Notation of structure types Flashcards
What is required for two compounds to be isotypic?
- Same space group
- Same number of atoms
- Atoms in same Wyckoff sites with same or similar positional coordinates
- Same or similar values of unit cell axial ratios and cell angles
How are structures typically described, and what kind of problems can this pose?
According to symmetry equivalent positions described in International Tables of Crystallography.
The problem is that equivalent crystal structures are described differently due to a shift of unit cell, a rotation or inversion of the coordinate system. This can lead to two identical crystal structures not being identified as such.
What are some alternative ways of describing crystal structures?
- Chemical formula of original compound found in that structure
- Strukturbericht
- Pearson code
- Space group number and Wyckoff positions
How are structures described by the chemical formula, and what is a pitfall with this way of describing structures?
Using the chemical formula or colloquial name of the compound that was originally found in a particular structure.
A problem can be that the same structure was identified in different compounds at about the same time, and both names are passed along in the literature.
How are structures described according to the Strukturbericht notation?
A capital letter prefix and number in that particular series.
Element = A, AB = B, AB2 = C etc.
This was discontinued in 1945, but might still see this in old papers.
How are structures described according to the Pearson code, and what is a pitfall with this way of describing structures?
Small letter that describes the crystal system (a, m, o, t, c, h) and a capital letter describing the centering (S, I, F, P, R), then followed by the number of atoms in the unit cell.
A pitfall here is that several different structures can have the same Pearson code, e.g. diamond and zinc blende.
Also, for rhombohedral space groups, the number of atoms sometimes refer to the rhombohedral unit cell and other times to the triple-hexagonal unit cell.
How are structures described according to space groups and Wyckoff sequences?
By listing the space group and the frequency of Wyckoff site occupation
E.g. Fd-3m - a = only a-site is used once
F-43m - ca = both c- and a-site is singly used
What are isopointal structures?
Geometrically unrelated structures that share space group and Wyckoff sequence.
How are a type and its antitype related?
Switched positions of cations and anions in same structure.
How is stacking described within ABC notation?
All different stacking positions are denoted with a capital letter. First layer is termed A. Next layer will be B. If the next layer is a new stacking position, it is C, or if it it’s directly above A, it will also be A.
How is stacking described within Jagodzinski-Wyckoff notation?
Notation consists of small letters c and h which are assigned depending on the side-wise displacements of two neighbourhing slabs.
h is assigned to each slab where the two neighbouring slabs are side-wise displaced in the same direction.
c is assigned to each slab where the two neighbouring slabs are side-wise displaced in different directions.
Notated for each layer going up a structure, then grouped in repeating structures. E.g. chhchhchhchh = (hhc)_3
When is Jagodzinski-Wyckoff notation applicable?
Only applicable to structures which allow not more than 3 stacking positions and where two subsequent slabs cannot have the same stacking position.
How is stacking described within Zhadnov notation?
Notation consists of a sqeunce of numbers each of which represents the number of repetitions or successions of slabs with a given sign for the side-wise displacement of subsequent slabs.
E.g.
(hhc) _3 → (21)_3
(hcchcchcchc) _3 → (3_3 2)_3
When is Zhadnov notation applicable?
Only applicable to structures which allow not more than 3 stacking positions and where two subsequent slabs cannot have the same stacking position.
How is stacking described within Hägg notation?
Using slashes and indicating which way you are moving from layer to layer.
E.g.
(hhc) _3 → (//)_3
(hcchcchcchc) _3 → ///\\///\
