The Lattice Parameters

The lattice constants of a crystal structure define the unit cell metric i.e. the translation lattice. The length of the basis vectors a, b, c must be given in Å, the angles a, b, g  in degrees. The agreement of the given lattice parameters with the defined crystal system derived from the space-group number and the used setting will be checked automatically to the greatest possible extent by PowderCell. It should be taken into consideration, that at first the correct space group or setting must be edited or changed, because the program uses the so defined symmetry to set the invariants of the lattice parameters. Sometimes it will be more complicated, if the setting of the former space group doesn't exist in the edited space group. In this case the setting will be corrected automatically to 1.

However, PowderCell doesn't check departures from the recommended rules for a general definition of basis vectors and angles between them. So e.g. the monoclinic angle should be selected higher than 90° but smaller than 120°. Otherwise it will be recommended to transform the basis vectors. For the definition of the orthorhombic basis vectors it will be recommended to define a < b < c. But very often this is impossible, especially if standard settings should be used. Therefore PowderCell don't try to fit this automatically.

 It is not correct to assume that the given lattice parameters define automatically the crystal system. But it is exactly the opposite: The crystal symmetry defines the relation between the lattice constants! That means, if the length of all three basis vectors are equal and the angles are 90° than it is an important hint that the present structure could be described by the cubic symmetry. But that's no proof! On the other hand, if you know the symmetry of the structure you are able to define the relation between the basis vectors. It follows that the metric of the unit cell is a necessary condition but no sufficient. As example some Cryolithes can be given. There only the monoclinic angle shows a small deviation from 90°, but the structure symmetry is clearly monoclinic and not orthorhombic (Na3AlF6 — b=90°...90.3°, Na3FeF6 — b=90.4°, Na3NiF6 — b=90.1°, Na3VF6 — b=90.5°).

© Dr. Gert Nolze & Werner Kraus (1998)

Federal Institute for Materials Research and Testing
Unter den Eichen 87, D-12205 Berlin,
Germany