Determining Profile Parameters from a Standard

 

  • A video version of the first two parts of this tutorial is available at https://anl.box.com/v/FindProfParamCW
  • Exercise files are found here

     

    The goal of this exercise is to determine approximate instrument profile parameters by a quick peak fit to a sample with a lab diffractometer. Ideally, one should use a material or mixture of materials that has peaks over the entire range where you collect data and use a material(s) that have negligible sample broadening (from crystallite size or microstrain). The NIST LaB6 standards (SRM 660, 660a and 660b) are good choices for this, as it has very little sample broadening and a relatively small number of peaks over a wide angular range, although it would be good to have peaks starting somewhat lower in 2theta.

     

    Note that it is highly recommended to collect reference data to a much higher 2theta angle than here. What is done in this part serves as an example, and is sufficient only if one will never collect and use data above 70 degrees (unlikely!).

     

    To get started, create a new project in GSAS-II, either by starting the program fresh or using File/New Project.

     

    Step 1: Read in the Diffraction Data

     

    Use Import/Powder Data/from Bruker RAW file to read file LaB6_Jan2018.raw from the Tutorials CWInstDemo/data directory (download from https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/CWInstDemo/data/). After selecting this file, answer yes to "Is this the file you want?"

     

    Step 2: Select Default Instrument Parameters

     

    The next dialog to appear is titled, "Choose inst. Param file for LaB6_Jan2018.raw Scan 1 (or Cancel for default)" since we do not have a set of parameters to read, we must use a default set. Press Cancel.

     

    This raises the default inst parms dialog, as below

    Here, choose the first option for CuKa lab data (which is for a standard instrument with Kalpha1 and Kalpha2 radiation) and press OK. A plot of the data will appear as below.

     

     

    Step 3: Change Data Range.

     

    Note that the data begins at 10 degrees, but the first peak is above 21 degrees, we can simplify the background fitting by changing the data limits. Click on the Limits data tree item, and either change the Tmin value from 10 to 20 or in the plot "drag" the green line to the right to approximately 20 degrees.

     

    Step 4: Add Peaks to Fit

     

    To define peaks, click on the "Peak List" data tree item. Note that as below, the peak list is initially empty.

     

    Move the mouse to any of the data points close to the top of the first peak and click the left mouse button. A line will be drawn through the peak and the position will be added to the peak table and a line marking this is added to the plot, as below.

     

    Repeat this for all 8 peaks in the pattern. Note that if a peak is entered in the wrong place it can be moved by "dragging" it with the mouse, or use a right-click to delete it. Be careful to make sure two peaks are not entered in the same place by accident.

    The peak table appears as:

     

    Step 5: Refine Peak Areas

     

    By default, the peak intensities are flagged as to be varied, but not any of the other parameters. It is wise to refine them all, but we want to make sure the parameters have a chance to converge one step at a time and we should start with only the intensities.  Use the Peak Fitting/Peakfit menu item to perform a peak refinement. You will be asked for a name to save the project (enter a name such as peakfit.gpx and press Save). The peaks are then fit, here optimizing only the intensity values. The console window shows the details of the refinement:

     

    The warning at the end is because the default peak parameters describe a peak shape that is significantly sharper than what is actually present for these data; the step size is actually fine. This warning will later go away, but if it did not this would indicate that it would be better to recollect the data with a step size decreased by a factor of 3-4.

     

    Step 6: Refine peak areas and heights

     

    In the peak list window, double click in the refine heading for the peak position flags, this will bring up a dialog that allows all peak positions to be varied.

     

    Select "vary all" and press OK. Now all peak positions and areas will be refined.

    Use the Peak Fitting/Peakfit menu item to start peak refinement.

     

    The fit improves significantly, as below, but further improvements are needed.

     

    Step 7: Refine peak areas, heights and widths (optional)

     

    Double-Click on the refine headings for the sigma (Gaussian width) and gamma (Lorentzian width) parameters so that all parameters can be refined. Use the Peak Fitting/Peakfit menu item to start peak refinement. The results in the console window are as below.  This is being done here just to see how the individual peaks vary before we fit them with a parametric equation. This step is not necessary, but provides a useful graphical reference to look for any anomalous peaks that one might not want to use. 

     

     

    Step 8: Add more Background terms

     

    Use the zoom feature (magnifying glass) to draw a box around the low intensity data

     

    Looking at the plot (see below), makes it clear that the background is not well fit. Adding more background terms will fix this.

     

    Select the Background tree item and change the number of coefficients to 6, as shown below.

