13.2 Electron crystallography and structure determination of nanomaterials

Electron crystallography uses electron waves to determine atomic structures of tiny crystals and nanomaterials. It's especially useful for small or delicate samples that X-rays can't handle, offering higher resolution and stronger interactions with matter.

This technique combines diffraction patterns and high-res imaging to reveal crystal structures, symmetry, and atomic positions. It's great for studying nanoparticles, graphene, and other cutting-edge materials, but faces challenges like radiation damage and multiple scattering effects.

Principles of Electron Crystallography

Fundamental Concepts and Instrumentation

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• Electron crystallography determines atomic structure of crystalline materials using wave-like properties of electrons
  • Particularly useful for small crystal sizes or beam-sensitive samples
• Diffraction of electrons by periodic arrangement of atoms in crystal lattice follows Bragg's law
• Primary instruments include transmission electron microscopes (TEM) and scanning transmission electron microscopes (STEM)
• Electron diffraction patterns reveal crystal structure information
  • Unit cell parameters
  • Symmetry
  • Atomic positions

Techniques and Data Collection

• Selected area electron diffraction (SAED) obtains diffraction patterns from specific regions
• Convergent beam electron diffraction (CBED) provides three-dimensional structural information
• Precession electron diffraction (PED) reduces dynamical scattering effects
• Data collection involves recording diffraction patterns and high-resolution images
  • Processed and analyzed to determine crystal structure
• Structure solution methods adapted from X-ray crystallography
  • Direct methods
  • Patterson methods
  • Charge flipping algorithms

Electron Crystallography vs Diffraction Methods

Advantages of Electron Crystallography

• Higher spatial resolution compared to X-ray and neutron diffraction
  • Enables study of nanoscale materials and local structural features
• Stronger interaction of electrons with matter than X-rays or neutrons
  • Allows analysis of very small crystals or single molecules
• Direct imaging of crystal structure through high-resolution TEM
  • Not possible with X-ray or neutron diffraction alone

Differences in Data Collection and Processing

• Electron diffraction patterns produce two-dimensional projections of reciprocal lattice
  • X-ray and neutron diffraction typically yield three-dimensional data sets
• Multiple scattering effects more pronounced in electron diffraction
  • Complicates structure determination
  • Requires specialized data processing techniques
• Sample preparation often more complex for electron crystallography
  • May involve focused ion beam (FIB) milling or ultramicrotomy

Limitations and Considerations

• Radiation damage more significant in electron crystallography
  • Particularly affects organic and biological samples
• Two-dimensional nature of electron diffraction data can limit structural information
  • Requires specialized techniques to obtain three-dimensional information

Structure Determination of Nanomaterials

Techniques for Nanostructure Analysis

• Combines electron diffraction data with high-resolution TEM imaging
  • Provides both reciprocal and real-space information
• Electron tomography reconstructs three-dimensional structure of nanomaterials
  • Combines multiple two-dimensional projections at different tilt angles
• Precession electron diffraction (PED) reduces dynamical scattering effects
  • Improves quality of diffraction data from nanocrystalline materials
• Automated diffraction tomography (ADT) and rotation electron diffraction (RED) collect three-dimensional electron diffraction data from nanocrystals

Applications to Specific Nanomaterials

• Analyzes defects, interfaces, and surface structures in nanomaterials
  • Combines diffraction, imaging, and spectroscopy techniques
• Studies atomic arrangement and bonding in novel nanomaterials
  • Graphene
  • Carbon nanotubes
  • Two-dimensional transition metal dichalcogenides
• Investigates nanoparticle structure and morphology
  • Determines size, shape, and internal structure of nanoparticles

Challenges of Electron Crystallography

Multiple Scattering and Data Interpretation

• Strong electron-matter interaction leads to multiple scattering effects
  • Complicates interpretation of diffraction patterns
  • Limits accuracy of structure determination
• Dynamical scattering effects violate kinematical approximation
  • Requires development of specialized data processing techniques
  • Necessitates advanced structure refinement methods

Radiation Damage and Sample Limitations

• Electron beam can alter crystal structure during data collection
  • Particularly problematic for beam-sensitive materials (organic compounds, biomolecules)
• Limited penetration depth of electrons restricts sample thickness
  • Requires specialized sample preparation techniques
  • May introduce artifacts

Data Completeness and Quantitative Analysis

• Limited tilt range in electron microscopes (typically ±70°) results in missing wedges of information
  • Affects completeness and accuracy of three-dimensional reconstructions
• Quantitative analysis of electron diffraction intensities challenging
  • Affected by multiple scattering, inelastic scattering, and sample thickness variations
  • Impacts reliability of atomic position and occupancy determinations
• Small sample volume increases sensitivity to crystal imperfections and surface effects
  • May not accurately represent bulk material properties