Laves phases are

intermetallic An intermetallic (also called an intermetallic compound, intermetallic alloy, ordered intermetallic alloy, and a long-range-ordered alloy) is a type of metallic alloy that forms an ordered solid-state compound between two or more metallic elemen ...

phases that have composition AB₂ and are named for Fritz Laves who first described them. The phases are classified on the basis of geometry alone. While the problem of packing spheres of equal size has been well-studied since Gauss, Laves phases are the result of his investigations into packing spheres of two sizes. Laves phases fall into three Strukturbericht types:

cubic Cubic may refer to: Science and mathematics * Cube (algebra), "cubic" measurement * Cube, a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex ** Cubic crystal system, a crystal system w ...

MgCu₂ (C15),

hexagonal In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°. Regular hexagon A '' regular hexagon'' has ...

MgZn₂ (C14), and hexagonal MgNi₂ (C36). The latter two classes are unique forms of the hexagonal arrangement, but share the same basic structure. In general, the A atoms are ordered as in diamond, hexagonal diamond, or a related structure, and the B atoms form

tetrahedra In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the o ...

around the A atoms for the AB₂ structure. Laves phases are of particular interest in modern metallurgy research because of their abnormal physical and chemical properties. Many hypothetical or primitive applications have been developed. However, little practical knowledge has been elucidated from Laves phase study so far. A characteristic feature is the almost perfect electrical conductivity, but they are not plastically deformable at room temperature. In each of the three classes of Laves phase, if the two types of atoms were perfect spheres with a size ratio of

\sqrt \approx 1.225

, the structure would be topologically tetrahedrally close-packed. At this size ratio, the structure has an overall packing volume density of 0.710. Compounds found in Laves phases typically have an atomic size ratio between 1.05 and 1.67. Analogues of Laves phases can be formed by the self-assembly of a colloidal dispersion of two sizes of sphere.

References

{{Reflist Intermetallics Crystal structure types