To help with determination of the optimal symmetry for a structure, GSAS-II provides a number of tools. Most utilize externally-created software. Further, there are also tools provided for working with distortion mode generated via representational analysis (see §28.2). In most cases, this software is accessed via web servers, but there are also codes included with GSAS-II. The access to these tools is located in the section of the GUI where their use would be most convenient. Below is a list of the tools that GSAS-II offers for symmetry analysis, listing the source of the actual computations and short description of what the tool does. The presentation is organized by the section of the GUI where the tools are located.
The GUI that is displayed when the Unit Cells List data tree sub-entry is selected for powder diffraction histograms provides tools for indexing powder diffraction patterns and considering extinctions arising from symmetry while graphically viewing the generated reflection positions superimposed on the powder diffraction pattern associated with the histogram . The upper part of the GUI in the data window is used for autoindexing and the lower portion of the window is used to provide the unit cell and space group used to generate the reflection positions that are shown with the selected powder diffraction pattern. Those unit cell parameters can be loaded from indexing results, from phases that have been imported into the project (using the “Cell Index/Refine”/“Load Phase” menu command), or a cell and space group can be entered from the keyboard into the appropriate text boxes and selection pull-down menus. When a Bravais lattice has been selected and unit cell contents are entered, the reflection positions are shown as vertical dashed orange lines. The location of extinct reflections will be shown in blue when “Show Extinct” is selected. Placing the mouse on a line causes the reflection indices to be displayed as a “tooltip.” The unit cell dimensions can be shifted with the arrows alongside of the text entry boxes for those dimensions and the “cell step” pull down menu dictates how much the parameters change when a arrow button is pressed. The “Try all?” button will generate a list of all the space groups consistent with the selected Bravais lattice; clicking on the entries in the list will show you the allowed reflections in that space group.
Note that the unit cell parameter text entry boxes will accept math expressions. One cute trick that this allows is a simple way to test if a superlattice can index unidentified peaks. If one edits the value of a, b, or c by adding “*2” at the end of the unit cell value, when the mouse is moved out of the box, the unit cell will be doubled. One can also multiply by \(\sqrt 2\) by adding *sqrt(2) at the end of the cell value. If a commensurate supercell is present, doubling a, b, or c in turn should index at least some of the “extra” peaks. The original value can be restored by entering “/2” at the end of the new unit cell value or using the “Cell Index/Refine”/“Load Phase” menu command.
In the menu labeled “Cell Index/Refine” the “Cell Symmetry Search” command runs the NIST*LATTICE program from Vicky Karen and the late Alan Mighell. This program will search for unit cells of higher symmetry that are close to the input unit cell dimensions as well as possible subcells and supercells. The generated unit cells are placed into the window where they can be compared to the histogram’s powder pattern. The value from this is that you may find a higher symmetry cell that indexes all the powder diffraction peaks, or, a supercell may index peaks that were previously unindexed.
The “Transform Cell” command in the menu labeled “Cell Index/Refine” brings up a dialog that can be used to transform the unit cell parameters that have been entered into the center section of the data window. In the common transformations pull-down list there are many common axes permutation options, for example, option a-cb will exchange the b and c axes, but an axis inversion is needed so that the system remains right handed. Likewise, option A-P will transform the unit cell from A-centered to primitive. These actions simply set the transformation matrix values. You can also manually enter any matrix you wish. The “Test xform” button to the right of the matrix will update the lattice parameters shown on the window to allow you to confirm that you are generating the cell you want.
In the menu labeled “Cell Index/Refine” the “Run Subgroups” command runs the SUBGROUPS program from the Bilbao Crystallographic Server (BCS). Note that before the web site can be used from within GSAS-II, an account must be created and entered into GSAS-II. How to do this is documented in the “Register for access to the Bilbao Crystallographic Server”1. The input for this includes an optional k-vector to expand the cell (due to supercell reflections). The default for this vector, (0,0,0), does not expand the cell. This will create a table of lowered symmetry settings, possibly with increased unit cell dimensions. Clicking on “Try” causes the reflections to be generated and displayed for that unit cell/symmetry setting. The results are ordered by highest to lowest symmetry, so typically the first result that indexes all peaks in the powder diffraction pattern is the cell/symmetry that will be of greatest interest. You are suggested to uncheck the “Keep” flag for any cells that do not index the pattern. Should you wish to transform a phase using the results from a row in the table, select that phase in the data tree and its General tab. The Compute/“Select magnetic/subgroup phase” will transform the phase to this lower symmetry. Alternately, the “Make subgroups project files(s)” in the same location creates new GSAS-II project (.gpx) files with the phase. With either, you will have to select from the list of subgroups that have “Keep” checked.
