Laboratory X-ray Powder Data - Fluroapatite

In this tutorial you will refine the structure of fluoroapatite, Ca5F(PO4)3, using constant wavelength laboratory X-ray powder diffraction data. At the completion of the refinement you will then prepare a drawing of the fluoroapatite structure. The structure is hexagonal with four different kinds of atoms spread over seven different sites. The data was taken on a conventional Bragg-Brentano powder diffractometer using CuKa radiation.

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

We suggest that you do the CW Neutron powder exercise first before doing this one. Some things are covered there in more detail that we will not cover here.

Step 1: read in the data file

1.      Use the Import/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). The xye format (angles in degrees) used by Topas, etc. can also be read via the Import/Import Powder Data menus.  Change the file directory to Exercises/fluroapatite to find the file; you will need to change the file type to any file (*.*) to find the desired file.

2.      Select the FAP.XRA 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_XRY.PRM instrument parameter file in the second dialog and press Open.

At this point the GSAS-II data tree window will have several entries and the plot window will show the powder pattern

Step 2: Create the phase

For this step we will take advantage of having an old GSAS experiment file with all the parameters for fluroapatite otherwise you’ll have to follow the steps used for the CW neutron example on garnet with the following information:

Phase name = ‘fap’, Space group = P 63/m, unit cell a = 9.372, c = 6.886

Atom coordinates:

TYPE

X

Y

Z

Ca

0.333333

0.666667

0.001

Ca

0.242

0.992

0.25

P

0.397

0.367

0.25

F

0.0

0.0

0.25

O

0.325

0.485

0.25

O

0.591

0.469

0.25

O

0.340

0.258

0.07

To import the fluroapatite phase information from the file FAP.EXP use the Import/Import Phase menu menu to see a pulldown menu. Select from GSAS .EXP file. The file selection dialog will still be set to the directory the data was found; click on FAP.EXP and Open to open it. A small dialog box with a phase name of ‘fap’ will appear. We didn’t change it so press OK to accept it.

Step 3 Add the powder data to the phase

The GSAS-II data tree should now have a Phase entry of fap. Select it.to view the fap phase information

You can see that the number of each kind of atom gives 2 formula units per cell. To add the powder data to this phase click on the Data tab and then select Edit/Add powder histograms from the menu. A Use data window will appear with only one choice PWDR FAP.XRA: BANK 1. Select it and press OK. The Data tab will change; press the Show PWDR FAP.XRA: BANK 1 check box; the window will change again

We will return to this window later when we consider the effect of crystallite size and mustrain broadening.

Step 4: Adjust background parameterization

You may have noticed that the background in this powder pattern rises significantly at low angles; there is also a less apparent rise at the high angle end as well. The default background function doesn’t handle this very well so find the Background item under PWDR FAP.XRA: BANK1 in the GSAS-II data tree and press it. The Background window will appear

Change the background function to log interpolate and the number of coefficients to 9. This will put background points at the two limits and at equal spaces in log(2Q) in between so there are more where the background is changing most rapidly. A linear interpolation is then used to compute the background for all points in the pattern during the Rietveld refinement.

Step 5 1st Rietveld refinement

You are now ready for the 1st Rietveld refinement; the histogram scale (found in Sample Parameters) and background will be refined. Press Calculate/Refine in the GSAS-II data tree menu. You will be asked for a project file name, we used ‘fap’ and made the file fap.gpx. The refinement proceeds and when complete (Rwp ~42.8%) a small dialog box will appear asking Load new result? Press OK; the windows will be updated and a new plot is displayed.

Expanding the plot shows that much of the difference is that the calculated peaks are out of place. This is due to lattice parameters and also that in this Bragg-Brentano experiment the sample position is offset from the focusing circle. Important: this is the most likely reason for peaks displacement errors in laboratory data, not the zero point. The lattice parameter flag is on the General tab for the Phase fap and the sample displacement is found on the Sample Parameters item under PWDR FAP.XRA: BANK1 in the GSAS-II data tree. Go to both places and set those flags.

