Help for GSAS-II

This is where to find help on various GSAS-II windows and plots. Note that GSAS-II operates with three windows: the main GSAS-II data tree section, which provides a hierarchical view of the current project on the left and the GSAS-II data editing section, which shows the contents of a particular section of the project, where values can be examined and changed; The second is the GSAS-II Plots window, which shows graphical representations of the results. The third is a console window, which has printout information that can be selected, cut & pasted into a document.

Help Index

1. Learning GSAS-II: tutorials
2. Application windows
3. Main menu commands
4. Data Tree headings, graphics windows and menu commands
1. Top-level Data Tree headings
2. Phase Data Tree headings
3. Image (IMG) Data Tree headings
4. Powder histogram (PWDR) Data Tree headings
• Comments
• Limits
• Background
• Instrument Parameters
• Sample Parameters
• Peak List
• Index Peak List
• Unit Cells List
• Reflection Lists
5. Single Crystal histogram (HKLF) Data Tree headings
• Instrument Parameters
• HKL Plot Controls
• Reflection List
6. Pair Distribution Functions (PDF) Data Tree headings
7. Powder Peaks (PKS) Data Tree headings
8. Small Angle Scattering (SASD) Data Tree headings
5. Other: Macintosh notes, Configuration options and Programmers documentation

Learning GSAS-II: Tutorials

The best way to learn about how different sections of GSAS-II is used is to work through tutorials. A list of available tutorial topics appears on a separate web page.

1. GSAS-II Data Tree

The data tree shows contents of a GSAS-II project (which can be read or saved as a .gpx file) in a hierarchical view. Clicking on any item in the tree opens that information on the right side of the window in the "Data Editing" section, where information in that item can be viewed or edited. For example, the "Sample Parameters" item under a ‘PWDR’ entry contains information about how data were collected, such as the sample temperature (see below). The arrow keys (up & down) move the selection to successive entries in the data tree; both the data window and the associated plot (if any) will change.

What can I do here?

The leftmost entries in the GSAS-II menu provide access to many features of GSAS-II. Other menu items will change depending on what type of entry is selected in the data tree. The menu commands that do not change and are described below in the main menu commands section.

2. GSAS-II Data Editing Window

Different information is displayed in the Data Editing Window, depending on which section of the data tree is selected. For example, clicking on the "Notebook" entry of the tree brings up the Notebook editing window, as described below in the data tree sections.

3. GSAS-II Plots Window

This window presents all the graphical material as a multipage tabbed set of plots utilizing the matplotlib python package. Each page has a tool with the controls

The first nine or ten icons have the following functions: Home, Back, Forward, Pan, Zoom, Resize plot, Save, Key Press and Help, respectively and are described below. The remainder (yellow arrows) move or rescale the plot. Note that Resize plot is removed from the toolbar where matplotlib allows this and should not be used.

Home

returns the plot to the initial scaling

Back

returns the plot to the previous scaling

Forward

reverses the action in the previous press(es) of the Back button

Pan

allows you to control panning across the plot (press left mouse button) and zooming (press right mouse button),

Zoom

allows you to select a portion of the plot (press right mouse button & drag for zoom box) for the next plot.

Save

allows you to save the currently displayed plot in one of several graphical formats suitable for printing or insertion in a document.

Key Press

Shows a menu of key press commands that can be used to interact with the plot. These actions can be initiated from the menu.

Help

accesses GSASII help on the specific plot type.

{less than}

Shifts the plot to the left, relative to the axes

{greater than}

Shifts the plot to the right, relative to the axes

{up arrow}

Shifts the plot up, relative to the axes

{down arrow}

Shifts the plot down, relative to the axes

{less than}+{greater than}

Zooms in on the plot (magnifies) along the horizontal (x) direction to show more details.

{greater than}+{less than}

Zooms out on the plot (demagnifies) along the horizontal (x) direction.

{up arrow}/{down arrow}

Zooms in on the plot (magnifies) along the vertical (y) direction to show more details.

{down arrow}/{up arrow}

Zooms out on the plot (demagnifies) along the vertical (y) direction.

Below the toolbar may be a status bar that on the left may show either an instruction for a keyed input or a pull down selection of keyed input; on the right may be displayed position dependent information that is updated as the mouse is moved over the plot region.

4. Main GSAS-II menu commands

1.      Menu File

Open project…

Open a previously saved GSAS-II project file ({project}.gpx). If you currently have a project file open, you are asked if it is OK to overwrite it; Cancel will cancel the read process.

Note that as files are saved, copies of the previous version are saved as backup files, named as {project}.bak{i}.gpx, where i starts as 0 and is increased after each save operation. NB: you may open a backup .gpx file (e.g. name.bak3.gpx) to return to a previous version of your project, but if you do so, it is best to immediately use the Save As... menu command (you may wish to use name.gpx to overwrite the current version or select a new name.) If you forget specify a project name, then name.bak3 will be considered the project name and backups will then be named name.bak3.bak0.gpx, etc.

Save project

Save the current project. If this is a new project that has not yet been saved, you will be prompted for a new name in a file dialog (you may optionally change the directory in that dialog). If the file exists, you will be asked if it is OK to overwrite it. Once a file name has been used to read or save a project, the name is shown after ‘Loaded Data:’ in the first item in the data tree.

Save Project as...

Save the current project in a specified project file. You will be prompted for a new name in a file dialog (you may optionally change the directory in that dialog). If the file exists, you will be asked if it is OK to overwrite it.

New Project

Discards any changes made to the current project since the last save and creates a new empty project.

Preferences

Provides access to GSAS-II configuration settings, as described in the Configuration Variables section.

Quit

Exit the GSAS-II program. Discards any changes made to the current project since the last save. You can also exit GSAS-II by pressing the red X in the upper right (Windows) or left (Mac).

2.      Menu Data

Read Powder Pattern Peaks…

Read in a list of powder pattern peak positions as either a d-spacing table or a set of 2theta positions; these can be used in GSAS-II powder pattern indexing.

Sum powder data

Form the sum of previously read powder patterns; each with a multiplier. Can be used to accumulate data, subtract background or empty container patterns, etc. Patterns used to form the sum must be of identical range and step size. Result is a new PWDR entry in the GSAS-II data tree.

Sum image data

Form the sum of previously read 2-D images; each with a multiplier. Can be used to accumulate data, subtract background or empty container patterns, etc. Images used to form the sum must be of identical size and source. Result is a new IMG entry in the GSAS-II data tree, and a GSAS-II image file is written for future use.

Add new phase

This begins the creation of a new phase in the data tree (under Phases). You are first prompted in a dialog box for a name to be assigned to the new phase. Then the Phase/General tab is opened for this phase, where you should first select the phase type, the enter the space group symbol and then the lattice parameters.
Note that nonstandard space group symbols are permitted; space group names must have spaces between the axial fields (e.g. use ‘P n a 21’ not ‘Pna21’).

Delete phase

This will remove a phase from the data tree. A dialog box will present the list of phases; pick one (or more) to delete.

Rename tree item

Rename a histogram entry. This should only be done before the histogram is used in any phases: e.g. only rename data immediately after reading.

Delete tree item

This will remove an item from the data tree. A dialog box with a list of choices for histograms is presented. Be sure to remove a histograms from all phases before deleting it from the tree.

Expand tree item

This will show child entries for specified type of items (Images, Powder patterns, etc.)

Move tree item

Move classes of Tree items around in the tree. Individual top-level tree items can be moved using the left mouse button.

3.      Menu Calculate

Setup PDFs

This creates the pair distribution function (PDF) controls for each powder pattern selected in the dialog box, but does not compute the PDF, which must be done from PDF tree entries. See PDF Controls for information on the PDF input.

View LS parms

This shows a dialog box with all the parameters for your project; those to be refined are flagged ‘True’, otherwise ‘False’. Blanks indicate parameters that are not refinable. The total number of refined parameters is also shown at the top of the list. The value of each parameter is also given. The parameter names are of the form ‘p:h:name:id’ where ‘p’ is the phase index, ‘h’ is the histogram index and ‘id’ is the item index (if needed). Indexes all begin with ‘0’ (zero).

Note that for atom positions, the coordinate values (named as ‘p::Aw:n’, where p is the phase number, n is the atom number and w is x, y or z) is not a refinable parameter, but the shift in the value is. The refined parameters are ‘p::Aw:n’. The reason this is done is that by treating an atom position as x+dx,y+dy,z+dz where the “d” values indicate shifts from the starting position and the shifts are refined rather than the x,y, or z values is that this simplifies symmetry constraints. As an example, suppose we have an atom on a symmetry constrained site, x,1/2-x,z. The process needed to define this constraint, so that if x moves positively y has to move negatively by the same amount would be messy. With refinement of shifts, all we need to do is constrain dy (‘0::dAy:n’) to be equal to -dx (-1*‘0::dAx:n’).

Press the window exit button to exit this dialog box.

Refine

This performs the refinement (Pawley/Rietveld or single crystal) according to the controls set in the Controls data tree item.

Sequential refine

This starts a sequential refinement with the data sets selected in the Controls data tree item.

4. Menu Import

GSAS-II uses separate routines to read in information from external files that can be created and customized easily. See the GSAS-II Import Modules section of the Programmers documentation for more information on this. Since it is easy to support new formats, the documentation below may not list all supported formats.

Image

Read in 2-D powder diffraction images (multiple patterns can be selected). A sub menu appears with choices for import of data. Each entry when selected with the mouse shows further submenus with specific imports that are available. Any of these files can be accessed from a zip file. GSAS-II can read many different image file formats including MAR345 files, Quantum ADSC files, and tiff files from Perkin-Elmer, Pilatus, and GE. Although many of these formats have data fields that should contain relevant information for the exposure (e.g. wavelength), these are rarely filled in correctly by the data acquisition software. Thus, you should have separately noted this information as it will be needed

Phase

Creates a new phase by reading unit cell/symmetry/atom coordinate information. GSAS-II can read information from a number of different format files including:

GSAS .EXP

This reads one phase from a (old) GSAS experiment file (name.EXP). The file name is found in a directory dialog; you can change directories as needed. Only .EXP (or .exp) file names are shown. If the selected file has more than one phase, a dialog is shown with the choices; only one can be chosen. If you want more than one, redo this command. After selecting a phase, a dialog box is shown with the proposed phase name. You can change it if desired.

PDB file

This reads the macromolecular phase information from a Protein Data Base file (name.PDB or name.ENT). The file name is found in a directory dialog; you can change directories as needed. Only .PDB (or .pdb) or .ENT (or .ent) file names are shown. Be careful that the space group symbol on the ‘CRYST1’ record in the PDB file follows the GSAS-II conventions (e.g. with spaces between axial fields). A dialog box is shown with the proposed phase name. You can change it if desired.

CIF file

This reads one phase from a Crystallographic Information File ({name}.CIF (or .cif). The file name is found in a directory dialog; you can change directories as needed. If the selected file has more than one phase, a dialog is shown with the choices; only one can be chosen. If you want more than one, redo this command. After selecting a phase, a dialog box is shown with the proposed phase name. You can change it if desired.

GSAS-II .gpx file

This reads one phase from a GSAS-II project file ({name}.gpx). The file name is found in a directory dialog; you can change directories as needed. If the selected file has more than one phase, a dialog is shown with the choices; If you want more than one, redo this command. After selecting a phase, a dialog box is shown with the proposed phase name. You can change it if desired.

guess format from file

This attempts to read one phase from a file trying the formats as described above. On occasion, this command may not succeed in correctly determining a file format. If it fails, retry by selecting the correct format from the list.

Powder Data

Reads a powder diffraction data set in a variety of formats. Results are placed in the GSAS-II data tree as ‘PWDR file name'. Information needed for processing a powder diffraction data set, such as data type, calibration constants (such as wavelength) and default profile parameters are read from a separate file, either a (old) GSAS instrument parameter file (usually .prm, .ins or .inst extension) or a new GSAS-II .instparm file.

Note that it is possible to apply corrections to the 2-theta, intensity or weight values by adding a Python command(s) to the instrument (.instprm) parameter with a variable named CorrectionCode. See the CorrectionCode.instprm.sample file provided in the GSAS-II source directory for an example of how this is done.

CIF file

This reads one powder pattern (histogram) from a Crystallographic Information File ({name}.CIF). The file name is found in a directory dialog; you can change directories as needed. Only one .cif can be chosen. If you want more than one, redo this command.

GSAS-II .gpx file

This reads powder patterns from a previously created GSAS-II gpx project file. If the selected file has more than one powder pattern, a dialog is shown with the choices; one or more can be selected. It will ask for an appropriate instrument parameter file to go with the selected powder data sets.

GSAS .fxye files

This reads powder patterns (histograms) from the defined GSAS format powder data files. GSAS file types STD, ESD, FXY and FXYE are recognized. Neutron TOF data with a ‘TIME-MAP’ are also recognized. The file names are found in a directory dialog; you can change directories as needed. If the selected files have more than one powder pattern, a dialog is shown with the choice(s).

TOPAS .xye files.

This format is a simple 3-column (2-theta, intensity & sig) text file. The file names are found in a directory dialog; you can change directories as needed.

guess format from file

This attempts to read one data set from a file trying the formats as described above. On occasion, this command may not succeed in correctly determining a file format. If it fails, retry by selecting the correct format from the list.

Structure Factor

Reads single crystal input from a variety of file types. Results are placed in the GSAS-II data tree as ‘HKLF file name’

F**2 HKL file

This reads squared structure factors (as F**2) and sig(F**2) from a SHELX format .hkl file. The file names are found in a directory dialog; you can change directories as needed. You must know the file contains structure factors (as F**2) as the file itself has no internal indication of this.

F HKL file

This reads structure factors (as F) and sig(F) from a SHELX format .hkl file. The file names are found in a directory dialog; you can change directories as needed. You must know the file contains structure factors (as F values) as the file itself has no internal indication of this.