    Then return to the Peak List data tree item and use the Peak Fitting/Peakfit menu item to perform a peak refinement. At this point it is instructive to click on the Instrument Parameters data tree item to see a plot of peak widths:

    Note that the solid curves here are plots of the profile coefficients from the default instrument parameters (which are unimportant here), but the fits for the individual peaks are shown (in units of Q/delta-Q vs Q), with Lorentzian widths (gamma) in green, Gaussian widths (sigma) in red and their convolution (total broadening) in blue.

     

    Step 9: Refine Profile Parameters

     

    Now, select the profile terms to be refined. Use Gaussian U, V, & W and Lorentzian X & Y (note that Z, which provides constant broadening, independent of Q, is provided as an option, but is rarely if ever needed.)

     

    Note that these U, V & W values will be used to set the Gaussian peak widths for those peaks where sigma is not being refined and likewise X, Y & Z will be used to determine the Lorentzian widths where gamma is not refined for that peak. If we had any peaks that were not consistent with the width of the others, we might choose to continue to refine their individual profile terms (sigma & gamma), if that is done the peaks varied individually would be excluded from the U, V, W, X & Y refinements. Here we will refine U, V, W, X & Y against all peaks. To do this, select the Peak List data tree item and remove refinement of sigma & gamma for all peaks by double-clicking on the refine column headers for each and select "N – vary none" so that the table appears as below:

     

    Use the Peak Fitting/Peakfit menu item to perform a peak refinement optimizing U, V, W, X & Y:

     

    Note that the sigma and gamma values are now computed from U, V, & W and X & Y, respectively. The difference curve shows very small deviations.

     

    Note that the background is also quite well fit now.

    Step 10: Save the Profile Parameters

     

    So that we can use these profile terms as the starting point for a future refinement, save the profile terms to a file by clicking on the Instrumental Parameters data tree item and use the Operations/Save Profile menu command. Give the file a name that will be helpful for future use (<MyInstrument>20-70deg.instparm might be good) and put this file in the directory(s) where you will keep your data files.

     

    Clicking on the Instrument Parameters data tree item will show the peak widths from U, V, W, X & Y, and also the individual peak widths generated from those values (not very useful). For a more useful plot we refining the individual peak widths independently again, as shown in the next section.

    Step 11: Plot Profile Parameters with Individual Peak Widths (optional)

     

    First we stop refining U, V, W, X & Y by clicking on Instrumental Parameters data tree item and turning the refinement flags off.

    In the Peak List data tree item, turn on refinement of all individual peak widths (as we did in Step 7)

    and use the Peak Fitting/Peakfit menu item to perform a peak refinement optimizing individual peak widths, as before. Returning to the Instrumental Parameters data tree item provides this plot:

     

    The displayed lines and points are as follows, where Lorentzian widths are shown in green, Gaussian widths are in red and their convolution (total broadening) is shown in blue:

    Š      Solid curves: profile terms from original instrument parameter file (here the CuKa lab data defaults). Note since X, Y & Z are zero, there is only Gaussian broadening and the total broadening is exactly the same as the Gaussian so the blue curve hides the red one.

    Š      Dashed curves: these values are generated by U, V & W and X, Y & Z. Note that the broadening from this instrument is significantly greater than the default values.

    Š      Plus signs (points): these are the widths for the individual reflections unconstrained. Note that they agree well with the fitted curves (dashed lines). 

     

    These profile terms are more than adequate for most structural fitting problems, but it should be noted that these values are not sufficient to obtain quantitative measurements of microstrain and/or crystallite size. To obtain even better terms the instrument profile is best determined by a Rietveld fit for (with a standard where microstrain and size are known to be negligible or at least have certified values) Those certified values should be set as input values and not refined to allow U, V, W, X, and Y to be further refined. Ideally, in addition to higher angle data, the sample would also have lower angle peaks and SH/L can also be refined.

     

    Part 2: Test the Profile Parameters

     

    The obvious question will be how well do these parameters fit the data? To test this, we can start a new refinement using these parameters and see how well they do.

     

    Step 2.1: Read in the Diffraction Data

     

    Use File/New Project to create an empty project. You can say Yes to the prompt to save the current project (No would not hurt.) As before, use Import/Powder Data/from Bruker RAW file to read file LaB6_Jan2018.raw from the Tutorials CWInstDemo/data directory (downloaded already from https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/CWInstDemo/data/). After selecting this file, answer yes to "Is this the file you want?"