Step 6 2nd Rietveld refinement

Now do the Rietveld refinement by Calculate/Refine menu on GSAS-II data tree window. The plot will be
 

noticeably improved (Rwp ~17%). Close inspection (see inset) shows that most of the differences are in the widths of the peaks so we should refine crystallite size and mustrain parameters next.

Step 7 3rd Rietveld refinement

Select the Phases/fap item in the GSAS-II data tree and then select the Data tab and set the refine flags for both size and mustrain. The window should look like

Now do the refinement; press the Calculate/Refine menu item on the GSAS-II data tree window. Do not be alarmed about how the Rwp jumps around on the progress bar; that is a consequence of how the Levenberg-Marquardt algorithm does a least squares minimization. The result in the end is noticeably better than before (Rwp=11.4%)

Step 8. 4th Rietveld refinement

Now we can refine atom parameters. Select Phases/fap and the Atoms tab; the Phase data for fap window will display

Double click the refine column header; a new window will show Refinement controls

Select X - coordinates and U - thermal parameters and press OK. The Atoms tab will show new refine flags

Now run the refinement; press the Calculate/Refine menu item on the GSAS-II data tree window. The result is a bit better (Rwp=10.20%) and the plot is pretty much the same as before

and the atom parameters are

The refinement is now essentially complete. The file fap.lst has the result of the last cycle of refinement with values and esds for all the parameters

Refinement results:
---------------------------------------------------------------------------------------------------
Number of function calls: 12  Number of observations:  5751  Number of parameters:  34
Refinement time =   18.062s,    4.516s/cycle, for 4 cycles
wRp =   10.20%, chi**2 =      18996.3, reduced chi**2 =   3.32
arning: invalid value encountered in divide

Phases:
Result for phase:  fap
Reciprocal metric tensor:
 names :            A11            A22            A33            A12            A13            A23
 values:    0.015177579    0.015177579    0.021087097    0.015177579    0.000000000    0.000000000
 esds  :    0.000000312                   0.000000250
New unit cell:
 names :           a           b           c       alpha        beta       gamma      Volume
 values:    9.372773    9.372773    6.886390     90.0000     90.0000    120.0000     523.912
 esds  :    0.000185                0.000041                                           0.008

Atoms:
  name      x         y         z      frac   Uiso     U11     U22     U33     U12     U13     U23
---------------------------------------------------------------------------------------------------
   CA1     Ca:
values:   0.33333   0.66667   0.00176   1.000 0.00811
sig   :                       0.00029         0.00036
   CA2     Ca:
values:   0.24157   0.99219   0.25000   1.000 0.00723
sig   :   0.00015   0.00019                   0.00028
    P3      P:
values:   0.39688   0.36762   0.25000   1.000 0.00759
sig   :   0.00020   0.00019                   0.00040
    F4      F:
values:   0.00000   0.00000   0.25000   1.000 0.01668
sig   :                                       0.00137
    O5      O:
values:   0.32553   0.48512   0.25000   1.000 0.00811
sig   :   0.00042   0.00043                   0.00104
    O6      O:
values:   0.58982   0.46887   0.25000   1.000 0.01071
sig   :   0.00044   0.00047                   0.00110
    O7      O:
values:   0.33994   0.25894   0.07098   1.000 0.01035
sig   :   0.00035   0.00034   0.00034         0.00077

Phase:  fap  in histogram:  PWDR FAP.XRA: BANK1
---------------------------------------------------------------------------------------------------
Final refinement RF, RF^2 = 3.27%, 7.65% on 325 reflections

Size model:     isotropic equatorial:       0.400, sig:   0.070 LG mix coeff.:      1.0000

Mustrain model: isotropic equatorial:       966.1, sig:     25.3 LG mix coeff.:      1.0000

Histogram:  PWDR FAP.XRA: BANK1  histogram Id:  0
---------------------------------------------------------------------------------------------------
Final refinement wRp = 10.20% on 5751 observations in this histogram
Instrument type:  Bragg-Brentano