CIF file

This reads structure factors (as F**2 or F) and sig(F**2 or F) from a .CIF (or .cif) or .FCF (or .fcf) format file. The file names are found in a directory dialog; you can change directories as needed. The internal structure of this file indicates in which form the structure factors are used.

guess format from file

This attempts to read one data set from a file trying the formats as described above. However, since it cannot be determined if SHELX format .hkl contaings F or F**2 values, do not use this command for those files. On occasion, this command may not succeed in correctly determining a file format. If it fails, retry by selecting the correct format from the list.

Small Angle Data

Reads small angle scattering data from files. At present these formats are not documented; See the importer routines (file .../GSASII/imports/G2sad_xye.py) for more details.

5. Menu Export

GSAS-II uses separate routines to write out files with information inside GSAS-II. These routines can be created and customized easily. See the GSAS-II Export Modules section of the Programmers documentation for more information on this. Since it is easy to support new formats, the documentation below may not list all supported formats.

Entire project as

At present the only supported format for a project is a Full CIF file. This brings up a separate window where information such as ranges for bond distances and angles can be selected.

Phase as

Phases can be exported in a variety of formats including a simplified CIF file that contains only the unit cell, symmetry and coordinates.

Powder data as

Powder data can be exported in number of formats. Note that this menu can also be used to export reflection lists from Rietveld and Pawley fits.

Single crystal data as

Single crystal reflection lists can be exported as text files or as a simplified CIF file that contains only structure factors.

Image data

This exports selected images as a portable networks graphics format (PNG) file. Alternately, the image controls and masks can be written for selected images. If strain analysis has been performed on images, the results can also be exported here as a spreadsheet (.csv file).

Maps as

Fourier maps can be exported here.

Export all Peak Lists...

This allows peak lists from selected powder histograms to be written to a simple text file. There will be a heading for each PWDR GSAS-II tree item and columns of values for position, intensity, sigma and gamma follow.

Export HKLs

This allows single crystal reflection lists from selected histograms to be written to a file.

Export PDF...

This allows computed PDFs peak lists from selected histograms to be written as two simple text files, {name}.gr and {name}.sq, containing g(r) and s(q), respectively as 2 columns of data; a header on each indicated the source file name and the column headings. The file name comes from the PDF entry in the GSAS-II data tree.

5. GSAS-II data tree items

Notebook

This window provides a place for you to enter whatever text commentary you wish. Each time you enter this window, a date/time entry is provided for you. A possibly useful technique is to select a portion of the project.lst file after a refinement completes (it will contain refinement results with residuals, new values & esds) and paste it into this Notebook window so it becomes a part of your project file.

What can I do here?

Use the notebook to keep track of information related to how you use GSAS-II.

Controls

This window provides access to the controls that determine how GSAS-II performs minimizations as well as few global parameters for GSAS-II. Note that many other customization settings are set as configuration variables in the Preferences menu. (See the Programmer's documentation for a description of those.)

Refinement Controls: These controls determine how refinements are performed. The first determines the computational engine used to minimize the structure.

Refinement type

This determines how refinements are performed. The choices are:

·         analytic Hessian: This is the default option and is usually the most useful. It uses a custom-developed least-squares minimizer that uses singular-value decomposition (SVD) to reduce the errors caused by correlated variables and the Levenberg-Marquardt algorithm to up-weight diagonal Hessian terms when refinements fail to lower χ².

·         analytic Jacobian: This uses a numpy-provided leastsq minimizer, which not applicable for problem with a large number of histograms as it requires much more memory than the Hessian routines. This because it creates a Jacobian matrix that is shaped N x M (N parameters x M observations) while the Hessian methods create a Jacobian matrix only each histogram.

·         numeric: This also uses the numpy leastsq minimizer, and is also not applicable for larger problems. Unlike, the "analytic Jacobian", numerical derivatives are computed rather than use the analytical derivatives that are coded directly into GSAS-II. This will be slower than the analytical derivatives and will is often less accurate which results in slower convergence. It is typically used for code development to check the accuracy of the analytical derivative formulations.

·         Hessian SVD: This is very similar to analytic Hessian but does not include the Levenberg-Marquardt algorithm. It can be faster, but is more prone to diverge when severe correlation is present. It is possible that it might be better for single-crystal refinements.

Note that the Jacobian refinement tools are the Fortran MINPACK lmdif and lmder algorithms wrapped in python as provided in the Scipy package. The Hessian routines are were developed for GSAS-II based on routines in numpy and scipy and using the material in Numerical Recipes (Press, Flannery, Teulosky & Vetterling) for the Levenberg-Marquardt. The purpose is to minimize the sum of the squares of M nonlinear functions in N variables by a modification of the Levenberg-Marquardt algorithm. The lmdif and lmder routines were written by Burton S. Garbow, Kenneth E. Hillstrom, Jorge J. More (Argonne National Laboratory, 1980).

Min delta-M/M

A refinement will stop when the change in the minimization function (M=Σ[w(Io-Ic)²]) is less than this value. The allowed range is 10^-9 to 1.0, with a default of 0.001. A value of 1.0 stops the refinement after a single cycle. Values less than 10^-4 cause refinements to continue even if there is no meaningful improvement.

Max cycles

This determines the maximum number of refinement cycles that will be performed. This is only available with the "Hessian" minimizers.

Initial lambda

Note that here λ is the Marquardt coefficient, where a weight of 1+λ is applied to the diagonal elements of the Hessian. When λ is large, this down-weights the significance of the off-diagonal terms in the Hessian. Thus, when λ is large, the refinement is effectively one of steepest-descents, where correlation between variables is ignored. Note that steepest-descents minimization is typically slow and may not always find the local minimum. This is only available with the "analytical Hessian" minimizer.

SVD zero tolerance

This determines the level where SVD considers values to be the same. Default is 10^-6. Make larger to where problems occur due to correlation. This is only available with the "Hessian" minimizers.

Initial shift factor

A “damping multiplier” applied during the first refinement cycle, for Jacobean/numeric refinements only. Should be in interval (0.1, 100). See the SciPy leastsq docs for more information.

Single Crystal: A set of controls is provided for control of single-crystal refinements. These only appear when single crystal (HKLF) histograms are present in the project.

Refine HKLF as F^2?

When checked, refinements are against F² rather than |F|.

Min obs/sig

Conventional cutoff for single crystal refinements as to what reflections should be considered observed, typical values are 2.0 (2σ) or 3.0 (3σ).

Min extinct.

(needs further work)

Max delt-F/sig

Removes reflections that are very poorly fit. Should be used only with extreme care, since poorly-fit reflections could be an indication that the structure is wrong.

Max d-spacing

Reflections with d-space values larger than this value are ignored.

Min d-spacing

Reflections with d-space values smaller than this value are ignored.

Sequential Settings: A set of controls is for sequential refinement. Settings here determine if a "normal" or "sequential" refinement is performed. If no datasets are selected here, then all histograms linked to phases in the project and that are flagged as "used" are included in one potentially large (combined) refinement. However, if any number of histograms are selected here, then a sequential refinement is performed, where a fit is made to the structural model(s) fitting each selected histogram in turn. Only the first item below is shown in "normal" mode.

Select datasets/Reselect Datasets

This brings up a menu where histograms can be selected, which potentially switches between a normal and a sequential refinement. If one or more histograms are selected, a sequential refinement is used. If none are selected, then the refinement be set as "normal". The button is labeled "Select" when in normal refinement mode and "Reselect" in sequential refinement mode.

Reverse order?

Normally, in a sequential histograms are fit in the order they are in the data tree (which can be reordered by dragging tree items), but when this option is selected, the sequential fit is performed with the last tree entry first.

Copy results to next histogram?

When this option is selected, the fitted parameters from each refinement are copied to the next histogram, so that the starting point for each refinement will be the results from fitting the previous. This works well for parametric experiments where parameters such as the lattice parameters change gradually over the course of successive measurements. This option is usually used only for the initial refinement after a sequential fit is started and the setting is reset once that refinement is completed. For subsequent refinements, it is usually better to start with the results from the previous fit.

Clear previous seq. results

When this button is pressed, the "Sequential Results" entry with the results from the last sequential fit is deleted from the tree.

Global Settings: This is a location for parameters that apply to an entire project. At present there is only one.

CIF Author

The value provided here is used when creating a CIF of an entire project.

What can I do here?

This offers a place to change how GSAS-II performs refinements, but has no specific menu commands or graphics.

Covariance

This window contains final residual information; the GSASII Plots window ‘Covariance’ shows a graphical representation of the variance-covariance matrix. A text window is displayed with statistical values and goodness of fit parameters.

What is plotted here?

The variance-covariance matrix as a color coded array is shown on this page. The color bar to the right shows the range of covariances (-1 to 1) and corresponding colors. The parameter names are to the right and the parameter numbers are below the plot.

What can I do with the plot?

Move the mouse cursor across the plot. If on a diagonal cell, the parameter name, value and esd is shown both as a tool tip and in the right hand portion of the status bar. If the cursor is off the diagonal, the two parameter names and their covariance are shown in the tool tip and the status bar.

Use the Zoom and Pan buttons to focus on some section of the variance-covariance matrix.

Press ‘s’ – A color scheme selection dialog is shown. Select a color scheme and press OK, the new color scheme will be plotted. The default is ‘RdYlGn’.

Press ‘p’ – Saves the covariance values in a text file.

Constraints

This window shows the constraints to be used in a refinement. It is organized into three tabbed pages. ‘Phase constraints’ contain those involving parameters that describe aspects of the crystalline phases to be used in the refinement (e.g. atom coordinates, thermal motion and site fraction parameters). ‘Histogram/Phase constraints’ are those which describe aspects of the pattern that depend on both the phase and the data set used in the refinement (e.g. microstrain and crystallite size parameters). ‘Histogram constraints’ are those that depend only on the data set (e.g. profile coefficients U, V, W, X and Y).

What can I do here?

1.      Select the tab for the parameter types you wish to constrain. Each will have the same possibilities in the ‘Edit’ menu.

2.      Menu ‘Edit’ –

a.       Add Hold – select a parameter that you wish to remain fixed although other parameters of the same type may be selected as a group for refinement. For example, if the space group for a phase has a polar axis (e.g. the b-axis in P2₁), then one atom y-parameter is arbitrary and should be selected for a Hold to keep the structure from drifting up or down the y-axis during refinement. If selected, a dialog box will appear showing the list of available parameters; select one and then OK to implement it, Cancel will cancel the operation. The held parameter will be shown in the constraint window with the keyword ‘FIXED’. A Delete button can be used to remove it.

b.      Add equivalence – select a list of parameters that should have the same value (possibly with a non-unitary multiplier for some). Examples are a list of atoms with the same thermal motion Uiso, sets of profile coefficients U,V,W across multiple data sets. If selected, a dialog box will appear with a list of the available parameters. Select one and press OK; a second dialog box will appear with only those parameters that can be made equivalent to the first one. Choose those and press OK. Cancel in either dialog will cancel the operation. The equivalenced parameters will show as an equation of the form M₁*P₁+M₂*P₂=0; usually M1=1.0 and M2=-1.0, but can be changed via the ‘Edit’ button. The keyword ‘EQUIV’ marks it as an equivalence. A Delete button can be used to remove it.

c.       Add constraint – select a list of parameters whose sum (with possible non-unitary multipliers) is fixed. For example, the sum of site fractions for atoms on the same site could be fixed to unity. If selected, a dialog box will appear with a list of the available parameters. Select one and press OK; a second dialog box will appear with only those parameters that can be used in a constraint with the first one. Choose those and press OK. Cancel in either dialog will cancel the operation. The equivalenced parameters will show as an equation of the form M₁*P₁+M₂*P₂+…=C; the multipliers M1, M2, … and C can be changed via the ‘Edit’ button. The keyword ‘CONSTR’ marks it as a constraint. A Delete button can be used to remove it.

d.      Add function – this is very similar the “Add constraint” type except that the result of the sum can be varied in the refinement. The keyword ‘FUNCT’ marks it as a function; the ‘Refine?’ box indicates your choice to refine the result of the sum. A Delete button can be used to remove it.

Restraints

This window shows the restraints to be used in a refinement. It is organized into several tabbed pages, one page for each type of restraint. Restraints are developed for an individual phase and act as additional observations to be “fitted” during the refinement.

What can I do here?

1.      Select the tab for the restraint type you wish to use. Each will have the same possibilities in the ‘Edit’ menu.

2.      You can change the Restraint weight factor – this is used to scale the weights for the entire set of restraints of this type. Default value for the weight factor is 1.0.

3.      You can choose to use or not use the restraints in subsequent refinements. Default is to use the restraints.

4.      You can change the search range used to find the bonds/angles that meet your criteria for restraint.

5.      You can examine the table of restraints and change individual values; grayed out regions cannot be changed. The ‘calc’ values are determined from the atom positions in your structure, ‘obs’ values are the target values for the restraint and ‘esd’ is the uncertainty used to weight the restraint in the refinement (multiplied by the weight factor).

6.      Menu ‘Edit’ – some entries may be grayed out if not appropriate for your phase or for the selected restraint.

a.       Select phase – active if there is more than one phase in your project. A dialog box will appear with a list of the phases, select the one you want for restraint development.

b.      Add restraints – this takes you through a sequence of dialog boxes which ask for the identities of the atoms involved in the restraint and the value to be assigned to the restraint. The esd is given a default value which can be changed after the restraints are created.

c.       Add residue restraints – if the phase is a ‘macromolecule’ then develop the restraints from a selected ‘macro’ file based on those used in GSAS for this purpose. A file dialog box is shown directed to /GSASIImacros; be sure to select the correct file.

d.      Plot residue restraints – if the phase is a ‘macromolecule’ and the restraint type is either ‘Torsion restraints’ or ‘Ramachandran restraints’, then a plot will be made of the restraint distribution; torsions as 1-D plots of angle vs. pseudopotential energy and Ramachandran ones as 2-D plot of psi vs phi. In each case a dialog box will appear asking for the residue types or specific torsion angles to plot. Each plot will show the observed distribution (blue) obtained from a wide variety of high resolution protein structures and those found (red dots) for your structure. The restraints are based on a pseudopotential (red curve or contours – favorable values at the peaks) which has been developed from the observed distributions for each residue type.

e.       Change value – this changes the ‘obsd’ value for selected restraints; a dialog box will appear asking for the new value.

f.        Change esd – this changes the ‘esd’ value for selected restraints; a dialog box will appear asking for the new value.

g.      Delete restraints – this deletes selected restraints from the list. A single click in the blank box in the upper left corner of the table will select/deselect all restraints.

