Neutron CW Powder Data - Yttrium Iron/Aluminium Garnet

A video version of this tutorial is available at https://anl.box.com/v/NeutronCWPowderData

In this tutorial you will refine the structure of yttrium iron/aluminum garnet using constant wavelength neutron data. The structure is cubic with four different atomic sites two of which are occupied by both iron and aluminum. The data was taken on the D1a powder diffractometer at the ILL, Grenoble, France using 1.909Ε wavelength neutrons.

If you have not done so already, start GSAS-II.

Step 1: read in the data file

1.      Use the Import/Powder Data/from GSAS file menu item to read the data file into GSAS-II. This read option is set to read any of the powder data formats (except neutron TOF time map files) defined for GSAS (angles in centidegrees). Other submenu items will read the cif format or the xye format (angles in degrees) used by Topas, etc.  Change the file directory to CWNeutron/data to find the file; you will need to change the file type to All files (*.*) to find the desired file.

2.      Select the garnet.raw data file in the first dialog and press Open. There will be a Dialog box asking Is this the file you want? Press Yes button to proceed.

3.      Select the inst_d1a.prm instrument parameter file in the second dialog and press Open.

At this point the left side of GSAS-II Data Window (the GSAS-II data tree) will have several entries and the plot window will show the powder pattern

Step 2: Create the phase

Use the Data/Add phase menu item to begin creation of the new phase for this garnet; enter a phase name in the dialog box, we assume ‘garnet’. The default phase information will immediately be displayed.

The General tab is visible; scroll bars can be used or you can resize the window to see the rest of the data. The Phase type is correctly set to “nuclear”; other options can be used for other structural problems (e.g. magnetic or faulted). Press the space group box (shows “P 1”), and enter the space group ‘I a 3 d’ (spaces between axial fields are required in GSAS-II) in the popup window and press OK, the space group information window will appear

Press OK to exit. The General tab display will change (principally changes in lattice parameter display). Enter the lattice parameter for garnet (a=12.19) in the appropriate field and press Enter. The display will change again to show the cell volume.

Click on the Data tab and select Edit Phase/Add powder histograms in the menu for this window. A Use data window will appear with only one choice PWDR garnet.raw: BANK 1. Select it and press OK. The Data tab will change

This window is the home of parameters that are both phase and data set dependent. These include phase fraction, crystallite size, mustrain & preferred orientation.

Step 3. Insert the atoms

Click on the Atoms tab; this is where you will insert the atoms for the garnet structure. The 6 sets of atom coordinates are:

TYPE

X

Y

Z

Y

0.12500

0. 00000

0. 25000

FE

0.00000

0.00000

0.00000

AL

0.00000

0.00000

0.00000

AL

0.37500

0.00000

0.25000

FE

0.37500

0.00000

0.25000

O

-0.03000

0.05000

0.15000

To begin use the Edit/Append atom in the menu on the Atoms tab 6 times to create the default set of atom places in the table; the table will look like

Then for each atom to be inserted, double click on the “H” in the Type column; a Periodic Table will appear

Each element has a small pull down selection for the possible valences (usually choose the “zero” one). Select “Y”, the Table will vanish and the Name and Type for that atom will change. Then enter the values for x, y and z; you can use Tab to move to the next one. You may use fractions for the atom coordinates (e.g. 1/4, 3/8). Do this for each atom in the Atoms table. NB: be careful about the signs for the O-atom positions. You can leave both frac and Uiso at the default values. Your result should look like


You can now do your first Rietveld refinement on this problem. To do this, do Calculate/Refine in the left side of the menu; a file dialog will ask you for a name for this project; you can change the directory if you wish. We assume the name “YAG”; the current project will be saved as YAG.gpx and the first backup file (YAG.bak0.gpx) will also be created and then the Rietveld refinement will be performed. By default, only the histogram scale factor (found under Sample Parameters for PWDR garnet.raw: BANK1 in the GSAS-II data tree) and 3 background coefficients are refined. The resulting powder pattern

shows a pretty poor fit (Rwp ~39%) and details can be found in the YAG.lst file. What appears to be in error includes some structural features (I’d first suspect site fractions for the Fe/Al sites) and something about the peak positions (may be lattice parameter). We can introduce all these parameters now.

