Cu type structure

Cr3Si-type structure W + / AgMgAs-type structure F + F + F" CaTi03-type structure P + P + J Cu2Mg-type structure T + D. For a few element structures Cu type structure F W-type structure 7 a-Po-type structure P Mg-type structure E C-diamond-type structure D. 

The sequence ABCABC... having a cubic symmetry is shown in Fig. 3.21. It is the cubic (face-centred cubic) close-packed structure, also described as cF4-Cu type structure. 

Another example of a superstructure based on a close-packed structure but related to the hexagonal close-packed one is that corresponding to the hP8-Ni3Sn prototype. Just as the AuCu3 type can be derived by ordering the Cu-type structure, so the Ni3Sn type can be obtained from the hP2-Mg type. Details of this structure and of some stacking variants are described in Chapter 7. 

Their normal crystal structure, at ambient conditions, corresponds to the body-centred cubic cI2-W-type structure. At very low temperatures, the close-packed hexagonal hP2-Mg-type structure has been observed for Li and Na, while for Rb and Cs the face-centred cubic close-packed cF4-Cu-type structure is known at high pressure. No polymorphic transformation has been reported for potassium. 

Figure 7.11. Section sequence parallel to the base plane of the cF4-Cu type structure.

Cu-derivative, substitutional and interstitial superstructures. As discussed in 3.8.1 ff, the Cu-type structure is also an important reference structure because it may be considered the ancestor of several derivative structures. 

The otherl4th group elements, Si, Ge and oSn have the diamond-type structure. The tI4- 3Sn structure (observed for Si and Ge under high pressure) can be considered a very much distorted diamond-type structure. Each Sn has four close neighbours, two more at a slightly larger and another four at a considerable larger distance. Fig. 7.13 shows the (3Sn unit cell. Lead, at ambient pressure, has a face-centred cubic cF4-Cu type structure. 

As pointed out in the description of the cubic close-packed structure (cF4-Cu type), this structure may be described (especially for certain values of the atomic diameter ratio) as a derivative of the Cu-type structure in which two sets of tetrahedral holes have been filled-in. 

The lanthanides (except Eu, Yb) and group 3b metals (Y, Sc, La, Ac) show a rather complex behavior on hydrogenation. They form nonstoichiometric dihydrides MH2 in which the metal atoms adopt a Cu type arrangement, in contrast to the parent metals, most of which crystallize in an Mg-type structure. All tetrahedral voids of the Cu-type structure of M are occupied by hydrogen, i.e., the dihydrides MH2 crystallize in a fluorite type structure (Fig. 3, left). 

Cupric sulfide, CuS, occurring as the mineral covellite (also known as covelline), exhibits a very unusual structure, in which the Cu is again partly 3-coordinate and partly 4-coordinate, with two-thirds of the sulfur atoms existing as S2 groups like those in pyrites. The low-temperature form of CuSe has also a covellite structure, the high-temperature modification (P-CuSe) being orthorhombic. All CuX2 compounds assume pyrite-type structures. 

Figure 3.20. A lateral view of different stacking sequences of triangular nets. They correspond to some typical close-packed structures. The first layer sequence shown corresponds to a superimposition according to the scheme ABABAB... (equivalent to BCBCBC... or CACACA... descriptions) characteristic of the hexagonal close-packed, Mg-type, structure. With reference to the usual description of its unit cell, the full stacking symbol indicating the element, the relative position of the superimposed layers and their distance is Mg Mg. The other sequences correspond to the schemes ABC.ABC. (Cu, cubic), ABAC.ABAC. (La, hexagonal), ACACBCBAB. (Sm, hexagonal). For Cu the constant ch of the (equivalent, non-conventional) hexagonal cell is shown which may be obtained by a convenient re-description of the standard cubic cell (see 3.6.1.3). ch = cV 3, body diagonal of the cubic cell.

Figure 3.21. The face-centred cubic close-packed structure (Cu type). On the left a block of eight cells is shown (one cell darkened). On the right a section of the structure is presented it corresponds to a plane perpendicular to the cube diagonal. Notice that the plane is the same presented on the left in Fig. 3.19. The sequence of the layers in this structure is shown in Fig. 3.20 in comparison with other close-packed elemental structures.

Figure 3.28. cP4-AuCu3 type structure. A block of eight unit cells is shown (Au white Cu grey). 

Figure 3.29. Analysis of the cP4-AuCu3 type structure. Typical fragments of a few adjacent cells are depicted in order to show the different coordinations (Au white Cu grey), (a) and (b) coordination around Au, (c) and (d) coordination around Cu. (a) octahedral coordination of 6 Au around Au,...

Figure 3.30. Analysis of the cP4-AuCu3 type structure. Coordination and interatomic (reduced) distances. The total number (n) of near-neighbour atoms around Au and Cu are plotted as a function of their reduced distances from the reference atom. The symbols of the surrounding atoms are indicated. Notice the similarity between the two histograms.

This filled-up superstructure may therefore be described in terms of the occupation by N of an interstice (centred in Vi, A, Vi) of a Cu-type (or AuCu3-type) structure. The N atom is octahedrally surrounded by 6 Fe atoms. This structure could also be described as a deficient NaCl-type derivative structure the Fe atoms are in the same positions as the Na atoms in NaCl and one out of the four Cl positions is occupied by the N atoms. 

In the preceding paragraphs examples of a number of so-called superstructures have been considered. Generally, it has been observed that a derivative structure has fewer symmetry operations than the reference structure it has either a larger cell or a lower symmetry (or both) than the reference structure. Typically the passage from the reference structure to the derivative structure (superstructure) may be related to the fact that a set of equipoints of a certain structure (the reference one) has to be subdivided into two (or more) subsets in order to obtain the description of the other structure. The structure of the Cu type (cF4 type), for instance, corresponds to 4 Cu atoms in the unit cell, placed in 0, 0, 0 14, 14, 0 14, 0, 14 0, 14, 14, whereas in the cP4-AuCu3 type structure the same atomic sites are subdivided, in another space group, into two sets with an ordered distribution of the two atomic species (1 Au atom in 0, 0, 0 and 3 Cu atoms in 14, 14, 0 14, 0,14 0,14,14). 

A special case of long-period structure to be considered is the oI40-AuCu(II) type structure which has ID substitutional and displacive modulations (Fig. 3.41). We must first mention that ordering of the Au-Cu face-centred cubic (cF4-Cu type) solid solution, having a 50-50 atomic composition, re-distributes Cu and Au atoms... 

In the cP2-W type (CN 8) structure Vsph is 0.68 Vat (only a portion of the available space is occupied by the atomic sphere ). In the cF4-Cu type and in the ideal hP2-Mg type (CN 12) structures, Vsph is 0.74 Vat. Considering now the previously reported relationship between RCs n and i CN8, we may compute for a given element very little volume (Vat) change in the allotropic transformation from a form with CN 12 to the form with CN 8, because the radius variation is nearly... 

Typical space-filling parameters of elemental structures are the following cF4-Cu type p = 0.740... 

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