Rigid bodies

This window shows the rigid body models that have been entered into GSAS-II for this project. There are two tabs; one is for vector style rigid bodies and the other is for flexible “Residue” rigid bodies. Note that these rigid bodies must be inserted into one of the phases before it can take effect in the crystal structure description.

What can I do here?

1.      Select the tab for the rigid body type you wish to use. Each will have the different possibilities in the ‘Edit’ menu depending on whether a rigid body has been defined.

2.      Menu ‘Edit’ – the entries listed below depend on which type of rigid body is selected.

a.      Add rigid body – (Vector rigid bodies) this creates a vector description of a rigid body. A dialog box asks the number of atoms (>2) and the number of vectors required to create the rigid body. An entry will be created showing a magnitude with the vector set to be applied for each vector needed to develop the rigid body.

b.      Import XYZ – (Residue rigid bodies) this reads a text file containing a set of Cartesian coordinates describing a rigid body model. Each line has atom type (e.g. C, Na, etc.) and Cartesian X, Y and Z.

c.       Define sequence – (Residue rigid bodies) this defines a variable torsion angle in a sequence of dialog boxes. The first one asks for the origin and the second asks for the pivot atom for the torsion from the nearest neighbors to the origin atom; the atoms that ride on the selected torsion are automatically found from their bond lengths.

d.      Import residues – (Residue rigid bodies) this reads a predetermined macro file that contains standard (Engh & Huber) coordinates for the amino acids found in natural proteins along with predetermined variable torsion angle definitions.

3.      Once a rigid body is defined you can plot it, change its name or manipulate any torsion angle to see the effect on the plot.

4.      The translation magnitudes in a vector rigid body can be refined.

Sequential refinement results

This tree entry is available after a sequential refinement has been run. (See the Controls tree item to set the histograms to be used in a sequential refinement and use the Calculate/Sequential refine menu command to run the refinement.) When this is selected, the window tabulates the sequential refinement results. The columns are the parameter names; the naming convention is ‘p:h:name:n’ where ‘p’ is the phase number,’ h’ is the histogram number, ‘name’ is the parameter name, and ‘n’ (if needed) is the item number (e.g. atom number). The rows are the data sets used in the sequential refinement.

What can I do here?

1.      Select a row – this will display the variance-covariance matrix for the refinement with that data set.

2.      Select a column – this will display a plot of that parameter across the sequence of data sets. Error bars for each value are also shown.

3.      Menu ‘Background’ –

a.       Save – this will create a text file of selected columns with values and corresponding esds. A file dialog box will appear; give a suitable file name; you may change directory if desired.

6. Histogram data tree items

These are shown in the data tree with a prefix of ‘PWDR’, ’HKLF’, ‘IMG’, or ‘PDF’ and usually a file name. These constitute the data sets (‘Histograms’) to be used by GSAS-II for analysis. Selection of these items does not produce any information in the data window but does display the data in the Plots Window. They are described below.

6A. Powder Histograms - type PWDR

When a powder diffraction dataset (prefix ‘PWDR’) is selected from the data tree the dataset is plotted. The observed data points are shown as blue crosses and where fit, the calculated pattern is shown as a green line; the background is shown as red line. The difference curve is shown as a cyan line. Reflection positions are shown with small vertical lines.

Each powder diffraction dataset has a number of children in the tree as are shown below. Clicking on any of them produces changes in the plot and allows access to different parameters associated with the dataset.

·         Comments

·         Limits

·         Background

·         Instrument Parameters

·         Sample Parameters

·         Peak List

·         Index Peak List

·         Unit Cells List

·         Reflection Lists

What can I do here?

Menu Commands

a.       a. Error Analysis – this produces a ‘normal probability’ plot for the refinement result as bounded by the limits. The slope and intercept of the curve in the central region (-1 < / < 1) are shown on the plot status line. The slope is the square root of GOF for the best fit set of data points (~68% of the data).

What is plotted here?

The powder patterns that are part of your project are shown on this page. They can be displayed as a stack of powder patterns, just a single pattern or as a contour image of the peak intensities. What can be done here will depend on home many patterns are shown as well as what mode is selected. Note that the tick marks and difference curve positions can be customized, as discussed below.

Similar plots to the one here are displayed when different subtree items are selected and on those plots it is possible to view and in some cases edit information associated with the histogram. As examples:

·         By selecting the Limits entry, range of data used, as well as possible excluded regions, can be set.

·         Selecting Reflection Lists allows display of reflection indicies (hkl values) for a selected phase. Letting the mouse rest unmoved at the position of a reflection in 2-theta, Q, etc. (the vertical position does not matter) will cause these to be displayed. After a short delay a "tool tip" will appear with indicies for any reflections close to the lateral mouse position.

·         Selecting Background allows a mouse to be used to define fixed points where a background curve can be fitted to those points.

·         Selecting Instrument Parametersdisplays plot of peak widths as a function of 2theta or Q.

·         Selecting Peak List allows postions of peaks to be defined for use in direct peak fitting.

·         Selecting Unit Cells List can show the positions of reflections for an arbitrary set of unit cell parameters, optionally with space group extinctions applied.

What can I do with the plot?

Move mouse

As the mouse cursor is moved across the plot, the plot status line will show the cursor position as 2Theta, d-spacing and the intensity. For a Q-plot, Q is shown instead of 2Theta.

Press keyboard keys

See below. The "s" and "w" modes are commonly used.

Drag tickmarks

Click on any tick mark and while holding the left mouse button down move them to where you want them to be displayed (press the s key for Sqrt(I) mode to reset to the defaults). With multiple phases, clicking on the 2nd phase, etc. changes the vertical spacing between phases. Tick marks can be dragged only when the main PWDR or Reflection Lists tree items are selected.

Drag the difference curve

When the "normal" obs-calc plot is shown (as opposed to the preferred "w" mode plot where (obs-calc)/sigma is displayed, click on any point in the difference curve and while holding the left mouse button down move the curve to where you want it to be displayed (press the s key for Sqrt(I) mode to reset it to the default). The difference curve can be dragged only when the main PWDR or Reflection Lists tree items are selected.

Display/edit histogram information

By selecting different tree items within the current histogram, it is possible to display and in some cases edit information associated with the histogram. See above.

Create a Publication-ready plot

Press the green "P" button to generate a customizable version of the displayed plot that can be exported at high resolution.

The following key press characters are defined (not for all plot modes). These actions can also be initiated from the Key Press button on the plot toolbar.

For line plots:

s: Sqrt(I) on/off

changes the y-axis to be the square-root of the intensity. The tick mark and the difference curve location is reset.

w: toggle diff plot mode

for the pattern selected from the data tree, this will replace the difference (obs-calc) curve with the differences divided by their standard uncertainty (esd) values [(obs-calc)/sigma], which shows the significance of the deviations in the fit of the pattern. (Recommended).

b: subtract background

Subtracts the fitted background from the powder pattern. Pressing this again turns the mode off.

n: log(I) on/off

changes the y-axis to be the log10 of the intensity; difference curve is not shown for log(I) on.

q: toggle Q plot

changes the x-axis from 2Theta to Q. This will put multiple powder patterns taken at different wavelengths/types on the same x-axis scale.

t: toggle D-space plot

changes the x-axis from 2Theta to d-space. This will put multiple powder patterns taken at different wavelengths/types on the same x-axis scale. May not be very useful with data over a wide range.

e: set excluded region

Defines a new excluded region: press the "e" key with the mouse on one side of the region. Move the mouse to the other side and and press "e" again. The region markers (magenta dashed lines) can be dragged to new positions. Available only when the Limits tree entry is selected.

x: show excluded region

Normally all observed data is plotted. When the "x" key is pressed, data inside excluded regions are not shown.

.: scaling diagnostic

When the '.' key is pressed, data are plotted where the intensity scale shows the equivalent number of counts so that uncertainty on each point is the sqrt(I).

g: grid lines

Draws vertical and horizontal grid lines at all axis label positions.

a: add magnification region

Adds a magnification region to the plot and sets the magnification amount to x2. This can be edited (or deleted) in the table that is shown when the main PWDR tree entry is selected.

For line plots with more than one powder pattern:

c: contour on/off

if multiple powder profiles, then a contour plot is shown of the observed intensities. All data sets must be the same length as the first one to be included in the contour plot.

S: set color Scheme

Select the color map used for contour plots

m: toggle single/multiple plot

for multiple powder profiles, this will show only the one selected from the data tree. The offset options (below) are not active.

f: select data

Allows only some powder patterns to be plotted, rather than all.

+,=: no selection

for multiple powder profiles, only the observed curve is shown when this mode is turned on ('+' and '=' do exactly the same thing).

/: normalize

for multiple powder profiles, all diffraction datasets are normalized so that the maximum intensity is 1.

Offset modes for line plots in waterfall mode (multiple patterns only):

l: offset left

for a waterfall plot of multiple powder profiles, increase the offset so that later plots are shifted more to the left relative to previous plots.

r: offset right

for a waterfall plot of multiple powder profiles, increase the offset to the right (or decrease the left offset.)

d,D: offset down

for a waterfall plot of multiple powder profiles, increase the offset down. (D does the same as d but to a much larger amount)

u,U: offset up

for a waterfall plot of multiple powder profiles, increase the offset up. (U does the same as u but to a much larger amount)

o: reset offset

for a waterfall plot of multiple powder profiles, reset to no offset.

For contour plots:

d: lower contour max

this lowers the level chosen for the highest contour color.

u: raise contour max

this raises the level chosen for the highest contour color

i: interpolation method

this changes the method used to represent the contours. If selected a dialog box appears with all the possible choices. Default is ‘nearest’; the other useful choice is ‘bilinear’, this will smooth out the contours.

s: color scheme

this changes the color scheme for the contouring. Default is ‘Paired’, black/ white options are ‘Greys’ and ‘binary’ (for black on white) or ‘gray’ (for white on black). Others can be very colorful (but not useful!)

c: contour off/on

this turns off contouring and returns to a waterfall plot with any offsets applied.

For display of reflections from magnetic unit space groups

j: show next; reset use flag

Show the next magnetic space group in the list, clearing the "Use" flag for the currently displayed space group. (available from Index Unit Cells only).

k: show next

Show the next magnetic space group in the list. The "Use" flag for the currently displayed space group is unchanged. (available from Index Unit Cells only).

Comments

This window shows whatever comment lines (preceded by “#”) found when the powder data file was read by GSAS-II. If you are lucky, there will be useful information here (e.g. sample name, date collected, wavelength used, etc.). If not, this window will be blank. The text is read-only.

Limits

This window shows the limits in position to be used in any fitting for this powder pattern. The ‘original’ values are obtained from the minimum & maximum values in the powder pattern. The ‘new’ values determine the range of data that will be used in fitting. Units are 2Theta for CW data and time (microsec) for TOF data.

What can I do here?

You can change the "new" values for Tmin and Tmax as needed. Change the upper and lower Tmin values by clicking on the appropriate vertical line and dragging it to the right or left or by typing values into the data window.

Menu ‘Edit Limits’

Copy

this copies the limits shown to other selected powder patterns. If used, a dialog box (Copy Parameters) will appear showing the list of available powder patterns, you can copy the limits parameters to any or all of them; select ‘All’ to copy them to all patterns. Then select ‘OK’ to do the copy; ‘Cancel’ to cancel the operation.

Add Exclude

Select this menu item and click on a data point. A pair of magenta lines is drawn to indicate a range that should be excluded. (No green solid line with the computed pattern is shown for those data). The magenta lines can be dragged, as described below for setting data limits.

What is plotted here?

The plot is the same as for Powder Histograms - type PWDR and the key press commands are all the same. However, two vertical lines are displayed, green for the lower Tmin value and red for the upper Tmin value. These can be dragged to set limits.

What can I do with the plot?

The upper and lower Tmin values can be changed by clicking on the appropriate vertical line and dragging it to the right or left.

Background

This window shows the choice of background functions and coefficients to be used in fitting this powder pattern. There are three types of contributions available for the background:

1). A continuous empirical function (‘chebyschev’, ‘chebyschev-1’, ‘cosine’, ‘lin interpolate’, ‘inv interpolate’ & ‘log interpolate’). The latter three select fixed points with spacing that is equal, inversely equal or equal on a log scale of the x-coordinate. The set of magnitudes at each point then comprise the background variables. All are refined when refine is selected. Note that ‘chebyschev-1' is a better choice than ‘chebyschev’.

2). A set of Debye diffuse scattering equation terms of the form:

where A,R & U are the possible variables and can be individually selected as desired; Q = 2π/d.

3). A set of individual Bragg peaks using the pseudo-Voigt profile function as their shapes. Their parameters are ‘pos’, ’int’, ‘sig’ & ‘gam’; each can be selected for refinement. The default values for sig & gam (=0.10) are for very sharp peaks, you may adjust them accordingly to the kind of peak you are trying to fit before trying to refine them.

What can I do here?

1.      Menu ‘Background’ –

a.       Copy – this copies the background parameters shown to other selected powder patterns. If used, a dialog box (Copy Parameters) will appear showing the list of available powder patterns, you can copy the background parameters to any or all of them; select ‘All’ to copy them to all patterns. Then select ‘OK’ to do the copy; ‘Cancel’ to cancel the operation.

b.      Copy flags – this copies only the refinement flags shown to other selected powder patterns. If used, a dialog box (Copy Refinement Flags) will appear showing the list of available powder patterns, you can copy the refinement flags to any or all of them; select ‘All’ to copy them to all patterns. Then select ‘OK’ to do the copy; ‘Cancel’ to cancel the operation.

