Laves phases are intermetallicphases 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: cubicMgCu2 (C15), hexagonal 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 around the A atoms for the AB2 structure.[1]
Unit cell of Laves phase with MgZn2 structure (Mg atoms are green).Laves polyhedron
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 ,[2] the structure would be topologically tetrahedrally close-packed.[3] At this size ratio, the structure has an overall packing volume density of 0.710.[4] Compounds found in Laves phases typically have an atomic size ratio between 1.05 and 1.67.[3] Analogues of Laves phases can be formed by the self-assembly of a colloidal dispersion of two sizes of sphere.[2]
^The Laves Phase Structures 2009-03-02 at the Wayback Machine. nrl.navy.mil. Accessed on 2009-2-26.
^ abHynninen, A. P.; Thijssen, J. H. J.; Vermolen, E. C. M.; Dijkstra, M.; Van Blaaderen, A. (2007). "Self-assembly route for photonic crystals with a bandgap in the visible region". Nature Materials. 6 (3): 202–205. Bibcode:2007NatMa...6..202H. doi:10.1038/nmat1841. PMID 17293851.
^ abZhu, J. H.; Liu, C. T.; Pike, L. M.; Liaw, P. K. (1999). "A thermodynamic interpretation of the size-ratio limits for Laves phase formation". Metallurgical and Materials Transactions A. 30 (5): 1449. doi:10.1007/s11661-999-0292-5. S2CID 98795110.
^Murray, M. J.; Sanders, J. V. (1980). "Close-packed structures of spheres of two different sizes II. The packing densities of likely arrangements". Philosophical Magazine A. 42 (6): 721. Bibcode:1980PMagA..42..721M. doi:10.1080/01418618008239380.
January 01, 1970
laves, phase, intermetallic, phases, that, have, composition, named, fritz, laves, first, described, them, phases, classified, basis, geometry, alone, while, problem, packing, spheres, equal, size, been, well, studied, since, gauss, result, investigations, int. Laves phases are intermetallic 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 MgCu2 C15 hexagonal 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 around the A atoms for the AB2 structure 1 Unit cell of Laves phase with MgZn2 structure Mg atoms are green Laves polyhedron 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 3 2 1 225 displaystyle sqrt 3 2 approx 1 225 2 the structure would be topologically tetrahedrally close packed 3 At this size ratio the structure has an overall packing volume density of 0 710 4 Compounds found in Laves phases typically have an atomic size ratio between 1 05 and 1 67 3 Analogues of Laves phases can be formed by the self assembly of a colloidal dispersion of two sizes of sphere 2 Laves phases are instances of the more general Frank Kasper phases References edit The Laves Phase Structures Archived 2009 03 02 at the Wayback Machine nrl navy mil Accessed on 2009 2 26 a b Hynninen A P Thijssen J H J Vermolen E C M Dijkstra M Van Blaaderen A 2007 Self assembly route for photonic crystals with a bandgap in the visible region Nature Materials 6 3 202 205 Bibcode 2007NatMa 6 202H doi 10 1038 nmat1841 PMID 17293851 a b Zhu J H Liu C T Pike L M Liaw P K 1999 A thermodynamic interpretation of the size ratio limits for Laves phase formation Metallurgical and Materials Transactions A 30 5 1449 doi 10 1007 s11661 999 0292 5 S2CID 98795110 Murray M J Sanders J V 1980 Close packed structures of spheres of two different sizes II The packing densities of likely arrangements Philosophical Magazine A 42 6 721 Bibcode 1980PMagA 42 721M doi 10 1080 01418618008239380 Retrieved from https en wikipedia org w index php title Laves phase amp oldid 1217085544, wikipedia, wiki, book, books, library,