1.      Go to Phases/garnet and check Refine unit cell in the General tab.

2.      Next go to Constraints in the main part of the GSAS-II data tree (near the top). You will see an empty window with 3 tabs; Phase is the one you want. Select Edit Constr./Add equivalence from the menu. You will see the following new window

select 0::AUiso:1 for Fe2… and press OK; a new window will appear

select 0::AUiso:2 for Al3 and press OK. That will form the first equivalence you need between the Fe and Al atoms that occupy the atom site at 0,0,0 in the cell. This shows up in the Constraints window.

Now do the same for the atoms 0::AUiso:3 for Al4 and 0::AUiso:4 for Fe5 to make that pair of atoms have the same Uiso.

3.      Next select Edit Constr./Add constraint equation. A now familiar window will appear; select 0::Afrac:1 for Fe2 and press OK. Again you will see the same second window; select 0::Afrac:2 for Al3 and press OK. Do the same thing for 0::Afrac:3 for Al4 – you may have to scroll down the list to see this – and 0::Afrac:4 for Fe5. When done the Constraints window should look like

This process set the equivalences/constraints for the two Fe/Al sites in the garnet so that refinement of frac and Uiso will succeed. GSAS-II constraints will correct the site fractions and Uiso values so that they conform to the constraints as written. You need not be concerned about their starting values beforehand. Also note the way each parameter was named; the general form is p:h:name:num where p is a phase number, h is a histogram number, name is the parameter name and num is an optional number (e.g. an atom number).

4.      Go to the Phases/garnet item in the GSAS-II data tree and select the Atoms tab. Note the frac values are unchanged from what you originally entered. Don’t worry, they will be corrected in the next refinement. We now have to set the refinement of frac for the Fe/Al sites. There are many ways to do this, we will show you one method now. Select row 1 for Fe(2) and then holding the Ctrl key down select rows 2-4; they will appear all blue or gray. Next select Edit Atoms/On selected atoms…/Refine selected; a new window will appear

 

For now select F – site fraction. You could select all three, GSAS-II would refine frac & Uiso but not the coordinates as they are fixed as special positions in this case. The Atom window will have an F in the refine column each of these atoms.

 

You are now ready for your second Rietveld refinement; select Calculate/Refine from the left side of the menu bar. There is now a much better fit with Rwp ~12% and a powder pattern that looks like (select PWDR garnet.raw from the GSAS-II data tree to see it)

There appears to be some differences in peak intensities and an interesting offset at the low end of the pattern. Let us add the remaining atom parameters (Uiso for each and the O(xyz) parameters. Go to Phases/garnet and select the Atoms tab.

Notice that the frac values for the Fe/Al atoms now conform to the constraints. For each atom in turn, double click on the refine box. A pull down list will appear, select U for the Y atom, FU for Fe/Al atoms and XU for the O atom. Your list should look like

when done. Now you can do your third Rietveld refinement; select Calculate/Refine. The resulting fit is

with Rwp ~10%. There is still an apparent peak offset at the ends of the pattern and perhaps some misfit of the peak widths.

The latter are determined by the U, V & W parameters found in the PWDR garnet.raw: BANK1/Instrument Parameters window. Go there and select their Refine? flags. Next go to Sample Parameters.

Notice that the Histogram scale factor is already being refined. Now you will want to refine both Sample X displacement and Sample Y displacement. The values will be in mm if the Goniometer radius is correct; enter 650 for that value. Now you can do another Rietveld refinement; the fit

is nearly perfect! Rwp = 5.18%. You can look at the YAG.lst output file for all the parameters and their respective esds. I’ve pasted some of my results in below for you to compare.

