8th Canadian Powder
Diffraction Workshop http://www.cins.ca/cpdw/
June 2010 notes by:
Lachlan Cranswick lachlan.cranswick@nrc.gc.ca
Ian Swainson ian.swainson@nrc.gc.ca
Michael Gharghouri
Michael.Gharghouri@nrc-cnrc.gc.ca
(File can be freely used and redistributed for those who wish to learn how to use GSAS for Rietveld refinement, or adapted to other
Rietveld software. Please keep the above notice intact.)
Workshop sponsored by http://www.uqtr.ca/ http://irh.uqtr.ca/ http://www.hydroquebec.com/ http://www.cins.ca/ http://lansce.lanl.gov/lujan/
01: P. 2
02: P. 3 to 14
02a: P. 15 to 16
Installing GSAS, EXPGUI and example files
An Easy start: refining the structure of corundum powder using data collected on a neutron powder diffraction system
Creating a GSAS neutron instrument parameter file using INSTEDIT
03: P. 17 to 30
Refining a standard for a dual wavelength X-ray diffractometer
03a: P. 31 to 32
Creating a GSAS XRD instrument parameter file using INSTEDIT
04: P. 31 to 35
05: P. 36 to 40
06: P. 41 to 44
Applying an existing GSAS EXP file to a new diffraction data file
Importing a Cif structure file and determining the polarisation of the X-ray beam using Y
2
O
3
Model based Le Bail fitting using GSAS for
“pre-structure refinement” whole profile fitting
07: P. 45 to 50
08: P. 51 to 60
True (model-less) Le Bail fitting using GSAS
Problems with space group settings and determining the neutron data wavelength by use of NIST Si 640c;
09: P. 61 to 74
10: P. 75 to 86
11: P. 87 to 93
and modelling a second trace phase
Combined Refinement of multiple datasets (X-ray and Neutron)
Importing a structure using a GSAS macro file, and using occupancy constraints and charge balance restraints
Quantitative Phase Analysis example using GSAS
12: P. 94 to 95
13: P. 96 to 101
Applying a QPA GSAS EXP file to a new diffraction file
Quantitative phase analysis involving preferred orientation
14: P 102 to 117
Multiphase refinement across neutron and X-ray datasets.
Fourier difference maps.
15: P 118 to 133
Simple rigid body in neutron diffraction
Appendix 1. P. 134:
Additions/corrections
(format of this document based on plagiarising (with permission) the Crystals Single Crystal workshop notes by Richard Cooper and David Watkin, Chemical Crystallography, Oxford University; http://www.xtl.ox.ac.uk/ ) http://www.nrc-cnrc.gc.ca/
1

Installing GSAS, EXPGUI
To install GSAS and EXPGUI on an MS-Windows PC:
 first download the GSAS and EXP installers from Brian Toby’s FTP site at ftp://ftp.ncnr.nist.gov/pub/cryst/gsas/ (or on the workshop CD in the
\gsas_install\ directory). Run gsas+expgui.exe
. Accept all the default options.

To update GSAS to the latest version, download the GSAS distribution
( gsaskit.exe
) from http://www.ccp14.ac.uk/ccp/ccp14/ftpmirror/gsas/public/gsas/ (or on the workshop CD in the \gsas_install\gsas_kits directory) and extract the files into the install directory. ( usually c:\gsas\ ).

To update to the latest version of EXPGUI, download the latest expgui_Alpha.zip
from ftp://ftp.ncnr.nist.gov/pub/cryst/gsas/ (or on the CD in the \gsas_install\gsas_kits directory)and extract it into the \gsas\expgui\ directory.
Important: For a Windows system: if the directory depth for the GSAS installation and/or the data files is too deep, GSAS functions such as Powpref and Genles may give an error and not run correctly.
The reference to use for GSAS in any resulting publications is: A.C. Larson and R.B.
Von Dreele, "General Structure Analysis System (GSAS)", Los Alamos National
Laboratory Report LAUR 86-748 (1994) .
The reference to cite in any resulting publications for using EXPGUI is: B. H. Toby,
EXPGUI, a graphical user interface for GSAS, J. Appl. Cryst. (2001). 34, 210-213
Installing tutorial example files
Extract the cpdw_prac_files.zip
file (located in the root directory of the CD-ROM provided with the tutorial manual) into the c:\cpdw directory of your PC.
They can also be found on the web at http://www.cins.ca/cpdw/files/cpdw.zip
2


2
3
Important: Before running your samples, the powder diffractometer should be aligned as well as possible. If the user of a diffraction system, check the alignment with suitable standard such as NIST Silicon 640c before running your samples. If the diffractometer is not well aligned, raise the problems with those responsible for the equipment and get the system aligned before continuing. It is easy to invalidate results by running samples on a poorly aligned and maintained equipment.
As a first (easy) example, we are going to refine on constant wavelength neutron powder diffraction data. Constant wavelength neutron powder diffraction data can be easy to fit using conventional Rietveld refinement due to symmetric peak-shapes and moderately broad peak widths (compared to X-ray systems). This corundum data is from the C2 neutron powder diffractometer at Canadian Neutron Beam Centre,
National Research Council, Chalk River, Ontario, Canada.
Double click the EXPGUI icon on the desktop, and the "Select an experiment file to read" dialog will be displayed. Browse to: c:\cpdw\al2o3_neutron directory, type in
“corundum” and click READ.
EXPGUI will give a message that the file does not exist. Select the Create button to create the CORUNDUM.EXP file.
Enter an experimental title “Corundum run on C2 NPD at Chalk River” and click
" OK" to give the following starting EXPGUI screen.
3

Important:
Before you can add any “histograms” (powder diffraction data), you must first add in a “phase” (crystal structure) data
Corundum has a Rhombohedral structure. For the convenience to both the GSAS software (which can only refine rhombohedral structures in the hexagonal setting) the following structure is in the hexagonal setting with the following crystallographic details:
Space group: R –3 c
Unit cell: a=b= 4.77
Å c= 13.02
Å : alpha=beta= 90 ° gamma = 120 °
Atom co-ordinates: (x, y, z)
Al : 0 0
O : .31 0
0.35
0.25
Select the Phase tab and then the “Add Phase” button. This will bring up an “add new phase” dialog where you input the Phase title (Corundum); the Space Group (R –
3 c) (make sure to include the spaces) and the unit cell constants. Then select the
“
Add
” button. GSAS will then give a symmetry analysis output for you to check and make sure you have entered the space group correctly (using the
International Tables or similar database to validate the output). Select
“ Continue ” once you are happy with this. This will give the following main
EXPGUI screen with the cell information but no atoms.
Now select the “ Add New Atoms ” button and add in the atom information using the keyboard. Select the “ More atom boxes ” to add an extra line to insert the Boron atom information.
Al : 0 0
O : .31 0
0.35
0.25
Select the “ Add Atoms ” button to go back to the main EXPGUI screen where all the crystallographic information is now visible. The GSAS default values of Uiso (0.025) are usually too large for inorganic structures. Often it is better to reset the starting UISO values to 0.01. Change the UISO values from 0.025 to 0.01 by selecting the UISO values one at a time with the mouse and changing to 0.01.
4

Important: Before you can add a histogram, you need to create or have an existing GSAS instrument parameter file ready. Assuming this is the first time you have used GSAS and you don’t have an instrument parameter file for this single wavelength neutron powder diffractometer, we will now create one.
From the top menu, select
“Powder, Instedit”
then the Cancel button to create a new
GSAS Instrument Parameter file. This will bring up the following screen. In the
“
Data type
”, select
CW Neutron for constant wavelength Neutron.
For title, give “ Generic prm file for C2 NPD using 531 of Silicon monochromator ” and for Instrument Name give “ C2 531 Silicon Mono ”. The wavelength is 1.33034
Å, give a zero correction of 7.77
centidegrees (normally this should be a constant of the diffractometer but if not determined, it can be refined). The zero correction offset for the diffractometer (which should be a constant), can be determined experimentally for a diffractometer by running NIST 640c silicon. The manager of the diffractometer should be able to provide the above information.
5

At this point DO NOT touch the Import Profile icon or the Add Profile icon. In the
Select Profile area, select Profile type“3”
(Pseudo-Voight/FCJ Assym). This will display a number of fields relating to fitting the peak profile (width, shape, asymmetry)
In the profile fields, add a peak cutoff of 0.001
and a GW (constant width) of 400 .
In this neutron diffraction example, we do not have to worry about the Finger Cox
Jephcoat (FCJ) peak asymmetry as there is negligible peak asymmetry in this neutron powder diffractometer.
Now select the “Save As” button and save the file with a suitable filename; in this case c2neutron.prm
. Then Close Instedit .
Select the “Histogram” tab followed by the “Add Histogram” button
To the right of “Data File” , use the “Select File” button and add the “corun531.gsa” dataset; following by the “Select File” button to the right of the “Instrument Parameter
File” to select the “ c2neutron.prm
” file. Make sure the “Select Bank” and “Select
Set” are set to 1 as pointed to in the screen image to the left of this text. Select the
“Add” button to add the histogram into GSAS.
6

Important: If you use a random GSAS instrument parameter file, there are no guarantees that it contains the correct information and the correct instrumental settings; and you should check things to make sure it has provided correct information.
Important: Many people are in the habit of choosing a type of background function out of habit. In this demonstration, a Shifted Chebyshev (Function 1) is used and can be very flexible for fitting bumpy backgrounds. Other people swear by a Cosine Fourier Series (Function 2)
At this point, it would be good to manually fit a background function to the background in preparation for us starting the refinement. For this we will use the bkgedit program. Prior to running bkgedit , powpref and genles must be run. Run the
Powpref icon in the top middle menu bar in EXPGUI, followed by GENLES .
After running powpref and genles , run “Powder, bkgedit ” to bring up the background editing screen. The main aim of this is to select background points by pointing and clicking with the mouse, then fit a GSAS background function to the data which is then fixed until you decide to let the background refine. This can save on quite a bit of tedium trying to immediately refine a GSAS background function at an early stage of the refinement.
Use the mouse, Add, Zoom and Delete options to visually select background points.
Which below are shown as pink triangles.
7

Then use the Fit icon to fit a line. Gradually increasing the number of terms until you get a good fit to the background function. In this case, 6 terms seem to be doing a good job. The dotted blue line shows the background function.
8

