Diffraction patterns are key to understanding crystal structures in crystallography. They reveal how X-rays, electrons, or neutrons interact with materials, helping us visualize atomic arrangements and determine properties like symmetry and spacing between crystal planes.
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Bragg's Law
- Describes the relationship between the angle of incidence, wavelength, and the distance between crystal planes.
- Given by the equation: nฮป = 2d sin(ฮธ), where n is an integer, ฮป is the wavelength, d is the interplanar spacing, and ฮธ is the angle of diffraction.
- Fundamental for determining crystal structures through X-ray diffraction.
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Reciprocal lattice
- A mathematical construct used to describe the periodicity of a crystal in momentum space.
- Each point in the reciprocal lattice corresponds to a set of crystal planes in real space.
- Essential for understanding diffraction patterns and the conditions for constructive interference.
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Ewald sphere
- A geometric representation that relates the reciprocal lattice to the diffraction condition.
- The radius of the sphere is inversely proportional to the wavelength of the incident beam.
- Helps visualize the relationship between the incident beam, scattered beam, and reciprocal lattice points.
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Structure factor
- A complex number that describes the amplitude and phase of scattered waves from a crystal.
- Depends on the arrangement of atoms within the unit cell and their scattering factors.
- Crucial for calculating the intensity of diffraction spots.
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Systematic absences
- Specific diffraction spots that are missing due to the symmetry and arrangement of atoms in the crystal.
- Can provide information about the space group and symmetry of the crystal structure.
- Important for determining the correct crystal structure from diffraction data.
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Laue equations
- A set of equations that describe the conditions for diffraction in terms of the crystal lattice and incident wave vector.
- Useful for analyzing diffraction patterns from single crystals.
- Provides insight into the orientation of the crystal with respect to the incident beam.
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Powder diffraction patterns
- Result from the diffraction of X-rays by a polycrystalline sample, producing a series of rings or peaks.
- Useful for identifying phases and determining crystal structures without needing single crystals.
- The pattern is a function of the d-spacing and the intensity of the diffracted beams.
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Single crystal diffraction patterns
- Produced by a single crystal, resulting in sharp, well-defined spots on a detector.
- Allows for precise determination of the crystal structure and atomic positions.
- Requires careful alignment of the crystal with respect to the incident beam.
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X-ray diffraction
- A technique that uses X-rays to probe the atomic structure of materials.
- Based on the interaction of X-rays with the electron cloud of atoms, leading to scattering.
- Widely used in crystallography for determining crystal structures.
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Electron diffraction
- Utilizes electrons instead of X-rays to probe crystal structures, providing higher resolution due to shorter wavelengths.
- Sensitive to the arrangement of atoms and can be used for thin films and nanostructures.
- Offers information on both the structure and electronic properties of materials.
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Neutron diffraction
- Employs neutrons to investigate crystal structures, particularly useful for locating light atoms like hydrogen.
- Neutrons interact with atomic nuclei rather than electron clouds, providing complementary information to X-ray diffraction.
- Effective for studying magnetic structures and dynamics in materials.
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Fourier transform and diffraction
- The mathematical tool used to relate real-space atomic positions to reciprocal-space diffraction patterns.
- Converts the intensity data from diffraction experiments into electron density maps.
- Essential for reconstructing the crystal structure from diffraction data.
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Miller indices
- A notation system for describing the orientation of crystal planes and directions.
- Defined by three integers (h, k, l) that are inversely proportional to the intercepts of the plane with the axes.
- Fundamental for indexing diffraction patterns and understanding crystal symmetry.
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Intensity of diffraction spots
- Proportional to the square of the structure factor and the multiplicity of the reflection.
- Provides information about the arrangement of atoms and their scattering power.
- Critical for determining the electron density and refining crystal structures.
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Resolution and d-spacing
- Resolution refers to the ability to distinguish between closely spaced features in a diffraction pattern.
- d-spacing is the distance between crystal planes, which can be calculated from the diffraction angle.
- Both are crucial for accurately determining the crystal structure and understanding material properties.