Crystal structure

A crystal structure is the ordered, repeating arrangement of atoms, ions, or molecules in a crystalline solid. Its geometry is described by a repeating unit cell and the symmetry operations that preserve the arrangement.

Crystal lattice: An idealized periodic array of points representing the translational repetition in a crystal. It separates the repeating geometry from the atoms or molecules placed at each point.
X-ray crystallography: A method that determines crystal structures by analyzing how crystals diffract X-rays. It uses diffraction intensities to infer the positions of atoms in a repeating structure.
Polymorphism (materials science): The ability of a solid substance to form multiple crystal structures. Different arrangements of the same substance can produce distinct material properties.
Amorphous solid: A solid lacking long-range periodic order in the arrangement of its constituent particles. It contrasts with a crystal by lacking a repeating structure throughout the material.
Unit cell: The smallest repeating volume that can generate a crystal’s periodic structure by translation. Its dimensions and contents specify how the full structure repeats.
Bragg's law: The relation between X-ray wavelength, crystal-plane spacing, and the angles of constructive diffraction. It connects observed diffraction angles to spacings between crystal planes.
Crystal defects: Departures from perfect periodic order, including vacancies, dislocations, and grain boundaries. Real structures contain defects that strongly influence mechanical and electrical behavior.
Quasicrystal: A solid with long-range order and sharp diffraction patterns but no periodic translational symmetry. It shows that ordered solids need not have a conventional repeating unit cell.
Basis (crystallography): A group of atoms, ions, or molecules assigned to each point of a crystal lattice. Combining a basis with a lattice produces the crystal’s atomic arrangement.
Structure factor: A quantity describing the amplitude and phase of waves scattered by the contents of a unit cell. It links atomic positions within the cell to the intensity of each diffraction reflection.

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