Crystallography unit cell, definition

The term monolayer (ML) must be defined clearly. In the work presented here, two definitions are used for surface studies, one ML indicates one adsorbate for each surface atom. For studies of compound formation, a monolayer is a slice of the compound s crystal structure, composed of one atomic layer of each of the constituent atoms. This does not necessarily mean a one unit-cell thick deposit is formed, as most compounds have larger unit cells from the point of view of crystallography, dependent on the orientation (Figure 8). 

The discovery of five-fold symmetry prompted the arf-interim Commission on Aperiodic Crystals of the International Union of Crystallography to change the definition of a crystal as a periodic three-dimensional arrangement of identical unit cells to the following ...by crystal we mean any solid having an essentially discrete diffraction diagram, and by aperiodic crystal we mean any crystal in which three-dimensional lattice periodicity can be considered to be absent . International Union of Crystallography. Report of the Executive Committee for 1991, Acta Cryst. A48,922 - 946 (1992). 

Note that this emphasis on the symmetry of the lattices has a profound effect on thinking about structures. Up to now, the lattice type has been characterised by the lattice parameters, the lengths of the lattice vectors and the inter-vector angles. Now, however, it is possible to define a lattice in terms of the symmetry rather than the dimensions. In fact this is the norm in crystallography. As we will see, the crystal system of a phase is allocated in terms of symmetry and not lattice parameters. To pre-empt future chapters somewhat, consider the definition of a monoclinic unit cell in terms of the lattice parameters a b c a = 90°, ft 90°, y = 90° (see Chapter 1). The unit cell may still be regarded as monoclinic (not orthorhombic) even if the angle /I is 90°, provide that the symmetry of the structure complies with that expected of a monoclinic unit cell. 

A space lattice is defined by either the three unit lattice vectors a, b, and c or the set of the six lattice parameters a, b,c, a, fi, and where the last three quantities represent the plane angles between the cell edges. The International Union of Crystallography (lUCr) has now standardized the notation and definition of space lattice parameters and this international standard nomenclature is listed below ... 

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