Laves phase

Laves phases have what is known as a topological close-packed (TCP) structure which is often undesirable because they can act as stress risers that initiate cracks because of their hardness and morphology and because they tie up atoms needed for the more desirable coherent y phases that are involved in precipitation hardening of alloys. 

3 Laves phases. hP12MgZn2 type (h), cF24 Cu2Mg type (c), hP24 Ni2Mg type (he), Laves polytypes (hhc, hhccc, etc.). 

The Laves phases form a homeotect structure type set (a family of polytypic structures). In all of them, described in terms of a hexagonal cell, three closely spaced 36 nets of atoms are followed (in the z direction of the same cell) by a 3636 net. The 36 nets are stacked on the same site as the kagome 3636 nets which they surround. For instance (3-BAC- -CAB in the two slabs MgZn2-type (h) structure, (3-BAC- -CBA-a-ACB in the three slabs MgCu2-type (c) structure, 

Layer stacking symbols (K + 3T slabs formed by kagome and triangular nets) of the main types of Laves phases  

Zn Mg 06Zn 25Mgo 44Zn 50Mg o 56Zn)( 75Mgo 94 

Details about general crystallography of the Laves phases and alternative descriptions and their polytypes and variants are given in 7.4.3.3 whereas some information about their occurrence and thermodynamics is reported in 3.9.3.1.3. 

The term Laves phases is used for certain alloys with the composition MM3, the M atoms being bigger than the M atoms. The classical representative is MgCu2 its structure is shown in Fig. 15.4. It can be regarded as a superstructure of the CsCl type as in Fig. 15.3, with the following occupation of the positions a, b, c, and d  

We thus have placed a tetrahedron of four Cu atoms instead of a single atom in the position b the same kind of Cu tetrahedron then also results at the position d. The magnesium atoms by themselves have the same arrangement as in diamond. 

In addition to this cubic Laves phase, a variant with magnesium atoms arranged as in hexagonal diamond exists in the MgZn2 type, and further polytypes are known. 

The space filling in the MgCu2 type can be calculated with the aid of equation (14.1) (p. 150) the geometric relations follow from the bottom image in Fig. 15.4 the four Cu spheres form a row along the diagonal of length a fl, therefore r(Cu) = s/2a two Mg 

The sketched model assuming hard spheres has a flaw the sum of the atomic radii of Mg and Cu is smaller than the shortest distance between these atoms r(Mg) + r(Cu) = ( /3 + /5)a = 0.393a 

The coordination polyhedra are Frank-Ka,s per polyhedra. These are polyhedra with 

When the atomic size ratio is near 1.2 some dense (i.e., close-packed) structures become possible in which tetrahedral sub-groups of one kind of atom share their vertices, sides or faces to from a network. This network contains holes into which the other kind of atoms are put. These are known as Laves phases. They have three kinds of symmetry cubic (related to diamond), hexagonal (related to wurtzite), and orthorhombic (a mixture of the other two). The prototype compounds are MgCu2, MgZn2, and MgNi2, respectively. Only the simplest cubic one will be discussed further here. See Laves (1956) or Raynor (1949) for more details. 

The other prototype Laves phases, MgZn2 and MgNi2, are formed similarly but have different symmetries. MgZn2 is hexagonal and derived as described 

Since these structures are formed by filling the open spaces in the diamond and wurtzite structures, they have high atomic densities. This implies high valence electron densities and therefore considerable stability which is manifested by high melting points and elastic stiffnesses. They behave more like metal-metalloid compounds than like pure metals. That is, like covalent compounds embedded in metals. 

Through X-ray scattering studies of the electron densities in MgCu2, Kubota et al. (2000) found concentrations of electrons between the Cu atom pairs, but not between Mg—Cu pairs. They interpreted this as p3d3 covalent hybrid Cu—Cu bonds embedded in Mg metal. 

An especially hard and stable Laves-type compound is cubic HfW2. Its melting point is 2650 °C, and its hardness at room temperature is 1900kg/mm2 (Stone, 1977). However, it has a high mass density, so its usefulness is limited. 

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The Tribaloy aUoy T-800, is from an aUoy family developed by DuPont in the eady 1970s, in the search for resistance to abrasion and corrosion. Excessive amounts of molybdenum and sUicon were aUoyed to induce the formation during solidifica tion of hard and corrosion-resistant intermetaUic compounds, known as Laves phase. The Laves precipitates confer outstanding resistance to abrasion, but limit ductUity. As a result of this limited ductUity the aUoy is not generaUy used in the form of plasma-sprayed coatings. 

XAS studies have also been carried out on C14 Laves phase alloys Ti05Zr05M2 and Ti075Zr025M2 (M= V05Ni, Feo2... 

It is in some measure demonstrated that the formation of A-B and B-B contacts provides the energy for the compression of the A atoms and permits AB2 phases with radius ratios so much larger (up to 1 -67) than the ideal (1-225) to adopt the MgCu2 type structure. At radius ratios somewhat lower than the ideal, the B atoms are insufficiently compressed for A-B and A-A contacts to form. This is probably a consequence of there being twice as many B atoms as A atoms, and it results in fewer known Laves phases with radius ratios below the ideal value than above it. 

There have been many reviews and discussions of the crystal chemistry of the Laves phases (among the more recent see Berry Raynor, 1953 Laves, 1956 Elliott Rostoker, 1958 Bardos, Gupta Beck, 1961 Dwight, 1961 Nevitt, 1963) but none of these explicitly discuss what we find to be their most remarkable features ... 

High-Pressure Investigations of Magnetic Properties (Examples Laves Phases and Iron Oxides)... 

Whereas the Mg atoms are in contact with each other and the Cu atoms are in contact with each other, the Cu partial structure floats inside the Mg partial structure. The hard sphere model proves to be insufficient to account for the real situation atoms are not really hard. The principle of the most efficient filling space should rather be stated as the principle of achieving the highest possible density. Indeed, this shows up in the actual densities of the Laves phases they are greater than the densities of the components (in some cases up to 50 % more). For example, the density of MgCu2 is 5.75 g cm-3, which is 1% more than the mean density of 5.37 g cm-3 for 1 mole Mg + 2 moles Cu. Therefore,... 

R. L. Johnston, R. Hoffmann, Structure bonding relationships in the Laves phases. Z Anorg. Allg. Chem. 616 (1992) 105. 

Figure 8.2 Structure (C15) of cubic Laves phases. MgCu2 is the prototype. Top—Mg sub-structure with the pattern of the diamond structure. Bottom—Cu sub-structure with four tetrahedral clusters in the tetroid holes of the diamond structure. The stars indicate the centers of the patterns.

According to Rajasekharan and Girgis on a A t>, A ws1/3 map, considerable resolution is obtained among the binary systems in which different structure types occur. The points corresponding to the systems in which the Laves phases (or the phases of types such as Cr3Si, TiAl3, etc.) occur show linear relationships on the... 

As a conclusive comment to the Miedema model, especially with reference to the enthalpy evaluation, we have to underline that while it may be useful in order to define a reference behaviour, however, its approximate (in a way qualitative) character cannot be forgotten. A critical discussion on the application and limits of this model has been published for instance by Chen et al. (2004) see the comments on the thermochemistry of the Laves phases in 3.9.3, see also a few more remarks on this subject in 4.4.7.1. 

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