Unit cell centred

Figure 7.20 Perspective view of the structure of a-Agl (a) the body-centred cubic arrangement of iodide ions in the unit cell (b) the anion centred polyhedron, (a truncated octahedron), around the iodide ion at the unit cell centre. [Note that the ions in part (a) are depicted smaller than ionic radii suggest, for clarity]...

There are only 14 possible three-dimensional lattices, called Bravais lattices (Figure 5.1). Bravais lattices are sometimes called direct lattices. The smallest unit cell possible for any of the lattices, the one that contains just one lattice point, is called the primitive unit cell. A primitive unit cell, usually drawn with a lattice point at each comer, is labelled P. All other lattice unit cells contain more than one lattice point. A unit cell with a lattice point at each corner and one at the centre of the unit cell (thus containing two lattice points in total) is called a body-centred unit cell, and labelled I. A unit cell with a lattice point in the middle of each face, thus containing four lattice points, is called a face-centred unit cell, and labelled F. A unit cell that has just one of the faces of the unit cell centred, thus containing two lattice points, is labelled A-face-centred if the faces cut the a axis, B-face-centred if the faces cut the b axis and C-face-centred if the faces cut the c axis. 

The large Sr ions are coordinated to 12 CF ions and are now situated at the unit cell centre (Figure 1.1c). For a discussion of the chemical and physical properties of this (and other) perovskites, it is convenient to think of the slmcture as built-up from an array of comer sharing TrO octahedra (Figure l.ld). The large Sr ions are located at... 

The first crystal structure to be detennined that had an adjustable position parameter was that of pyrite, FeS2 In this structure the iron atoms are at the comers and the face centres, but the sulphur atoms are further away than in zincblende along a different tln-eefold synnnetry axis for each of the four iron atoms, which makes the unit cell primitive. 

Figure Bl.21.1. Atomic hard-ball models of low-Miller-index bulk-temiinated surfaces of simple metals with face-centred close-packed (fee), hexagonal close-packed (licp) and body-centred cubic (bcc) lattices (a) fee (lll)-(l X 1) (b)fcc(lO -(l X l) (c)fcc(110)-(l X 1) (d)hcp(0001)-(l x 1) (e) hcp(l0-10)-(l X 1), usually written as hcp(l010)-(l x 1) (f) bcc(l 10)-(1 x ]) (g) bcc(100)-(l x 1) and (li) bcc(l 11)-(1 x 1). The atomic spheres are drawn with radii that are smaller than touching-sphere radii, in order to give better depth views. The arrows are unit cell vectors. These figures were produced by the software program BALSAC [35]-...

In the face-centred cubic structure tirere are four atoms per unit cell, 8x1/8 cube corners and 6x1/2 face centres. There are also four octahedral holes, one body centre and 12 x 1 /4 on each cube edge. When all of the holes are filled the overall composition is thus 1 1, metal to interstitial. In the same metal structure there are eight cube corners where tetrahedral sites occur at the 1/4, 1/4, 1/4 positions. When these are all filled there is a 1 2 metal to interstititial ratio. The transition metals can therefore form monocarbides, niU ides and oxides with the octahedrally coordinated interstitial atoms, and dihydrides with the tetrahedral coordination of the hydrogen atoms. 

Fig. 8.12. The structure of 0.8% carbon martensite. During the transformation, the carbon atoms put themselves into the interstitial sites shown. To moke room for them the lattice stretches along one cube direction (and contracts slightly along the other two). This produces what is called a face-centred tetragonal unit cell. Note that only a small proportion of the labelled sites actually contain a carbon atom.

The ultimate covalent ceramic is diamond, widely used where wear resistance or very great strength are needed the diamond stylus of a pick-up, or the diamond anvils of an ultra-high pressure press. Its structure, shown in Fig. 16.3(a), shows the 4 coordinated arrangement of the atoms within the cubic unit cell each atom is at the centre of a tetrahedron with its four bonds directed to the four corners of the tetrahedron. It is not a close-packed structure (atoms in close-packed structures have 12, not four, neighbours) so its density is low. 

Figure 13.2 The cubic structure of skutterudite (C0AS3). (a) Relation to the ReOs structure (b) unit cell (only sufficient Co-As bonds are drawn to show that there is a square group of As atoms in only 6 of the 8 octants of the cubic unit cell, the complete 6-coordination group of Co is shown only for the atom at the body-centre of the cell) and (c) section of the unit cell showing CoAsg octahedra comer-linked to form AS4 squares.

Figure 14.11 Crystal structure of HPF6.6H2O showing the cavity formed by 24 H2O molecules disposed with their O atoms at the vertices of a truncated octahedron, The PFe octahedra occupy centre and comers of the cubic unit cell, i.c. one PFr, at the centre of each cavily. ...

The largest protonated cluster of water molecules yet definitively characterized is the discrete unit lHi306l formed serendipitously when the cage compound [(CyHin)3(NH)2Cll Cl was crystallized from a 10% aqueous hydrochloric acid solution. The structure of the cage cation is shown in Fig. 14.14 and the unit cell contains 4 [C9H,8)3(NH)2aiCUHnOfiiai- The hydrated proton features a short. symmetrical O-H-0 bond at the centre of symmetry und 4 longer unsymmetrical O-H - 0 bonds to 4... 

Fig. 20.25 Unit cells of (a) the face-centred cubic (f.c.c.), (b) the close-packed hexagonal (c.p.h.) and (c) the body-centred cubic (b.c.c.) crystal structures...

The prefixes c and p mean centred and primitive , respectively, where centred refers to when an adsorbate is added in the centre of the primitive unit cell. 

---