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  2. Quasicrystal - Wikipedia

    en.wikipedia.org/wiki/Quasicrystal

    The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled, e.g., the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two directions.

  3. Crystal structure - Wikipedia

    en.wikipedia.org/wiki/Crystal_structure

    Vectors and planes in a crystal lattice are described by the three-value Miller index notation. This syntax uses the indices h, k, and â„“ as directional parameters. [4] By definition, the syntax (hkâ„“) denotes a plane that intercepts the three points a 1 /h, a 2 /k, and a 3 /â„“, or some multiple thereof. That is, the Miller indices are ...

  4. Diamond cubic - Wikipedia

    en.wikipedia.org/wiki/Diamond_cubic

    Rotating model of the diamond cubic crystal structure 3D ball-and-stick model of a diamond lattice Pole figure in stereographic projection of the diamond lattice showing the 3-fold symmetry along the [111] direction. In crystallography, the diamond cubic crystal structure is a repeating pattern of 8 atoms that certain materials may adopt as ...

  5. Crystal system - Wikipedia

    en.wikipedia.org/wiki/Crystal_system

    A lattice system is a set of Bravais lattices. Space groups are classified into crystal systems according to their point groups, and into lattice systems according to their Bravais lattices. Crystal systems that have space groups assigned to a common lattice system are combined into a crystal family.

  6. Bravais lattice - Wikipedia

    en.wikipedia.org/wiki/Bravais_lattice

    For example, a crystal, viewed as a lattice with a single kind of atom located at every lattice point (the simplest basis form), may also be viewed as a lattice with a basis of two atoms. In this case, a primitive unit cell is a unit cell having only one lattice point in the first way of describing the crystal in order to ensure the smallest ...

  7. Particle in a one-dimensional lattice - Wikipedia

    en.wikipedia.org/wiki/Particle_in_a_one...

    In quantum mechanics, the particle in a one-dimensional lattice is a problem that occurs in the model of a periodic crystal lattice. The potential is caused by ions in the periodic structure of the crystal creating an electromagnetic field so electrons are subject to a regular potential inside the lattice.

  8. Lattice (group) - Wikipedia

    en.wikipedia.org/wiki/Lattice_(group)

    A lattice in the sense of a 3-dimensional array of regularly spaced points coinciding with e.g. the atom or molecule positions in a crystal, or more generally, the orbit of a group action under translational symmetry, is a translation of the translation lattice: a coset, which need not contain the origin, and therefore need not be a lattice in ...

  9. Hexagonal lattice - Wikipedia

    en.wikipedia.org/wiki/Hexagonal_lattice

    The honeycomb point set is a special case of the hexagonal lattice with a two-atom basis. [1] The centers of the hexagons of a honeycomb form a hexagonal lattice, and the honeycomb point set can be seen as the union of two offset hexagonal lattices. In nature, carbon atoms of the two-dimensional material graphene are arranged in a honeycomb ...