15.9: Crystal Systems

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    From LibreTexts, under CC BY-NC-SA 2.0, as the source states it; its equations are written in TeX, which the PDF shows typeset. This page at LibreTexts.

    The rotational symmetry of a crystal places constraints on the shape of the conventional unit cell we choose to describe the structure. On this basis we divide all structures into one of 7 crystal systems. For example, for crystals with 4 fold symmetry it will always be possible to choose a unit cell that has a square base with a = b and γ = 90°:

    4-fold symmetry example

    There are 14 unique combinations of the 7 crystal systems with the possible types of primitive and non-primitive lattices. These are referred to as the 14 Bravais lattices.

    Crystal systems, lattices and symmetry elements

    Crystal System

    Defining Symmetry

    Unit Cell Geometry

    		  

    Triclinic

    Translational Only

    a≠b≠c; α≠β≠γ

    a

    Monoclinic

    A diad axis
    (parallel to [010])

    a≠b≠c; α=γ=90°; β>90°

    a

    Orthorhombic

    3 diads
    (each should be parallel to each axis)

    a≠b≠c; α=β=γ=90°

    a

    Trigonal

    For more information click here

    1 triad
    (parallel to [001])

    a=b≠c; α=β=90°;
    γ=120°
    ( or
    a=b=c;
    120° > α=β=γ ≠ 90°)

    a

    Hexagonal

    1 hexad (parallel to [001])

    a=b≠c; α=β=90°;
    γ=120°

    a

    Tetragonal

    One tetrad
    (parallel to the [001] vector)

    a=b≠c; α=β=γ=90°

    a

    Cubic

    4 triads
    (all parallel to <111> directions)

    a=b=c; α=β=γ=90°

    a

    Bravais Lattice Structures

     

     

     

     

     

     

     

     

     

     

     

     

     

     

     

    		  

    And you can use the Wolfram Demonstration Project Viewer to look at the Bravais lattices

           

    This page titled 15.9: Crystal Systems was last modified on Thu, 24 Aug 2023 21:17:35 GMT and is shared under a CC BY-NC-SA 2.0 license and was authored, remixed, and/or curated by Dissemination of IT for the Promotion of Materials Science (DoITPoMS) via source content that was edited to the style and standards of the LibreTexts platform.