Sample Parameters:
names :         Scale         Shift  Transparency
values:       42.2328       67.4518        0.0000
sig   :        0.1416        0.3528

Background function:  log interpolate
value :      623.3     404.2     262.4     153.8     104.4     71.28     50.69     49.62     61.33
sig   :      5.265     3.069     2.323     1.753     1.311    0.9978    0.9045     1.121     1.425

Step 9. Draw the structure

What we like to show is the unit cell contents with the PO4-3 ions as tetrahedra and the Ca and F atoms as balls. Begin by finding Phases/fap in GSAS-II data tree and selecting the Drawing Options tab. The Phase data for fap window shows Drawing controls

The plot will show a new tab marked fap showing some balls in various colors.

Notice the slider controls in Drawing controls; you can change them to change the how the structure is displayed. Set the Show unit cell? check box if needed (the drawing will show the unit cell edges) and then press the Draw atoms tab; this will show the list of atoms that are drawn in the picture.

This is a copy of what is in the Atoms table; there are columns that allow you to change how the atoms are displayed, their labels and their color all controlled on an atom-by-atom basis. Now if the contents of the Atoms table change (e.g. by refinement) then you must manually update the Draw Atoms table by erasing all the Draw Atoms. They are then automatically refreshed from the Atoms table with the new values. Do this by selecting all the Draw Atoms; double click the blank in the upper left corner of the table. All atoms will be highlighted in dark gray. Then press Edit/Delete atoms in the Draw Atoms menu. All the atoms will vanish and then reappear with updated values. Now we can draw the structure assured that we are using the final result from the refinement.

To build the structure model we want to show with PO4 tetrahedra and balls for the F and Ca atoms in a unit cell box (the box should already be visible) do the following steps:

1.      Select all the atoms in the Draw Atoms tab by double clicking in upper left corner box of the table. All atoms in the table are then displayed in dark gray and they all are green on the drawing indicating their selection.

2.      Select Edit/Fill unit cell from the Draw Atoms menu. The drawing will show the unit cell filled with atoms in positions equivalent to the original set and the Draw Atoms table will have all of them listed. The Sym Op column in the table shows the symmetry operator number and unit cell translation used to generate that position.

3.      Double click on the column label Type. A small dialog window will appear with a list of element types in this structure. Select P by checking the box and then press OK. All the P atoms will be bright green and they will be highlighted in dark gray in the table

4.      Select Edit/Fill CN-sphere in the Draw Atoms menu. Each P atom will now have its full complement of 4 O atoms.

5.      Repeat step 3 to select all the P atoms again.

6.      Select Edit/Atom style from the Draw Atoms menu. A small dialog bow will appear with a list of possible atom drawing styles. Notice the first one is blank; that will cause the atom to not be drawn. Select polyhedral and press OK. Each P atom will be drawn as a brass colored polyhedron (with too many faces to be a tetrahedron because a nearby Ca atom was included – this will be fixed in a moment).

7.      Now do step 3 yet again but this time select the O atoms.

8.      Select Edit/Atom style and pick the blank entry and press OK; the O atoms will vanish leaving some odd polyhedra and the Ca and F atoms.

9.      Select the Drawing Options tab and change the Bond search factor to 0.80 and press Enter; the odd polyhedra will immediately change to tetrahedra.

10.  You can adjust the van der Waals scale to make all the balls any size you desire.

11.  If you don’t like the fact that both Ca and F are in a very similar green, you can change this. Select the Draw Atoms tab, then do step 3 selecting the Ca atoms.

12.  Select Edit/Atom color in the Draw Atoms menu. A color selection dialog box will appear (NB: this dialog is operating system dependent – we will assume you are using a Windows7 machine). The dialog box looks like (I pressed Define Custom Colors)

The steps for changing a color is to either a) choose your color by finding it in Basic colors and then press OK or b) press Define Custom Colors, move the cross around on the spectrum display, set the vertical slider for the luminosity (ColorSolid will show the result), and then press OK. The drawing will now show that color for the atoms and the color will appear in the Draw Atoms table. If you don’t like your colors select Edit/Reset atom colors to put them back to their default colors. In my drawing I’ve made the Ca atoms a medium gray

Step 10. Calculate bond distances and angles

GSAS-II will compute all the distances and angles among all the atoms you select in the Atoms table with controls on the range of atom-atom distances to consider either globally or by atom type.

