrons in crystalline materials typically much smaller than X-rays
• Makes electron diffraction more surface-sensitive and suitable for studying thin films and nanostructures
• Penetration depth depends on accelerating voltage and sample composition
  • Typical range: 10-100 nm for 100-300 keV electrons in most materials

Dynamical Diffraction Effects

• Arise from strong interaction between electrons and crystal lattice
• Provide information about crystal orientation and perfection
• Examples of dynamical effects include:
  • Kikuchi lines (formed by inelastically scattered electrons)
  • Channeling (enhanced transmission along specific crystallographic directions)
• Dynamical effects can be used for precise crystal orientation determination

Electron Diffraction Setup

Electron Source and Beam Formation

• Electron source typically thermionic or field emission gun
• Produces coherent beam of electrons with controlled energy and wavelength
• Condenser lens system focuses and collimates electron beam
  • Controls beam intensity and convergence angle
  • Allows for formation of parallel or convergent beam for different diffraction techniques

Sample Manipulation and Imaging System

• Sample holder maintains specimen in correct orientation
• Allows for precise manipulation of sample position and tilt
• Objective lens forms initial magnified image of specimen and diffraction pattern in back focal plane
• Intermediate and projector lenses further magnify and project diffraction pattern onto viewing screen or detector

Beam Control and Detection

• Apertures select specific regions of sample or diffraction pattern for analysis
  • Control angular range of scattered electrons
  • Examples: selected area aperture, objective aperture
• Detector system captures diffraction pattern
  • Options include fluorescent screen, CCD camera, or direct electron detector
  • Modern detectors allow for high dynamic range and fast acquisition rates

Interpreting Diffraction Patterns

Reciprocal Space Analysis

• Geometry of diffraction spots corresponds to reciprocal lattice of crystal
• Allows determination of lattice parameters and crystal symmetry
• Spot spacing inversely proportional to real space lattice dimensions
• Pattern symmetry reflects point group symmetry of crystal

Intensity Analysis and Structure Determination

• Intensity variations among diffraction spots provide information about atomic structure factor
• Used to refine atomic positions within unit cell
• Presence of forbidden reflections or systematic absences indicate specific space group symmetries or structural motifs
• Intensity analysis complicated by dynamical effects in thick samples

Advanced Diffraction Techniques

• Higher-order Laue zone (HOLZ) reflections provide precise information about lattice parameters and strain
• Convergent beam electron diffraction (CBED) patterns contain additional information about:
  • Crystal thickness
  • Space group symmetry
  • Local atomic arrangements
• Precession electron diffraction techniques obtain more kinematical diffraction data
  • Simplifies structure solution and refinement processes
  • Reduces dynamical effects by averaging over rocking curve