Crystal lattice body centred

The experimental techniques outlined in the previous sections allow the lattice parameters of a crystal to be determined. However, the determination of the appropriate crystal lattice, face-centred cubic as against body-centred, for example, requires information on the intensities of the diffracted beams. More importantly, in order to proceed with a determination of the complete crystal structure, it is vital to understand the relationship between the intensity of a beam diffracted from a set of (hkl) planes and the atoms that make up the planes themselves. 

Every ionic crystal can formally be regarded as a mutually interconnected composite of two distinct structures cationic sublattice and anionic sublattice, which may or may not have identical symmetry. Silver iodide exhibits two structures thermodynamically stable below 146°C sphalerite (below 137°C) and wurtzite (137-146°C), with a plane-centred I- sublattice. This changes into a body-centred one at 146°C, and it persists up to the melting point of Agl (555°C). On the other hand, the Ag+ sub-lattice is much less stable it collapses at the phase transition temperature (146°C) into a highly disordered, liquid-like system, in which the Ag+ ions are easily mobile over all the 42 theoretically available interstitial sites in the I-sub-lattice. This system shows an Ag+ conductivity of 1.31 S/cm at 146°C (the regular wurtzite modification of Agl has an ionic conductivity of about 10-3 S/cm at this temperature). 

Figure 7.1 Three common crystal lattices adopted by elements (a) body-centred cubic packing, (b) cubic closest packed (or face-centred cubic) and (c) hexagonal closest packed...

The true unit cell is not necessarily the smallest unit that will account for all the reciprocal lattice points it is also necessary that the cell chosen should conform to the crystal symmetry. The reflections of crystals with face-centred or body-centred lattices can be accounted for by unit cells which have only a fraction of the volume of the true unit cell, but the smallest unit cells for such crystals are rejected in favour of the smallest that conforms to the crystal symmetry. The... 

An extreme type of defect structure is the a form of Agl, which is stable above 146° C, In this crystal the iodine atoms form a cubic body-centred arrangement, but the silver atoms apparently have no fixed positions at all they wander freely through the iodine lattice (Strock, 1934, 1935). 

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. 

Iron has a body-centred cubic lattice (see Figure 5.16) with a unit cell side of 286 pm. Calculate the number of iron atoms per cm2 of surface for each of the Fe(100), Fe(110) and Fe(lll) crystal faces. Nitrogen adsorbs dissociatively on the Fe(100) surface and the LEED pattern is that of a C(2 x 2) adsorbed layer. Assuming saturation of this layer, calculate the number of adsorbed nitrogen atoms per cm2 of surface. 

Thus, there are seven crystal types for which fourteen different types of lattices (7 primitive, 3 body centred, 2 face centred and 2 end centred) are possible. These fourteen different types of lattices are known as Bravais lattices. 

Not all types of lattice are allowable within each crystal system, because the symmetrical relationships between cell parameters mean a smaller cell could be drawn in another crystal system. For example a C-centred cubic unit cell can be redrawn as a body-centred tetragonal cell. The fourteen allowable combinations for the lattices are given in Table 1.4. These lattices are called the Bravais lattices. 

The other crystal lattices can be generated by adding to some of the above-defined cells extra high-symmetry points by the so-called centering method. TableB.2 shows the new systems added to the simple crystal lattices (noted s, or P, for primitive) and the numbers of lattice points in each conventional unit cell. The body-centred lattices are noted be or I (for German Innenzentrierte), the face-centred, fc or F, and the side-centred or base-centred lattices are noted C (an extra atom at the Centre of the base). These 14 lattice systems are known as the Bravais lattices (noted here BLs). A representation of their unit cells can be found in the textbook by Kittel [7]. 

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