Institut Jean Barriol
Plateforme de mesures de diffraction X - Service Commun de RMN - Logiciel MoPro

Geminography

Current build No. 2012, released June 7, 2011

A software package to explore twin laws in non-merohedric twins and to analyze hybrid twins

Geminography - a mixed-origin term, from Latin gemini (twins), and Greek γραφια (writing) - is the term introduced by J.D.H. Donnay to indicate the branch of crystallography dealing with twinning. This term made its appearance in the literature in 1975, in an article in Japanese (Takeda, 1975), but it was only in 2003 that it began to be used in the English literature (Nespolo and Ferraris, 2003).

The program geminography aims at finding possible twin laws in non-merohedric twins. It takes in input the cell parameters and the indices of a (known or supposed) twin element (plane or axis), plus a few parameters described in the documentation, and looks for lattice elements quasi-perpendicular to the twin element, in order to find the possible twin lattice(s). It calculates the twin index and the obliquity and the (pseudo)-symmetry of the twin lattice(s) obtained. The peculiarity of this program, with respect to other software packages that analyse twinned crystals, is the systematic search for co-existing sublattices and the interpretation of twinned edifices as hybrid twins whenever this gives a better description of the lattice quasi-restoration.

The program geminography is not a black-box tool. A blind use may easily result in meaningless conclusions. The user is expected to be familiar with concepts like twin index and obliquity, sublattice, holohedry and merohedry, as well as the reticular classification of twins. A suitable introduction can be found at this address. You can download an electronic reprint of the article where the theory, the computation algorithm and some examples are presented and analyzed (330 Kb).

What are hybrid twins?

The degree of lattice (quasi)-restoration in a twin is inversely related to the twin index and the obliquity; a large part of known non-merohedric twins correspond to low obliquity and low twin index, the empiric limiting values being 6º for the obliquity and 6 for the twin index (Friedel, 1926). Twins that correspond to this criterion are called "Friedelian twins" (Nespolo and Ferraris, 2005).

A number of examples of non-Friedelian twins are known, which are hardly understandable on the basis of the classical reticular theory. Actually, many of them can again be rationalized in terms of the lattice (quasi)-restoration, provided the classical approach is extended to consider the coexistence of N quasi-restored sublattices. These concurrent sublattices correspond to the same twin law, are defined by different pairs (hkl)/[uvw], all based on the common twin element and differing for the quasi-perpendicular lattice element, and show different degrees of quasi-restoration. A twin where multiple concurrent sublattices correspond to the same twin element are called hybrid twins.

Downloadable archive

The program geminography runs under the MicrosoftTM WindowsTM operating system and has been tested in the 2000 and XP versions. It should however run also under previous versions, The graphic interface is written in python. The compressed archive contains the executable (geminography.exe), the graphic interface (gui.exe), the user manual, one example of input file (that is read in when the graphic interface is run), and all the libraries needed to run the graphic interface. Simply unzip the archive in a folder: there is no installer, the program runs by double-clicking the gui.exe file. If you use the geminography.exe file then graphic interface is bypassed: the program reads the input.in file (details in the user manual).

DOWNLOAD GEMINOGRAPHY.ZIP (compressed archive - 4.4 Mb)
download electronic reprint (pdf - 330Kb)

Disclaimer

The program should be considered in beta-test. Despite the number of tests already done by the author, it is possible that some bugs are still present. Several checks for consistencies are done: when an unexpected situation occurs, a warning is printed in the results. In this case, please contact the author and send your input file. Also in the case that for any reason you think the results obtained are incorrect, please contact the author. The success of the debugging process depends on the number of bugs reported by different users. I apologise for any bug and mistake you may find and thank you in advance for your help in improving this program.

Changelog

Build numbers have nothing to do with the year. Builds 1xxx were only for internal development; builds 2xxx indicate release candidates; the first public build was No. 2005.

7 June 2011: build 2012 released. Major update (build 2011 is an intermediate development build, not for public release).

3 February 2009: build 2010 released. Bug fix and improvement for the exploration of a set of possible twin elements over an interval of indices.

  1. Bug fix: results were sometimes printed without reduction of the twin element to coprime factors; only the printed indices were wrong, the results were correct.
  2. Added a check to avoid analyzing twice the same twin element during the (hkl) or [uvw] exploration.
  3. A few minor code inconsistencies fixed thanks to the new Fortran compiler.

8 July 2008: build 2009 released. One bug fix and two presentation improvements.

  1. Fixed a bug affecting the check for I-centring of the twin lattice.
  2. Added a transformation to avoid acute angles.
  3. Sublattices are now presented in the order of decreasing twin index

7 May 2008: build 2008 released. Bug fix: added a missing flag for i-TLS twinning in crystals with rhombohedral lattice

10 March 2008: build 2007 released. Added a check against input error in case orthorhombic crystals

4 March 2008: build 2006 released. Two bugs related to the numerical treatment have been fixed

  1. When the lowest-obliquity element is eliminated because it defines a too large cell, one or more elements which are within this cell but outside the smaller one remain in the list. In the new build they are correctly eliminated
  2. When the intermediate effective twin index is equal to or lower than the twin index of a component, in some cases the program does not stop calculation but keeps the result as final effective twin index. Fixed. Also, a further limit has been introduced: when the effective twin index is within 0.5 of the twin index of a component, the hybrid interpretation is withdrawn.

29 August 2006: build 2005 released.





References