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13.13: Crystal Systems

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     High quality crystals are often used to generate precise laser beams
    Figure \(\PageIndex{1}\) (Credit: Courtesy of the National Cancer Institute; Source: http://commons.wikimedia.org/wiki/File:Photodynamic_therapy.jpg(opens in new window); License: Public Domain)

    What are the different uses of lasers?

    The development of modern lasers has opened many doors to both research and applications. A laser beam was used to measure the distance from the Earth to the moon. Lasers are important components of CD players. As the image above illustrates, lasers can provide precise focusing of beams to selectively destroy cancer cells in patients. The ability of a laser to focus precisely is due to high-quality crystals that help give rise to the laser beam. A variety of techniques are used to manufacture pure crystals for use in lasers.

    Crystalline Solids

    The majority of solids are crystalline in nature. A crystal is a substance in which the particles are arranged in an orderly, repeating, three-dimensional pattern. Particles of a solid crystal may be ions, atoms, or molecules, depending on the type of substance. The three-dimensional arrangement of a solid crystal is referred to as the crystal lattice. Different arrangements of the particles within a crystal cause them to adopt several different shapes.

    Crystal Systems

    Crystals are classified into general categories based on their shapes. A crystal is defined by its faces, which intersect one another at specific angles; these intersections are characteristic of the given substance. The seven crystal systems are shown below, along with an example of each. The edge lengths of a crystal are represented by the letters \(a\), \(b\), and \(c\). The angles at which the faces intersect are represented by the Greek letters \(\alpha\), \(\beta\), and \(\gamma\). Each of the seven crystal systems differ in terms of the angles between the faces, and in the number of edges of equal length on each face.

    Table \(\PageIndex{1}\): Seven Basic Crystal Systems and Examples of Each

    Seven Basic Crystal Systems and Examples of Each
    Crystal System Diagram Example

    Cubic

    \(a = b = c\); \(\alpha = \beta = \gamma = 90^\text{o}\)
    Structure of a cubic crystal
    Figure \(\PageIndex{2}\): (Credit: Christopher Auyeung; Source: CK-12 Foundation; License: CC  by-NC 3.0(opens in new window))
    An example of a cubic crystal is pyrite
    Figure \(\PageIndex{3}\): Pyrite. (Credit: User: Teravolt/Wkipedia; Source: http://en.wikipedia.org/wiki/File:Pyrite_Cubes.JPG(opens in new window); License: CC by 3.0(opens in new window))

    Tetragonal

    \(a = b \neq c\); \(\alpha = \beta = \gamma = 90^\text{o}\)
    Structure of a tetragonal crystal
    Figure \(\PageIndex{4}\): (Credit: Christopher Auyeung; Source: CK-12 Foundation; License: CC  by-NC 3.0(opens in new window))
    An example of a tetragonal crystal is wulfenite
    Figure \(\PageIndex{5}\): Wulfenite. (Credit: Courtesy of the "Minerals in Your World Project" by the  US Geological Survey and the Mineral Information Institute; Source: http://commons.wikimedia.org/wiki/File:WulfeniteUSGOV.jpg(opens in new window); License: Public Domain)

    Orthorhombic

    \(a \neq b \neq c\); \(\alpha = \beta = \gamma = 90^\text{o}\)
    Structure of an orthorhombic crystal
    Figure \(\PageIndex{6}\): (Credit: Christopher Auyeung; Source: CK-12 Foundation; License: CC  by-NC 3.0(opens in new window))
    An example of an orthorhombic crystal is aragonite
    Figure \(\PageIndex{7}\): Aragonite. (Credit: Christoph Radtke; Source: http://commons.wikimedia.org/wiki/File:Aragonite_-_crystal_ball.jpg(opens in new window); License: Public Domain)

    Monoclinic

    \(a \neq b \neq c\); \(\alpha \neq 90^\text{o} = \beta = \gamma\)
    Structure of a monoclinic crystal
    Figure \(\PageIndex{8}\): (Credit: Christopher Auyeung; Source: CK-12 Foundation; License: CC  by-NC 3.0(opens in new window))
    An example of a monoclinic crystal is azurite
    Figure \(\PageIndex{9}\): Azurite. (Credit: Stephanie Clifford (Flickr: sdixclifford); Source: http://www.flickr.com/photos/30486689@N08/3561497998/(opens in new window); License: CC  by 2.0(opens in new window))

    Rhombohedral

    \(a = b = c\); \(\alpha = \beta = \gamma \neq 90^\text{o}\)
    Structure of a rhombohedral crystal
    Figure \(\PageIndex{10}\):  (Credit: Christopher Auyeung; Source: CK-12 Foundation; License: CC  by-NC 3.0(opens in new window))
    An example of a rhombohedral crystal is calcite
    Figure \(\PageIndex{11}\): Calcite. (Credit: Mike Beauregard (Flickr: subarcticmike); Source: http://www.flickr.com/photos/31856336@N03/3108675089/(opens in new window); License: CC BY 2.0(opens in new window))

     

    Triclinic

    \(a \neq b \neq c\); \(\alpha \neq \beta \neq \gamma \neq 90^\text{o}\)
    Structure of a triclinic crystal
    Figure \(\PageIndex{12}\):  (Credit: Christopher Auyeung; Source: CK-12 Foundation
    License: CC BY-NC 3.0(opens in new window))
    An example of a triclinic crystal is microcline
    Figure \(\PageIndex{13}\): Microcline. (Credit: Courtesy of the "Minerals in Your World Project" by the US Geological Survey and the Mineral Information Institute; Source: http://commons.wikimedia.org/wiki/File:Feldspar%2528Microcline%2529USGOV.jpg(opens in new window); License: Public Domain)

    Hexagonal

    \(a = b \neq c\); \(\alpha = \beta = 90^\text{o}\), \(\gamma = 120^\text{o}\)
    Structure of a hexagonal crystal
    Figure \(\PageIndex{14}\):  (Credit: Christopher Auyeung; Source: CK-12 Foundation; License: CC BY-NC 3.0(opens in new window))
    An example of a hexagonal crystal is beryl
    Figure \(\PageIndex{15}\): Beryl. (Credit: Parent Gery; Parent Géry; Source: http://commons.wikimedia.org/wiki/File:H%25C3%25A9liodore_2_%2528Russie%2529_.jpg(opens in new window); License: Public Domain)

    Summary

    • A crystal is a substance in which the particles are arranged in an orderly, repeating, three-dimensional pattern.
    • The crystal lattice is the three-dimensional arrangement of a solid crystal.

    Review

    1. What is a crystal?
    2. List the seven crystal systems.

    This page titled 13.13: Crystal Systems is shared under a CK-12 license and was authored, remixed, and/or curated by CK-12 Foundation via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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