Transcript Attachment 2

Structure Type Assignments
Suri Kabekkodu
Structure Type Notation
• LPF uses a longer notation: Structure Type Formula,
Pearson Symbol, Space group number
• Examples: Cu3 Au,cP4,221; Cu3 As,cI64,220;
NaCl,cF8,225
Structure Type requirements
• Must crystallize in the same space group
• Similar cell parameter ratio
• Same Wyckoff positions (Wyckoff
sequence)
• When all the above 3 conditions satisfy, we
have similar atomic environments
Wyckoff sequence
Wyckoff notation of a given space group
changes with
1. Choice of origin
2. Alternative setting
Hence it is required to standardize the
crystal structure prior to the “atomic
environment” comparison
Standardization of Crystal
Structure
• First proposed by Parthe and Gelato (Acta
Cryst. (1984), A40, 169-183)
• The method calculated standardization
parameter  based on
• Shift of origin
• Rotation of the coordinate system
• Inversion of the basis vectors
The smallest  represents the standard description
Standardization
• Program STRUCTURE TIDY (Parthe and
Gelato) to standardize the structure
• Standardization procedure criteria
Space group setting
Cell parameters
Origin of the coordinate system
Order of the atom sites
Standardization Criteria (-Contd)
• Additional constraints
• Triclinic space groups: Niggli reduced cell
• Monoclinic with b-axis unique
• Orthorhombic a b  c (when not fixed by the space
group)
• Trigonal space group with R lattice (triple hexagonal
cell)
• Choice of origin: at the inversion center
• Enantiomorphic space groups: smallest index on the
relevant screw axis
Special Cases
• In general standardization procedure can
directly compare candidates for isotypic
compounds. However there are some
special cases:
• Refinable coordinate very close to zero