In the menu labeled “Cell Index/Refine” the “Run k-SUBGROUPSMAG” command runs the k-SUBGROUPSMAG program from the Bilbao Crystallographic Server (BCS). Note that, as described before, the web site can be used from within GSAS-II, an account must be created and entered into GSAS-II. This is used to generate the color space group settings associated with the given unit cell and symmetry that is supplied. Commonly, one or more cell expansion coefficients in the form of up to three k-vectors can be specified. This will create a table of lowered symmetry settings, possibly with increased unit cell dimensions. Clicking on “Try” causes the reflections to be generated and displayed for that unit cell/symmetry setting. The results are ordered by highest to lowest symmetry, so typically the first result that indexes all peaks in the powder diffraction pattern is the cell/symmetry that will be of greatest interest. You are suggested to uncheck the “Keep” flag for any cells that do not index the pattern. Should you wish to transform a phase using the results from a row in the table, select that phase in the data tree and its General tab. The Compute/“Select magnetic/subgroup phase” will apply the phase transformation to create a new magnetic phase from the parent chemical (nuclear) phase. You will be offered a list of the magnetic groups where “Keep” has been selected.
There are a number of symmetry-related tools provided in the Phase GUI associated with the General tab. These are primarily used to transform the existing phase into a new one. The are invoked by commands in the “Compute” menu.
The “Transform” command in the menu labeled “Compute” brings up a dialog that can be used to transform the unit cell parameters that have been entered into the center section of the data window, creating a new phase. In the common transformations pull-down list there are many common axes permutation options, for example, option a-cb will exchange the b and c axes, but an axis inversion is needed so that the system remains right handed. Likewise, option A-P will transform the unit cell from A-centered to primitive. These actions simply set the transformation matrix values. You can also manually enter any matrix you wish. The “Test xform” button to the right of the matrix will update the lattice parameters shown on the window to allow you to confirm that you are generating the cell you want. Unlike the “Transform Cell” command associated with the Unit Cells List data tree sub-entry, this command will transform both unit cell dimensions and atom coordinates. Note that for atom transformations, there are two coordinate shift vectors, U and V. The values in U are subtracted before the transformation matrix is applied and the V values are added afterwards. This command will expand the unit cell contents and remove duplicate atoms, to match the target space group provided near the bottom of the window.
The button at the top of the window labeled “Make unit cell magnetic?” is used to create a magnetic phase from a chemical (nuclear) phase. This adds some additional options to the window. You should select the target space group as the parent, non-color space group. The generators for that group are then displayed immediately below and you select the spin flip setting for each of those symmetry operations. Note that while all operators may be black (a gray group); but, not all are allowed to be red. If an internally conflicting set of operators are set to red, operator(s) that are in conflict will be reset to black. The BNS color space group name is generated from the spin flip settings.
For magnetic phases, only the potentially magnetic atoms will be transformed, but a list of the generated positions is shown and you can select to only include the atoms that you think can carry a spin in that phase. For non-magnetic phase generation, all atoms are transformed.
The “Make constraints between phases?” option will generate constraints so that the unit cell dimensions and atom parameters will be kept synchronized between the two phases. If the phases are used in histograms, phase fractions and isotropic sample broadening terms will also be constrained. This is unlikely to be needed for non-magnetic transforms, where the new phase will be used to replace the original phase, but is very likely to useful with a magnetic phase. Thus, the default for this changes.
GSAS-II is will handle non-standard space group settings, and these settings can be very useful (as discussed in §3.15), but it is also useful to have the unit cell and coordinates in the standard setting. The “Std Setting” menu command in the “Compute” menu runs the “IDENTIFY GROUP” program from the Bilbao Crystallographic Server. If the structure is already set into the standard setting, a message saying this will be displayed. If structure is not in the standard setting, a new GSAS-II project file will be created, named Filename_std.gpx when the original project had been named Filename.gpx with the cell and coordinates are transformed for that phase. Note that, as described before, the web site can be used from within GSAS-II, an account must be created and entered into GSAS-II.