2.      You can select a different Background function from the pull down tab.

3.      You can choose to refine/not refine the background coefficients.

4.      You can select the number of background coefficients to be used (1-36).

5.      You can change individual background coefficient values. Enter the value then press Enter or click the mouse elsewhere in the Background window. This will set the new value.

6.      You can introduce one or more Debye scattering terms into the background. For each one you should enter a sensible value for ‘R’ – an expected interatomic distance in an amorphous phase is appropriate. Select parameters to refine; usually start with the ‘A’ coefficients.

7.      You can introduce single Bragg peaks into the background. For each you should specify at least the position. Select parameters to refine; usually start with the ‘int’ coefficients.

What is plotted here?

The plot is the same as for Powder Histograms - type PWDR and the key press commands are largerly the same. Specific to this plot are fixed background points. These can be added, deleted and moved. Once that is done the background parameters for the selected function can be fitted to the fixed points.

Instrument Parameters

This window shows the instrument parameters for the selected powder data set. The plot window shows the corresponding resolution curves. Solid lines are for the default values (in parentheses), dashed lines from the refined values and ‘+’ for individual entries in the ‘Peak_List’.

What can I do here?

1.      Menu ‘Operations’ –

a.       Load profile… - loads a GSAS-II instrument parameter file (name.instprm), replacing the existing instrument parameter values. All refinement flags are unset.

b.      Save profile… - saves the current instrument parameter values in a simple text file (name.instprm); you will be prompted for the file name – do not change the extension. This file may be edited but heed the warning to not change the parameter names, the order of the parameter records or add new parameter records as this will invalidate the file. You may only change the numeric values if necessary. You can change or add comment records (begins with ‘#’).

c.       Reset profile – resets the values for the instrument parameters to the default values shown in parentheses for each entry.

d.      Copy – this copies the instrument parameters shown to other selected powder patterns. If used, a dialog box (Copy parameters) will appear showing the list of available powder patterns, you can copy the instrument parameters to any or all of them; select ‘All’ to copy them to all patterns. Then select ‘OK’ to do the copy; ‘Cancel’ to cancel the operation. The copy will only work for instrument parameters that are commensurate with the one that is shown, e.g. single radiation patterns will not be updated from K_a1/K_a2 ones.

e.       Copy flags - – this copies the instrument parameter refinement flags shown to other selected powder patterns. If used, a dialog box (Copy refinement flags) will appear showing the list of available powder patterns, you can copy the instrument parameter refinement flags to any or all of them; select ‘All’ to copy them to all patterns. Then select ‘OK’ to do the copy; ‘Cancel’ to cancel the operation. The copy will only work for instrument parameters that are commensurate with the one that is shown, e.g. single radiation patterns will not be updated from K_a1/K_a2 ones.

2.      You can change any of the profile coefficients

3.      You can choose to refine any profile coefficients. NB: In certain circumstances some choices are ignored e.g. Zero is not refined during peak fitting. Also some choices may lead to unstable refinement, e.g. Lam refinement and lattice parameter refinement. Examine the ‘Covariance’ display for highly correlated parameters.

What is plotted here?

This plot shows the contributions to the powder pattern peak widths as delta-Q/Q (=delta-d/d) vs. Q for the Gaussian and Lorentzian parts of the profile function, in addition to the overall widths. The solid curves are based on the default values of U, V, W, X and Y shown in the Instrument Parameters window (shown in parentheses; these are the values for the instrument contribution that were set when the powder pattern was first read in to GSAS-II.) The dashed values are based on the refined values, if different. If individual peak fitting has been performed, the values of ‘sig’ & ‘gam’ for those peaks are plotted as ‘+’; these are computed from the fitted values of U, V, W, X and Y as well as any sig or gam values that are individually refined.

Sample Parameters

This window shows the various sample-dependent parameters for the selected powder pattern. The presence of a refine button indicates that a parameter can be refined (all others are fixed.) All values shown in this window can be edited. Note that the last three parameters (named FreePrmX, X=1,2,3) have labels that can be changed. If changed in one histogram, the same label is used for all histograms. When a label is changed, the Comments tree item for each PWDR histogram is searched for a matching "Label=value" pair (differences in letter case between the two label strings is ignored). When found, the value is converted to a float and saved as the appropriate Sample Parameter. NB: for powder data be sure the correct instrument type is selected (Debye-Scherrer or Bragg-Brentano).

What can I do here?

Command Menu items

In this window you can change parameters associated with a histogram or set them to be refined. The histogram scale factor is usually refined. For Debye-Scherrer mode the "Sample X displacement" is also ususally refined but the "Sample Y displacement" can only be refined when data are collected over a two-theta range that extends to greater than ~140 degrees (typically for CW Neutron). Sample absorption should not be refined when all atomic displacement parameters (Uiso or Uaniso values) are varied, as the correlation is very high. For Bragg-Brentano, "Sample displacement" is usually refined and for low-Z samples "Sample transparency" is usually refined. "Surface roughness" parameters are not usually refined. Remaining parameters are of use for texture or parametric studies and may be changed with the menu commands described here.

Set scale

Rescales a pattern by multiplying by the current scale factor.

Load

This loads sample parameters from a previously saved .samprm file.

Save

This saves the sample parameters to a file with the extension ’.samprm’. A file dialog box will appear to ask for the name of the file to be written.

Copy

This copies the sample parameters shown to other selected powder patterns. If used, a dialog box (Copy parameters) will appear showing the list of available powder patterns, you can copy the sample parameters to any or all of them; select ‘All’ to copy them to all patterns. Then select ‘OK’ to do the copy; ‘Cancel’ to cancel the operation.

Copy selected...

This copies only the sample parameter that are selected to other selected powder patterns, but is otherwise similar to "Copy".

Copy flags

This copies the sample parameter refinement flags shown to other selected powder patterns. If used, a dialog box (Copy refinement flags) will appear showing the list of available powder patterns, you can copy the sample parameter refinement flags to any or all of them; select ‘All’ to copy them to all patterns. Then select ‘OK’ to do the copy; ‘Cancel’ to cancel the operation.

Set one value

This is used to set a single selected sample parameter for a selected set of PWDR histograms. The same value can be used for all histograms or a dialog can be used to provide a table where you can set the values differently for each of selected histograms.

Load all

Reads a file containing a table of sample parameters and copies them to matching PWDR entries. The file will look something like the example here:

#filename       temperature pressure ignore-me  humidity

LaB6_dc250.tif      100          1      test       .2

LaB6_dc300.tif      150          1      test       .25

Note that the first line(s) in the file can be a header, but each header line must start marked with a hash (#). A header is not required. "Columns" in the table are separated by one or more delimiters (which may be a comma, tab or space). Note that columns do not need to be aligned, as long as each entry is spaced by at least one delimiter. The first column in the table is used to look up PWDR entries where the initial space-delimited string after the PWDR tag ("myfile" in "PWRD myfile AZM=180...") must match the table. Subsequent columns can then be mapped to sample parameters or can be ignored, using a dialog window.

Rescale all

Allows a series of selected PWDR histograms to be put on a common scale by integrating them over a specific two-theta region and then scaling them so that the integration range will match the first pattern.

Peak List

The Peak List data tree entry is used to fit diffraction peaks at user-supplied positions (not generated from a unit cell). Peak positions and intensities may be selected for individual refinement. Gaussian (sigma) and Lorentzian (gamma) peak widths may be varied individually or the values may be generated from the U,V & W (sigma) and X & Y (gamma) values in the Instrument Parameters tree item: If individual values are refined, then the value in the table is used. If values are not refined, then those determined by U,V & W and/or X & Y are placed in the table and are used. Likewise, the background is generated using the parameters in the Background data tree entry and the range of data used in the fit is set from the Limits tree item. Note that optionally the parameters on the Background and in the Instrument Parameters tree items may be refined as peak settings are fitted.

What can I do here?

There are three ways to interact with Peak List data tree item: through its menu, labeled Peak Fitting, through interaction with the peak list table, and through interactions with the plot.

The following interactions are available with the peak table:

·  You can change individual peak coefficient values. Enter the value then press Enter or Tab or click the mouse elsewhere in the Peak List window. This will set the new value.

·  You can change the individual refine flags either by clicking on the check boxes.

·  You can change all refine flags in a column by clicking on a single one and then click on the column label above. The entire column should be highlighted in blue. Type ‘y’ to set the refine flags or ‘n’ to clear the flags. This can also be done by double-clicking on the column label, which brings up a menu.

·  You can delete peaks in the Peak List by selecting a row by clicking on the row label to the left (multiple selection of rows is allowed). Selected rows will be highlighted in the plot (see below). Then press the Delete or backspace key. (Note that peaks can also be deleted from the plot, see below.)

·  You can highlight a peak by clicking or double-clicking on the row label (to the left) for a peak. The color of the line will change from blue to green.

The Peak Fitting menu contains the following commands:

Set sel. ref flags

If one or more row of peaks are selected by clicking on the peak label to the left, this menu item can be used to set the refinement flags for the selected reflections.

Set all ref flags

This sets refinement flags for all peaks in the table.

Auto search

This fills the table with peak positions. These are selected based on peak tops that are substantially above background. Noisy data will give spurious peaks and small peaks or shoulders will not be found. Examine results & modify as needed.

UnDo

Resets peak parameters, background and instrument parameter values varied in the last peak fitting refinement back to their original values. Use this to recover from a failed refinement. Note: only one previous refinement is saved, so this cannot be pressed twice to return to the refinement before the previous.

PeakFit

Performs a least squares fit of the peaks in Peak List to the data. Any peak parameters, background parameters and instrument parameters with refine checked will be varied in this refinement. The refinement will proceed until convergence. We suggest you vary the intensity along with the background first (the default), then vary the position and instrument parameters after. The order will depend on how poor is the initial estimate of the instrument parameters (U, V, W, X, Y & SH/L). To determine how to proceed, examine in detail the powder pattern difference curve displayed in the GSASII Plots window. If individual peaks show peak widths that are widely different, their individual sigma and gamma parameters may be refined. If the refinement results in negative peak coefficients, these will be highlighted in red. If this happens, you should use the UnDo menu item (above) to return to the refinement and reconsider your choice of parameters to be varied.

LSQ one cycle

Perform a single cycle of least squares refinement. This can be used in difficult cases to get a refinement started toward convergence.

Reset sig and gam

This resets the values of sigma and gamma in the table to those computed from the instrument parameters U, V, W, X & Y.

Peak copy

Copy the current set of peaks to other histogram(s)

Seq PeakFit

Fit peaks for multiple histograms

Clear peaks

This removes all the peaks from the Peak List.

Move selected peak

A peak may be moved using the following process: select it in the table by clicking on its label (to left), use this menu item. The peak line will then follow movement of the mouse in the plot window. Click with the left mouse button to set a new position. Click with the right mouse button to delete that peak. Click outside the axes to abort the move and return to the previous position. (Note that peak movement is also possible with the plot window, see below.)

What is plotted here?

The plot window shows the observed and computed patterns, as well as the background and peak positions. Observed points are shown as blue crosses (+) and the fitted pattern is shown as a solid green line. The background is shown as a red line and the difference curve is shown as a cyan (turquoise) line, below the observed and computed pattern. Peak positions are shown as vertical blue lines (or green when selected). The upper and lower data limits are shown as red and green dashed vertical lines, respectively.

What can I do with the plot?

For all actions involving mouse clicks such as those below, be sure that the Zoom/Pan buttons are not selected on the Plot window, as the mouse clicks will be used for zooming or panning, not the desired action.

·  You can add peaks to the Peak list using the mouse on the plot by: position the cursor pointer onto a cross for an observed point and pressing the left mouse button. The selected peak will be added to the Peak List in the appropriate position to keep peaks sorted and a blue vertical line will be plotted on that position. We recommend that you begin picking peaks from the right side of the pattern; that way the tool tip won’t be in your way as you select peaks.

·  You can delete peaks using the mouse on the plot by positioning the pointer on the blue line for the peak to be deleted and then pressing the right mouse button. The blue line should vanish and the corresponding peak will be removed from the Peak List.

·  You can move a Peak List item using the mouse on the plot by: position the pointer on the blue line for the peak you wish to move and then hold the left mouse button down, dragging the line to the desired position. When the mouse button is released, the peak line will be drawn in the new position.

·  The fit limits can be changed without selecting the Limits item in the data tree from the plot. Change the upper and lower Tmin values by clicking on the appropriate vertical line and dragging it to the right or left.

Index Peak List

This window shows the list of peaks that will be used for indexing (see Unit Cells List). It must be filled before indexing can proceed. When indexing is completed, this display will show the resulting hkl values for every indexed reflection along with the calculated d-spacing (‘d-calc’) for the selected unit cell in Unit Cells List. .

What can I do here?

1.      Menu ‘Operations’ – Load/Reload – loads the peak positions & intensities from the Peak List to make them available for the indexing routine. The d-obs is obtained from Bragg’s Law after applying the Zero correction shown on the Instrument Parameters table to the position shown here.

2.      You may deselect individual peaks from indexing by unchecking the corresponding ‘use’ box.

Unit Cells List

This tree item has several purposes, it can be used to perform autoindexing and it can be used to show the positions of peaks from unit cells which may be results from autoindexing or may be entered from a phase or manually. It can be used to refine unit cell parameters. It can also be used to search for cells/symmetry settings related to a specified unit cell & space group.

What can I do here?

