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Aditya posted an Question
April 04, 2020 • 13:59 pm 30 points
  • IIT JAM
  • Geology (GG)

Hermann -mauguin symbol

hermann -mauguin symbol. what is it. how to write these symbols. characteristics of hm symbol , its importance in crystallography.

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    Rahul kumar Best Answer

    Hermann-Mauguin symbols (also called the international symbols) used to describe the crystal classes from the symmetry content. One, two, or three symbols describe a point group; they combine in different ways for different systems. These symbols are conventional and are used worldwide. For different crystal systems different positions represents different symmetry as discussed below. For cubic point groups, the first symbol describes three mutually perpendicular principal symmetry axes, oriented perpendicular to cubic faces (if cubic faces are present). The second describes four axes oriented at angles of 54 degrees 44 minutes to the principal axes. They correspond to the “body diagonals” of a cube, a diagonal from a corner through the center to the opposite corner. The third symbol, if present, describes six 2-fold axes or mirror planes oriented at angles of 45 degrees to the principal axes. They correspond to “edge diagonals” of a cube, diagonals from the center of edges through the center of the cube to the opposite edge. For hexagonal point groups, the first symbol describes the single principal axis. The second, if present, describes three secondary rotation axes oriented at to each other and perpendicular to the principal axis, or three mirror planes oriented at to each other and parallel to the principal axis. The third symbol, if present, represents mirror planes or 2-fold axes oriented between the secondary axes. For tetragonal point groups, the first symbol represents the principal axis. The second, if present, represents two secondary axes perpendicular to each other and to the principal axis, or two mirror planes oriented at to each other and parallel to the principal axis. The third represents axes or mirror planes between the secondary axes. Only three orthorhombic point groups are possible. Point group 222 has three mutually perpendicular 2-fold axes. Point group mm2 has one 2-fold axis with two mutually perpendicular mirror planes parallel to it. Point group 2/m2/m2/m has three perpendicular 2-fold axes with mirror planes perpendicular to each. For monoclinic point groups, only one symmetry element is included in the Hermann-Mauguin symbols because the only possible symmetries are a 2-fold axis, a mirror, or a 2-fold axis with a mirror perpendicular to it. Similarly, for triclinic crystals, the only possible point groups are 1 and bar1. For more details please go through attachment.

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