Laves structures

Figure 8.3 Contiuation of Figure 8.2 showing super-position of the two sub-structures to yield the C15 Laves structure. The star indicates the center. 

In the Fe-Be alloys the Laves structures are observed for Be-rich alloys Q Mg type for the 8 phase (82-93Be) and MgZn2 type for the C, phase (63-89Be). 

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. 

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 ... 

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. 

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. 

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.

F. Laves, Crystal Structure and Atomic Size, p. 124 in Theory of Alloy Phases, Amer. 

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... 

These concepts and their historical development were summarized in a contribution by Laves (1944), translated and reported by Hellner (1979), in which conditions for calling crystal structures equal (isotypism), similar (homeotypism) or different (heterotypism) are discussed and exemplified. 

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