For autoindexing, the peaks in the Index Peak List are used. Select one or more Bravais lattice types to use and use the "Cell Index/Refine"/"Index Cell" menu command to start indexing. Output will appear on the console and a progress bar dialog will appear which tracks trial volume. A Cancel button will terminate indexing; it may need to be pressed more than once to fully terminate the indexing process. Console output shows possible solutions with a computed M20 for each; good solutions are indicated by high M20 values. X20 gives number of unindexed lines out of the 1^st 20 lines and Nc gives total number of reflections generated for each solution.

The "Copy Cell" menu commnd copies a selected solution to the Unit cell values; the Bravais lattice shown for the choice is copied. Press Show hkl positions to generate the allowed reflection positions, which are visually superimposed on the displayed powder pattern to visually confirm the indexing. Pay particular attention to any unmatched peaks in the pattern. A Space group can be from the pulldown box to remove reflections based on space group extinctions and visually eliminate possiblities.

1.      Max Nc/Nobs: – this controls the extent of the search for the correct indexing. This may need to be increased if an indexing trial terminates too quickly. It rarely needs to be changed.

2.      Start Volume: – this sets an initial unit cell volume for the indexing. It rarely needs to be changed.

3.      Select "keep" in the table for a cell that should be preserved when an additional indexing run is tried; all without that are erased before the indexing trial begins.

To display a unit cell, optionally with space group extinctions, set a Bravais class to determine a unit cell type (see list below), optionally select a space group (by default the lowest symmetry space group for the class is selected) and enter the unit cell contents. Or use the "Cell Index/Refine"/"Load Phase" menu command to read this information from a phase that has been read into a project or from a file (such as a CIF) using the "Cell Index/Refine"/"Import Cell" menu command.

For symmetry exploration, once a phase/cell has been loaded, use the "Run SUBGROUPS", "Cell Symmetry Search" or "Run k-SUBGROUPSMAG" commands from the "Cell Index/Refine" menu. These commands look for: subgroups, higher symmetry cells or magnetic subgroups, respectively. Also note the "Transform Cell" commnd in that menu that can perform namy common lattice transformations, apply a user-supplied cell transformation or create a magnetic phase.

To optimize a cell, to fit the peaks in the Index Peak List, use the "Cell Index/Refine"/"Refine Cell" menu command. The results will be placed in the Indexing Result table with ‘use’ selected.

Other: The "Make new phase" command creates a new phase from the selected unit cell and chosen space group. A dialog box will appear asking for a name for this phase. See the new entry under Phases and the new lattice parameters will be in the General window for that phase.

GSAS-II Laue classes (note that some redundant entries are included for convenience.)

·         Cubic: Fm3m, Im3m & Pm3m

·         Rhombohedral: R3-H (hexagonal axes)

·         Hexagonal: P6/mmm

·         Tetragonal: I4/mmm, P4/mmm

·         Orthorhombic: Fmmm, Immm, Ammm, Bmmm, Cmmm, Pmmm

·         Monoclinic: I2/m, C2/m, P2/m (b-unique)

·         Triclinic: P1, C1

Reflection Lists

This window shows the reflections for the selected phase (selected by the tab at top) found in this powder data set. It is generated by a Rietveld (including Pawley and LeBail) refinements. Reflection d-spaces are generated directly from lattice parameters but 2θ values will incorporate corrections, such as for sample displacement, zero, etc.

The indicies (hkl values) for reflections can be displayed by letting the mouse rest at the position of a reflection in 2-theta, Q, etc. (the vertical position does not matter). After a short delay, a "tool tip" will be displayed for any reflections close to the lateral mouse position.

What can I do here?

1.      Menu ‘Reflection List’ –

a.       Select phase – if there is more than one phase; you can select another phase; the window title will show which phase is shown.

6B. Single Crystal Histograms – type HKLF

Instrument Parameters

This window shows the histogram type (SXC or SNC) and the wavelength. You may change the wavelength but rarely will need to do so.

HKL Plot Controls

This controls the display of the single crystal reflections on the plot. If available a green ring is shown for F-observed, a blue ring for F-calculated and a central disk for ΔF (green for Fo>Fc and red for Fo<Fc).

What can I do here?

1.      Change the scale – move the slider, the rings will change their radius accordingly.

2.      Select the zone – select between 100, 010 or 001; plot axes will be labeled accordingly.

3.      Select plot type – the choices are either F or F², ΔF²/σ(F²), ΔF²>σ(F²) or ΔF²>3σ(F²).

4.      Select layer – move the slider for upper layers for the selected zone.

Reflection List

This window shows the reflections for this single crystal data set.

6C. Pair Distribution Functions - type PDF

A PDF entry is created from a powder histogram (PWDR entry) using the Setup PDFs entry in the Calculate menu. The main PDF data tree item displays the same window as the PDF Controls, below. When this item is selected, the S(Q) function is plotted, see below.

PDF Controls

This window provides parameters for computing the pair distribution function [PDF, G(r)] from the I(Q) function. This can only be done when a chemical formula and appropriate control values are provided. If so, clicking on this menu item causes the I(Q), S(Q), F(Q) and G(R) functions to be plotted, as described below.

The Optimize PDF button can be used to refine the values of the "Flat Bkg", "Background ratio" and "Ruland width" parameters to best agree with the -4*pi*r line that is plotted for r < Rmin. Rmin should be set to a distance below the shortest expected interatomic distance for the material.

What can I do here?

The PDF parameters can be changed, triggering recomputation of the I(Q), S(Q), F(Q) and G(R) functions. Available menu commands are:

Add element

Adds a new element to the chemical formula by clicking on a periodic table. Note that the number of atoms of this type in the empirical formula must still be entered.

Delete element

Removes a previously-entered element from the chemical formula.

Copy Controls

Copies the current PDF control values to other PDF data entries

Load Controls

Replaces the current PDF control values with values read from a file (see Save controls).

Save Controls

Saves the current PDF control values into a file.

Compute PDF

Recomputes the PDF for the current entry. This is usually done automatically when values are changed, but if not this can be forced with this menu item.

Compute all PDFs

Recomputes the PDFs for all selected PDF entries. This is usually done after Copy Controls is used. By default PDFs are optimized to reduce the low G(r) region, but this can be turned off.

What is plotted here?

When a chemical formula and appropriate control values are provided, clicking on this menu item causes the I(Q), S(Q), F(Q) and G(R) functions to be plotted, as described separately, below.

What can I do with the plot?

For each of the plots, the following keyboard shortcuts are available:

For line plots with more than one powder pattern:

c: contour on/off

if multiple PDFs are available, then a contour plot is shown for the displayed function. All data sets must be the same length as the first one to be included in the contour plot.

m: toggle multiple plot

for multiple PDFs, this will show only the one selected from the data tree. The offset options are not active. Or all selected items will be plotted on a single axis.

s: toggle single plot

for multiple PDFs, this will show only the one selected from the data tree. The offset options are not active. Or all selected items will be plotted on a single axis.

f: select data

Allows only some PDFs to be plotted, rather than all.

t: toggle legend

provides a legend with the line type and name for each PDF.

For line plots in waterfall mode (multiple patterns are shown) these key press items are defined:

t: toggle legend

provides a legend with the line type and name for each PDF.

l: offset left

for a waterfall plot of multiple powder profiles, increase the offset so that later plots are shifted more to the left relative to previous plots.

r: offset right

for a waterfall plot of multiple powder profiles, increase the offset to the right (or decrease the left offset.)

d: offset down

for a waterfall plot of multiple powder profiles, increase the offset down.

u: offset up

for a waterfall plot of multiple powder profiles, increase the offset up.

o: reset offset

for a waterfall plot of multiple powder profiles, reset to no offset.

I(Q) Function

This shows the I(Q) function. See the PDF Controls for information on menu commands and plot options,

S(Q) Function

This shows the S(Q) function. See the PDF Controls for information on menu commands and plot options,

F(Q) Function

This shows the F(Q) function. See the PDF Controls for information on menu commands and plot options,

G(r) Function

This shows the PDF, G(r) function. See the PDF Controls for information on menu commands and plot options,

6D. 2-D Images – type IMG

Comments

This window shows whatever comment lines found in a “metadata” file when the image data file was read by GSAS-II. If you are lucky, there will be useful information here (e.g. sample name, date collected, wavelength used, etc.). If not, this window will be blank. The text is read-only.

Image Controls

This window displays calibration values needed to convert pixel locations to two-theta and azimuth. Also shown are controls that determine how integration is performed.

Menu command for this window are used to perform calibration (fitting the calibration values from a diffraction pattern image taken with a calibrant) and for integration. Other menu commands allow the values on the window to be saved to a file, read from a file or copied to other images. The "Xfer Angles" menu command scales the current integration range for other images located at different detector distances.

Masks

Image masks are used designate areas of an image that should not be included in the integration, typically used due to detector irregularities, shadows of the beamstop, single-crystal peaks from a mounting, etc. Masks can be created with a menu command or with keyboard/mouse shortcuts. There are five types of masks:

1.      Spot masks: occlude a circle with a selected center and diameter in image coordinates (mm).

2.      Ring masks: occludes a specific Bragg reflection (a ring placed relative to the image center). The location and thickness of the ring are specified in degrees 2-theta.

3.      Arc masks: occlude a section of a Bragg reflection, similar to a ring mask, except that in addition to the location and thickness of the ring, the mask has a starting and ending azimuthal angle.

4.      Polygon masks: occlude an arbitary region created by line segments joining a series of points specified in image coordinates (mm). Pixels inside the polygon mask are not used for integration.

5.      The Frame mask: occludes an arbitary region created by line segments joining a series of points specified in image coordinates (mm). Typically a point is placed near each corner of the image. Only pixels inside the frame mask are used for integration. Only one frame mask can be defined.

What can I do here?

Masks of each type are created using the appropriate menu commands and then clicking as described in the section on "What can I do with the plot?" below, or by using keyboard shortcuts, also described in that section.

What is plotted here?

The image is shown, as described above. Note that The frame mask, if defined, is displayed in green, while the other types of masks are shown in red.

What can I do with the plot?

There are menu commands to create masks as well as keyboard shortcuts. If a menu command is used, then use left and right mouse clicks as described below.

1.      Spot masks:

Create Spot masks after a menu command by clicking on the location on the image that should be masked. There are also two ways to create spot masks with the keyboard:

o    Press the 's' key and then left-click successively on multiple locations for spot masks. Press the 's' key again or right-click* to stop adding spot masks.

o    Alternately, move the mouse to the position for a new spot mask and press the 't' key. (Note that this can be used while the plot is in Zoom or Pan mode.)

The default size for newly-created spot masks is determined by the Spot_mask_diameter configuration variable or 1.0 mm, if not specified.

Edit Spot mask location by left-clicking inside or on the edge the of the mask and then drag the spot mask to a new location.

Edit Spot mask radius by right-clicking* inside the mask and then dragging to change the mask size.

2.      Ring masks:

Create Ring masks with a menu command and then by left-clicking on the mask center; Or, by pressing the 'r' key and then left-clicking. (Right-click* to cancel.)

The default thickness for newly-created ring masks is determined by the Ring_mask_thickness configuration variable or 0.1 degrees (2theta) if not specified.

Edit Ring mask location by left-clicking on either the inner or outer circle and drag the circle to the new radius.

Edit Ring mask thickness by right-clicking* either on the inner or outer circle and drag the the circle change spacing between the inner and outer circle.

3.      Arc masks: occludes a section of a Bragg reflection, similar to a ring mask, except that in addition to the location and thickness of the ring, the mask has a starting and ending azimuthal angle.

Create Arc masks with a menu command and then by left-clicking on at the mask center; Or, by pressing the 'a' key and then left-clicking. (Right-click* to cancel.)

The default size for newly-created ring masks is determined by configuration variables
thickness: Ring_mask_thickness (0.1 degrees 2theta if not specified) and
azimuthal range: Arc_mask_azimuth (10.0 degrees if not specified.)

Edit Arc mask location by left-clicking on either the inner or outer circle and drag the circle to the new radius. Alternately, left-click on the upper or lower arc limit (the straight lines) and drag them to rotate the center of the arc azimuthal range to a new position.

Edit Arc mask thickness or range by right-clicking* either on the inner or outer circle and drag the the circle change spacing between the inner and outer circle. Alternately, right-click* on the upper or lower arc limit (the straight lines) and drag them to change the arc azimuthal range.

4.      Polygon masks: occludes an arbitary region created by line segments joining a series of points specified in image coordinates (mm). Pixels inside the polygon mask are not used for integration.

Create Polygon masks with a menu command and then by left-clicking successively on the vertices of the polygon shape surrounding pixels to be excluded. After the last point is defined, right-click* anywhere to close the mask. Alternately, press the 'p' key and then left-click, as before, to define the mask and right-click* anywhere to close the mask.

Edit Polygon mask by left-clicking on any point at a vertex in the polygon mask and drag that point to a new position. If the vertex is dragged to the same position as any other vertex in the mask the dragged point is deleted.

Add a point to Polygon mask by right-clicking* on any vertex and dragging. A new point is added to the mask immediately after the selected point at the position where the mouse is released.

5.      The Frame mask: occludes an arbitary region created by line segments joining a series of points specified in image coordinates (mm). Typically a point is placed near each corner of the image. Only pixels inside the frame mask are used for integration. Only one frame mask can be defined.

Create a Frame mask with a menu command and then by left-clicking successively on the vertices of a polygon. After the last point is defined, right-click* anywhere to close the frame mask. Alternately, press the 'f' key and then left-click, as before, to define the mask and right-click* anywhere to close the mask. Note that if a Frame mask already exists, using the 'f' key or the "Create Frame" menu item causes the existing frame mask to be deleted.

Edit the Frame mask by left-clicking on any point at a vertex in the frame mask and drag that point to a new position. If the vertex is dragged to the same position as any other vertex in the mask the dragged point is deleted.

Add a point to the Frame mask by right-clicking* on any vertex and dragging. A new point is added to the mask immediately after the selected point at the position where the mouse is released.

* Note that on a Mac with a one-button mouse, a right-click is generated by pressing the control button while clicking the mouse.

Stress/Strain

What can I do here?

