Crystallographic cell converter
Nicolas Schoeni and Gervais Chapuis
École Polytechnique Fédérale de Lausanne, Switzerland
![](https://www.epfl.ch/schools/sb/research/iphys/wp-content/uploads/2019/07/CellConverter-applet.png)
It is often necessary to describe a crystal structure in a new unit cell different from the original.
![](https://www.epfl.ch/schools/sb/research/iphys/wp-content/uploads/2019/07/cellconv_graph.png)
If a, b and c are the lattice vectors defining the unit cell, the new lattice vectors a’, b’ and c’ are obtained from the following matrix transformation P
![](https://www.epfl.ch/schools/sb/research/iphys/wp-content/uploads/2019/07/cellconv_equ1.png)
where P is the matrix
![](https://www.epfl.ch/schools/sb/research/iphys/wp-content/uploads/2019/07/cellconv_equ2-300x103.png)
In some cases, the new origin of the unit cell is not identical to the old one. The origin shift is given by the column vector
![](https://www.epfl.ch/schools/sb/research/iphys/wp-content/uploads/2019/07/cellconv_equ3-300x96.png)
In the new unit cell, the atomic coordinates are given by the following relation
![](https://www.epfl.ch/schools/sb/research/iphys/wp-content/uploads/2019/07/cellconv_equ4-300x101.png)
where
![](https://www.epfl.ch/schools/sb/research/iphys/wp-content/uploads/2019/07/cellconv_equ5-300x81.png)
and
![](https://www.epfl.ch/schools/sb/research/iphys/wp-content/uploads/2019/07/cellconv_equ6.png)
In the absence of a CIF file, the user can select on the existing one in the menu and edit the file ignorer to introduce the original lattice constants. The P and p arrays can introduced in the applet along wth the atomic coordinates. After transformation a new CIF file is created with the new atomic coordinates referring to the new unit cell.