Placing an atom

A crystal is not, in actual fact, a simple array of points, each of which is a pattern-unit. In the first place, an atom is not a point its electrons, which scatter the X-rays, are distributed over distances commensurable with the interatomic distances. Secondly, each pattern-unit in a crystal often consists, not of one atom, but a group of atoms. The pattern-unit is thus not a point, but has a diffuse and often irregular form. However, for the purpose of diffraction theory, as far as it is carried in this chapter, the diffuse pattern-unit may be mentally replaced by a point. It will be shown in Chapter VII that the form of the pattern-unit affects the intensities of the diffracted beams but it does not affect their positions, which depend only on the space-lattice, the fundamental arrangement of identical pattern-units. 

Suppose, however, we place an atom on one of the planes of symmetry, m2, at position xOz. Plane m2 does not create a second atom it merely makes one-half of the atom the mirror image of the other half. But plane m does create another atom, at position xOz (Fig. 152, right). Similarly, if an atom were placed on mt at position 0yz, only one more atom would be created, at 0yz. Thus positions on planes of symmetry are twofold positions. It should be noted that there are also planes of symmetry half-way along a and b edges of the cell, and therefore x z is a twofold position (reflected by m as x z), as is also yz (reflected by m2 as yz). 

Physical Properties.7—Tantalum is a white metal with a greyish tinge and is very similar to platinum in colour and general appearance. When it is heated to 1600° C. in vacuo it assumes a crystalline form.8 Examination of the powdered metal by X-ray analysis has shown that the arrangement of the atoms is on the plan of a body-centred cube of side 3 272 A, obtained by dividing the space of a crystal into equal closely packed cubes and placing an atom at each cube comer and each cube centre the distance between the nearest atoms is 2 883 A. The specific gravity of the fused metal is 16 6, - a sample drawn into wire 0 05 mm. diameter had a density of 16 5 10 the density calculated from X-ray data is 17 09.u... 

In a more specialized case, Horjales and Branden (90) determined a preferred orientation of cyclohexanol in the active site of liver alcohol dehydrogenase for what was believed to be a productive enzyme-substrate complex. By using the positions of the atoms of the bound cyclohexanol ring as a starting point, an extended diamond lattice was constructed to fill the available space in the enzyme site. Each of the lattice points could then be examined to determine the steric possibility of placing an atom at that position. This framework could then be used to design and dock additional structures. 

People have succeeded in placing an atom inside a cage molecule. The smallest such system so far synthesized was obtained by subjecting... 

All crystal structures can be built up from a lattice by placing an atom or a group of atoms at each lattice point. The crystal structure of a simple metal and that of a complex protein may both be described in terms of the same lattice, but whereas the number of atoms allocated to each lattice point is often just one for a simple metallic crystal, it may easily be thousands for a protein crystal. 

To better understand the origin of Eq. (12.4), consider the situation depicted schematically in Fig. 12.2, where four pistons are attached to four sides of a cube of material such that the pressures in the pistons are unequal with, say, > Pb- These pressures will result in normal compressive forces -removed from surface A (e.g., by having it fill in a vacancy just below the A surface), piston A will move by a volume 0, and the work done on the system is Q,P = Ucrj). By placing an atom on surface B (e.g., by having an atom from just below the surface diffuse to the surface), work is done by the system CtPs = -f cr22- The net work is thus... 

There are three basic packing arrangements, which we can describe by again imagining a tiny box. If we place an atom at each of the eight vertices of this box, the arrangement is referred to as simple cubic. If we take a simple cubic unit cell and add an atom to the center of each face, we have a face-centered cubic arrangement. If we instead add an atom to the center of the cube, it s called a body-centered cubic unit cell. There are more possibilities, but these three simple ones described here cover a lot of the crystals that chemists encounter. 

This algorithm places an atom a, which is adjacent to the seed atom, at a standard distance from the seed atom, at an angle equal to the CFS/q of the seed atom. 

This can be done, fa- example, by placing an atom at the center of a large box and repeating this box periodically... 

Let us place an atom in an external electric field. Under the action of this field, the centers of charges of both signs will shift away from each other and an induced dipole moment will appear (Figure 4.24)... 

---