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  2. Crystal system - Wikipedia

    en.wikipedia.org/wiki/Crystal_system

    A crystal system is a set of point groups in which the point groups themselves and their corresponding space groups are assigned to a lattice system. Of the 32 crystallographic point groups that exist in three dimensions, most are assigned to only one lattice system, in which case both the crystal and lattice systems have the same name. However ...

  3. Crystal structure - Wikipedia

    en.wikipedia.org/wiki/Crystal_structure

    A crystal system is a set of point groups in which the point groups themselves and their corresponding space groups are assigned to a lattice system. Of the 32 point groups that exist in three dimensions, most are assigned to only one lattice system, in which case the crystal system and lattice system both have the same name.

  4. Crystallographic point group - Wikipedia

    en.wikipedia.org/wiki/Crystallographic_point_group

    Each crystallographic point group defines the (geometric) crystal class of the crystal. The point group of a crystal determines, among other things, the directional variation of physical properties that arise from its structure, including optical properties such as birefringency , or electro-optical features such as the Pockels effect .

  5. Hermann–Mauguin notation - Wikipedia

    en.wikipedia.org/wiki/Hermann–Mauguin_notation

    These are the crystallographic point groups 1 and 1 (triclinic crystal system), 2, m, and ⁠ 2 / m ⁠ , and 222, ⁠ 2 / m ⁠ ⁠ 2 / m ⁠ ⁠ 2 / m ⁠, and mm2 (orthorhombic). (The short form of ⁠ 2 / m ⁠ ⁠ 2 / m ⁠ ⁠ 2 / m ⁠ is mmm.) If the symbol contains three positions, then they denote symmetry elements in the x, y, z ...

  6. Crystallography - Wikipedia

    en.wikipedia.org/wiki/Crystallography

    Before the 20th century, the study of crystals was based on physical measurements of their geometry using a goniometer. [4] This involved measuring the angles of crystal faces relative to each other and to theoretical reference axes (crystallographic axes), and establishing the symmetry of the crystal in question.

  7. Crystal - Wikipedia

    en.wikipedia.org/wiki/Crystal

    Crystals of amethyst quartz Microscopically, a single crystal has atoms in a near-perfect periodic arrangement; a polycrystal is composed of many microscopic crystals (called "crystallites" or "grains"); and an amorphous solid (such as glass) has no periodic arrangement even microscopically.

  8. Centrosymmetry - Wikipedia

    en.wikipedia.org/wiki/Centrosymmetry

    In crystallography, a centrosymmetric point group contains an inversion center as one of its symmetry elements. [1] In such a point group, for every point (x, y, z) in the unit cell there is an indistinguishable point (-x, -y, -z). Such point groups are also said to have inversion symmetry. [2] Point reflection is a similar term used in geometry.

  9. List of space groups - Wikipedia

    en.wikipedia.org/wiki/List_of_space_groups

    The superscript doesn't give any additional information about symmetry elements of the space group, but is instead related to the order in which Schoenflies derived the space groups. This is sometimes supplemented with a symbol of the form Γ x y {\displaystyle \Gamma _{x}^{y}} which specifies the Bravais lattice.