Now select the “
Save in EXP File & Exit
” icon at the bottom right of the screen to save the fitted background profile. When EXPGUI prompts that the EXP file has been modified, select the “
Load new
” file (unless you have made a mistake). If you have made a mistake, select the “continue with old” button. EXPGUI will recognise the new background parameters by giving the new number of terms you used to fit the background profile. It is recommended that the background should not be refined until everything else is pretty much under control.
In the Profile tab, make sure the profile type is profile 3 (Pseudo-Voight with Finger-
Cox-Jephcoat peak asymmetry function). It is possible that the instrument parameter file you used defaults to another profile type, so you should check this. If it is not profile number 3, then change it to profile type 3 . Now run powpref and genles to do some cycles of refinement with only the scale factor refining.
Now run liveplot (and keep this window open) to see the state of the refinement in terms of how well the calculated pattern based on the structure model is fitting the data. By default, the scale factor is set to refine . The black crosses are the raw data; the red line is the calculated pattern and the blue line below is the difference. The aim is to get the calculated pattern matching the observed pattern with the difference being as close to a flat line as possible.
Using the “ File, Tickmarks ” option in Liveplot, you can also overlay where HKLs are expected, and the [Control] [Shift] and left click on the left Mouse button near the
HKL will label the HKL. (To have HKL labels near the peaks, you have to enable the tickmarks via “File, Tickmarks” in Liveplot).
If you have extra peaks in the raw diffraction data that are not matched up by a calculated HKL, this can mean you have the wrong cell or spacegroup, or an impurity phase.
Important: There is no fixed method of performing a Rietveld refinement in terms of the order of parameters to be released. The following is just a suggestion, and should not be blindly followed in all cases. Each refinement may require its own custom refinement sequence for parameters to refine in a stable manner.
In the LS controls Tab, set the number of cycles to 8 and in the Profile Tab , set the profile cutoff to 0.001
(if it is not already at 0.001). By default many GSAS parameter files default to 0.01, which is not adequate for many X-ray and neutron diffractometers.
9

Set the unit cell parameter to refine (in the Phase tab) and the Zero parameter to refine in the Histogram Tab. Performing a refinement on NIST silicon should give you the zero offset of the diffractometer which should be a constant, however, to get the best fit to the neutron data using GSAS, it might vary slightly.
If you find that you have mucked up the refinement where parameters have gone to unreasonable values, it might be easier to go to a previous version of the EXP file. In
EXPGUI, go into “ File Open” menu and then select the “Include Archived Files”; this lists the previous archived files by time and date. Just select a previous EXP file you expect to be OK. If this turns out to be too late or early an EXP file, just try selecting another one.
Important: Whenever you change the profile cutoff, powpref needs to be run for this change to take effect in the refinement. (when in doubt, run powpref prior to running genles ). Now run powpref followed by genles
Now run powpref followed by genles . The fit will get slightly better due to the calculated peaks better lining up with the observed peaks. While the following may vary depending on your starting peak width and shape values, the a=b unit cell has changed from 4.77
to around 4.7688
; the c unit cell value from 13.02
to 13.0248
; with a zero changed from 7.77
of 9.85
.
Important: If after refining unit cell and Zero , the fit looks almost as bad as when you started, use the mouse to zoom up on a relatively low angle peak in
Liveplot and take a look at the observed vs calculated profiles. In the below left frame, you can see the red calculated profile is too wide. Resetting the GW width to half of its value will help get a better starting fit; if that does not work, try half again. In the initial stages of the refinement, manual tweaking of starting parameters may be required. Below we see the tweaking of the GW width value from 400 to 300 to 100 (In the Profile Tab) to give a decent visual starting fit to the refinement.
10

Now we are going to refine width, shape and peak asymmetry; but it has to be done in a slow sequence to keep the refinement stable. In the Profile Tab, release the GW peak width parameter, then run Genles . Initially the fit may only improve marginally.
In the Profile Tab, release the LY shape parameter, then run Genles .
For an X-ray diffraction system, you might next released the GV width parameter.
However, for this neutron diffractometer, it can be best to next release the GU width parameter. The sequence to release parameters is often found experimentally by trying things out. In the Profile Tab, release the GU shape parameter, then run Genles .
The width and shape parameters are getting better, but the intensities are moderately out. In another practical, we will learn on how to do Le Bail whole profile fitting, prior to structure refinement, which helps solve these initial peak profiling problems. But for now, the solution is to refine some atomic parameters. This reinforces how on occasion, the refinement pathway may only be elucidated during the refinement. Some
11

Rietveld guidelines suggest getting the best profile fit to the data before releasing atom parameters.
If this was X-ray diffraction data, you should slowly release the atoms in reverse order of atomic number (heavy atoms first). However, the atomic scattering factors in
Neutron diffraction for Aluminium and Oxygen are quite similar, so the atoms can be released at roughly the same time. In the Phase tab, release the UISO (thermal) parameters for the Al and O atoms. The Al and O atoms are both on special positions so are restricted in their movements. E.g., with the Aluminium x and y positions at the special position of zero, GSAS would still keep these two co-ordinates fixed as required by the space group. Be wary that other Rietveld programs would move the atoms on special positions, even if spacegroup does not allow this. When performing a
Rietveld structure refinement a good knowledge of crystallographic fundamentals is assumed and Rietveld programs can not be used in substitute for crystallographic knowledge.
If the thermals for atoms do go negative, this could be indicative of problems such as incorrect atoms having been entered or systematic errors in the data. Also, if the calculated peak shape near the peak tails are concatenated, run powpref followed by genles which should fix this up where the intensities now roughly match up over the length of the powder pattern.
As this data has a wide angular range, now release the LX shape parameter followed by some cycles of refinement, then release the GU width parameter followed by cycles of refinement.
12

All of this should give the following decent fit to the whole profile.
Up till now the background has been fixed. Now refine the background via the
Histogram Tab.
Again, if this was X-ray diffraction data, you should slowly release the atoms in reverse order of atomic number (heavy atoms first). However, the atomic scattering factors in Neutron diffraction for Aluminium and Oxygen are quite similar, so the atoms can be released at roughly the same time. In the Phase tab, now release the
X’s for the Al and O atoms and perform some cycles of refinement. If the atoms have strange negative or very large thermals, this could be telling you that there is something wonky with the structure model; or systematic errors in the data.
The refinement is pretty much over.
13

Now examine the Rietveld plot, being on the lookout for misfits at low and high angle, as well as other misfitting peaks and any spurious peaks.
One of the main validations of a refined structure is to check the bond lengths and angles to see if they make sense. If new to a phase system and not sure what are physically reasonable results for certain atom types, the bond lengths and angles from structures from the relevant structure database can be used as a guide (i.e., the
Inorganic Crystal Structure Database via http://www.fizinformationsdienste.de/en/DB/icsd/ ). To get a list of bond lengths and angles from
GSAS, from the top menu select “ Results, Disagl ”.
14

Important: the sample dependent parameters should NOT be incorporated into the Instrument Parameter file. This means trans (if refined) and shft (if refined – not relevant for neutron cylindrical samples) should be set to zero after importing the profile information.
Important: Before running your samples, the diffractometer should be aligned as well as possible. If the user of a diffraction system, check the alignment with an appropriate standard (NIST Silicon) before running your samples. If the diffractometer is not well aligned, raise the problems with those responsible for the diffractometer and get the system aligned before continuing.
Run “
Powder, Instedit
” and load the previously created Instrument Parameter file
( c2neutron.prm
).
Select the Import Profile button and select the Corundum.exp
file; and confirm the importing of the profile determined from the Corundum refinement you have just previously performed.
15

Save and overwrite the existing c2neutron.prm
with this new updated version of the instrument parameter file. This instrument parameter file can now serve as the instrument parameter file for data collected on this same instrument. The trans (if refined) and shft should be set to zero as these are dependent on the individual sample, not the instrument. This is not relevant for neutron data in a cylindrical sample holder, but is for Bragg-Brentano X-ray diffractometers.
16

2

Important: the sample dependent parameters should NOT be incorporated into the Instrument Parameter file. This means trans and shft should be set to zero after importing the profile information.
Important: Before running your samples, the diffractometer should be aligned as well as possible. If the user of a diffraction system, check the alignment with standard (NIST Silicon and NIST LaB6) before running your samples. If the diffractometer is not well aligned, raise the problems with those responsible for the laboratory and get the system aligned before continuing. It is easy to invalidate results by running samples on a poorly aligned diffractometer.
Double click the EXPGUI icon on the desktop, and the "Select an experiment file to read" dialog will be displayed. Browse to: c:\cpdw\ceo2newxrd directory, type in
“ceo2” and click
READ.
EXPGUI will give a message that the file does not exist. Select the Create button to create the CEO2.EXP file.
Enter an experimental title “CEO2” and click "
OK" to give the following starting
EXPGUI screen.
Important:
Before you can add any “histograms” (powder diffraction data), you must first add in a “phase” (crystal structure) data
17

CeO2 is a Cubic structure with the following crystallographic details:
Spacegroup: F M 3 M
Unit cell: a=b=c= 5.410
Å : alpha=beta=gamma =
90
°
Atom co-ordinates: (x, y, z)
Ce : 0 0 0
O : 0.25 0.25 0.25
Select the Phase tab and then the “Add Phase” button. This will bring up an “add new phase” dialog where you input the Phase title (CeO2); the Space Group (F M 3 M)
(make sure to include the spaces) and the unit cell constants. Then select the “Add” button. GSAS will then give a symmetry analysis output for you to check and make sure you have entered the spacegroup correctly (using the International Tables or similar database to validate the output). Select “Continue” once you are happy with this. This will give the following main EXPGUI screen with the cell information but no atoms.
Now select the “Add New Atoms” button and add in the atom information using the keyboard. Select the “More atom boxes” to add an extra line to insert the Boron atom information.
Ce 0 0 0
O 0.25 0.25 0.25
Select the “Add Atoms” button to go back to the main EXPGUI screen where all the crystallographic information is now visible. The GSAS default values of Uiso (0.025) are usually too large for heavy metal structures. Often it is better to reset the starting
UISO values to 0.01.
18

