Harold T. Stokes and Dorian M. Hatch
Department of Physics and Astronomy
Brigham Young University, Provo, Utah 84606

ISOTROPY is a software package which applies group theoretical methods to the analysis of phase transitions in crystalline solids.

When this software is used in research that results in published papers, please include a reference which contains the following information:

H. T. Stokes and D. M. Hatch, (2002). ISOTROPY,


ISOTROPY User's Manual
Introduction to Isotropy Subgroups and Displacive Phase Transitions (unpublished)

Internet Versions

ISOTROPY: Main interactive program.

ISODISPLACE: Explore and visualize displacive distortions of a crystalline structure associated with space group irreducible representations.

FINDSYM: Identify the space group of a crystal, given the positions of the atoms in a unit cell.

COPL: Find a complete list of order parameters for a phase transition, given the space-group symmetries of the parent and subgroup phases.

INVARIANTS: Generate invariant polynomials of the components of order parameters.

SMODES: Find the displacement modes in a crystal which brings the dynamical matrix to block-diagonal form, with the smallest possible blocks.

FROZSL: Calculate phonon frequencies and displacement modes using the method of frozen phonons.

COMSUBS: Find common subgroups of two structures in a reconstructive phase transition

Downloadable Versions


DOS. Version 6.4.2. August 2001. Includes ISOTROPY, FINDSYM, SMODES, SYMSEARCH.


June 2006, ISOTROPY, version 8.5. Fixed minor bugs.

June 2006, ISODISPLACE, version 3.2.10. Made minor improvements.

June 2006, all programs are now compiled using Intel Fortran Compiler for Linux, version 9.1.

June 2006, RELATIONS, no longer available.

June 2006, SYMSEARCH, no longer available.

May 2006, ISODISPLACE, version 3.2.8. Finds ESDs for mode and strain amplitudes. Also new compiler results in faster program.

May 2006, ISODISPLACE, version 3.2.7. Now able to read general CIF files.

April 2006, ISODISPLACE, version 3.2.6. New features and some bugs fixed.

April 2006, FINDSYM, version 3.2.1. Fixed bug for R-centered lattices.

March 2006, ISOTROPY, version 8.4. Fixed some minor bugs concerning coupled irreps.

February 2006, COMSUBS, version 3.1. Implemented preservation of bonds.

February 2006, ISOTROPY, version 8.3. Fixed some minor bugs. Also fixed a major bug affecting the calculation of isotropy subgroups for coupled irreps where the second (or third or fourth, etc.) irrep belongs to a non k point of symmetry (non special k point).

February 2006, ISODISPLACE, version 3.2. Many new features.

January 2006, ISOTROPY, version 8.2. Fixed incorrect ferroics types for some cases in the cubic space groups.

November 2005, ISODISPLACE, version 3.0. Included strain and a few other miscellaneous new features.

October 2005, ISODISPLACE, version 2.0. Included order-disorder transitions and a few other miscellaneous new features.

August 2005, ISODISPLACE, version 1.0.

July 2005, COMSUBS, version 3.0. Redefined meaning of maximum atomic shuffle. This helped the program run faster.

July 2005, FINDSYM, version 3.2. Added monoclinic and orthorhomic settings.

July 2005, ISOTROPY, version 8.1. Added monoclinic and orthorhomic settings.

April 2005, COMSUBS, version 2.2. Fixed some minor bugs.

November 2004, FINDSYM, version 3.1. Added option to use different settings for space groups.

November 2004, FINDSYM, version 3.0. Fixed how tolerance is handled. Added a centering option for basis vectors of the unit cell. Removed unnecesary data from output. Inserted more user-friendly error messages.

July 2004, COMSUBS, version 2.1.1. Fixed various minor bugs.

March 2004, ISOTROPY, version 8.0.4. Fixed various minor bugs.

November 2003, FINDSYM, version 2.6. Added graphical rendition of the unit cell (internet version only).

May 2003, COMSUBS, version 2.0.1. Fixed bug in determining origin of common subgroup in crystal 2.