...

What is plotted here?

...

What can I do with the plot?

...

6E. Powder Peaks – type PKS

6F. Small Angle Scattering – type SASD

7. Phase data tree items

When a phase is selected from the data tree, parameters are shown for that selected phase in a tabbed window. Clicking on each tab raises the windows listed below. Each tab is identified by the underlined phrase in the following:

General Phase Parameters

This gives overall parameters describing the phase such as the name, space group, the unit cell parameters and overall parameters for the atom present in the phase. It also has the controls for Pawley intensity extraction and for computing Fourier maps for this phase. It can also be used to compute new structures based on the unit cell and atom poistions.

What can I do here?

1.      Menu ‘Compute’ – The compute menu shows computations that are possible for this phase.

a.       Fourier maps

compute Fourier maps according to the controls set at bottom of General page.

Search maps

search the computed Fourier map. Peaks that are above ‘Peak cutoff’ % of the maximum will be found in this procedure; they will be printed on the console and will be shown in the ‘Map peaks’ page. This page will immediately be shown and the peaks will be shown on the structure drawing for this phase as white 3-D crosses.

Charge flipping

This performs a charge flipping ab initio structure solution using the method of Oszlanyi & Suto (Acta Cryst. A60, 134-141, 2004). You will need to select a source for the reflection set and perhaps select an element for normalization by its form factor, a resolution limit (usually 0.5A) and a charge flip threshold (usually 0.1); these are found at the bottom of the General window. A progress bar showing the charge flip residual is shown while the charge flip is in operation. When the residual is no longer decreasing (be patient – it doesn’t necessarily fall continuously), press the Cancel button to stop the charge flipping. The resulting map will be positioned to properly place symmetry operators (NB: depends on the quality of the resulting phases), searched for peaks and the display shifts to Map peaks to show them.

Clear map

This clears any Fourier/charge flip map from memory; the Fourier map controls are also cleared.

Transform

This allows for a change in axes, symmetry or unit cell. It is also used to create a magnetic phase from a chemical (nuclear) phase. One important transformation that can be done here is for Origin 1 settings to Origin 2 (described below)

 

2.      The items in the upper part of the General page that can be changed are Phase name, Phase type, Space group, unit cell parameters & refine flag. These are described in turn:

a.       Phase name – this is the name assigned to this phase. It should only be changed when the phase is initialized or imported.

b.      Phase type – this can only be set when there are no atoms in the Atoms page for this phase. Select it when the phase is initialized.

c.       Space group – this should be set when the phase is initialized; it can be changed later. Be careful about the impact on Atom site symmetry and multiplicity if you do. GSAS-II will recognize any legal space group symbol using the short Hermann-Mauguin forms; put a space between the axial fields (e.g. ‘F d 3 m’ not ‘Fd3m’). For space groups with a choice of origin (e.g. F d 3 m), GSAS-II always uses the 2^nd setting where the center of inversion is located at the origin. The choice of space group will set the available unit cell parameters.

d.      Refine unit cell – set this flag to refine the unit cell parameters in a Rietveld or Pawley refinement. The actual parameters refined are the symmetry allowed terms (A₀-A₅) in the expression

e.       a, b, c, alpha, beta, gamma – lattice parameters; only those permitted by the space group are shown. The volume  is computed from the values entered.

3.      If there are entries in the Atoms page then the Elements table is shown next on the General page; you may select the isotope (only relevant for neutron diffraction experiments). The density (just above the Elements) is computed depending on this choice, the unit cell volume and the atom fractions/site multiplicities in the entries on the Atoms page.

4.      Next are the Pawley controls.

a.       Do Pawley refinement? – This must be chosen to perform a Pawley refinement as opposed to a Rietveld refinement for this phase. NB: you probably should clear the Histogram scale factor refinement flag (found in Sample parameters for the powder data set) as it cannot be refined simultaneously with the Pawley reflection intensities.

b.      Pawley dmin – This is the minimum d-spacing to be used in a Pawley refinement. NB: be sure to set this to match the minimum d-spacing indicated by the powder pattern limits (see Limits for the powder data set).

c.       Pawley neg. wt. – This is the weight for a penalty function applied during a Pawley refinement on resulting negative intensities. Use with caution; initially try very small values (e.g. .01). A value of zero means no penalty is applied.

5.      Fourier map controls are shown next on the General page. A completed Rietveld or Pawley refinement is required before a Fourier map can be computed. Select the desired type of map, the source of the reflection set and the map resolution desired. The peak cutoff is defined as a percentage of the maximum and defines the lowest level considered in the peak search.

6.      Charge flip controls are below the Fourier map controls.

a.       Reflection set from – This is the source of structure factors to be used in a charge flip calculation. These may be either a single crystal data set, or structure factors extracted from a powder pattern via a Pawley refinement or a Rietveld refinement.

b.      Normalizing element – This is an element form factor chosen to normalize the structure factors before charge flipping. None (the default) can be selected from the lower right of the Periodic Table display shown when this is selected.

c.       Resolution – This is the resolution of the charge flip map; default is 0.5A. The set of reflections is expanded to a full sphere and zero filled to this resolution limit; this suite of reflections is then used for charge flipping.

d.      k-Factor – This is the threshold on the density map, all densities below this are charge flipped.

e.       k-Max – This is an upper threshold on the density may; all densities above this are charge flipped. In this way the “uranium solution” problem is avoided. Use k-Max = 10-12 for equal atom problems and larger for heavy atom ones.

7.      Monte Carlo/Simulated Annealing controls are at the bottom of the window. (Future capability & under development).

a.       Reflection set from – This is the source of structure factors to be used in a charge flip calculation. These may be either a single crystal data set, or structure factors extracted from a powder pattern via a Pawley refinement or a Rietveld refinement.

b.      d-min - This restricts the set of reflections to be used in the MC/SA run.

c.       MC/SA algorithm – This selects the type of jump to be used for each MC/SA trial.

d.      Annealing schedule – This selects the beginning MC/SA “temperature”, final “temperature”, slope and number of trials at each step.

e.       A-jump & B-jump – If the “Tremayne” algorithm is chosen these determine the jump components for each trial.

Origin 1 -> Origin 2 Transformations

An important transformation may be needed in certain cases when space groups that two alternate origin settings (listed here). These are centrosymmetric space groups where the highest symmetry point in the structure does not contain a center of symmetry. Origin 1 places the origin at the highest symmetry setting while Origin 2 places the origin at a center of symmetry (creating a -x,-y,-z symmetry operator, which means that reflection phases can only be 0 or π.) GSAS-II requires use of the Origin 2 settings because computations are much faster and simpler without complex structure factors. Alas, the literature contains a number of structures reported in Origin 1, where the origin choice may not be clearly communicated. (The CIF standard does not require that origin choice be indicated.) When a structure is imported that uses any of the space groups where an origin choice is possible, a message is shown in GSAS-II notifying the user that they must confirm that the origin choice is correct.

Example: An example of what can go wrong is illustrated with the structure of anatase. The space group is I 4₁/a m d. In Origin 1 the coordinates are:

Origin 1
atom	coordinates
Ti	0	0	0
O	0	0	0.208

and in Origin 2 the coordinates are:

Origin 2
atom	coordinates
Ti	0	1/4	-1/8
O	0	1/4	0.083

where the origin is shifted by (0,0.25,-0.125).

Since GSAS-II always the symmetry operators for Origin 2, if structure is input incorrectly with the coordinates set for Origin 1, there are several fairly obvious signs of problems: (1) the site symmetries and multiplicities are wrong, often giving an incorrect chemical formula, (2) the interatomic distances are incorrect, and (3) a plot of the structure is improbable. In this case incorrect multiplicities gives rise to a density of 7.9 g/cc, double the correct value. Impossible interatomic distances of 1.88Å for Ti-Ti, and 1.39Å for Ti-O are seen. The unit cell contents with the wrong space group operators is shown to the right.

With coordinates that match the space group operations, the correct Ti-O distances are 1.92Å and 1.97Å and the shortest Ti-Ti distance is 3.0Å. (Note that interatomic distances can be computed in GSAS-II using the Phase Atoms tab and the Compute/"Show Distances & Angles" menu item.)

Transform Origin: To transform a space group setting from Origin setting 1 to 2, use the Transform option in the Compute menu and then select the last option in the "Common transformations" pulldown menu, which will be setting 1->2 for space groups where both origins are available, as shown to the right. The transformation matrix will be set to the identity and the "V" vector will have the required origin shift loaded. Press OK. The changes can be seen by selecting the Atoms tab.

Data

This tab serves several purposes. It is used to link histograms to the selected phase and it allows the values and refinement flags to be set for the parameters that are defined for each histogram-phase pair, labeled as HAP parameters. [Note that some GSAS-II parameters are defined for each phase (atomic positions, for example), other parameters are defined for each histogram (scale factors and instrumental constants, for example) but the HAP parameters have values for each histogram in each phase.] It can also be used to show a graphical representation of an HAP parameter set.

The HAP parameters include: the phase fraction; the sample contribution to peak broadening: microstrain and crystallite size; a LeBail intensity extraction flag; hydrostatic/elastic strain shifts to lattice parameters; corrections to peak intensities due to experimental effects (preferred orientation, extinction and disordered solvents).

Use flag

When the Use flag is selected, the currently selected phase is used to compute intensities as a contribution to the selected histogram (single-crystal histograms can have only one phase; powder histograms can have any number of associated phases). When not set, the phase is not present in the selected histogram.

Phase fraction

used in powder histograms: a multiplier that determines the relative amount of the selected phase to a histogram. Note that when the histogram scale factor is varied, these values are on a relative scale. Conventional practice it to vary the scale factor and to not vary the phase fraction for one phase in a histogram. Do not refine the scale factor and all phase fractions unless a constraint is defined so the phase fractions add to 1.

Crystallite size peak broadening

is computed from size factor(s) in microns (10^-6 m), with the Scherrer constant assumed as unity. Sizes can be computed in three ways: isotropic, uniaxial and ellipsoidal. In isotropic broadening, crystallites are assumed to average as uniform in all directions and a single size value is supplied; with uniaxial broadening, a preferred direction (as a crystallographic axis, such as 0,0,1 is supplied) -- note that for most crystal systems only one axis makes sense -- and two size parameters are defined, one for along the axis and one for in the perpendicular plane; with ellipsoidal, six terms are used to define a broadening tensor that has arbitrary orientation -- this model may require constraints and is seldomly needed. Note that size broadening is usually Lorentzian, which corresponds to a LGmix value of 1.0; if this value is between 0. and 1., both Gaussian and Lorentz size broadening is modeled and a value of 0.0 is pure Gaussian. Values less than 0. or greater than 1. make no physical sense.

Microstrain peak broadening

is computed as unitless fraction of delta d-space/d-space (or equivalently delta-Q/Q) times 10⁶. Microstrain can be computed in three ways: isotropic, uniaxial and generalized. In isotropic broadening, microstrain broadening assumed to be the same in all crystallographic directions and a single value is supplied; with uniaxial broadening, a preferred direction (as a crystallographic axis, such as 0,0,1) is supplied -- note that for most crystal systems only one axis makes sense -- and two microstrain parameters are defined, one for along the axis and one for in the perpendicular plane; with generalized, the Peter Stephens second-order expansion model is used and the number of terms will depend on the crystal system. It is typically possible to refine all terms when significant anisotropic strain broadening is present. Note that microstrain broadening is usually Lorentzian, which corresponds to a LGmix value of 1.0; if this value is between 0. and 1., both Gaussian and Lorentz broadening is modeled and a value of 0.0 is pure Gaussian. Values less than 0. or greater than 1. make no physical sense.

LeBail intensity extraction

When this is selected, intensities are set to values that are best-fit using the LeBail intensity determination method rather than are computed from the atomic information for the phase.

Hydrostatic/elastic strain

shifts the lattice constants for the contribution of a phase into a histogram (powder diffraction only). The values are added to the reciprocal lattice parameter tensor terms. They must be refined in sequential refinements or where the lattice constants are slightly different in different histograms (as an example see the Combined X-ray/CW-neutron refinement of PbSO4 tutorial.

Preferred orientation

is treated in one of two ways. Intensity corrections can be added to the model here or a full texture model is possible with the "Texture" tab (which usually requires multiple histograms at different sample or detector settings). The approaches available here are March-Dollase, which requires a definition of a unique axis (in crystallographic coordinates) and the relative amount of excess or depletion of crystallites in that direction; or Spherical Harmonics, where the selection of an order determines the shape of the probability surface (which is always constrained to match the symmetry of the crystal system).

Extinction

can occur when crystals/crystallites have minimal mosaic character, which results in lowering of diffraction intensities for the most intense reflections. This is not commonly seen in powder diffraction.

Disordered solvent

This correction, using the Babinet model, is typically used to treat scattering from water that is not well-ordered in protein structures. It probably makes no sense in any other application.

What can I do here?

1.      In this tab, menu items allow copying values or refinement flags to histograms/phases and selection of which histograms are used in the current phase.

2.      The plot selection items allow for three dimensional representations of the microstrain or crystallite size distributions (which are spheres for isotropic treatments); preferred orientation can be plotted as a Psi scan (a plot of relative crystallite abundance for a particular reflection as a function of azimuthal angle) or as an inverse pole figure (which shows in a stereographic projection the probability distribution for different reciprocal lattice directions for a particular sample orientation).

Atoms

This is the table of parameters for the atoms in this crystal structure model. The menu controls allow manipulation of the values, refinement flags as well as initiate calculations of geometrical values (distances & angles) among the atoms.

What can I do here?