Important: Before you can add a histogram, you need to create or have an existing GSAS instrument parameter file ready. Assuming this is the first time you have used GSAS and you don’t have an instrument parameter file for this single wavelength diffractometer, we will now create one.
From the top menu, select
“Powder, Instedit”
then the Cancel button to create a new
GSAS Instrument Parameter file. This will bring up the following screen. In the
“
Data type
”, select
CW X-ray for constant wavelength X-ray.
For title, give “Generic prm file for Cuk alpha 1+2 Bragg-Brentano
Diffractometer” and for Instrument Name give “cukal1_2” . The radiation type is Cu, it is monochromatic (dual wavelength), give a zero correction of -0.07 centidegrees
(Zero correction offset for the diffractometer, which should be a constant, as distinct to the sample displacement error, can be determined for a diffractometer by running NIST
640c silicon). A POLA value of 0.911
. ( IPOLA should be set to 1 which defines the use of the Azaroff function, but currently there is not an option to do this in the Instedit screen, so it needs to be set in the EXP file during refinement). Paraphrasing a note from Bob von Dreele,
“IPOLA=1 is in there to match the "traditional" Azaroff function for diffracted beam monochromators. The IPOLA=0 function is my adaption so that POLA is the polarized fraction. POLA=0.50 for no polarization and POLA=1.0 for perfect polarization nearly realized in synchrotron radiation & vertical diffraction.
”. Polarization fraction can be calculated, but it can be good to determine this experimentally by running a suitable phase such as cubic Y
2
O
3
from the lowest to highest angle of the diffractometer – e.g., 5 to 150 degrees 2-theta).
In the Select Profile area, select Profile type“3” (Pseudo-Voight/FCJ Assym), with a peak cutoff of 0.001 and a GW (constant width) of 400. The Finger Cox Jephcoat
(FCJ) peak asymmetry is defined by two parameters, S/L and D/L, where S/L is the source size to sample-detector distance ratio and D/L is the detector size to sample-
19

detector distance ratio, as per the following figure taken from L. W. Finger, D. E. Cox and A. P. Jephcoat, “A correction for powder diffraction peak asymmetry due to axial divergence”, J. Appl. Cryst. (1994). 27, 892-900.
It is best if you calculated these values from measuring these values on the diffractometer. If you received the data from someone else and cannot get these diffactometer values, take a best guess (e.g., for this type of medium resolution diffractometer, 173mm for sample-detector distance and 5mm for source size and detector size. This gives starting S/L and D/L ratios of 0.029.
Now select the “Save As” button and save the file with a suitable filename; in this case cuka12xrd.prm
. Then Close Instedit .
Select the “Histogram” tab followed by the “Add Histogram” button
To the right of “Data File” , use the “Select File” button and add the
“ceo2newxrd.gsa” dataset; following by the “ Select File ” button to the right of the
“Instrument Parameter File” to select the “ cuka12xrd.prm
” file. Make sure the
“ Select Bank ” and “ Select Set ” are set to 1 as pointed to in the screen image to the left of this text. Select the “ Add ” button to add the histogram into GSAS.
20

In the above screen image, if the Ratio of the wavelengths is at zero instead of 0.5, set the Ratio to 0.5
(the correct value). As POLA is set at a value for a curved graphite diffracted beam monochromator based on using the Azaroff function (0.911) , IPOLA should be set to 1 to get GSAS to use the Azaroff function.
Important: If you use a random GSAS instrument parameter file (or even one that looks correct), there are no guarantees that it will import the correct information and the correct instrumental settings; and you should check things to make sure it has provided correct information.
Important: Many people are in the habit of choosing a type of background function out of habit. In this demonstration, a Shifted Chebyshev (Function 1) is used and can be very flexible for fitting bumpy backgrounds. Other people swear by a Cosine Fourier Series (Function 2)
At this point, it would be good to manually fit a background function to the background in preparation for us starting the refinement. For this we will use the bkgedit program. Prior to running bkgedit , powpref and genles must be run. Run the
Powpref icon in the top middle menu bar in EXPGUI, followed by GENLES.
After running powpref and genles, run
“Powder, bkgedit ” to bring up the background editing screen. The main aim of this is to select background points by pointing and clicking with the mouse, then fit a GSAS background function to the data which is then fixed until you decide to let the background refine. This can save on quite a bit of tedium trying to immediately refine a GSAS background function at an early stage of the refinement.
Use the mouse, Add, Zoom and Delete options to visually select background points.
Which below are shown as pink triangles.
21

Then use the Fit icon to fit a line, gradually increasing the number of terms until you get a good fit to the background function. In this case, 6 terms seem to be doing a good job. The dotted blue line shows the background function.
Now select the “Save in EXP File & Exit” icon at the bottom right of the screen to save the fitted background profile. When EXPGUI prompts that the EXP file has been modified, select the “Load new” file (unless you have made a mistake). If you have made a mistake, select the “continue with old” button. EXPGUI will recognise the new background parameters by giving the new number of terms you used to fit the background profile. It is recommended that the background should not be refined until everything else is pretty much under control.
22

In the Profile tab, make sure the profile type is profile 3 (Pseudo-Voight with Finger-
Cox-Jephcoat peak asymmetry function). It is possible that the instrument parameter file you used defaults to another profile type, so you should check this. If it is not, then change it to profile type 3 . Now run powpref and genles to do some cycles of refinement with only the scale factor refinining.
Now run liveplot (and keep this window open) to see the state of the refinement in terms of how well the calculated pattern based on the structure model is fitting the data. By default, the scale factor is set to refine . The black crosses are the raw data; the red line is the calculated pattern and the blue line below is the difference. The aim is to get the calculated pattern matching the observed pattern with the difference being as close to a flat line as possible.
Using the “File, Tickmarks” option in Liveplot, you can also overlay where HKLs are expected, and the [Control] [Shift] and left click on the left Mouse button near the
HKL will label the HKL. (To have HKL labels near the peaks, you have to enable the tickmarks via “File, Tickmarks” in Liveplot).
If you have extra peaks in the raw diffraction data that are not matched up by a calculated HKL, this can mean you have the wrong cell or spacegroup, or an impurity phase.
Important: There is no fixed method of performing a Rietveld refinement in terms of the order of parameters to be released. The following is just a suggestion, and should not be blindly followed in all cases. Each refinement may require its own custom refinement sequence for parameters to refine in a stable manner.
Also, if you find that you have mucked up the refinement where parameters have gone to unreasonable values, it might be easier to go to a previous version of the EXP file.
In EXPGUI, go into “ File Open”
menu and then select the
“Include Archived Files”; this lists the previous archived files by time and date. Just select a previous EXP file you expect to be OK. If this turns out to be too late or early an EXP file, just try selecting another one.
23

In the LS controls Tab, set the number of cycles to 8 and in the Profile Tab , set the profile cutoff to 0.001
(if it is not already at 0.001). By default many GSAS parameter files default to 0.01, which is not adequate for many X-ray diffractometers.
Important: Whenever you change the profile cutoff, powpref needs to be run for this change to take effect in the refinement. (when in doubt, run powpref prior to running genles ). Now run powpref followed by genles
Important: If after refining the scale factor, the fit looks very bad, it is best to evaluate what is going on and base your refinement strategy on this. If the observed peaks do not match up with the calculated, this could be telling you your unit cell needs to be tweaked manually or you have the wrong unit cell or spacegroup.
In the below left frame, you can see the red calculated profile is too wide. So it is best to manually adjust the width before releasing any further parameters.
Resetting the GW width to half of its value will help get a better starting fit; if that does not work, try half again. In the initial stages of the refinement, manual tweaking of starting parameters may be required. Below we see the tweaking of the GW width value (In the Profile Tab ) to give a decent visual starting fit to the refinement. In the following we have had to do a lot of interations, eventually going down to a GW of 10.
24

Now that we have got the peak width in roughly the right range, set the unit cell parameter to refine (in the Phase tab) and the shft parameter to refine in the Profile Tab
( shft = sample displacement ). For a Bragg-Brentano diffractometer, it is better to use the shft parameter over the zero parameter as most of the variation in an aligned diffractometer is due to accurate placement of the sample. Performing a refinement on
NIST silicon should give you the zero offset of the diffractometer which should be a constant.
Now run powpref followed by genles. The fit will get better due to the calculated peaks better lining up with the observed peaks. While the following may vary depending on your starting peak width and shape values, the unit cell has changed from
5.4100 to around 5.4108
, with a sample displacement value of -0.664E+01 . The following screen images show the level of improvement.
Now we are going to refine width, shape and peak asymmetry; but it has to be done in a slow sequence to keep the refinement stable. In the Profile Tab, release the GW peak width parameter, then run Genles . Initially the fit may only improve marginally.
In the Profile Tab, release the LY shape parameter, then run Genles.
25

In the Profile Tab, release the GV shape parameter, then run Genles.
The width and shape parameters are getting better, but the intensities are out. In another practical, we will learn on how to do Le Bail whole profile fitting, prior to structure refinement, which helps solve these initial peak profiling problems. But for now, the solution is to refine some atomic parameters. This reinforces how on occasion, the refinement pathway may only be elucidated during the refinement. Some
Rietveld guidelines suggest getting the best profile fit to the data before releasing atom parameters.
In the Phase tab , release the U (thermal) parameter for the heavy Ce atom (not the light Oxygen atom). The Ce is on a special position so cannot move, but even if you tried to refine the Ce x,y,z, GSAS would still keep it fixed as required by the space group. Be wary that other Rietveld programs would move the special position atoms, even if spacegroup does not allow this. When performing a Rietveld structure refinement a good knowledge of crystallographic fundamentals is assumed and
Rietveld programs can not be used in substitute for crystallographic knowledge.
If the thermal for the heavy atom of a
“standard material”
does go negative, this could be indicative of problems such as the polarization of the X-ray beam being incorrect or the wrong atom type. Also, if the peak shape is concatenated, run powpref followed by genles which should fix this up where the intensities now roughly match up over the length of the powder pattern.
26

As this data has a very wide angular range, now release the LX shape parameter followed by some cycles of refinement, then release the GU width parameter followed by cycles of refinement.
Via the Profile tab, now release the trns (sample transparency parameter) which is relevant for Bragg-Brentano flat plate systems.
This should give the following decent fit to the whole profile.
27

