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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_Cartn_transform.matrix
Name:_atom_sites_Cartn_transform.matrix
Definition:
Matrix used to transform fractional coordinates in the ATOM_SITE
category to Cartesian coordinates. The axial alignments of this
transformation are described in _atom_sites_Cartn_transform.axes.
The 3 x 1 translation is defined in _atom_sites_Cartn_transform.vector.
x' |11 12 13| x | 1 |
( y' ) Cartesian = mat|21 22 23| * ( y ) fractional + 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 lies in the YZ plane.
Reference: Rollett, J. S. (1965). Computing Methods in Crystallography,
p. 22. Oxford: Pergamon Press.
Type: Real
Values appear in Matrix context.
Dimension: [3,3]
Units: angstroms
Evaluation method:
With a as atom_sites_Cartn_transform
_atom_sites_Cartn_transform.matrix = [[a.mat_11, a.mat_12, a.mat_13],
[a.mat_21, a.mat_22, a.mat_23],
[a.mat_31, a.mat_32, a.mat_33]]
Category:
atom_sites_Cartn_transform