Structure types hexagonal close-packed

Fig. 2.56 Twin structure of hexagonal close packing projected on (OlO)oh - Twin plane is (101),. Note that a new type of interstice (trigonal prism) appears on the twin plane.

In a concise nomenclature for c.p. structures a layer is denoted by h if the two neighbouring layers are of the same type (i.e. both A, both B, or both C) or by c if they are of different types. Hexagonal close-packing is then denoted simply by h (i.e. hhh. ..) and cubic close-packing by c. The symbols for more complex sequences include both h and c. Now the spheres in h and c layers have different arrangements... 

The mica structure provides an interesting variation of the types of close-packing observed for large ions in crystals. The two central layers of 0 , OH-, and F- ions form close-packed planes with three spheres in a hexagonal unit of edge 5.2 A, at positions 00, l/i2/i, and VsVa relative... 

Side and expanded views of hexagonal and cubic close-packed crystal types. In the hexagonal close-packed structure, spheres on both sides of any plane are in the same positions, and the third layer is directly above the first. In the cubic close-packed structure, layers take up three different positions, and the fourth layer is directly above the first. 

In either of these close-packed structures, each sphere has 12 nearest neighbors 6 in the same plane, 3 in the dimples above, and 3 in the dimples below. The expanded views in Figure 11-30 show the different arrangements of the hexagonal and cubic close-packed crystalline types, hi the hexagonal close-packed structure, notice that the third layer lies directly above the first, the fourth above the second, and so on. The layers can be labeled ABAB. 

The chemical bonding and the possible existence of non-nuclear maxima (NNM) in the EDDs of simple metals has recently been much debated [13,27-31]. The question of NNM in simple metals is a diverse topic, and the research on the topic has basically addressed three issues. First, what are the topological features of simple metals This question is interesting from a purely mathematical point of view because the number and types of critical points in the EDD have to satisfy the constraints of the crystal symmetry [32], In the case of the hexagonal-close-packed (hep) structure, a critical point network has not yet been theoretically established [28]. The second topic of interest is that if NNM exist in metals what do they mean, and are they important for the physical properties of the material The third and most heavily debated issue is about numerical methods used in the experimental determination of EDDs from Bragg X-ray diffraction data. It is in this respect that the presence of NNM in metals has been intimately tied to the reliability of MEM densities. 

One aspect that remains to be explored is the extent to which the packing of X atoms alone governs the structural characteristics of the FeS2—m type. As variously pointed out in the literature e.g. (9, 10)], the location of the X atoms in the FeS2—m type structure, in common with the TiOa—r (r=rutile) type, bears some resemblance to hexagonal close-packing. 

Fig. 1 Atomic arrangement of X (open circles) and T (filled circles) in projection for (a) hexagonal close-packing of X with T occupying half the octahedral holes (positions of the other half being indicated by crosses), and (b) the FeS2—m type structure, where the X—X pairs are emphasized by connecting bars...

Figure 9. Simplified model of the (111) surface of the corundum-type structure, (a) A view of the surface from a direction slightly shifted from <111>. Only metal ions of the zeroth, first, and second layers are shown, (b) A section of the surface along the arrows depicted in part a. Hexagonally close-packed oxide ion layers are shown with lines. Surface protons are not shown, (c) A divalent Co-57 or pentavalent Sb-119 ion on the zeroth metal ion layer, (d) Aquo or hydroxyl complex of divalent Co-57 or pentavalent Sb-119 hydrogen-bonded to the surface oxide ion layers of hematite.

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.

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. 

Titanium, zirconium and hafnium in normal conditions crystallize in the hexagonal close-packed structure (a modification) with a c/a slightly smaller than the ideal one c/a = 1.587 (Ti), 1.593 (Zr) and 1.581 (Hf). At high temperature they have the bcc W-type structure ((3 modification). High-pressure transformations are known (Tables 5.21-5.23). 

Physical properties of the element are anticipated or calculated. Sdvery metal having two aUotropic forms (i) alpha form that should have a double hexagonal closed-packed structure and (ii) a face-centered cubic type beta form density 14.78 g/cm (alpha form), and 13.25 g/cm (beta form) melting point 985°C soluble in dilute mineral acids. 

Most of the metallic elements of the Periodic Table crystallize in one or more of the highly symmetric structure types A1 (cubic close packed, ccp ), A2 (body-centered cubic, bcc) and A3 (hexagonal close packed, hcp) ... 

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