1.      1. Atom selection from table - These are controlled by the mouse and the Shift/Ctrl/Alt keys. Note that for most purposes (one exception is atom reordering which requires an Alt-Left-click on the rows), selection of any cell for an atom will work equivalently with selection of the entire row:

a.       Left Mouse Button (LMB) – on a row number selects the atom.

b.      Shift LMB – on a row number selects all atoms from last selection to the selected row (or top is none previously selected).

c.       Ctrl LMB – on a row number selects/deselects the atom.

d.      Alt LMB – on a row number selects that atom for moving; the status line at bottom of window will show name of atom selected. Use Alt LMB again to select a target row for this atom; insertion will be before this row and the table will be updated to show the change. NB: the Draw Atoms list is not updated by this change.

2.      Double left click a Type column heading: a dialog box is shown that allows you to select all atoms with that type.

3.      Double click a refine or I/A column heading: a dialog box will be shown with choices to be applied to every atom in the list.

4.      Atom data item editing tools – These are controlled by the mouse (Alt ignored, Shift & Ctrl allow selection of multiple cells but no use is made of them). An individual data item can be cut/pasted anywhere including from/to another document. Bad entries are rejected. If any entry is changed, press Enter key or select another atom entry to apply the change.

a.       Name – can change to any text string.

b.      Type – causes a popup display of the Periodic Table of the elements; select the element/valence desired; the atom will be renamed as well.

c.       refine – shows a pulldown of allowed refinement flag choices to be shown; select one (top entry is blank for no refinement).

d.      x,y,z – change atom coordinate. Fractions (e.g. 1/3, 1/4) are allowed.

e.       frac,Uiso,Uij – change these values; numeric entry only.

f.        I/A – select one of I(sotropic) or A(nisotropic); the Uiso/Uij entries will change appropriately.

5.      Menu ‘Edit’ - The edit menu shows operations that can be performed on your selected atoms. You must select one or more atoms before using many of the menu items.

a.       Append atom – add an H atom (name= Unk) at 0,0,0 to the end of the atom table, it is also drawn as an H atom in the structure plot.

b.      Append view point – add an H atom (name= Unk) to the end of the atom table with coordinates matching the location of the view point, it is drawn as an H atom in the structure plot

c.       Insert atom – insert an H atom (name= Unk) at 0,0,0 before the selected atom, it is also drawn as an H atom in the structure plot.

d.      Insert view point – insert an H atom (name= Unk) before the selected atom with coordinates matching the location of the view point, it is also drawn as an H atom in the structure plot.

e.       Delete atom – selected atoms will be deleted from the atom list, they should also vanish from the structure drawing.

f.        Set atom refinement flags – A popup dialog box appears; select refinement flags to apply to all selected atoms.

g.      Modify atom parameters – A popup dialog box appears with a list of atom parameter names; select one to apply to all atoms. Name will rename selected atoms according to position in table (e.g. Na(1) for Na atom as 1^st atom in list in row ‘0’). Type will give periodic table popup; selected element valence will be used for all selected atoms and atoms names will be changed. I/A will give popup with choices to be used for all selected atoms. x,y,z will give popup for shift to be applied to the parameter for all selected atoms. Uiso and frac will give popup for new value to be used for all selected atoms.

h.      Transform atoms – A popup dialog box appears; select space group operator/unit cell translation to apply to the selected atoms. You can optionally force the result to be within the unit cell and optionally generate a new set of atom positions.

i.        Reload draw atoms –

6.      Menu ‘Compute’ –

a.       Distances & Angles – compute distances and angles with esds (if possible) for selected atoms. A popup dialog box will appear with distance angle controls. NB: if atoms have been added or their type changed, you may need to do a Reset of this dialog box before proceeding.

What can I do with the plot?

A plot will be displayed only if the Draw Options or Draw Atoms tabs are visited before use of the Atoms tab. In that case the crystal structure is shown. Use of the mouse buttons changes the view of the structure and can be used to select atoms.

·  Left drag: Holding down left button rotates axes around screen x & y

·  Right drag: Holding down right button translates the fractional coordinates assigned to the view point (which is kept at the center of the plot). The structure will appear to translate. The view point can also be entered directly in the Draw Options.

·  Middle drag: Holding down center button rotates axes around screen z (direction perpendicular to screen).

·  Wheel: Rotating the scroll wheel: changes “camera position” (zoom in/out)

·  Shift+Left click: Holding down the shift key while clicking on an atom with the left mouse button causes that atom to be selected (Shift + a Right click does the same). Any previously selected atoms will be reset. If two atoms are overlapped in the current view, then the top-most atom will usually be selected. Only atoms in the asymmetric unit can be selected from the plot in this way.

·  Shift+Right click: Holding down the shift key while clicking on an atom with the right mouse button causes the atom to be selected if previously unselected and unselected if previously selected. Any previously selected atoms will be continue to be selected so shift-right click can be used to add atoms to the selection list. If two atoms are overlapped in the current view, then the top-most atom will usually be selected. Only atoms in the asymmetric unit can be selected from the plot in this way.

Draw Options

What can I do here?

The Draw Options window provides access to a number of items that control how the structure is displayed.

What is plotted here?

A plot that shows the atoms of the crystal structure is generated. The atoms are displayed according to the controls in the in this page as well as options on the Draw Atoms page.

What can I do with the plot?

Use of the mouse buttons when viewing a crystal structure changes the view of the structure:

·  Holding down left button (left drag): rotates axes around screen x & y

·  Holding down right button (right drag): translates the fractional coordinates assigned to the view point (which is kept at the center of the plot). Note that the view point coordinates can also be entered directly.

·  Holding down center button (center drag): rotates axes around screen z

·  Rotating the scroll wheel: changes “camera position” (zoom in/out)

Draw Atoms

This gives a list of the atoms and bonds that are to be rendered as lines, van der Waals radii balls, sticks, balls & sticks, ellipsoids & sticks or polyhedra. There are two menus for this tab; Edit allows modification of the list of atoms to be rendered and Compute gives some options for geometric characterization of selected atoms.

What can I do here?

1.      Atom Selection from table: select individual atoms by a left click of the mouse when pointed at the left most column (atom numbers) of the atom display; hold down the Ctrl key to add to your selection; a previously selected atom will be deselected; hold down Shift key to select from last in list selected to current selection. A selected atom will be highlighted (in grey) and the atoms will be shown in green on the plot. Selection without the Ctrl key will clear previous selections. A double left click in the (empty) upper left box will select or deselect all atoms.

2.      Atom Selection from plot: select an atom by a left click of the mouse while holding down the Shift key and pointed at the center of the displayed atom, it will turn green if successful and the corresponding entry in the table will be highlighted (in grey); any previous selections will be cleared. To add to .your selection use the right mouse button (Shift down); if a previously selection is reselected it is removed from the selection list. NB: beware of atoms that are hiding behind the one you are trying to select, they may be selected inadvertently. You can rotate the structure anytime during the selection process.

3.      Double left click a Name, Type and Sym Op column heading: a dialog box is shown that allows you to select all atoms with that characteristic. For example, selecting the Type column will show all the atom types; your choice will then cause all those atoms to be selected.

4.      Double left click a Style, Label or Color column: a dialog box is shown that allows you to select a rendering option for all the atoms. For Color a color choice dialog is displayed that covers the entire color spectrum. Choose a color by any of the means available, press the “Add to Custom Colors”, select that color in the Custom colors display and then press OK. NB: selecting Color will make all atoms have the same color and for Style “blank” means the atoms aren’t rendered and thus the plot will not show any atoms or bonds!

5.      Menu ‘Edit’ - The edit menu shows operations that can be performed on your selected atoms. You must select one or more atoms before using any of the menu items. Most of these items can also be accessed by selecting one or more atoms and right-clicking the mouse.

a.       Atom style – select the rendering style for the selected atoms

b.      Atom label – select the item to be shown as a label for each atom in selection. The choices are: none, type, name or number.

c.       Atom color – select the color for the atom; a color choice dialog is displayed that covers the entire color spectrum. Choose a color by any of the means available, press the “Add to Custom Colors”, select that color in the Custom colors display and then press OK.

d.      Reset atom colors – return the atom color back to their defaults for the selected atoms.

e.       View point – position the plot view point to the first atom in the selection.

f.        Add atoms – using the selected atoms, new ones are added to the bottom of the list after applying your choice of symmetry operator and unit cell translation selected via a dialog display. Duplicate atom positions are not retained. Any anisotropic thermal displacement parameters (Uij) will be transformed as appropriate.

g.      Transform atoms – apply a symmetry operator and unit cell translation to the set of selected atoms; they will be changed in place. Any anisotropic thermal displacement parameters (Uij) will be transformed as appropriate.

h.      Fill CN-sphere – using the atoms currently in the draw atom table, find all atoms that belong in the coordination sphere around the selected atoms via unit cell translations. NB: symmetry operations are not used in this search.

i.        Fill unit cell - using the atoms currently selected from the draw atom table, find all atoms that fall inside or on the edge/surface/corners of the unit cell. This operation is frequently performed before Fill CN-sphere.

j.        Delete atoms – clear the entire draw atom table; it is then refilled from the Atoms table. You should do this operation after any changes in the Atoms table, e.g. by a structure refinement.

6.      Menu ‘Compute’ - The compute menu gives a choice of geometric calculations to be performed with the selected atoms. You must select the appropriate number of atoms for these to work and the computation is done for the atoms in selection order.

a.       View pt. dist. - this calculates distance from view point to all selected draw atoms; result is given on the console window.

b.      Dist. Ang. Tors. – when 2-4 atoms are selected, a distance, angle or torsion angle will be found for them. The angles are computed for the atoms in their selection order. The torsion angle is a right hand angle about the A2-A3 vector for the sequence of atoms A1-A2-A3-A4. An estimated standard deviation is given for the calculated value if a current variance-covariance matrix is available. The result is shown on the console window; it may be cut & pasted to another application (e.g. Microsoft Word).

c.       Best plane – when 4 or more atoms are selected, a best plane is determined for them. The result is shown on the console window; it may be cut & pasted to another application (e.g. Microsoft Word). Shown are the atom coordinates transformed to Cartesian best plane coordinates where the largest range is over the X-axis and the smallest is over the Z-axis with the origin at the unweighted center of the selection. Root mean square displacements along each axis for the best plane are also listed. The Z-axis RMS value indicates the flatness of the proposed plane. NB: if you select (e.g. all) atoms then Best plane will give Cartesian coordinates for these atoms with respect to a coordinate system where the X-axis is along the longest axis of the atom grouping and the Z-axis is along the shortest distance. The origin is at the unweighted center of the selected atoms.

What is plotted here?

A plot that shows the atoms of the crystal structure is generated. The atoms are displayed according to the controls in the in this page as well as options on the Draw Options page.

What can I do with the plot?

Use of the mouse buttons when viewing a crystal structure changes the view of the structure:

·  Left drag: Holding down left button rotates axes around screen x & y

·  Right drag: Holding down right button translates the fractional coordinates assigned to the view point (which is kept at the center of the plot). The structure will appear to translate. (On Mac control+mouse drag will also do this). The view point can also be entered directly in the Draw Options.

·  Middle drag: Holding down center button rotates axes around screen z (direction perpendicular to screen).

·  Mouse Wheel: Rotating the scroll wheel: changes “camera position” (zoom in/out)

·  Shift+Left click: Holding down the shift key while clicking on an atom with the left mouse button causes that atom to be selected. Any previously selected atoms will be reset. If two atoms are overlapped in the current view, then the top-most atom will usually be selected. Atom selection requires that either the "Atoms" or "Draw Atoms" phase be displayed.

·  Shift+Right click: Holding down the shift key while clicking on an atom with the right mouse button causes the atom to be selected if previously unselected and unselected if previously selected. Any previously selected atoms will be continue to be selected so shift-right click can be used to add atoms to the selection list. (On Mac control+mouse click will also do this). If two atoms are overlapped in the current view, then the top-most atom will usually be selected. Atom selection requires that either the "Atoms" or "Draw Atoms" phase be displayed.

RB Models

This is used to insert rigid bodies into a structure. The rigid bodies must first be defined for the project using the Rigid bodies tree item. It also allows control of the location of the rigid body and in this phase

What can I do with the plot?

Use of the mouse buttons when viewing a crystal structure changes the view of the structure:

·  Holding down left button (left drag): rotates axes around screen x & y

·  Holding down right button (right drag): translates the fractional coordinates assigned to the view point (which is kept at the center of the plot). The structure will appear to translate. The view point can also be entered directly in the Draw Options.

·  Holding down center button (center drag): rotates axes around screen z

·  Rotating the scroll wheel: changes “camera position” (zoom in/out)

When a rigid body is being inserted into a structure, both the rigid body and the crystal structure are displayed. It is useful to plan for this by preselecting the atoms in the Draw Atoms list and to have atoms displayed as "Sticks" or "Ball-and-Sticks." The rigid body will be displayed as "Ball-and-Sticks" but bonds will be in green. Use of the Alt key causes the above mouse movements to reposition the rigid body rather than change the view of the crystal structure:

·  Alt+Left drag: Holding Alt while dragging the mouse with the left button down rotates the rigid body around screen x & y axes

·  Alt+Middle drag: Holding Alt while dragging the mouse with the middle button down rotates the rigid body around screen z axis (out of screen)

·  Alt+Right drag: Holding Alt while dragging the mouse with the right button down translates the rigid body in the screen x & y directions (rotate the plot to see and move in the rigid body in the third direction.) Pressing the "Lock" checkbox next to the origin location prevents the origin from being changed in this way.

Texture

 

This tab is used to control settings used for a texture study of a material. This type of characterization requires diffraction data recorded with multiple detector orientations (the number of orientations will depend on sample and material symmetry). Do not confuse this with applying a preferred orientation correction (found in the "Data" tab) in a structural study. The sample orientation relative to the detector axes is specified here and the detector orientation is specified for each histogram as goniometer omega, chi, phi and azimuth values (details below). These values must be specified.

