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4.2: Single crystals- Shape and anisotropy

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    A single crystal often has distinctive plane faces and some symmetry. The actual shape of the crystal will be determined by the availability of crystallising material, and by interference with other crystals, but the angles between the faces will be characteristic of the material and will define an ideal shape. Single crystals showing these characteristic shapes can be grown from salt solutions such as alum and copper sulphate.

    Gemstones are often single crystals. They tend to be cut artificially to obtain aesthetically pleasing refractive and reflective properties. This generally requires cutting along crystallographic planes. This is known as cleaving the crystal. A familiar example is diamond, from which decorative stones can be cleaved in different ways to produce a wide range of effects.

    To see a variety of symmetrical naturally formed minerals, visit the mineral galleries website.

    Consider the following three-dimensional shapes:

    Diagram of a cube
    Cube: 6 identical squares
    Diagram of a tetrahedron
    Tetrahedron: 4 identical equilateral triangles
    Diagram of an octahedron
    Octahedron: 8 identical equilateral triangles
    Diagram of a rhomohedron
    Rhombohedron: 6 identical parallelograms with sides of equal length

    You can make your own cube, octahedron and tetrahedron by printing the following pages and following the instructions on them.

    These three shapes are the most important in materials science, and you should be very familiar with them!

    The symmetry exhibited by real single crystals is determined by the crystal structure of the material. Many have shapes composed of less regular polyhedra, such as prisms and pyramids.

    Diagram of a hexagonal prism
    Hexagonal prism: 2 hexagons and 6 rectangles
    Diagram of a square-based pyramid
    Square-based pyramid: 4 triangles and a square

    Not all single crystal specimens exhibit distinctive polyhedral shapes. Metals, for example, often have crystals of no particular shape at all.