The “SUBGROUPS search” menu command in the “Compute” menu runs the “SUBGROUPS” program from the Bilbao Crystallographic Server. This duplicates the “Cell Index/Refine”/“Run Subgroups” command from the histogram “Index Cells List” data tree entry. You can then transform the phase using the search results from a row in the table using the Compute/“Select magnetic/subgroup phase,” which adds a new phase with this lower symmetry to the project or the “make subgroups project files(s)” command, which creates new project files for the located and selected subgroups. Note that, as described before, the web site can be used from within GSAS-II, an account must be created and entered into GSAS-II.
The “Select magnetic/subgroup phase” menu command is used after the Compute/“SUBGROUPS search” menu command for the General tab of the phase or after running the “Cell Index/Refine”/“Run Subgroups” or the “Cell Index/Refine”/“Run k-SUBGROUPSMAG” menu commands from the histogram “Index Cells List” data tree entry. This adds a new phase with this lower symmetry to the project.
The “Select magnetic/subgroup phase” menu command is used after the Compute/“SUBGROUPS search” menu command for the General tab of the phase or after running the “Cell Index/Refine”/“Run Subgroups” menu command from the histogram “Index Cells List” data tree entry. This creates new project files for the selected subgroups.
The “Bilbao Supergroup search” command from the Compute menu command for the General tab of the phase runs the “PSEUDO’ program from the Bilbao Crystallographic Server and is used to find possible higher symmetry versions of the current phase. This program requires that the phase be in a standard setting, so that is checked first and the phase is transformed, if needed, and then uploaded. This process requires a series steps, where unit cells are generated and if the cell parameters are sufficiently close to the original cell (or the standard setting cell) or you decide to include that cell anyway, the coordinates checked for compatibility with the new cell. If the coordinates can be transformed within acceptable error limits, the structure is generated and saved in a GSAS-II project (.gpx) file. The previous supercell search is then performed on all the newly created structures until no further candidate structures are found. At the end, a summary is presented showing all created files.
At the time this is being written, I have not completed revisions to GSAS-II to work with updates to the BCS web site. This means that a step needed to locate potential higher symmetry cells for triclinic and monoclinic cells can not be performed as part of this search process. There are warning messages shown should this be tried. For now, in these cases, one must use the web site directly.
The “ISOCIF Supergroup search” command from the Compute menu command for the General tab of the phase runs the “ISOCIF’ program from the Brigham Young University’s ISOTROPY Software Suite web site. This will search for a possible higher symmetry versions of the current phase. It has succeeded in cases where the Bilbao PSEUDO search has not, but provides much less information on what is being done. I believe there is value in trying both.
The ISODISTORT tab associated with each phase provides a mechanism for running the “ISODISTORT” program from the Brigham Young University’s ISOTROPY web site. This can be used in two different ways. In the first, a single structure is uploaded to the website and then displacive distortion modes for that structure are generated as single irrep modes. The structure can be read from a CIF or can be the current phase. Select the input and then use the Operations/“Run ISODISTORT” to submit that information to the web server. A table of subgroups is created and CIFs for any of those child structures can be written.
The second mode offered here is for comparison of two related structures. The parent structure is the high symmetry version of the structure and the child will be a lower symmetry version. Both can be read from CIFs or either can be the current phase. The result of this is a series of distortion modes that can be viewed in this tab or used to create a model for PDFfit.
One other way that GSAS-II can interact with the Brigham Young University’s ISOTROPY web site is that the ISODISTORT program creates CIFs that have additional information in them that describes the distortion modes, When the GSAS-II CIF importer encounters these distortion modes they are converted to “new variable” constraints (see §24.2.3). This allows selected distortion modes to be refined in place of individual atomic parameters. Note that if all distortion modes are refined simultaneously, the result is the same as if all the constrained atomic parameters are refined. At present, GSAS-II supports displacive, occupancy and magnetic distortion modes but not ADP and strain distortion modes).
When magnetic distortion modes are read, if the parent chemical phase is present, constraints are also generated to keep the lattice parameters and the positions of atoms occurring in both phases as equivalent. Such constraints can be somewhat complex when the unit cell relationships are not simple. Likewise, when histogram(s) are linked to the magnetic phase, constraints are generated to keep phase fraction and isotropic phase broadening terms also synchronized.
Finally, when such constraints are present, in the Constraints data tree entry, the “Edit Constr.”/“Show ISODISTORT modes” menu command can be used to see a tabulation of these modes and the dependent atomic parameters they control.