4: X-ray Crystallography
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- 4.2: Unit Cells
- The construction of a simple powder diffractometer was first described by Hull in 19171 which was shortly after the discovery of X-rays by Wilhelm Conrad Röntgen in 18952. Diffractometer measures the angles at which X-rays get reflected and thus get the structural information they contains. Nowadays resolution of this technique get significant improvement and it is widely used as a tool to analyze the phase information and solve crystal structures of solid-state materials.
- 4.3: Miller Indices (hkl)
- The orientation of a surface or a crystal plane may be defined by considering how the plane (or indeed any parallel plane) intersects the main crystallographic axes of the solid. The application of a set of rules leads to the assignment of the Miller Indices (hkl), which are a set of numbers which quantify the intercepts and thus may be used to uniquely identify the plane or surface.
- 4.4: Sample and data collection
- X-ray Crystallography is a scientific method used to determine the arrangement of atoms of a crystalline solid in three dimensional space. This technique takes advantage of the interatomic spacing of most crystalline solids by employing them as a diffraction gradient for x-ray light, which has wavelengths on the order of 1 angstrom (10-8 cm).
- 4.5: Crystallography quick reference
- The branch of science devoted to the study of molecular and crystalline structure and properties, with far-reaching applications in mineralogy, chemistry, physics, mathematics, biology and materials science.
- 4.5.1: Fundamental Crystallography
- 4.5.1.1: Abelian group
- 4.5.1.2: Absolute structure
- 4.5.1.3: Affine Isomorphism
- 4.5.1.4: Affine mapping
- 4.5.1.5: Aperiodic crystal
- 4.5.1.6: Aristotype
- 4.5.1.7: Arithmetic crystal class
- 4.5.1.8: Asymmetric Unit
- 4.5.1.9: Automorphism
- 4.5.1.100: Friedel's law
- 4.5.1.101: Geometric crystal class
- 4.5.1.102: Geometric element
- 4.5.1.103: Voronoi domain
- 4.5.1.104: Group
- 4.5.1.105: Weissenberg complex
- 4.5.1.106: Group homomorphism
- 4.5.1.107: Wigner-Seitz cell
- 4.5.1.108: Group isomorphism
- 4.5.1.109: Wyckoff position
- 4.5.1.10: Laue classes
- 4.5.1.110: H centered cell
- 4.5.1.111: Wyckoff set
- 4.5.1.112: Image
- 4.5.1.113: Lattice
- 4.5.1.114: Lattice system
- 4.5.1.115: Bravais flock
- 4.5.1.11: Local symmetry
- 4.5.1.12: Brillouin zones
- 4.5.1.13: Mapping
- 4.5.1.14: Center
- 4.5.1.15: Centralizer
- 4.5.1.16: Complex
- 4.5.1.17: Conjugacy class
- 4.5.1.18: Coset
- 4.5.1.19: Crystallographic orbit
- 4.5.1.20: Hemihedry
- 4.5.1.21: Displacive modulation
- 4.5.1.22: Domain of influence
- 4.5.1.23: Double coset
- 4.5.1.24: Flack parameter
- 4.5.1.25: Form
- 4.5.1.26: Groupoid
- 4.5.1.27: Holohedry
- 4.5.1.28: Incommensurate composite crystal
- 4.5.1.29: Incommensurate magnetic structure
- 4.5.1.30: Incommensurate modulated structure
- 4.5.1.31: Merohedral
- 4.5.1.32: Miller Indices
- 4.5.1.33: Lattice complex
- 4.5.1.34: Limiting complex
- 4.5.1.35: Merohedry
- 4.5.1.36: Order
- 4.5.1.37: Mesh
- 4.5.1.38: Patterson methods
- 4.5.1.39: Patterson vector
- 4.5.1.40: Modulated crystal structure
- 4.5.1.41: Point configuration
- 4.5.1.42: Normalizer
- 4.5.1.43: Point group
- 4.5.1.44: Normal subgroup
- 4.5.1.45: Point space
- 4.5.1.46: OD structure
- 4.5.1.47: Primitive cell
- 4.5.1.48: Ogdohedry
- 4.5.1.49: Priority rule
- 4.5.1.50: Pseudo symmetry
- 4.5.1.51: Point symmetry
- 4.5.1.52: Reciprocal lattice
- 4.5.1.53: Partial symmetry
- 4.5.1.54: Reciprocal Space
- 4.5.1.55: Site symmetry
- 4.5.1.56: Space group
- 4.5.1.57: Symmetry element
- 4.5.1.58: Symmetry operation