 

Texture analysis using GSAS-II employs spherical harmonics modeling, as described by Bunge, "Texture Analysis in Materials Science" (1982), and implemented by Von Dreele, J. Appl. Cryst., 30, 517-525 (1997) in GSAS. The even part of the orientation distribution function (ODF) via the general axis equation

is used to give the intensity corrections due to texture. The two harmonic terms,  and , take on values according to the sample and crystal symmetries, respectively, and thus the two inner summations are over only the resulting unique, nonzero harmonic terms. These unique terms are automatically selected by GSAS-II according to the space group symmetry and the user chosen sample symmetry. The available sample symmetries are cylindrical, 2/m, mmm and no symmetry. The choice of sample symmetry profoundly affects the selection of harmonic coefficients. For example, in the case of cylindrical sample symmetry (fiber texture) only k_L⁰(y) terms are nonzero so the rest are excluded from the summations and the set of C_L⁰ⁿ coefficients is sufficient to describe the effect on the diffraction pattern due to texture. The crystal harmonic factor, , is defined for each reflection, h, via polar and azimuthal coordinates (f, b) of a unit vector coincident with h relative to the reciprocal lattice. For most crystal symmetries, f is the angle between h and the n-th order major rotation axis of the space group (usually the c-axis) and b is the angle between the projections of h and any secondary axis (usually the a-axis) onto the normal plane.  In a similar way the sample harmonic factor, , is defined according to polar and azimuthal coordinates (y, g) of a unit vector coincident with the diffraction vector relative to a coordinate system attached to the external form of the sample. For example, in the case of a rolled steel plate having mmm symmetry, the polar angle, y, is frequently measured from the normal direction (ND, parallel to K_s) and g is then measured from the rolling direction (RD, parallel to I_s) in the TD (transverse direction, parallel to J_s) - RD plane.  Thus, the general axis equation becomes

Note that this version of the general axis equation differs from that shown in Von Dreele (1997) in that the assignment of m and n are reversed.

In a diffraction experiment the crystal reflection coordinates (f, b) are determined by the choice of reflection index (hkl) while the sample coordinates (y, g) are determined by the sample orientation on the diffractometer. To define the sample coordinates (y, g), we have defined an instrument coordinate system (I, J, K) such that K is normal to the diffraction plane and J is coincident with the direction of the incident radiation beam toward the source. We further define a standard set of right-handed eulerian goniometer angles (W, C, F) so that W and F are rotations about K and C is a rotation about J when W  = 0.  Finally, as the sample may be mounted so that the sample coordinate system (I_s, J_s, K_s) does not coincide with the instrument coordinate system (I, J, K), we define three eulerian sample rotation offset angles (W_s, C_s, F_s) that describe the rotation from (I_s, J_s, K_s) to (I, J, K).  The sample rotation angles are defined so that with the goniometer angles at zero W_s and F_s are rotations about K and C_s is a rotation about J.  The zeros of these three sample rotation angles can be refined as part of the Rietveld analysis to accommodate any angular offset in sample mounting. For the specific case of cylindrical sample symmetry, the cylinder axis is coincident with K_s as is the 2-fold in 2/m sample symmetry. After including the diffraction angle, Q, and a detector azimuthal angle, A, the full rotation matrix, M, is

M = -QAWC(F+F_s)C_sW_s

By transformation of unit Cartesian vectors (100, 010 and 001) with this rotation matrix, the sample orientation coordinates (y, g) are given by

cos(y) =  and   tan(g) =

The harmonic terms,  and , are developed from (those for  are similar)

where the normalized associated Legendre functions, , are defined via a Fourier expansion as

for n even and

for n odd.  Each sum is only over either the even or odd values of s, respectively, because of the properties of the Fourier coefficients, .  These Fourier coefficients are determined so that the definition

is satisfied.  Terms of the form  and  are combined depending on the symmetry and the value of n (or m) along with appropriate normalization coefficients to give the harmonic terms  and .  For cubic crystal symmetry, the term  is obtained directly from the Fourier expansion

using the coefficients, , as tabulated by Bunge (1982).

The Rietveld refinement of texture then proceeds by constructing derivatives of the profile intensities with respect to the allowed harmonic coefficients, , and the three sample orientation angles, W_s, C_s, F_s, all of which can be adjustable parameters of the refinement. Once the refinement is complete, pole figures for any reflection may be constructed by use of the general axis equation, the refined values for  and the sample orientation angles W_s, C_s, F_s.

The magnitude of the texture is evaluated from the texture index by

If the texture is random then J = 1, otherwise J > 1; for a single crystal J = ¥.

In GSAS-II the texture is defined in two ways to accommodate the two possible uses of this correction. In one, a suite of spherical harmonics coefficients is defined for the texture of a phase in the sample; this can have any of the possible sample symmetries and is the usual result desired for texture analysis. The other is the suite of spherical harmonics terms for cylindrical sample symmetry for each phase in each powder pattern (“histogram”) and is usually used to accommodate preferred orientation effects in a Rietveld refinement. The former description allows refinement of the sample orientation zeros, W_s, C_s, F_s, but the latter description does not (they are assumed to be zero and not refinable). The sample orientation angles, (W, C, F) are specified in the Sample Parameters table in the GSAS-II data tree structure and are applied for either description.

Some useful examples:

1) Bragg-Brentano laboratory powder diffractometer

The conventional arrangement of this experiment is to have a flat sample with incident and diffracted beams at equal angles (theta) on opposite sides of the sample. The sample is frequently spun about its normal to improve powder statistics and impose cylindrical symmetry on any preferred orientation (texture). Thus, the diffraction plane (source, diffraction vector & detector) contains the K-vector which is parallel to the diffraction vector and W, C, F = 0.

2) Debye-Scherrer diffractometer with point detector(s)

The usual arrangement here is to have a capillary sample perpendicular to the diffraction plane. The capillary may be spun about its cylinder axis for powder averaging and to impose cylindrical symmetry on the texture which is perpendicular to the diffraction plane. Thus, W, F = 0 and C =90.

3) Debye-Scherrer diffractometer with 2D area detector

The area detector is presumed to be directly behind the sample with the incident beam somewhere near the center of the detector. The detector axes are defined (for a synchrotron) with the X-axis toward the synchrotron ring and the Y-axis vertical “up”; one views the detector image as if looking from the x-ray source. The sample is assumed to be a capillary (which may be spun to impose cylindrical symmetry), although other sample shapes may be used, and is aligned with the cylinder axis horizontal. Integration of the image from a series of “caked” slices gives a set of powder patterns, each assigned an azimuthal angle where zero is along the X-axis. Thus, at azimuth=0 the diffraction plane is horizontal and contains the cylinder axis so W, C, F = 0.

What can I do here?

1. Menu ‘Texture/Refine texture’ – refines the spherical harmonics texture model using the predetermined values of Prfo for all histogram reflection sets as demonstrated in 2DTexture tutorial.

 

2. Texture settings:

 

The texture index, J is shown on the 1^st line. The Texture model can be chosen from [‘cylindrical’, ’none’, ‘shear - 2/m’, or ‘rolling – mmm’].

 

The Harmonic order (even integer 0-34), refine flag & show coefficients flag are next.

 

The Texture plot type is one of:

·         as an "Axial pole distribution" which simulates the intensity of a reflection during a phi scan.

·         as a "pole figure," where a projection of the probability of finding a pole (hkl) is plotted as a function of sample orientation.

·         as a "inverse pole figure," where a projection of the probability of finding all poles (hkls) is plotted for a selected sample orientation.

·         or as a "3D pole distribution" that shows the probability of finding a pole (hkl) is plotted as a function of sample orientation.

For Axial distribution, pole figure and 3D pole distribution one must next select the hkl of the desired pole, for Inverse pole figure one must select a sample direction (typically 0 0 1).

One can choose the contour (pole & inverse pole figures) color scheme (default “Paired”) and make a CSV file of the image for import into other software.

The spherical harmonics coefficients are shown next; they may be edited. They may be cleared by setting harmonic order to zero and then back to desired value.

Lastly, the sample orientation angle zeros (W_s, C_s, F_s) are shown with their individual refinement flags.

Map peaks

This gives the list (magnitude, x y & z) of all peaks found within the unit cell from the last Fourier/charge flip map search sorted in order of decreasing peak magnitude. The crystal structure plot shows each peak position as a white to dark gray cross; the shade is determined from the magnitude for the peak relative to the maximum peak magnitude. Negative peaks shown in orange.

What can I do here?

1.      Peak Selection from table: select individual atoms by a left click of the mouse when pointed at the left most column (atom numbers) of the atom display; hold down the Ctrl key to add to your selection; a previously selected atom will be deselected; hold down Shift key to select from last in list selected to current selection. A selected atom will be highlighted (in grey) and the atoms will be shown in green on the plot. Selection without the Ctrl key will clear previous selections. A left click in the (empty) upper left box will select or deselect all atoms.

2.      Select the mag column – the entries will be sorted with the largest at the top.

3.      Select the dzero column – the entries will be sorted with the smallest (distance from origin) at the top.

4.      Select the dcent column – the entries will be sorted with the smallest distance from the unit cell center at the top.

5.      Menu ‘Map peaks’  –

a.       Move peaks – this copies selected peaks to the Atoms list and the Draw Atoms list. They will be appended to the end of each list each with the name ‘UNK’ and the atom type as ‘H’. They will also be drawn as small white spheres at their respective positions in the structure drawing. You should next go to the Atoms page and change the atom type to whatever element you desire; it will be renamed automatically.

b.      View point – this positions the view point (large 3D RGB cross) at the 1^st selected peak.

c.       View pt. dist. – this calculates distance from view point to all selected map peaks.

d.      Hide/Show bonds – toggle display of lines (bonds) between peaks

e.       Calc dist/ang – if 2 peaks are selected, this calculates the distance between them. If 3 peaks are selected this calculates the angle between them; NB: selection order matters. If selection is not 2 or 3 peaks this is ignored. Output is on the console window.

f.        Equivalent peaks – this selects all peaks related to selection by space group symmetry.

g.      Invert peak positions – inversion through cell center of map and all positions.

h.      Roll charge flip map – popup allows shifting of the map & all peak positions by unit cell fractions; can be along combinations of axes.

i.        Unique peaks – this selects only the unique peak positions amongst those selected; a popup allows selection of atom subset closest to x=0, y=0, z=0 origin or center.

j.        Save peaks – saves the peak list as a csv file.

k.      Delete peaks – this deletes selected peaks. The shading on the remaining peaks is changed to reflect any change in the maximum after deletion.

l.        Clear peaks – this deletes all the peaks in the map peak list; they are also removed from the crystal structure drawing plot.

Pawley reflections

This gives the list of reflections used in a Pawley refinement and can only be seen if the phase type is ‘Pawley’ (see General).

What can I do here?

1.      Menu ‘Operations’ –

a.       Pawley create – this creates a new set of Pawley reflections, over writing any preexisting Pawley set. They are generated with d-spacings larger than the limit set as ‘Pawley dmin’ in the General tab for this phase. By default the refine flags are not set and the Fsq(hkl) = 100.0.

b.      Pawley estimate – this attempts an estimate of Fsq(hkl) from the peak heights of the reflection as seen in the 1^st powder pattern of those selected in the Data tab.

c.       Pawley delete – this clears the set of Pawley reflections.

2.      You can change the refine flags either by clicking on the box or by selecting one and then selecting the column (a single click on the column heading). Then type ‘y’ to set the refine flags or ‘n’ to clear the flags. You should deselect those reflections that fall below the lower limit or above the upper limit of the powder pattern otherwise you may have a singular matrix error in your Pawley refinement.

3.      You can change the individual Fsq(hkl) values by selecting it, typing in the new value and then pressing enter or selecting somewhere else in the table.

Layers

What can I do here?

Wave Data

What can I do here?

MC/SA

What can I do here?

Pawley reflections

What can I do here?

Macintosh notes:

GSAS-II can be run on Windows, Linux and Macintosh/OS X computers, but the GUI follows the native style of Mac OS X. On Windows and some versions of Linux, the menu bars appears on top of the main window. On the Mac, the menu appears at the location that has been configured for menus (usually at the top of the screen). GSAS-II defines actions for both the left and right buttons on a two-button mouse, If a two or three-button mouse is used with a Mac, these mouse buttons will work as intended. If using a Mac touchpad or single-button mouse, clicking the touchpad or mouse button will generate a "left button" click. Hold down the control-key to generate a "right button" click.

Configuration Variables:

GSAS-II provides a number of configuration settings that can be changed via variables that can be set and saved. These are controlled in the File/Preferences menu item (on Mac the Preferences menu is found in the usual place on Macs, in the main application menu). These settings are optionally saved from for subsequent runs in a file named config.py. More information about this can be found in the appropriate section of the Programmer's documentation.

Programmers documentation

The routines and classes used within GSAS-II are documented in a set of web pages and in a PDF document. This documentation is created from the Python source code files using Sphinx.

Access to fullrmc

The fullrmc program is a large-box pair distribution function modeling library developed by Bachir Aoun ["Fullrmc, a Rigid Body Reverse Monte Carlo Modeling Package Enabled with Machine Learning and Artificial Intelligence", B. Aoun, Jour. Comp. Chem. (2016), 37, 1102-1111. DOI: 10.1002/jcc.24304]. Extensive information about fullrmc is found, including a number of explanatory videos, along with the source code on GitHub: https://bachiraoun.github.io/fullrmc/. Use of fullrmc requires a set of Python packages that can be installed along with the packages needed for GSAS-II, but Windows and MacOS users will likely find it easier to install a pre-compiled version of fullrmc by downloading it from here. To locate a version of Python containing fullrmc, the following locations are checked (in the order specified):

1.      The GSAS-II configuration variable fullrmc_exec can point to a Python image.

2.      The Python interpreter running GSAS-II is checked if fullrmc can be imported

3.      The location where GSAS-II is installed, the location where Python is installed, the location where the GSAS-II binaries are found, the current default location and all directories in the system path are all checked for a file named "fullrmc*macOS*i386-64bit" (MacOS), "fullrmc*.exe" (Windows) or "fullrmc*" (Linux).

Last modified: Tue Apr 27 22:21:15 CDT 2021