     

    Step 2.2: Select New Instrument Parameters

     

    The next dialog to appear is titled, "Choose inst. Param file for LaB6_Jan2018.raw Scan 1 unlike before, we do have profile terms to read, from the file created in Step 10, above. Select the file written before (such as <MyInstrument>20-70deg.instparm ) and press OK.  Note that you may need to change the file filter to see files of type .instparm.

     

    At present, the instrument type is not saved, so go to the Sample Parameters data tree item for the new histogram and change the Diffractometer type from Debye-Scherrer to Bragg-Brentano.

     

    (before)

     

    (after)

    Step 2.3: Add Phase

     

    We will add a phase for LaB6, since this is a simple material we will input this by hand rather than trying to import it. Use Data/Add new phase to create a new phase. Enter any name you choose, though LaB6 is a good choice and press OK.

     

    The symmetry and cell need to be edited on the new phase's General tab. Click on the Space Group Button (which defaults to P1) and enter P m -3 m (note use of spaces to separate symmetry axes – though in this case since this is a standard setting, omitting the spaces works too. The space group symmetry information is displayed, click OK.

     

    Change the lattice constant (a) from 1.0 to 4.15689 A. (The value for SRM 660b)

     

     

    Finally add atoms to the phase by clicking on the Atoms tab. Use the Edit Atoms/Append atom menu item to insert an atom. A new atom is included in the table.

    Double-Click on the Type value (H) and which opens a periodic table window. Click on the arrow next to La to bring up a menu of the defined valences

     

    Select La (neutral atoms are usually preferred) from that pull-down and the period table window closes. This atom is located at position 0,0,0 so no further editing is needed. For completeness add the second by using the Edit Atoms/Append atom menu item again. to insert an atom. For the second atom, change the type to boron by Double-Clicking on the Type value (H) and selecting B (the only choice) from the pull-down. The coordinates for this atom are 0.1975,0.5,0.5 so the x, y and z values must be edited.

    Note that the site multiplicities indicate that the stoichiometry is La1B6, as is expected.

     

    Step 2.4: Link Histogram and Phase

     

    Click on the Data tab for the phase. Note that there are no associated histograms:

     

    Use the Edit Phase/Add Powder Histogram menu command. Select the one histogram and press OK. 

    Nothing needs to be changed of the new parameters added here:

     

    Step 2.5: Refine Histogram Parameters

     

    We will first change a few histogram parameters. For data tree item Limits change Tmin to 20 degrees, as was done before in step 3.

    For data tree item Background change the Number of coeff. to 6, as was done before in step 8.

     

    Note that the refinement flag is on by default. We will not refine any of the Instrument parameters but we will refine the histogram scale factor (only) on the Sample Parameters.

     

    Use the Calculate/Refine menu item to start refinement.  The program will prompt requesting a name for the newly-created .gpx file.

     

    The fit is not very good. Clicking on the histogram's (PWDR) data tree item and zooming in shows that the tick are not well aligned with the peaks. This is due to sample displacement.

     

    Step 2.6: Refine an additional Histogram Parameter

     

    The position of the sample is never well determined in a Bragg-Brentano instrument, so the sample displacement should always be varied. Click on Sample Parameters and turn on refinement of Sample displacement.

     

    Use the Calculate/Refine menu item to start another refinement.  Significant improvement is seen and even more if Calculate/Refine is used a second time.

    Step 2.6: Turn on Le Bail fitting

    Part of the problem in the fit is that the intensities are not well fit in the model. Rather than fitting the few free structural parameters (x for B and Uiso values), we will treat the intensities are arbitrary using Le Bail fitting. This is done by clicking on the Phase tree item and the Data tab and setting the do LeBail extraction flag.

     

     

    Use the Calculate/Refine menu item to start another refinement.  A warning message that "Steepest Descents dominates" this is because a high degree of parameter correlation occurs as the reflection intensities change. The fit does not improve very much if Calculate/Refine is used a second time but the warning goes away.

     

    Step 2.7: Fit Lattice

    While this should not be needed for a standard, it is clear by looking at the plots that peaks are still not quite line up. In a less dense sample it might be reasonable to refine the sample transparency, but here the only reasonable parameter is to refine the lattice. On the Phase's General tab press the Refine unit cell control.

    Use the Calculate/Refine menu item to start another refinement and the positioning of the peaks improves significantly.

    Step 2.8: Fit MicroStrain

    The remaining major problem is that we have not treated the sample broadening and LaB6 does have some microstrain. That can be refined with the Phase's Data tab with the microstrain control.