- 4.5.1.59: Unit cell
- 4.5.1.60: Polytypism
- 4.5.1.61: Vector module
- 4.5.1.62: Primitive basis
- 4.5.1.63: Vector space
- 4.5.1.64: Bragg's Law
- 4.5.1.65: Bravais-Miller indices
- 4.5.1.66: Bravais class
- 4.5.1.67: Bravais lattice
- 4.5.1.68: Cartesian product
- 4.5.1.69: Centered lattices
- 4.5.1.70: Semidirect product
- 4.5.1.71: Conventional cell
- 4.5.1.72: Crystal
- 4.5.1.73: Subperiodic group
- 4.5.1.74: Crystallographic basis
- 4.5.1.75: Crystallographic symmetry
- 4.5.1.76: Stabilizer
- 4.5.1.77: Crystal family
- 4.5.1.78: Statistical descriptors
- 4.5.1.79: Crystal pattern
- 4.5.1.80: Subcell
- 4.5.1.81: Crystal system
- 4.5.1.82: Subgroup
- 4.5.1.83: Direct Lattice
- 4.5.1.84: Sublattice
- 4.5.1.85: Direct product
- 4.5.1.86: Supercell
- 4.5.1.87: Direct space
- 4.5.1.88: Supergroup
- 4.5.1.89: Dual basis
- 4.5.1.90: Superlattice
- 4.5.1.91: D centered cell
- 4.5.1.92: Eigensymmetry
- 4.5.1.93: Euclidean mapping
- 4.5.1.94: Symmorphic space groups
- 4.5.1.95: Factor group
- 4.5.1.96: Tetartohedry
- 4.5.1.97: Family structure
- 4.5.1.98: Fixed-point-free space groups
- 4.5.1.99: Binary Operation
- 4.5.2: Structure Determination
- 4.5.2.1: Bragg R factor
- 4.5.2.2: Constrained refinement
- 4.5.2.3: Direct methods
- 4.5.2.4: Free R factor
- 4.5.2.5: Harker section
- 4.5.2.6: Heavy-Atom Method
- 4.5.2.7: Phase problem
- 4.5.2.8: Refinement
- 4.5.2.9: Restrained refinement
- 4.5.2.10: Rietveld method
- 4.5.2.11: R factor
- 4.5.2.12: Sharpened Patterson function
- 4.5.2.13: Structure-factor coefficient
- 4.5.2.14: Structure amplitude
- 4.5.2.15: Structure determination
- 4.5.2.16: Superposition methods
- 4.5.3: Twinning
- 4.5.3.1: Allotwin
- 4.5.3.2: Corresponding Twins
- 4.5.3.3: Hybrid twin
- 4.5.3.4: Inversion twin
- 4.5.3.5: Mallard's Law
- 4.5.3.6: Reflection twin
- 4.5.3.7: Rotation Twin
- 4.5.3.8: Selective merohedry
- 4.5.3.9: TLQS twinning
- 4.5.3.10: TLS twinning
- 4.5.3.11: Twinning
- 4.5.3.12: Twinning(effects of)
- 4.5.3.13: Twinning (consequences of)
- 4.5.3.14: Twinning (endemic conditions of)
- 4.5.3.15: Twinning by inversion
- 4.5.3.16: Twinning by merohedry
- 4.5.3.17: Twinning by metric merohedry
- 4.5.3.18: Twinning by psuedomerohedry
- 4.5.3.19: Twinning by reticular merohedry
- 4.5.3.20: Twinning by reticular polyholohedry
- 4.5.3.21: Twinning by reticular pseudomerohedry
- 4.5.3.22: Twin element
- 4.5.3.23: Twin index
- 4.5.3.24: Twin lattice
- 4.5.3.25: Twin law
- 4.5.3.26: Twin obliquity
- 4.5.3.27: Twin operation
- 4.5.4: X-rays
- 4.5.4.1: Absorption edge
- 4.5.4.2: Anomalous absorption
- 4.5.4.3: Anomalous dispersion
- 4.5.4.4: Anomalous scattering
- 4.5.4.5: Borrmann Effect
- 4.5.4.6: Bragg's law
- 4.5.4.7: Bragg angle
- 4.5.4.8: Cromer–Mann coefficients
- 4.5.4.9: Dynamical diffraction
- 4.5.4.10: Dynamical theory of Scattering
- 4.5.4.11: Electron density map
- 4.5.4.12: Ewald sphere
- 4.5.4.13: F(000)
- 4.5.4.14: Friedel's Law
- 4.5.4.15: Friedel pair
- 4.5.4.16: Integral reflection conditions
- 4.5.4.17: Kinematical theory
- 4.5.4.18: Laue equations
- 4.5.4.19: Lorentz–polarization correction
- 4.5.4.20: Mosaic crystal
- 4.5.4.21: Primary extinction
- 4.5.4.22: Reflection conditions
- 4.5.4.23: Resolution
- 4.5.4.24: Resonant scattering
- 4.5.4.25: Secondary extinction
- 4.5.4.26: Serial reflection conditions
- 4.5.4.27: Structure Factor
- 4.5.4.28: Systematic absences
- 4.5.4.29: Zonal reflection conditions
Thumbnail: 3D depiction of electron density (blue) of a ligand (orange) bound to a binding site in a protein (yellow).[131] The electron density is obtained from experimental data, and the ligand is modeled into this electron density. (CC BY-SA 4.0; Theislikerice via Wikipedia)