Cubic (crystal system)

In crystallography, the cubic crystal system (or isometric crystal system) is the most symmetric of the 7 crystal systems. The system is composed of the three Bravais lattices whose symmetry group is that of a cube.

Related Topics:
Crystallography - Symmetric - Crystal system - Bravais lattice - Symmetry group - Cube

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The three Bravais lattices that form the cubic crystal system are:

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The cubes drawn are the conventional unit cells. For a cube whose vertices include 000 and 200, bcc has additional lattice point 111, while fcc has 110, 101, and 011. For bcc the primitive cells have a volume of 1/2 of the cube, e.g. the parallelepiped 000 200 020 220 111 311 131 331 with primitive translation vectors 200, 020, and 111, with determinant 4. For fcc the primitive cells have a volume of 1/4 of the cube, e.g. the parallelepiped 110 220 020 130 101 211 011 121 with primitive translation vectors 110, -1 1 0, and 0 -1 1, with determinant 2.

Related Topics:
Lattice - Primitive cell - Parallelepiped

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As can be seen by turning the base plane 45°, bcc and fcc only differ by a vertical scaling: in both cases the lattice points in the middle layer are above the centers of the squares of the base layer. Both scales are "special", allowing a cubic symmetry: for bcc the middle layer has a height of 1/2 of the grid size of the square grid of each layer, while for fcc the middle layer has a height of 1/2 √2 of that grid size. For other scalings both are the same, body-centered

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tetragonal.

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Perpendicular to each body diagonal, fcc has hexagonal layers, with three positionings, which are cyclically changed. Two opposite vertices of the cube have two layers in between. See also: close-packing

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The point groups that fall under this crystal system are listed below, followed by their representations in international notation and Schoenflies notation, and mineral examples.

Related Topics:
Point groups - Schoenflies notation - Mineral

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There are 36 cubic space groups, of which 10 are hexoctahedral: Fd3c, Fd3m, Fm3c, Fm3m, Ia3d, Im3m, Pm3m, Pm3n, Pn3m, and Pn3n. Other terms for hexoctahedral are normal class, holohedral, ditesseral central class, galena type.

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