Up till now the background has been fixed. Now refine the background via the
Histogram Tab.
When performing a refinement using X-ray diffraction data, you should slowly release the atoms in reverse order of atomic number (heavy atoms first). In the Phase tab, now release the U’s for the oxygen atom and perform some cycles of refinement (the
Oxygen is on a special position, so there is no point trying to refine the X’s / atom coordinates). Pay careful attention to the thermal parameter of the oxygen. If the light atoms have strange negative or very large thermals, this could be telling you that there is something wonky with the data; either bad sample packing, or something wrong with the diffractometer.
The refinement is pretty much over. One more thing that is possible is to tweak the
H/L and S/L peak asymmetry parameters. These parameters are unstable if refined together, so first refine one and turn it off, then the other and turn it off, then repeat the sequence until the refinement converges and (via Liveplot) you see the best fit with the low angle peaks.
28

The fit to the lowest angle peaks seems to be OK. Though often such things can be in the eye of the beholder. It can be good to run some NIST standards on a variety of diffraction systems to get a feel for what fits are possible on various instruments.
The very high angle peaks also seem OK.
One of the main validations of a refined structure is to check the bond lengths and angles to see if they make sense. If new to a phase system and not sure what are physically reasonable results for certain atom types, the bond lengths and angles from structures from the relevant structure database can be used as a guide (i.e., the
Inorganic Crystal Structure Database). To get a list of bond lengths and angles from
GSAS, from the top menu select “
Results, Disagl
”.
29

30

Run “ Powder, Instedit ” and load the previously created Instrument Parameter file
( cuka12xrd.prm
).
Select the Import Profile button and select the CeO2.exp
file; and confirm the importing of the profile determined from the CeO2 refinement you have just previously performed. The trans and shft should be set to zero as these are dependent on the individual sample, not the instrument. Overwrite the existing cuka1xrd.prm
with this version with the updated information. This instrument parameter file can now serve as the instrument parameter file for data collected on this same instrument.
31

Using the Windows explorer (or your favourite file manager), copy the CEO2.EXP and cuka12xrd.prm from the \cpdw\ceo2newxrd directory to the \cpdw\ceo2oldxrd directory.
Either double click on the ceo2.exp
file to automatically open it in EXPGUI, or run
EXPGUI and load the cpdw\ceo2oldxrd\ceo2.exp file
At present, replacing histogram files is done via the EXPEDT program (the comprehensive GSAS EXP file editor by Bob von Dreele and Allen Larson). Select the EXPEDT ICON from the top left menu.
Then to get to the point where you can replace the histogram, type K P H R 1 (note the descriptors within EXPEDT which explain what these mean while you are doing this). When prompted with Enter raw histogram input file name (<?>,$,QUIT), type the name of the data file: ceo2oldxrd.gsa
and when prompted, confirm this is correct by typing Y . When prompted with Enter POWDER instrument parameter file name (<?>,$,QUIT) , type the name of the GSAS instrument parameter file: cuka12xrd.prm
and when prompted, choose scan number 1
. Don’t bother previewing it. Then type T (Set max 2-Theta or Energy or min TOF), and then / to confirm the maximum angle is acceptable. To exist EXPEDT, type X X X and
[RETURN], the X and [RETURN].
Check the EXP file is OK, especially in the Histogram tab as some of the Instrument parameters may not have been imported correctly. Referring to the following screen image, if the Ratio of the wavelengths is at zero, set this to 0.5
. Reset the Ratio to 0.5
(the correct value). As POLA is set at a value for a curved graphite diffracted beam monochromator based on using the Azaroff function (0.911) , IPOLA should be set to
1 to get GSAS to use the Azaroff function. Correct these. This data was actually
32

taken on an older diffractometer (though pretty much identical in setup and configuration), so it can be expected the Zero will be different. We will probably work on this later in the refinement.
The new dataset has pretty much the same counting statistics of its replacement. So it can be pretty much refined in one step using all the parameters. If it had very different counting statistics, it would be best to do the refinement slowly as per the previous practicals by turning off all the parameters and turning them back on in a similar sequence. Though two things to turned off are S/L and H/L as these parameters can be very unstable.
Now run powpref followed by genles . The refinement is done! Now you should check things out and see if anything needs tweaking of there have been any problems doing a refinement as quickly as this may have caused; validate the structure using disang ; and check if there are some nuances or problems with the data file that might only be revealed in a post refinement examination.
33

Be wary on just releasing parameters “willy nilly” without regard to the physical reality of the sample and possible consequences. Normally, you should not have to refine trns (sample transparency) with a heavy metal inorganic phase like CeO2.
Though in this example this is what we have done, blindly. Releasing parameters inappropriately may hide systematic errors in the data and also skew the final results.
If we release the sample transparency parameter, the high angle reflections look OK.
Though both fits seem to be having minor problems.
Old B-B Diffractometer (left) vs new B-B diffractometer (right)
Diffractometer
Uiso*100 Ce
Old
0.24(2)
New
0.16(1)
NIST Certificate*
Uiso*100 O
Unit cell
0.68(13) 0.77(7)
5.41253(3) 5.41004(2) 5.4111(1)
(* http://ois.nist.gov/srmcatalog/certificates/view_cert2gif.cfm?certificate=674a )
However, if you do not release the sample transparency parameter (keep it at zero), and look closely at the high angle fit of the “old” Bragg-Bretano diffractometer compared to the
“new” Bragg-Bretano diffractometer
, you can see problems with the high angle fit. The old diffractometer was based on stepper motors and had a retrofit of a diffracted beam curved graphite monochromator. It looks like the updated anti-backlash springs are not strong enough to take the extra weight; or there are some other goniometer problems. The new diffractometer theta and 2-theta axes were driven by DC motors guided by direct drive optical encoders.
Old B-B Diffractometer (left) vs new B-B diffractometer (right)
34

Diffractometer
Uiso*100 Ce
Old
0.30(2)
New
0.15(1)
NIST Certificate*
Uiso*100 O 0.79(13) 0.73(8)
Unit cell 5.41311(2) 5.41062(2) 5.4111(1)
(* http://ois.nist.gov/srmcatalog/certificates/view_cert2gif.cfm?certificate=674a )
The ESDs given by Rietveld analysis are only indicators of probable error assuming there are no systematic errors. Systematic errors or over simplifications in the model can make the ESDs meaningless in terms of “probable error”. With X-ray data, thermal parameters are well known as sinks for many types of systematic errors in the peak intensities. For the unit cell discrepancies, errors due to temperature of the data collection, misalignment of the sample and diffractometer are most likely. To get an indicator of probable error due to the diffractometer and sample packing, it can be more sensible to run the same sample with multiple packings, multiple times on different instruments to get a “Standard Deviation”, as well as running the sample with an internal position standard such as NIST Silicon 640c.

If you look closely at the background, you will notice some peaks that do not have calculated HKLs. This could imply impurity phases; but in this case is Cuk

satellite reflections from the most intense CeO2 Cuk

reflections; in this case the 111 and 220 respectively in the left plot from the newer diffractometer. In the older diffractometer
(right plot), it is more difficult to see as the counting stats are less, and Tungsten contamination from the (possible older?) X-ray tube is also visible.
35

2
3
The aim of this section is to show how i) easy it is to import an existing structure file into GSAS (minimizing the risk of typographical errors) and ii) refining the polarisation of the X-ray beam. Normally to refine the polarisation of the X-ray bean, you need to use a standard of decent peak density, and the entire range of the diffractometer up to the highest angle possible (between 140 to 150 degrees 2-theta).
But be wary that after importing an existing structure, you still need to check that the structure from the literature is OK and kosher before starting the refinement.
Double click the EXPGUI icon on the desktop, and the "Select an experiment file to read" dialog will be displayed. Browse to: c:\cpdw\y2o3_pola directory, type in
“Y2O3” and click
READ.
EXPGUI will give a message that the file does not exist. Select the Create button to create the Y2O3.EXP
file and add the title.
Under the Phase tab, click on the “
Add Phase
” button, but instead of inputting all the information by hand, use the Import Phase From button and select Crystallographic
Information File (CIF) .
Then select and import the y2o3_icsd_26190.cif
file in the c:\cpdw\y2o3_pola directory. EXPGUI will give a warning that the I a –3 setting of the I a 3 space group is unlikely to be understood.
Change I a –3 to I a 3 . Under more complicated circumstances, the space group and structure may have to be changed or transformed to a setting that GSAS does understand.
36

Press Continue . GSAS will output the spacegroup information which you can check with the IUCr International Tables or other suitable spacegroup database.
This brings up the Adding Atoms dialogue box. Some CIFS can have blank input for the Uiso values. If they do, has some default values like 0.01. The following values of zero will be OK, and we will be refining these.
Select Add Atoms to finish importing the structure into GSAS.
37

Now add the histogram as done in previous sections. The datafile is c:\cpdw\ y2o3_pola\ y2o3.gsa
and the instrument parameter file is c:\cpdw\ y2o3_pola\ cuka12xrd.prm
. If required, correct any problems such as the ratio not being correct
(it should be 0.5). IPOLA should be set to 1 which defines the use of the Azaroff function. Note the existing value of POLA has been set to 0.81, the theoretical value of the polarisation correction using the Azaroff function for a curved graphite monochromator with CukAlpha X-rays. This is the parameter we will eventually be refining to get a better value. Paraphrasing a note from Bob von Dreele, “IPOLA=1 is in there to match the "traditional" Azaroff function for diffracted beam monochromators. The IPOLA=0 function is my adaption so that POLA is the polarized fraction. POLA=0.50 for no polarization and POLA=1.0 for perfect polarization nearly realized in synchrotron radiation & vertical diffraction.
” A cos 2 2

of the 002 graphite reflection (For Cu X-rays this is at an angle of 26.6 degrees 2-theta / d=3.3480Å) gives a calculated POLA value of around 0.81.
Now set the number of cycles to 8 , check the profile cutoff is 0.001, fit the background and refine the profile, background and structure as per the previous sections. This should leave you with the following fit.
38

Don’t forget to validate the refined structure by using disang to check the refined structure makes physical sense.
In the Histogram tab, now refine the POLA parameter (which was set at its theoretical
Azaroff function value of 0.81). If you reset the values of the thermal parameters and reset POLA to different values, it should still converge onto the same value of near
0.90(1), showing the refinement of this parameter is robust.
As there are correlations between parameters such Uiso, and POLA, it can be a good idea to check the Correlation Matrix is the LSTVIEW output, as it is possible that correlations are excessive and affecting the accuracy of the result. It can also indicate
39

where due care is required as parameters may be unexpected correlated. In the LS
Controls tab, click on the Print Options Icon and select Print correlation matrix (2) .
Now run Powpref and Genles for these new listing options to take effect. Viewing the output via LSTVIEW will show which parameters have a correlation greater than 0.5.
HSCL is the Histogram Scale factor; PF are profile parameters and BK are background parameters.
40