1.      To start select the Atoms tab in Phases/fap.

2.      Select the first Ca atoms by clicking on its row label (an “0”). Add to the selection the other Ca atom and the P atom in the same way with the Ctrl key down; all will be highlighted in dark gray.

3.      Select Compute/Distances Angles from the Atoms menu. A small dialog box will appear

Here you have individual controls on various atom radii to consider for both distance and angle calculations as well as global search factors. Considering our experience with drawing the PO4 tetrahedra the Bond and Angle search factors may be too large for this case. Change both to 0.8 and press OK. GSAS-II will then display on the console formatted tables of individual atom distances and angles with esds as appropriate for the two Ca atoms and the P atom.

********************************************************************************
   Interatomic Distances and Angles for phase fap
********************************************************************************

 Space Group: P 63/m
 The lattice is centrosymmetric primitive hexagonal
 Multiplicity of a general site is 12
 The Laue symmetry is 6/m
 The inversion center is located at 0,0,0

 The equivalent positions are:
 ( 1)     X ,    Y ,    Z               ( 2)    X-Y,    X ,1/2+Z
 ( 3)    -Y ,   X-Y,    Z               ( 4)    -X ,   -Y ,1/2+Z
 ( 5)    Y-X,   -X ,    Z               ( 6)     Y ,   Y-X,1/2+Z


 Unit cell: a = 9.37277(18) b = 9.372773 c = 6.88639(4) alpha = 90. beta = 90. gamma = 120. Volume = 523.912(8)

 Distances & angles for  CA1  at      0.333333    0.666667 0.00176(29)
********************************************************************************
  To       cell +(sym. op.)      dist.       CA1         CA1          O5          O5          O5          O6          O6
  CA1     [ 0 1 0]  +(  -2)  3.4674(30)
  CA1     [ 0 1 1]  +(  -2)  3.4190(14)    180.000
  O5      [ 0 0 0]  +(   1)  2.3872(28)   135.73(14)  44.27(14)
  O5      [ 1 1 0]  +(   3)  2.3872(3)    135.73(14)  44.27(14)   74.38(21)
  O5      [ 0 1 0]  +(   5)  2.3872(3)    135.73(14)  44.27(14)   74.38(21)   74.38(21)
  O6      [ 0 0-1]  +(   2)  2.4603(30)   45.20(15)   134.80(15)  124.33(22)  154.25(23)  92.82(17)
  O6      [ 1 1-1]  +(   4)   2.460(4)    45.20(15)   134.80(15)  92.81(17)   124.33(22)  154.25(23)  75.83(23)
  O6      [ 0 1-1]  +(   6)   2.460(4)    45.20(15)   134.80(15)  154.25(23)  92.82(17)   124.33(22)  75.83(23)   75.83(23)

 Distances & angles for  CA2  at   0.24157(15) 0.99219(19)        0.25
********************************************************************************
  To       cell +(sym. op.)      dist.        F4          O6          O7          O7          O7
  F4      [ 0 1 0]  +(   1)  2.3016(11)
  O6      [ 1 1 0]  +(   3)   2.355(4)    152.08(23)
  O7      [ 0 1 0]  +(   1)  2.5131(29)   81.13(14)   74.61(21)
  O7      [ 0 1 0]  +(   6)  2.3441(29)   102.87(15)  85.36(16)   135.16(23)
  O7      [ 0 1 0]  +(  -3)  2.3441(26)   102.87(15)  85.36(16)   77.52(11)   141.11(28)
  O7      [ 0 1 1]  +(  -4)  2.5131(25)   81.13(14)   74.61(21)   58.75(24)   77.52(11)   135.16(23)

