Body-centred cubic close-packed structure

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. 

When the a phase, i.e, the primary solid solution, has only a limited range of stability, other intermediate phases are formed. At particular concentrations of the second component a transformation from one crystal structure to another takes place. In a large number of binary systems, e.g. Gu-Au, Cu-Al, Cu-Sn, a transition from the cubic close packed structure of copper to a body centred cubic structure ()3 phase) occurs at a particular concentration. The phase is stable over a particular range of concentration and at higher concentrations is generally converted to the y-phase which has a complex structure, followed by the e and >) phases which are... 

This group of more than 50 elements, including the 4f and 5f elements, comprises most of the metals. The structure of at least one form of most of these metals is known (Table 29.3), and with few exceptions they crystallize with one or more of three structures. These are the hexagonal and cubic close-packed structures and the body-centred cubic structure. 

A substance is said to be polymorphous when it is capable of existing in two or more forms with different crystal structures. We have already encountered numerous instances of this phenomenon as, for example, carbon, selenium, some of the metallic elements, zinc sulphide, ferric oxide, silica, and many others. In some of these examples one form alone is found under a given set of physical conditions and a reversible transition between forms is brought about by a change in these conditions, in which case the forms are said to be enantiotropic. Thus iron has the cubic close-packed structure between the temperatures 906 and 1401 °C, and the cubic body-centred structure at temperatures outside this range. Even so, the rate at which the transition takes place may vary between wide limits at the one extreme it may be virtually instantaneous and at the other it may be so slow that a form is capable of indefinite existence under conditions in which it is, strictly speaking,... 

Another example of polymorphic change involving a change in co-ordination is that between the cubic body-centred and cubic close-packed structures of a- and y-iron. Although a change in co-ordination takes place, it should nevertheless be noted that the transformation can be achieved by a purely displacive mechanism, and accordingly takes place readily. In fig. 9.02 four unit cells of the cubic body-centred a-iron... 

The crystal chemistry of the iron-carbon system is especially complex on account of the relatively small size of the iron atom, resulting in a carbon iron radius ratio of about o 6o, which is so close to the critical value 0 59 discussed above that both interstitial structures and structures of greater complexity may be expected. Added to this is the further complication that iron is dimorphous. Below about 910 °C, and from about 1400 °C to the melting point, the structure is cubic body centred, and is known as a iron. Between these two temperatures a cubic close-packed structure, termed y iron, is formed. The ferromagnetism of iron... 

Figure 6.1 The crystal structures of the metallic elements. Note unit cell parameters are in nanometres. The figure given for cubic structures is Oq, A1 = copper (cubic close-packed) structure A2 = tungsten (body-centred cubic) structure A3 = magnesium (hexagonal close-packed) structure...

Metals atoms (cations) pack closely together in a regular structure to form crystals. Arrangements in which the gaps are kept to a minimum are known as close-packed structures. X-ray diffraction studies have revealed that there are three main types of metallic structure hexagonal close packed, face-centred cubic close packed and body-centred cubic. 

Figure Al.3.23. Phase diagram of silicon in various polymorphs from an ab initio pseudopotential calculation [34], The volume is nonnalized to the experimental volume. The binding energy is the total electronic energy of the valence electrons. The slope of the dashed curve gives the pressure to transfomi silicon in the diamond structure to the p-Sn structure. Otlier polymorphs listed include face-centred cubic (fee), body-centred cubic (bee), simple hexagonal (sh), simple cubic (sc) and hexagonal close-packed (licp) structures.

We begin by looking at the smallest scale of controllable structural feature - the way in which the atoms in the metals are packed together to give either a crystalline or a glassy (amorphous) structure. Table 2.2 lists the crystal structures of the pure metals at room temperature. In nearly every case the metal atoms pack into the simple crystal structures of face-centred cubic (f.c.c.), body-centred cubic (b.c.c.) or close-packed hexagonal (c.p.h.). 

Mono- or single-crystal materials are undoubtedly the most straightforward to handle conceptually, however, and we start our consideration of electrochemistry by examining some simple substances to show how the surface structure follows immediately from the bulk structure we will need this information in chapter 2, since modern single-crystal studies have shed considerable light on the mechanism of many prototypical electrochemical reactions. The great majority of electrode materials are either elemental metals or metal alloys, most of which have a face-centred or body-centred cubic structure, or one based on a hexagonal close-packed array of atoms. 

According to the Frank-Kasper definition, the coordination number is unambiguously 12 in the hexagonal close-packed metals and assumes the value 14 in a body-centred cubic metal. Generally in several complex metallic structures this definition yields reasonable values such as 14, even when the nearest-neighbour definition would give 1 or 2. 

Some metals do not adopt a close-packed structure but have a slightly less efficient packing method this is the body-centred cubic structure (bcc), shown in Figure 1.8. (Unlike the previous diagrams, the positions of the atoms are now represented here—and in subsequent diagrams—by small spheres which do not touch this is merely a device to open up the structure and allow it to be seen more clearly—the whole question of atom and ion size is discussed in Section 1.6.4.) In this structure an atom in the middle of a cube is surrounded by eight identical and equidistant atoms at the corners of the cube—... 

Below 146°C, two phases of Agl exist y-Agl, which has the zinc blende structure, and (3-Agl with the wurtzite structure. Both are based on a close-packed array of iodide ions with half of the tetrahedral holes filled. However, above 146°C a new phase, a-AgI, is observed where the iodide ions now have a body-centred cubic lattice. If you look back to Figure 5.7, you can see that a dramatic increase in conductivity is observed for this phase the conductivity of a-Agl is very high, 131 S m , a factor of 10 higher than that of (3- or y-AgI, comparable with the conductivity of the best conducting liquid electrolytes. How can we explain this startling phenomenon ... 

Not all structures are based on close packed lattices. Ions that are large and soft often adopt structures based on a primitive or body centred cubic lattice as found in CsCl (22173) and a-AgI (200108). Others, such as perovskite, ABO3 (Fig. 10.4), are based on close packed lattices that comprise both anions and large cations. The larger and softer the ions, the more variations appear, but the lattice packing principle can still be used. Santoro et al. (1999,2000) have shown how close-packing considerations combined with the use of bond valences can give a quantitative prediction of the structure of BaRuOs (10253). 

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).

Crystalline solids consist of periodically repeating arrays of atoms, ions or molecules. Many catalytic metals adopt cubic close-packed (also called face-centred cubic) (Co, Ni, Cu, Pd, Ag, Pt) or hexagonal close-packed (Ti, Co, Zn) structures. Others (e.g. Fe, W) adopt the slightly less efficiently packed body-centred cubic structure. The different crystal faces which are possible are conveniently described in terms of their Miller indices. It is customary to describe the geometry of a crystal in terms of its unit cell. This is a parallelepiped of characteristic shape which generates the crystal lattice when many of them are packed together. 

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