Close-packed element structure types

1 Close-packed element structure types. The structures of the close-packed metals are a simple well-known example of homeotect structure types. We have seen that the following metals can be considered as reference types. 

Their polytypic nature may be represented by a series of close-packed stacking variants of similar triangular atomic nets (A, B, C nets) corresponding to the following symbols  

Details about these structure types and lists of metals belonging to them are presented in 7.3.2.1. 

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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.

The La- and Sm-type structures belong to the same homeotect type set as Mg and Cu. All these close-packed element structures are stacking variants of identical slab types (monatomic triangular nets). 

Nitrides can be sub-divided into ionic, covalent and interstitial types.An alternate general classification of nitrides, based on bonding classification, as ionic, covalent and metallic has also been applied. Ionic or salt-like nitrides are formed by electropositive elements such as Li, Mg, Ca, Sr, Ba, Cu, Zn, Cd and Hg and possess formulae which correspond to those expected on the basis of the combination of the metal ion with ions. A range of covalent nitrides are known and are exhibited by less electropositive elements such as B, S, P, C and Si. Interstitial nitrides are formed by some transition metals and refer to compounds which can be described in terms of the occupancy of interstitial sites in close packed metallic structures by nitrogen atoms. Oxygen can also be accommodated within these structures and a range of oxynitrides are known to... 

Fig. 1.1 The three commonest elemental structure types (a) face-centred cubic, (b) hexagonal close-packed, and (c) body-centred cubic. From Wells (1986).

Metallic elements are normally found forming close packed lattice structures of types body centered, face centered, or hexagonal close packed. All of them display high coordination numbers, either eight or twelve nearest neighbors. Furthermore metals show a number of other characteristic physical properties such as metallic luster and high thermal and electrical conductivities. Theories dealing with metals must therefore be able to explain these properties. 

The best way to determine the type of unit cell adopted by a metal is x-ray diffraction, which gives a characteristic diffraction pattern for each type of unit cell (see Major Technique 3 following his chapter). However, a simpler procedure that can be used to distinguish between close-packed and other structures is to measure the density of the metal we then calculate the densities of the candidate unit cells and decide which structure accounts for the observed density. Density is an intensive property, which means that it does not depend on the size of the sample (Section A). Therefore, it is the same for a unit cell and a bulk sample. Hexagonal and cubic close packing cannot be distinguished in this way, because they have the same coordination numbers and therefore the same densities (for a given element). 

Intuitively, one would expect a volume contraction on forming a strongly bonded compound from the elements. Indeed, Richards 190, 191) regarded heats of formation as heats of compression. The fractional volume contraction, AV = (molecular volume - 2 atomic vol-ume)/2(atomic volume), has been related to formation heats for NaCl or CsCl type structures 151). Even nonpolar compounds in the condensed state cohere in close-packed arrays. The packing density of difluorine, derived from the ratio of the van der Waals envelope to the molecular volume, is especially low, and a larger contraction would be expected for fluorides than for other halides. This approach has yet to be systematically examined. 

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.

Crystal data summarized first are those characteristic of structures of metallic elements, typically having highly symmetric and dense atomic arrangements. Only a few notes are reported for the close-packed structures (Mg, Cu types), since for these structures several details are presented in 3.7.6 and 3.9.2.I. Subsequently, particular structures observed for a few selected specific metals and, finally, a few typical structures of non-metallic elements are described. 

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) ... 

The 17 rare-earth metals are known to adopt five crystalline forms. At room temperature, nine exist in the hexagonal closest packed structure, four in the double c-axis hep (dhep) structure, two in the cubic closest packed structure and one in each of the body-centered cubic packed and rhombic (Sm-type) structures, as listed in Table 18.1.1. This distribution changes with temperature and pressure as many of the elements go through a number of structural phase transitions. All of the crystal structures, with the exception of bep, are closest packed, which can be defined by the stacking sequence of the layers of close-packed atoms, and are labeled in Fig. 18.1.1. 

MnS and MnSe are the only transition-element compounds which have a zinc blende modification. The ZnS structure is the cubic version of the ZnO structure, i. e. the cations occupy half the tetrahedral holes in a cubic close-packed anion sublattice. As in the rocksalt structure the anion and the cation sublattices are identical to one another, i.e. the NaCl and ZnS structures are their own antitype. Like in the case of ZnS itself one should expect several polytypes to occur for MnS and MnSe. MnTe can be stabilized in the zinc blende structure by adding B3-type tellurides. Cubic mixed crystals Zni Mn Te were synthesized up to x = 0.86 171), Cdi-zMnzTe up to x — 0.75 172) and Hgi- Mn Te up to x = 0.8 172). 

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