Refinement results:

---------------------------------------------------------------------------------------------------------------------------------------

 Number of function calls: 7  Number of observations:  2677  Number of parameters:  20

 Refinement time =    3.448s,    0.862s/cycle, for 4 cycles

 wR =    5.18%, chi**2 =      10072.9, reduced chi**2 =   3.79

----------------------------------------------------------------------------------------------------------------------------------

Variables generated by constraints

 

 name  :     0::AUiso:1     0::AUiso:3          0::A0      ::constr0      ::constr1

 value :         0.0035        -0.0004         0.0067        -0.1083        -0.2843

 sig   :         0.0006         0.0007         0.0000         0.0127         0.0104

 

 Phases:

 Result for phase:  garnet

 Reciprocal metric tensor:

  names :            A11            A22            A33            A12            A13            A23

  values:    0.006738782    0.006738782    0.006738782    0.000000000    0.000000000    0.000000000

  esds  :    0.000000268                                                                          

 New unit cell:

  names :           a           b           c       alpha        beta       gamma      Volume

  values:   12.181739   12.181739   12.181739     90.0000     90.0000     90.0000    1807.706

  esds  :    0.000242                                                                   0.036

 

 Atoms:

   name      x         y         z      frac   Uiso     U11     U22     U33     U12     U13     U23

---------------------------------------------------------------------------------------------------------------------------------------

   Y(1)      Y:

 values:   0.12500   0.00000   0.25000   1.000 0.00442

 sig   :                                       0.00035

  Fe(2)     Fe:

 values:   0.00000   0.00000   0.00000   0.577 0.00347

 sig   :                                 0.009 0.00059

  Al(3)     Al:

 values:   0.00000   0.00000   0.00000   0.423 0.00347

 sig   :                                 0.009 0.00059

  Al(4)     Al:

 values:   0.37500   0.00000   0.25000   0.701-0.00041

 sig   :                                 0.007 0.00074

  Fe(5)     Fe:

 values:   0.37500   0.00000   0.25000   0.299-0.00041

 sig   :                                 0.007 0.00074

   O(6)      O:

 values:  -0.02942   0.05390   0.15059   1.000 0.00472

 sig   :   0.00006   0.00006   0.00007         0.00027

 

 Phase:  garnet  in histogram:  PWDR garnet.raw Bank 1

----------------------------------------------------------------------------------------------------------------------------------

 Final refinement RF, RF^2 = 2.27%, 3.70% on 89 reflections

 Bragg intensity sum = 2.74e+05

 

 Histogram:  PWDR garnet.raw Bank 1  histogram Id:  0

---------------------------------------------------------------------------------------------------------------------------------------

 PWDR histogram weight factor = 1.000

 Final refinement wR = 5.18% on 2677 observations in this histogram

 Other residuals: R = 4.22%, Rb = 3.40%, wRb = 3.55% wRmin = 2.67%

 Instrument type:  Debye-Scherrer

 

 Sample Parameters:

 names :         Scale    Absorption     DisplaceX     DisplaceY

 values:      612.9203        0.0000     1242.4926    -2837.8867

 sig   :        3.4719                     53.7322      117.5487

 

 Instrument Parameters:

 names :         Lam    Polariz.        SH/L           U           V           W           X

 value :    1.909000    0.000000    0.002000  258.609371 -645.406449  572.149553    0.000000

 sig   :                                        4.221864   10.112266    5.820126           

 

 Instrument Parameters:

 names :           Y        Zero

 value :    0.000000   -0.129218

 sig   :                0.005984

 

 Background function:  chebyschev

 value :      121.3    -27.19     27.04

 sig   :     0.2834     0.537    0.9925

 Background sums: empirical 2.41e+04, Debye 0, peaks 0, Total 2.41e+04

A useful display to examine is given by selecting Covariance in the GSAS-II data tree

This is a graphical rendering of the variance-covariance matrix from the last refinement. This matrix is symmetric about the diagonal; moving your cursor about it will display parameter names, values and esds on the diagonal and the covariance between a pair of parameters off the diagonal. Intense red or green indicates high covariance (green for + and red for -) and yellow is for close to zero covariance. High covariances naturally occur for profile coefficients and for background parameters. You can change the color scheme, the default is RdYlGn. If during the course of one of your refinements you see white bands in this display: that is the signature of some singularities in your refinement. The offending parameter(s) should not be refined independently; perhaps a constraint/equivalence is needed.