     

    Use the Calculate/Refine menu item to start another refinement. A second refinement cycle brings the Rw to circa 5.8%. The fit improves dramatically and microstrain refines to a non-physical negative value. This is because our somewhat naive approach above assumed no sample broadening.

     

    This shows why if you are planning to measure microstrain and/or crystallite size quantitatively, you should determine instrument profile using a Rietveld fit with a standard with known values for the microstrain and size. Fix the size and microstrain to the known values when fitting the data from the standard.

    Step 2.9: Additional Parameters

    For these data, it appears the ratio of Kalpha1 and Kalpha2 is not exactly the theoretical value of 0.5. This can happen due to monochromator tuning. Allowing this to shift slightly by including brings the Rw to circa 4.9%.

    The fit is quite good without fitting the instrumental profile terms:

     

    Step 2.10: Profile Term Quality Check

    The quality of the profile parameters we previously fit can be demonstrated by turning off refinement of the microstrain term and refining the U, V, W and X & Y terms. This produces a small improvement in the fit (expected as one fitting parameter as been replaced by 5), but the changes are very small, as noted by the Instrument Parameter terms plot:

    Part 3: Fitting data over a wider range

     

    In this section we fit a pattern with a wider range of data. This proceeds quite simply.

    Step 3.1: Start new project and read in data

     

    Restart GSAS-II or use the File/New Project  to create a new empty project.

    Use Import/Powder Data/from GSAS powder data file to read file NIST660CBI.gsas from the Tutorials CWInstDemo/data directory (download from https://subversion.xray.aps.anl.gov/pyGSAS/Tutorials/CWInstDemo/data/). After selecting this file, answer yes to "Is this the file you want?". As before, use Cancel to select the default CuKa lab data instrument parameters.

    Step 3.2: Change Data Range

     

    Since the background is quite curved at lower angles, reducing the angular range to be fit will require fewer background terms. Select Limits in the data tree and then set Tmin to 20.  Then select Background in the tree and change the number of background parameters to 8.

    Step 3.3: Add Peaks

     

    Select Peak List from the tree allows adding peaks. Zooming in on the lower portion of the pattern makes it easier to see all the peaks. Be sure to click on magnification icon a second time to turn off zoom mode. Then click on a point for each of the 20 peaks in the pattern. You should have a plot that looks like this:

    Step 3.3: Fit Peaks

     

    As the peaks are initially added to the table, the refine flag is set for the peak intensity. Fit the individual peak intensities by using Peak Fitting/Peakfit menu command. Provide a file name and the Rwp drops to ~40% with a reasonable background level, but not good peak shapes.

     

    Select the Instrument Parameter tree item, select the refinement flag for U, V, W, X, Y and SH/L, then select the Peak List tree entry again and use the Peak Fitting/Peakfit menu command. The fit improves a bit, but since the peak positions have not been refined, a good fit is not to be expected. Click on the refine column heading to the immediate right of the peak positions, then select “Y – vary all” and again use the Peak Fitting/Peakfit menu command. The fit improves significantly with an Rwp value of ~8%. The fit shows very small difference plot:

     

     

    However, pressing the w key in the plot window changes the plot appearance and it can be seen that the fit at low angle is significantly worse than at high angle. This suggests that log angle asymmetry may not be well fit.

    To improve this, we can force the SH/L value to be larger. Instead of the local minimum that was found with SH/L of ~0.003, we can select the Instrument Parameter tree item and set SH/L to a larger value, say 0.03. Then select the Peak List tree entry again and use the Peak Fitting/Peakfit menu command. The  Rwp improves somewhat, to circa 5%, but now the difference plot is greatly improved at low angle with SH/L increasing to 0.063:

    Step 3.4: Save Instrument Parameters

     

    Select the Instrument Parameter tree entry and then use the Operations/Save Profile… menu command to write a file. This can be used as the starting point for future refinements. The plot shown at this point compares the mostly meaningless default starting profile terms (as solid lines) to the fit here (as dashed lines). Using Operations/Load Profile… resets the default values to the current refinement parameters, which makes for a simpler plot.

    Step 3.5: Compare individual peaks widths to fit profile

     

    While the Instrument Parameter tree entry is selected, turn off refinement of the U, V, W X, and Y refinement flags (SH/L can be left to continue to refine) and then select the Peak List tree entry.  Double-click on the refine headings for the sigma and gamma columns to refine the individual peak widths and again and use the Peak Fitting/Peakfit menu command. The fit quality does not change very significantly, and selecting the Instrument Parameter tree entry generates a plot that shows that the individual peak fits are quite close to the fitted curves.