The unit cell is an essential parameter for studying crystalline solids because knowing the unit cell allows us to understand the atomic structure of the entire crystalline solid. In this section, we will discuss the 14 unique unit cells that are the basis for all crystal structures.
The orientation of a surface or a crystal plane may be defined by considering how the plane (or indeed any parallel plane) intersects the main crystallographic axes of the solid. The application of a set of rules leads to the assignment of the Miller Indices , (hkl) ; a set of numbers which quantify the intercepts and thus may be used to uniquely identify the plane or surface.
The structures of crystals and molecules are often identified using x-ray diffraction studies, which are explained by Bragg’s Law. The law explains the relationship between an incoming x-ray beam and its reflection off a crystal.
It has been observed that some hkl planes do not produce reflections and that other hkl planes produce reflections that are less intense than the reflections from other lattice planes. These systematic absences and variations in reflection intensities will be discussed in this section.
In the previous section, we treated the lattice points as individual, localized electron densities. In reality, the electron density of a unit cell is distributed over a much larger space. The Fourier transform process relates the collected structure factor data of x-ray diffraction to the electron density around the crystalline atoms in real space.
We can address the question of what happens when a molecule becomes adsorbed onto a surface at two levels; specifically we can aim to identify the nature of the adsorbed species and its local adsorption geometry (i.e., its chemical structure and co-ordination to adjacent substrate atoms) the overall structure of the extended adsorbate/substrate interface (i.e., the long range ordering of the surface).
The Langmuir isotherm was developed by Irving Langmuir in 1916 to describe the dependence of the surface coverage of an adsorbed gas on the pressure of the gas above the surface at a fixed temperature. Whilst the Langmuir isotherm is one of the simplest, it still provides a useful insight into the pressure dependence of the extent of surface adsorption.
It is possible to predict how the kinetics of certain heterogeneously-catalysed reactions might vary with the partial pressures of the reactant gases above the catalyst surface by using the Langmuir isotherm expression for equilibrium surface coverages.
The kinetics and thermodynamics of the chemical and physical processes that occur on the surface of a solid are greatly dependent on the structure of the surface. Few, if any surfaces are perfectly flat, and thus the cavities, protrusions, ridges, and edges of the surface must be treated differently when studying chemisorption and physisorption.
The Haber-Bosch process for the synthesis of ammonia is one of the most important catalyzed syntheses in the chemical industry. The process takes advantage of the low activation energies required for the dissociative chemisorption of nitrogen and hydrogen molecules that have been physisorbed onto a metal oxide surface.
