Unit cell sides

It is important in defining the monodromy matrix, which quantifies changes in the unit cell in Figs. 4 and 5, to specify the lengths of the unit cell sides that define the basis. The monodromy theorem—that the monodromy index is equal to the number of pinch points on the pinched torus [40]—applies in a basis in which the cell sides represent unit changes in the relevant quantum number. 

The minimum amount of information needed to specify a crystal structure is the unit cell type, that is, cubic, tetragonal, and so on, the unit cell parameters, and the positions of all of the atoms in the unit cell. The atomic contents of the unit cell are a simple multiple, Z, of the composition of the material. The value of Z is equal to the number of formula units of the solid in the unit cell. Atom positions are expressed in terms of three coordinates, x, y, and z. These are taken as fractions of a, b, and c, the unit cell sides, say and j. The x, y, and z coordinates are plotted with respect to the unit cell axes, not to a Cartesian set of axes. The space group describes the symmetry of the unit cell, and although it is not mandatory when specifying a structure, its use considerably shortens the list of atomic positions that must be specified in order to built the structure. 

Unit Cell Side Length, Radius of Atom (Ion),... 

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. 

We repeat and complete some concepts introduced in Section 2.4. Given the unit cell sides a, b, c and angles a (between b and c), /> (between c and a), and y (between a and b), we recall the inner product or dot product... 

Figure 2. Evolution of order parameters Hx(z) (left axisX ( ) (right axis) through bcc 100 crystal-melt interface. Distance z is measured in reduced units of crystal cubic unit cell side length. (From Haymet and Oxtoby. )... 

The square (tp) lattice, (Figure 3.5g), has, as principle symmetry element, a tetrad rotation axis through the lattice point at the unit cell origin, which necessitates a tetrad through each lattice point. This generates additional diads at the centre of each unit cell side, and another tetrad at the cell... 

Assuming the transport number of oxygen is unity, estimate the electrical conductivity at 1000°C. Assume the unit cell side of 513 pm. State all assumptions. 

Figure 1.18. Experimental (hkO) data (solid line) for a ftilly iodine-vapour-doped polyacetylene sample as compared to the calculated structure factor (circles) from the representative intermediate doping model (containing two unit cells side by side) shown in the inset with y = 0.10. The arrows point to residual polyacetylene double layers and the numbers identify single polyacetylene layers. (Reproduced from ref. 132 with kind permission. Copyright (1992) American Physical Society.)...

Unit Cell Details — The analysis will yield the dimensions of the unit cell (a, b, c) and the angles between the unit cell sides (oc, P, y). 

Fig. 3.1 A schematic representation of the structure of a bulk hexagonal graphite crystal showing the bulk unit cell. Side insets. Top view of the basal plane of graphite and a schematic representation of the surface structure (carbon atoms) of graphite, where every other atom is enhanced (right-side inset) and viewed under ideal conditions, and where every single atom is seen (left-side inset). Figure reproduced from Ref. [3]...

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