Before using any of the atomic information, it can be convenient to do a structureless
Le Bail fit to the data and get the best whole profile fit before proceeding on to refine the atomic positions. GSAS has two options, a model biased Le Bail fit, and a true Le
Bail fit. For getting a good fit prior to structure refinement, it can be more convenient to use the model biased Le Bail fit. This avoids the tediousness of having all the reflections set to zero after running powpref as with the true Le Bail fitting. The following Calcium Niobium Oxide example has over 100 atoms (depending on which model is used, (L.M.D. Cranswick, W.G. Mumme, I.E. Grey, R.S. Roth, P. Bordet, “A new octahedral tilt system in the perovskite phase Ca3Nb2O8”, Journal of Solid State Chemistry, 172 (1): 178-187 April
2003
)) and it is more convenient to fit the whole profile before trying to sort out the structural refinement problems. In reality, this was done via a combined refinement using both X-ray data to lock down the heavy atoms, and neutron data to lock down the light oxygen atoms. The atom list given with this example is not 100% correct, which is why refinement of the structure is required.
Important: If you find the following dataset refines to slowly on your PC, you can do the same tutorial using the Y2O3 data and CIF file.
Because we are going to use an Instrument parameter file with the starting profile values determined from refining the CeO2 standard, this should be a moderately painless profile fitting exercise.
Important: Whenever you run powpref while in Le Bail mode, this resets the
HKL intensities. This can mean that you need to fix the profile parameters while you run a few cycles of Genles to get the intensities roughly matching the diffraction data, then start releasing profile parameters again.
Double click the EXPGUI icon on the desktop, and the "Select an experiment file to read" dialog will be displayed. Browse to: c:\cpdw\lebail_model directory, type in
“CANBO” and click READ followed, when prompted, by Create to create a new EXP file. Put in the extra title information as required.
Rather than type in the positions of over 100 atoms manually, we will import the structure from a CIF file as per the previous example on this topic. Use the c:\cpdw\lebail_model\starting_canbo_structure.cif
file.
41

Now add in the diffraction data/histogram. c:\cpdw\lebail_model\canbo-v.
gsa is the diffraction data file (a variable count time dataset converted into the GSAS ESD format) and c:\cpdw\lebail_model\cuka12xrd.prm is the instrument parameter file.
As usual, fix up any problems with the Ratio of the wavelengths (0.5). As POLA is set at a value for a curved graphite diffracted beam monochromator based on using the
Azaroff function (0.911), IPOLA should be set to 1 to get GSAS to use the Azaroff function. (1).
Run Powpref and Genles , then fit the background graphically using Powder , Bkgedit as per previous sections.
42

In the LS Controls tab, now enable the F(calc) Weighted button. And turn off the
Scale Factor, which is meaningless to refine during a Le Bail fit as all the HKL intensities are free to go to whatever value it takes to get the best fit to the data.
Via the Scaling tab, turn off the Scale parameter refinement flags for the X-ray and
Neutron data. (These are turned back on after the Le Bail fitting) Now run Powpref once, the Genles a few times to get calculated intensities into the observed peaks. As this is a large cell, this could take a while. You should get a starting fit similar to the following.
Now slowly release the unit cell, shft, and other profile parameters as per the previous sections. If the refinement goes unstable, you may have to run powpref again to reset the Le Bail intensities.
After refining the unit cell and shft , it should look something like the following.
43

After refining the profile parameters, it should look similar to the following.
Now you can turn off all the profile and unit cell parameters and turn back on the
Rietveld refinement to try and get a good initial fit of the trial structure to the data.
Remember to turn back on the Scale Factor.
Run powpref and run genles to start refining the structure. Though you may like to go to the next exercise. It took around 6 to 12 months to solve this structure, then around
2 years to refine it to completion, from whence it could be published. While the X-ray data may look like it has a decent fit at the moment, including the neutron diffraction data was very important to reliably refine the oxygen positions, and work out problems with the model. The starting neutron fit is included below with the corresponding starting X-ray fit.
44

If you know the cell and space group but not the structure, you can obtain a set of intensities from powder diffraction data for structure solution by using Le Bail fitting.
Using model-less Le Bail fitting, all the intensities are set to zero prior to the start of the fitting procedure, and thus are un-biased by any atoms you may have put in the unit cell.
Important: If you find the following dataset refines to slowly on your PC, you can do the same tutorial using the Y2O3 data and CIF file.
Important: Whenever you run powpref while in true Le Bail mode, this resets the HKL intensities to zero. This can mean that you need to fix the profile parameters while you run a few cycles of Genles to get the intensities roughly matching the diffraction data, then start releasing profile parameters again.
For this example, we will use a synchrotron dataset of tetracycline hydrochloride from the 1 st Structure Solution from Powder Diffractometry Round Robin (SDPDRR, http://sdpd.univ-lemans.fr/SDPDRR/ ). The instrument profile were not provided with the data from the synchrotron, so you will have to slowly fit the peak profile parameters as part of the Le Bail process. If you obtain data from a third party, it would save some tedium if you could also obtain a good instrument parameter file of the diffractometer. You will have to create a starting instrument parameter file for this example.
Important: This data was collected from a capillary, thus parameters relevant to flat plate Bragg-Brentano instruments (trns and shft) should not be used. The
Refine Zero in the Histogram Tab should be used.

Wavelength = 0.692
Angstrom; Polarisation of the X-ray beam (IPOLA=0) of
1.

The orthorhombic spacegroup of tetracycline hydrochloride is P 21 21 21

The unitcell of tetracycline hydrochloride is 10.981 12.853 15.733 90 90 90
Double click the EXPGUI icon on the desktop, and the "Select an experiment file to read" dialog will be displayed. Browse to: c:\cpdw\lebail_modeless directory, type in “tetcy” and click READ followed, when prompted, by Create to create a new EXP file. Put in the extra title information as required.
Then via the Phases tab, add a new phase with the above parameters.
45

Important: When adding a cell and spacegroup, GSAS still needs one atom for it to run Genles, even when doing structureless Le Bail fitting. Thus to keep
GSAS happy, a “dummy” atom needs to be added.
Thus as per the above, add a dummy Hydrogen atom at 0 0 0 .
Now create a default Instrument parameter file for this synchrotron data file using
Powder Instedt
. Give a title similar to “
Daresbury 9.1 in image plate mode at 0.692
Angstrom ” and an Instrument name of something like “ Daresbury 9.1
”. It is a constant wavelength X-ray instrument with radiation type of Other . The wavelength is 0.692
and the polarisation fraction is 1. As this is synchrotron data with good resolution, give the GW parameter a value of 2 . Then Save As to save the file with the name synca.prm
.
Now in the Histogram tab, add the diffraction data file ( ALDSYNC.gsa
) and instrument parameter file ( synca.prm
)
46

In the Scaling tab, turn off the Scale Factor and in the L S Controls tab, enable Equally
Weighed (Le Bail method).
Now run powpref and then genles . Then view the plot in Liveplot .
As the very low angle data (where there are no Bragg peaks) has a strange background which would be tedious to try and fit a function to, and there are hardly any reflections above 36 degrees, we are going to exclude these areas. Now run the Powder, Excledt program. Using the Add Region ICON and the click and drag with the mouse to add the two excluded areas at the extreme ends of the data. When completed, click Save and Finish. Then run Powpref (so this change takes effect) and genles .
47

Making sure you have run Powpref and genles after excluding the lower and upper angle regions, now run Powder, Bkgedit to manually fit a background function to the data. Because a glass capillary was used to hold the powder sample, the background has humps in the data that need to be fitted as part of the background function. In the following screen image, a 18 term function seems to be doing the job. Click on Save in EXP file & Exit to continue on.
Now run powpref (which resets the Le Bail intensities to zero). Then run genles twice.
It will normally take running genles twice to get a decent about of intensity into the peaks, as the following two screen images show. Genles will only do one cycle each time as no parameters have been set to refine at this point.
(Left: first run of genles; Right: second run of genles)
48

Now refine the Unit Cell and Zero where you should get the following style of fit.
Continue on as with the previous sections for refining the profile parameters. Though remember to NOT release shft or trns . Use you best judgement to how many parameters need to be released, and whether the peak asymmetry parameters S/L and
H/L need to be released. At some point, you will most likely have to release the background to refine. Be very careful when doing this with Le Bail fitting.
If you see evidence of peak concatenation, you may have to change the peak cutoff (in the Profile tab) to 0.0001
. If you do this, turn off ALL the refined parameters
(including the background) , run powpref , run genles 2 to 4 times , then turn the parameters back on . If you do not turn off all the parameters, the parameters that have been left to refine will go tend to go completely beserk.
(with peak concatenation with peak cut-off at 0.001)
(setting the peak cut-off at 0.0001)
49

After refining the 3 width and 2 shape parameters (with background, zero and unit cell), you should be at the following point in the Le Bail fit.
You can now use Results, Reflist to export the list of HKL and intensities. After some minor sorting and reediting, these can be passed into favourite HKL based structure solution software in an attempt to solve the structure.
50

The aim of this section is to show how i) easy it is to import an existing structure file into GSAS (minimizing the risk of typographical errors); ii) recognize problems with the imported structure, including the space-group setting and iii) refining the value of the wavelength by the use of a NIST Si 640c standard. Note that if there are not enough reflections to refine the wavelength, mixing in a phase like annealed cubic
Y
2
O
3
can allow the wavelength to be refined as the Y
2
O
3
add more observations for the refinement of the zero offset. This data was taken from the 5 3 1 reflection of a Silicon monochromator at a take-off angle of -92.732°, which will result in a wavelength of around 1.33Å.
Double click the EXPGUI icon on the desktop, and the "Select an experiment file to read" dialog will be displayed. Browse to: c:\cpdw\silicon_neutron directory, type in “silicon” and click
READ.
EXPGUI will give a message that the file does not exist. Select the Create button to create the SILICON.EXP
file and add the title.
Under the Phase tab, click on the “
Add Phase
” button, but instead of inputting all the information by hand, use the Import Phase From button and select Crystallographic
Information File (CIF) .
Then select and import the si_icsd_51688.cif
file in the c:\cpdw\silicon_neutron directory. EXPGUI will give a warning that the F d -3 m S is unlikely to be understood, as GSAS only understands standard Hermann-Maugin space group symbols.
Change F d -3 m S to F d -3 m Under more complicated circumstances, the space group and structure may have to be changed or transformed to a setting that GSAS does understand.
51

