OD Explorer is a "virtual laboratory" for the analysis of Order/Disorder (OD) structures. The OD theory was developed in the 1950s to explain unusual diffraction phenomena and disorder in minerals like wollastonite and isotypic inorganic compounds like Madrell's salt (NaPO3) and the isotypic sodium polymetaarsenate. The arguments of OD theory apply to all classes of compounds and it has been fruitfully applied to minerals, synthetic inorganic compounds, organic compounds and even biological macro-molecules.

OD theory is based on the geometric equivalence of pairs of layers. A structure is said to fulfill the vicinity condition (VC) if

Structures which fulfill the VC and allow for different stacking possibilities are said to be proper OD structures, otherwise fully ordered structures. All resulting stacking possibilities belong to an OD family. If interatomic interactions of atoms distanced by more than a layer width are neglected, all members of an OD family are energetically equivalent, thus leading to polytypism.

For more details on OD theory see:


Inspired by the Superspace Group Finder, we decided to provide similar functionality for OD groupoid families. The aim of the project is twofold:

  1. Provide crystallographers a tool to analyze OD families. Since there are an infinity of OD families, it will never be possible to publish an equivalent to the International Tables of Crystallography Vol. A. Help in preparation of graphics and symbols for publication.
  2. Provide a code base which enables the testing of conjectures and thus the advancement of OD theory (i.e. a "virtual lab").


OD Explorer is alpha-level software in development. So far only rudimentary features have been implemented and the software is practically untested.

Design decisions

A list of design decision which will or will not be met and may or may not be useful. Time will tell.


Usage at the moment is very simple: The user inputs the symbol of an OD family. The software outputs a number of statistics. At the moment special parameters and the corresponding stacking possibilities are listed.