 Distances & angles for  P3  at   0.39688(20) 0.36762(19)        0.25
********************************************************************************
  To       cell +(sym. op.)      dist.        O5          O6          O7
  O5      [ 0 0 0]  +(   1)   1.548(4)
  O6      [ 0 0 0]  +(   1)  1.5668(3)     110.3(5)
  O7      [ 0 0 0]  +(   1)  1.5161(26)   110.23(29)  108.59(29)
  O7      [ 0 0 1]  +(  -4)  1.5161(24)   110.23(29)  108.59(29)   108.8(4)

There is probably too many bonds shown for the Ca1 atom; you can repeat the calculation with somewhat smaller Ca radii to fix this. Setting the Bond and Angle Ca radii to 2.1 and 1.9, respectively, gave

********************************************************************************
   Interatomic Distances and Angles for phase fap
********************************************************************************

 Space Group: P 63/m
 The lattice is centrosymmetric primitive hexagonal
 Multiplicity of a general site is 12
 The Laue symmetry is 6/m
 The inversion center is located at 0,0,0

 The equivalent positions are:
 ( 1)     X ,    Y ,    Z               ( 2)    X-Y,    X ,1/2+Z
 ( 3)    -Y ,   X-Y,    Z               ( 4)    -X ,   -Y ,1/2+Z
 ( 5)    Y-X,   -X ,    Z               ( 6)     Y ,   Y-X,1/2+Z


 Unit cell: a = 9.37277(18) b = 9.372773 c = 6.88639(4) alpha = 90. beta = 90. gamma = 120. Volume = 523.912(8)

 Distances & angles for  CA1  at      0.333333    0.666667 0.00176(29)
********************************************************************************
  To       cell +(sym. op.)      dist.        O5          O5          O5          O6          O6
  O5      [ 0 0 0]  +(   1)  2.3872(28)
  O5      [ 1 1 0]  +(   3)  2.3872(3)    74.38(21)
  O5      [ 0 1 0]  +(   5)  2.3872(3)    74.38(21)   74.38(21)
  O6      [ 0 0-1]  +(   2)  2.4603(30)   124.33(22)  154.25(23)  92.82(17)
  O6      [ 1 1-1]  +(   4)   2.460(4)    92.81(17)   124.33(22)  154.25(23)  75.83(23)
  O6      [ 0 1-1]  +(   6)   2.460(4)    154.25(23)  92.82(17)   124.33(22)  75.83(23)   75.83(23)

 Distances & angles for  CA2  at   0.24157(15) 0.99219(19)        0.25
********************************************************************************
  To       cell +(sym. op.)      dist.        F4          O6          O7          O7          O7
  F4      [ 0 1 0]  +(   1)  2.3016(11)
  O6      [ 1 1 0]  +(   3)   2.355(4)    152.08(23)
  O7      [ 0 1 0]  +(   1)  2.5131(29)   81.13(14)   74.61(21)
  O7      [ 0 1 0]  +(   6)  2.3441(29)   102.87(15)  85.36(16)   135.16(23)
  O7      [ 0 1 0]  +(  -3)  2.3441(26)   102.87(15)  85.36(16)   77.52(11)   141.11(28)
  O7      [ 0 1 1]  +(  -4)  2.5131(25)   81.13(14)   74.61(21)   58.75(24)   77.52(11)   135.16(23)

 Distances & angles for  P3  at   0.39688(20) 0.36762(19)        0.25
********************************************************************************
  To       cell +(sym. op.)      dist.        O5          O6          O7
  O5      [ 0 0 0]  +(   1)   1.548(4)
  O6      [ 0 0 0]  +(   1)  1.5668(3)     110.3(5)
  O7      [ 0 0 0]  +(   1)  1.5161(26)   110.23(29)  108.59(29)
  O7      [ 0 0 1]  +(  -4)  1.5161(24)   110.23(29)  108.59(29)   108.8(4)

which is probably more reasonable.

This concludes this tutorial for Rietveld refinement of fluroapatite.