Press Continue . GSAS will output the spacegroup information which you can check with the IUCr International Tables or other suitable spacegroup database.
This brings up the Adding Atoms dialogue box.
GSAS will complain if the “Atom Type” of Si (neutron atom) has its charge labelled as Si0+ . Change this to Si . Some CIFS can have either blank input or have Biso values instead of the GSAS required Uiso values. In this case, there is a Biso value present in the structure information. Biso = 8
 2
Uiso : Uiso = Biso/78.96.
So just this formula to convert the Biso to Uiso values: a Biso of 0.54
becomes a Uiso of 0.0068
.
52

Now add the histogram as done in previous sections. The datafile is c:\cpdw\ silicon_neutron\ si_531.gsa
and the instrument parameter file is c:\cpdw\ silicon_neutron\ c2neutron.prm
.
Now set the number of cycles to 8 ; and check the profile cutoff is 0.001. Run
Powpref and Genles and fit the background.
53

Set the unit cell for NIST 640c Silicon at its certificate value of (when measured at
22.5°C - https://srmors.nist.gov/view_cert.cfm?srm=640C ) of 5.4311946Å. This is done by going to the Phase Tab and selecting Edit Cell icon.
Now refine, via the Histogram Tab , refine the Wavelength and Zero offset (the unit cell of Silicon remains FIXED at its NIST value). As you have changed the unit cell manually, run Powpref followed by Genles .
As per the following screen image, the fit is very woeful given this is a standard material with a single atom located on a special position. (The peak at 52° where there is no calculated HKL is a Vanadium peak from the Vanadium sample can).
54

To cut a long story shorter, if you have not encountered this problem before, it is easy to waste a lot of time trying to figure out what is going on. Is this really the correct sample? Was the correct wavelength set? Some strange bug in the program?
Occupancies, thermal and position correct? Is it possible that “severe” preferred orientation/texture will be reponsible for this? (in the case of Silicon powder:
“not bloody likely”) The solution to this is the default space-group setting used by
GSAS. GSAS assumes the a setting of the F d –3 m space group which has the Origin at 0,0,0 . However, if you look up F d –3 m (No 227) in the IUCr International Tables
Vol A, it puts the Origin at 1/8, 1/8, 1/8. So if you translate the Silicon atom to 1/8,
1/8, 1/8 (0.125, 0.125, 0.125) the calculated pattern will probably start fitting the observed much better.
As another check, if you look inside the Silicon CIF file with a text editor, it includes the Wyckoff position for the Silicon atom: 8a . In the International Tables, 8a is the
1/8, 1/8, 1/8 position.
As another, another check, if you run the GSAS DISAGL program (via Results,
Disagl), when Silicon is located at 1/8, 1/8, 1/8, all the Si to Si bond distances are
2.352Å with Si-Si-Si bond angles of 109.47°. If you put the Si at 0, 0, 0, then the bond distance is 1.92Å and the bond angles are all over the place in a manner that would be unexpected for a diamond structure type.
In the Phases Tab , click on the Silicon atom line, then in the bottom details box, change 0 to 0.125 for X Y and Z .
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Run Powpref and Genles . This gives a much better fit as per the following screen image.
Now, as with previous examples, complete the refinement by fitting the profile, refining the background and releasing the silicon thermal/Uiso parameter.
To record the wavelength, Zero and ESDs, open LSTVIEW (ICON 2 nd from the right on the top EXPGUI program bar) and scroll down to the bottom to find the
C/L1/R/2Th (wavelength) and Zero.
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It is not good practise to have an impurity phase un-modelled in the Rietveld analysis.
Thus, similar to before, now add in the Vanadium phase and finish off the refinement.
The Vanadium structure is given in the vanadium_icsd_52537.cif
file in the c:\cpdw\silicon_neutron directory. As the Vanadium peaks are present in trace amounts, we will most likely have to constrain the thermals and profile values to be equal to the major phase.
In the Phases Tab , import the vanadium_icsd_52537.cif
file. Change V0+ to V and give the Vanadium thermal/Uiso the same as the Silicon (this can be changed later in the Phases Tab ( phase 2 ICON ) for the Vanadium)
The scale factors for the two phases have to refine separately. Thus to into the Scaling
Tab and fix the overall scale factor, and refine the individual phase fraction scale factors (as shown in the following screen image).
If you have a LivePlot window already open, close it as the HKL’s for the new
Vanadium phase will not be displayed. Run Powpref (to generate the HKL’s for
Silicon and Vanadium) then run Genles.
Open LivePlot and zoom up to the background. Display the HKLs for the Vanadium via the Liveplot menu (File, Tickmarks, Phase 2 ; and Option, Configure Tickmarks,
Manual Placement). In the following screen image, it is easy to see that the intensities for the Vanadium metal are not matching up.
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As this is a metal can, it can very likely be suffering from very severe texture/preferred orientation. But first, we had better check the International Tables Vol A information on I M –3 M (No 229) and make sure we have the space group setting correct for
Vanadium. It is easy to get confused here as if the Vanadium does have very severe preferred orientation (which would be expected), it could be that putting the Vanadium atom into another site (using trial and error to determine which setting GSAS uses as a default for I M –3 M) might improve the fit by mis-modelling the preferred orientation as an origin shift of some sort (e.g., by putting the Vanadium at 0, 1/2, 1/2: the 6b
Wyckoff site).
If International Tables Vol A are consulted, 0,0,0 is the origin, as is consistent with the
GSAS symmetry check out put. The CIF file states the Vanadium site is a 2a site; and in the International Tables 2a is 0,0,0. If you do a Results, Disagl then bond distances and angle make sense with the Vanadium on the 2a 0,0,0. The bond distances and angles do not make sense by putting the Vanadium sites other than the 2a 0,0,0 site.
Following are screen dumps of powder patterns of Vanadium calculated using the userfriendly Powder Cell program (left) and Poudrix program (right) (both are distributed on the CD-ROM). Both allow you to cross validate the GSAS calculated powder pattern and Powder Cell also allows you to input the Wyckov position.
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Thus a conclusion to make of all of this is you have to be very careful with space groups and Rietveld refinement. You also have to be careful to be on the lookout for bugs in space group generation code.
Rather than try to model the texture on this trace phase, we will fit the Vanadium intensity by doing a model biased Le Bail fit which allows all the intensities to freely float. To fit the Vanadium intensities using a model biased Le Bail fit, go to the LS
Controls tab and select F(calc) Weighted (model Biased) for phase 2 (the
Vanadium).
Run Powpref and Genles and evaluate the result in LivePlot . The intensities now match quite well.
Under the Phase Tab, Phase 2 ICON , Release the UnitCell for Vanadium and run
Genles . The fit might improve a trivial amount, as the Unit Cell given in the ICSD is quite accurate for this diffraction pattern. From the point of view of trying to refine the
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wavelength of silicon, don’t spend too much time on the Vanadium. It is unlikely to significantly affect the determination of the wavelength.
Again, to record the wavelength, Zero and ESDs, open LSTVIEW (ICON 2 nd from the right on the top EXPGUI program bar) and scroll down to the bottom to find the
C/L1/R/2Th (wavelength) and Zero.
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Important: Combined X-ray and Neutron refinement can seem quite nifty and high-tech, but it should be done for a well defined and definite reason. Often, it can be best to just refine on the neutron powder diffraction data as, in comparison to X-ray data, it can be less affected by systematic errors. If the individual X-ray or neutron data is not adequate by themselves, combined refinement can be beneficial. In practise, the following structure would normally just be refined using the neutron data.
Important: If the Sum(w*d**2) for the histograms/diffraction patterns are very unequal, histogram weighting may be required so the datasets are equally weighted and this is shown in the following tutorial. A rule of thumb can be to weight the neutron data such that the Sum(w*d**2) for the neutron data is 1.2 times that of the X-ray data. Histogram weighting is enabled via the Expedt program (via the expedt menu: k p h f). Powpref must be run after setting any new histogram weighting.
Important: In joint refinements, other Rietveld users would usually not start with both data sets, but get one looking OK before introducing the additional data. A suggestion would be to follow this strategy if the following guide does not work.
Adding multiple diffraction datasets into GSAS is just as easy as adding a single dataset. Using both X-ray and Neutrons together can be very useful, though some thought can be required. The datasets should be on an identical sample, run at the same temperature, and the diffraction data should be seeing consistent properties of the structure (refer: I.E. Grey, L.M.D. Cranswick and C. Li, Accurate site occupancies for light atoms from powder X-ray data? Oxygen vacancy ordering in 6H-BaFe0.67Ti0.33O3-delta (delta = 0.08 and 0.32),
Journal of Applied Crystallography, 1998, Vol.31, No.Pt5, pp.692-699) . In this example, we are going to refine the structure of IUCr Rietveld Round Robin PbSO4 using both the
X-ray and neutron data (R. J. Hill, “Rietveld refinement round robin. I. Analysis of standard X-ray and neutron data for PbSO4”, J. Appl. Cryst. (1992). 25, 589-610) .
Double click the EXPGUI icon on the desktop, and the "Select an experiment file to read" dialog will be displayed. Browse to: c:\cpdw\lebail_xray_neutron directory, type in
“pbso4”
and click READ followed, when prompted, by Create to create a new EXP file. Put in the extra title information as required.
Add a phase and import the structure from the file named c:\cpdw\lebail_xray_neutron\pbso4_icsd_76925.cif
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Now add the X-ray dataset by using the Add New Histogram icon in the Histogram tab. The data file is c:\cpdw\lebail_xray_neutron\pbso4xrd.gsa
and the instrument parameter file is c:\cpdw\lebail_xray_neutron\cuka12xrd.prm
. Again, fix up any problems with the Ratio of the wavelengths (0.5). As POLA is set at a value for a curved graphite diffracted beam monochromator based on using the Azaroff function
(0.911), IPOLA should be set to 1 to get GSAS to use the Azaroff function. (1).
Now repeat the same procedure to add the neutron dataset by using the Add New
Histogram icon in the Histogram tab. The data file is c:\cpdw\lebail_xray_neutron\pbso4neu.gsa
and the instrument parameter file is c:\cpdw\lebail_xray_neutron\neu_d1a.prm
. The Instrument parameter file has two banks, select bank one (EXPGUI will not let you proceed until you choose a bank).
If you look in the Histogram tab you will now see one line per histogram (one X-ray histogram and one neutron histogram). To see the parameters for a particular histogram, click on that line.
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(Left: X-ray histogram; Right: neutron histogram)
For the profile fitting, we are going to do this in Model Biased Le Bail mode. Go into the LS Controls tab. Click on Histogram 1 (X-ray data) , and select F(calc)
Weighted .
Now click on Histogram 2 (Neutron data) , and select F(calc) Weighted .
Now, prior to fitting the background, run Powpref and Genles
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Now, select Powder, Bkgedit and fit the background for Histogram 1 (the X-ray data).
If the X-ray histogram is not selected, via the top Bkgedit menu, select File,
Histogram 1 .
Now, making sure Histogram 2 (Neutron data) is selected via the L S Controls, select
Powder, Bkgedit and fit the background for the Neutron data. If the X-ray histogram is not selected, via the top Bkgedit menu, select File, Histogram 2 .
Getting the best fit to the multiple diffraction patterns can be more tedious than just fitting a single diffraction dataset but it is not that difficult. One trick when fitting a combined X-ray and Neutron dataset is to let the wavelength for the neutron dataset refine along with the unit cell. Normally the wavelength for the X-ray dataset is more well determined, so the X-ray wavelength can be used to anchor the unit cell.
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Via the Scaling tab, turn off the Scale parameter refinement flags for the X-ray and
Neutron data. (These are turned back on after the Le Bail fitting) Now run Powpref once, the Genles a few times to get calculated intensities into the observed peaks.
To help the positions of the calculated reflections match up with the observed:

Refine Cell (Phase tab)

Refine both the Zero and Wavelength for the Neutron data (Histogram Tab,
Histogram 2)

Refine the shft parameter for the X-ray data (ProfileTab, Histogram 1)
In Liveplot, to view the Rietveld plot for the 2 nd Histogram, select File, Histogram, 2 from the top Liveplot menu. It is possible to open multiple Liveplot screens so you can simultaneously follow the Rietveld plots of the various histograms.
As per the previous sections, slowly release the width and shape parameters for the
X-ray and Neutron data. You may find you need to play with the X-ray parameters as releasing all the Width and Shape parameters may go into a false minima where the peaks are too broad at high angle (not helped by a possible goniometer offset problem at high angle). It may be best to not release any more width and shape parameters at this point and only try releasing the other width and shape parameters in the final stage of the structure refinement where the calculated intensities are constrained to the atomic structure.
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For both X-ray and Neutron datasets, now refine the background parameters
( Histogram tab).
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For the moment, turn off the refinement flags for all the profile parameters, wavelength, zero offset and unitcell (but keep the background refinement flags on.
In the LS Controls , for histogram 1 (X-ray) and histogram 2 (neutron), go back into
Rietveld mode ; and in Scaling , refine the scale factor for histogram 1 (X-ray) and histogram 2 (neutron).
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Now run powpref following be Genles .
If you were only refining X-ray data, you would release the atoms positions and thermals slowly in reverse order of atomic number. As this is a smallish structure and the neutron data is also being used, refine all the atomic positions of the atoms. In the
Phase Tab, put your mouse of the atoms and click the right mouse button. This selects all the atoms.
Now select the “X” refinement flags box.
Now run genles .
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Most of the above difference plot looks due to thermal parameters needing refinement.
But it does not hurt to run Results, Disang to check that none of the atoms have gone a-wandering and are in physically unreasonable positions.
If you were only refining X-ray data, you would release the atoms positions and thermals slowly in reverse order of atomic number. As this is a smallish structure and the neutron data is also being used, refine all the thermal positions of the atoms. In the
Phase Tab, put your mouse of the atoms and click the right mouse button. This selects all the atoms. Now select the “U” refinement flags box.
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Now run genles.
Now could be a good time to again release the profile parameters, unit cell, neutron zero, neutron wavelength, and profile parameters for the X-ray and neutron data. Then run Genles .
Near the final stages of the refinement, visual changes to the Rietveld plot can be quite trivial. Thus a better guide can be to look at the fit indices and the refined parameters
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via the Lstview program and Disang as a judge of how well the refinement is now progressing.
Cycle 179 There were 8918 observations.
Powder data statistics Fitted -Bknd Average
Bank Ndata Sum(w*d**2) wRp Rp wRp Rp DWd Integral
Hstgm 1 PXC 1 6000 24606. 0.1001 0.0785 0.0984 0.0780 0.724 0.956
Hstgm 2 PNC 1 2918 24061. 0.0561 0.0454 0.0594 0.0487 0.219 0.915
Powder totals 8918 48667. 0.0694 0.0683 0.0761 0.0713 0.474
Cycle 180 There were 8918 observations.
Powder data statistics Fitted -Bknd Average
Bank Ndata Sum(w*d**2) wRp Rp wRp Rp DWd Integral
Hstgm 1 PXC 1 6000 24162. 0.0992 0.0778 0.0971 0.0770 0.729 0.956
Hstgm 2 PNC 1 2918 26884. 0.0593 0.0478 0.0633 0.0516 0.208 0.915
Powder totals 8918 51046. 0.0711 0.0685 0.0774 0.0712 0.455
Cycle 182 There were 8918 observations.
Powder data statistics Fitted -Bknd Average
Bank Ndata Sum(w*d**2) wRp Rp wRp Rp DWd Integral
Hstgm 1 PXC 1 6000 23562. 0.0980 0.0767 0.0954 0.0756 0.735 0.956
Hstgm 2 PNC 1 2918 26541. 0.0589 0.0475 0.0628 0.0513 0.210 0.915
Powder totals 8918 50102. 0.0704 0.0677 0.0764 0.0701 0.457
Cycle 183 There were 8918 observations.
Powder data statistics Fitted -Bknd Average
Bank Ndata Sum(w*d**2) wRp Rp wRp Rp DWd Integral
Hstgm 1 PXC 1 6000 23354. 0.0976 0.0763 0.0948 0.0751 0.737 0.956
Hstgm 2 PNC 1 2918 24885. 0.0571 0.0461 0.0606 0.0496 0.216 0.915
Powder totals 8918 48238. 0.0691 0.0670 0.0750 0.0693 0.468
Cycle 184 There were 8918 observations.
Powder data statistics Fitted -Bknd Average
Bank Ndata Sum(w*d**2) wRp Rp wRp Rp DWd Integral
Hstgm 1 PXC 1 6000 23197. 0.0972 0.0760 0.0943 0.0747 0.739 0.956
Hstgm 2 PNC 1 2918 26280. 0.0586 0.0473 0.0625 0.0510 0.210 0.915
Powder totals 8918 49476. 0.0700 0.0672 0.0757 0.0694 0.458
Important: Be very careful when refining thermals anisotropically using powder diffraction data. Normally this is only possible with good Neutron data, and even then due care must be shown to make sure the results are physically reasonable and releasing these parameters is supported by the data.
Besides looking at the shift/ESDs and ESDs in the GSAS LIST file (via Lstview ). If the shift/ESD for a parameter is not very near zero after a good number of cycles, this can imply that the data will not support the refinement of this parameter (either alone or in combination with other parameters). Also run the structure through validation in
Platon and visually inspect the structure using either Platon or GUI WinORTEP 3
(WinORTEP 3 can read GSAS files directly)
To refine the atoms anisotropically that are already refining isotropically, select all the atoms then click on the Xform Atoms icon. Then select the Set Anisotropic icon which will convert the Isotropic values to Anisotropic values. Select Close to get back to the main EXPGUI screen.
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It would not hurt to run Powpref at this point, followed by Genles to continue the refinement.
While the shift/ESDs look OK (via lstview ) for the anisotropic thermal parameters, it would be good if the refinement was weighted more on the Neutron data than the
X-rays. The Sum(w*d**2) for the X-ray data is double that of the neutron data, so it is possible that noise or systematic error in the X-ray data is having more of an influence on some of the thermal parameters than the better high angle intensities of the neutron data.
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Based on the above Sum(w*d**2), it would be good to double the weighting of the neutron data. Via Expedt , type k p h f 2 (2 is the second histogram, which in this case is the neutron data). Then enter a new histogram weighting factor of 2 (the default is
1). Now keep typing X [RETURN key] until Expedt exits. Powpref must be run after changing a histogram weighting. The following Genles screen shows the neutron data (Histgm 2) is now upweighted compared to the X-ray data, which is what we want.
ORTEP-3 for Windows for Windows can be obtained from http://www.chem.gla.ac.uk/~louis/software/ortep3/ (is included on the CD-ROM) and can imported GSAS EXP files. It can be good to graphically inspect the structure to see if the ORTEPs make sense, as show in the following screen image.
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Platon (by Ton Spek) can perform visualisation of crystal structures as well as a large variety of structure validation. At minimum you should do an Addsym check to see if the structure may have too low a symmetry spacegroup. Addsym analysis should be considered mandatory for all solved and refined structures. Platon can also check for intra and inter molecular bonds that are suspiciously short, and suspicious anisotropic thermals. The UNIX version of Platon is available via http://www.cryst.chem.uu.nl/platon/ and the Windows version at: http://www.chem.gla.ac.uk/~louis/software/platon/ . Platon can read Platon, Shelx and
CIF files, and EXPGUI can export Platon SPF files (via the Import/Export, Coord
Export menu). It can often be best to export CIF files for reading into Platon, as
Platon can then use the ESDs as part of the validation analysis.
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In this example, there will be a brief example of using the GSAS Expedt macro facility as well as showing the use of constraints for refinement of site occupancies.
The crystal structure is that of Barium Iron Titanate (I.E. Grey, C. Li, L.M.D.
Cranswick, R.S. Roth and T.A. Vanderah, Structure analysis of the 6H-
Ba(Ti,Fe3+,Fe4+)O3-delta solid solution, Journal of Solid State Chemistry, 1998,
Vol.135, No.2, pp.312- 321.)
Hexagonal; Spacegroup = P 63/M M C
Cell a=b= 5.6915 c= 13.9521 gamma = 120
Following are the starting co-ordinates and occupancies in GSAS macro format. The text after the “!” are comments. i 1 Ba+2 0.00 0.00 0.25 1 Ba1 i 0.025 !Insert atom 1 i 2 Ba+2 0.33333 0.66667 0.09 1 Ba2 i 0.025 !Insert atom 2 i 3 Ti+4 0.00 0.00 0.00 0.5 Ti1 i 0.025 !Insert atom 3 i 4 Fe+3 0.00 0.00 0.00 0.5 Fe1 i 0.025 !Insert atom 4 i 5 Ti+4 0.33333 0.66667 0.84 0.5 Ti2 i 0.025 !Insert atom 5 i 6 Fe+3 0.33333 0.66667 0.84 0.5 Fe2 i 0.025 !Insert atom 6 i 7 O-2 0.52 0.04 0.25 1 O1 i 0.025 !Insert atom 7 i 8 O-2 0.83 0.66 0.08 1 O2 i 0.025 !Insert atom 8
Double click the EXPGUI icon on the desktop, create a new EXP file (directory and title of c:\cpdw\occ_constraints\titanate.exp
) and add the above Cell information
(but don’t add any atoms).
Then add the histogram / powder X-ray diffraction data c:\cpdw\occ_constraints\titanate.gsa
and instrument parameter file of c:\cpdw\occ_constraints\ cuka12xrd.prm
. Again, fix up any problems with the
Ratio of the wavelengths (0.5). As POLA is set at a value for a curved graphite diffracted beam monochromator based on using the Azaroff function (0.911), IPOLA
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should be set to 1 to get GSAS to use the Azaroff function. (1). Set the number of refinement cycles to 8, etc.
The idea behind GSAS macro files is that of files that contain the keystrokes of the commands and parameters you would use if you were inputting the information by hand. The advantage of using a Macro file is you avoid tedium and possible typographical errors, especially if you have a large structure.
To enter the above coordinates in the c:\cpdw\occ_constraints\struct.mac
, run
Expedt , and enter the atom editing menu by typing k l a .