July 2002, ISOTROPY, version 8.0.1. Fixed bug in show macroscopic for hexagonal groups. Bug introduced in version 7.0.

July 2002, ISOTROPY, version 8.0. Added domain sets capability.

March 2002, ISOTROPY, version 7.0. Changed all 8-byte real numbers to 16-byte real numbers. This should make no difference in the output.

August 2001, ISOTROPY, version 6.7. Added show subgroup and show size commands to display direction.

July 2001, ISOTROPY, version 6.6. Added option to obtain maximal subgroups and minimal supergroups.

September 2000, ISOTROPY, version 6.5. Fixed some minor bugs.

August 2000, FINDSYM, version 2.3.3. Fixed another bug relating to the identification of the Wyckoff positions and the origin.

August 2000, ISOTROPY, version 6.4.2. Fixed some minor bugs.

July 2000, FINDSYM, version 2.3. Fixed another bug relating to the identification of the Wyckoff positions.

June 2000, ISOTROPY, version 6.4. Expanded to include ferroic nature of phase transitions.

June 2000, FINDSYM, version 2.2. Fixed a bug relating to the identification of the Wyckoff positions.

May 2000, FINDSYM, version 2.0. This program now works for any arbitrary orientation of axes.

March 2000, ISOTROPY, version 6.3.4. Fixed some minor bugs.

February 2000, ISOTROPY, version 6.3.2. Expanded various routines to include irreps at non k points of symmetry.

October 1999. ISOTROPY tutorial in isotut.pdf. Wrote Session 6 on domains and updated the other sessions to reflect changes made in more recent versions of ISOTROPY.

October 1999, ISOTROPY, version 6.3.1. Fixed minor bug introduced in last version. Implemented Smith normal form in the method for identifying space group symmetry of subgroup.

September 1999, ISOTROPY, version 6.3. Coupled order parameters can now be generated for irreps at non-k-points of symmetry ("displace isotropy coupled").

August 1999, ISOTROPY, version 6.2.1. Fixed bug in "show subgroup alternate" command.

August 1999, ISOTROPY, version 6.2. Added "show subgroup alternate" command.

August 1999. FINDSYM, version 1.2. Fixed bug in origin of space group. Also changed setting to Origin Choice 2 so that it would match the default setting in ISOTROPY.

August 1999, ISOTROPY, version 6.1.1. Fixed bug in "value direction" command. Also improved routine for generating isotropy subgroups at non k points of symmetry.

June 1999, ISOTROPY, version 6.1. Fixed some minor bugs. File affected: iso.exe.

February 1999, ISOTROPY, version 6.0.3. Fixed some minor bugs and some incorect generators for three point groups in the data base. Files affected: iso.exe and d_space.bin.

January 1999, ISOTROPY, version 6.0.2. Fixed some minor bugs and added some error messages. Files affected: iso.exe.

January 1999, SMODES, version 1.2.4. Made some minor changes.

January 1999, FINDSYM, version 1.1.1. Made some minor changes.

June 1998, SMODES, version 1.1.3. Made some minor changes in output format.

June 1998, FINDSYM, version 1.1. Fixed a bug.

June 1998, ISOTROPY, version 6.0.1. Fixed a bug in DISPLAY BUSH. Files affected: iso.exe.

April 1998, FINDSYM, version 1.0-2. Fixed some bugs.

March 1998, SMODES, version 1.2.2. Recompiled to be compatible with a change made in d_wyck.bin.

March 1998, ISOTROPY, version 6.0. Introduced new features, including the incorporation of GET_ISOTROPY, which used to be a separate program. Also made a change in d_wyck.bin, the data base associated with Wyckoff positions.

February 1998, SMODES, version 1.2.1. Fixed bug introduced by a change in an ISOTROPY library routine, November 1997.

February 1998, ISOTROPY, version 5.6.1. Fixed some bugs in DISPLAY BUSH. Files affected: iso.exe.

January 1998, FINDSYM, version 1.0. First version made available at this internet site.

January 1998, ISOTROPY, version 5.6. First version made available at this internet site.

September 1995, SMODES, version 1.2. First version made available at this internet site.