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International
Tables for Crystallography Volume G Definition and exchange of crystallographic data Edited by J. R. Hester and B. McMahon © International Union of Crystallography 2026 |
International Tables for Crystallography (2026). Vol. G. Early view chapter
https://doi.org/10.1107/97809553602060001011 Chapter 4.2 Core dictionary (coreCIF) |
Core dictionary version 3.3.0
_atom_sites_fract_transform.mat_31
Name:_atom_sites_fract_transform.mat_31
Aliases:
_atom_sites_fract_tran_matrix_31
_atom_sites.fract_transf_matrix[3][1]
Definition:
Matrix used to transform Cartesian coordinates in the ATOM_SITE category
to fractional coordinates. The axial alignments of this transformation are
described in _atom_sites_fract_transform.axes. The 3 x 1 translation is
defined in _atom_sites_fract_transform.vector.
x' |11 12 13| x | 1 |
( y' )fractional = mat|21 22 23| * ( y )Cartesian + vec| 2 |
z' |31 32 33| z | 3 |
The default transformation matrix uses Rollett's axial assignments with
cell vectors a,b,c aligned with orthogonal axes X,Y,Z so that c||Z and
b in plane YZ.
Ref: Rollett, J. S. (1965). Computing Methods in Crystallography, p. 22.
Oxford: Pergamon Press.
Type: Real
Units: reciprocal_angstroms
Category:
atom_sites_fract_transform