Then to use a macro file type @r ( this is the “use macro" command), and GSAS will prompt you to enter a macro file, type struct.mac
. After running the macro file, type
L to examining the atom list.
Now keep typing X [RETURN key] until Expedt exits.
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Run powpref , then Genles and then fit the background using Powder, bkgedit .
Then do a F(calc) weighted Le Bail fit to the data, including refining the background.
Note that with the screen images below, the fit to the high angle data should be very good.
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Then lock down all the profile refinement parameters as before, except the background. Note that with the screen images below, the fit to the high angle data should be very good. Turn GSAS back to Rietveld mode. And refine the scale factor
Before we can refine the titanium – iron shared positions, they have to be linked to refine to move together and have the same thermal factors. (the summed occupancy values should be made consistent with the known composition of the material, unless you tare trying to determine the chemistry from the diffraction data itself)
Note that in reality the Iron and Titanium most likely do not move identically or have the same thermal factors, but this is a constraint that is necessary due to not having enough information in the diffraction pattern to model the shared atom sites in an unrestrained manner.
The assumption with the following restraints is that the two metal sites are fully occupied. To make these types of assumptions on your materials, some crystal chemical knowledge must be applied and tested against the diffraction data.
In this case, the two separate metal sites will not have their fractional occupancies linked. This can be used to help use the diffraction data to refine the chemistry.
Though it can be better to have an elemental analysis to constrain the composition in the refinement. Metal site one contains atoms 3 (Ti1) and 4 (Fe1). Metal site two contains atoms 5 (Ti2) and 6 (Fe2).
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Go to the Constraints Tab and select New Constraint . Select atoms 3 and 4, then
XYZU-F from the Variables List and save the constraint. Repeat this procedure for atoms 5 and 6. This means while X,Y,Z and thermals will be constrained to move together, adding Fe into the site with take out an equivalent amount of Ti; and visa versa.
Now slowly refine the atom positions and thermals. And Fractional occupancies for the shared metal sites. It may not be possible to release thermal parameters and occupancies at the same time. This is something you may find out the hard way. Be wary to make sure things charge balance (we will be doing this later). This structure is more complicated as there may be Fe+4 as well as Fe+3. Also, vacancies in the oxygen positions may be possible as well. The large thermals for the Oxygens might be indicating oxygen vacancies, or may be just large thermals. This can be difficult to determine with confidence from X-ray data alone.
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Important: It can be beneficial to set the occupancy values in the shared sites
(consistent with the known composition of the material) to different values and see if they consistently refine to the same value. This is a good check on the robustness of the refinement, and also if there might be some dangerous false minima in the refinement you should be aware of.
We will use the cell composition restrains to set up a change balance constraint. It can be easier doing this as a GSAS macro ( c:\cpdw\occ_constraints\chbal.mac
). And this appears below. Even if you don’t wish to apply the constraint, it can be a good way to do an easy check on whether the refinement charge balances. k !don't make backup file l !least squares setup s !edit soft restraint data c !edit chemical composition restraints i 0 0.1 !insert new constraint, it should sum to zero with 0.1 esd
1 1 2 !phase one, atom 1 (Barium), value of 2
1 2 2 !phase one, atom 2 (Barium), value of 2
1 3 4 !phase one, atom 3 (Titanium), value of 4
1 4 3 !phase one, atom 4 (Iron), value of 3
1 5 4 !phase one, atom 5 (Titanium), value of 4
1 6 3 !phase one, atom 6 (Iron), value of 3
1 7 -2 !phase one, atom 7 (Oxygen), value of -2
1 8 -2 !phase one, atom 8 (Oxygen), value of -2
0 !end inputting the charge balance constraint
To insert the constraint within the chbal.mac
file, run Expedt, then type @r and when prompted, chbal.mac
. Then type L and keep pressing the [ENTER] key to list the restraint. This is telling us that there are too many negative charges. In this exercise, we are going to assume this is due to oxygen vacancy in the oxygens surrounding the
Fe/Ti sites.
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Now keep typing X [RETURN key] until Expedt exits. In the Histogram Tab, click on the Set Histogram Use Flags . This shows the chemical composition/charge balance restraints are being applied. If you only wanted to use the restraint diagnostically, you could deselect this.
Run Results, Disang. This shows that O1 is bonded to the Bariums but not O2. Given the model has Barium fully occupied, any oxygen vacancies are more likely to be in the O2 site.
Thus release the O2 Fractional refinement parameter. The charge balance restraint should keep the parameters from going beserk. Again, we might be finding out the hard way if we need to fix the O2 thermal, or constrain it to be equal to the O1 thermal.
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Just in case, run powpref ; then run Genles to refine. The Oxygen occupancy goes to greater than 1 (physically unreasonable). It looks like we have to increase the weighting on the charge balance restraint. Run Expedt and go k l s c . After listing the restraint, type F 100 to increase the restraint weighting from 1 (default) to 100. Type
X [Return] until you exit Expedt.
If you now run Genles, it still wants to keep the Oxygen occupancy around 1. (full occupancy). Disabling the charge balance restraint and manually setting the Oxygen
O1 occupancy at various values also upsets the refinement and drives the metal occupancies to unreasonable values. This could imply our model of Oxygen vacancies in the O2 site is not valid and that we should look for the problem elsewhere. Often when a restraint is fighting against the diffraction data, it implies the model behind the restraint has some flaws or mistakes. E.g., it could imply we have Fe+4 in the structure; and or we have refined the Ti/Fe ratio off the actual composition.
Important:
“What type of crap tutorial is this where the tutorial restraint does not work!?” we hear you ask? Often the logic and assumptions behind the adding of restraints (and some constraints) are not correct, but this may not be obvious at the time the restraint was added. It is helpful to get used to the idea that initial versions and assumptions of the structure model may not be correct.
Forcing pre-conceived ideas about the model onto uncooperative data is not a good way to progress. Instead, consider if there are more appropriate models that may give a better explanation of the fine points of the diffraction data.
Think of restraints as being like having nuclear weapons: just because you have the technology does not mean it should be used. Careful thought on if/when it is appropriate to use a restraint should be considered, and whether it might be better to collect extra or improved data so the restraint does not have to be used.
One thing that could be tried could be to add another Fe atom to each of the Ti/Fe sites and define this as Fe+4 using the charge balance restraint and see what values of Fe+4 this might give in the two sites. (it is of course just as easy to do this calculation on a sheet of paper – working out how much Fe+4 would have to be present to “charge balance” the structure). This of course assumes the composition has been refined correctly. This may not be a valid assumption. This is where the analyst has to think about things, and perhaps get a microprobe or other quantitative chemical analysis of the sample to fully constrain the composition in the refinement.
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Important: The following assumed you know the composition of the material, and that the initial occupancy values have been setup in GSAS such that it matches the known elemental chemistry of the sample.
Here, we will enter constraints that if any Iron is taken out of the first shared metal site, it will be put into the second shared site, and visa versa with the Titanium. This is not as straight forward in this case as it might initially seem, as the two shared sites have different multiplicities (i.e., different numbers of atom positions within the unit cell)
In the Constraint Tab, delete the old Fractional constraints that were set up in the previous section.
Then go to the Phase tab and turn off all the atom coordinate refinement parameters.
Also, reset the occupancies of the two shared sites to 0.5
, either by typing them manually, or selecting the atoms, clicking on the Xform Atoms icon.
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Type 0.5 in the occupancy box and select Set Occupancies . Doing this when you need to change a number of atoms can be very convenient. It can also make it easy to set the thermal and occupancy atom parameters are various values to check the robustness of the refinement.
Do the same with the thermals of ALL the atoms. This can be a good habit to make sure we don’t slowly go down into a false minima based on the previous refinement.
Reset them all to 0.1
To add the new fractional occupancy constraint where atom occupancy taken out of one metal site into another, the following logic must be considered.

The metal position at 0, 0,0 has a site Mult/multiplicity of 2 . (there are two of these sites in the full unit cell

The metal position at 1/3, 2/3,0.84 has a site Mult/multiplicity of 4 . (there are four of these sites in the full unit cell
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
This means that if you took 0.25 of occupancy from the 4 fold site and put it into the 2 fold site, you would be taking 0.25x4= 1 atom’s worth of scattering power.
But 1 atom’s worth of scattering power in the 2 fold site is 0.5. So the act of taking 0.25 occupancy out of the 4 fold site puts 0.5 occupancy in the 2 fold site.

Thus in the new occupancy constraint, if the multiplier for the 4 fold site is 1, the multiplier for the 2 fold site is 2.
Now here comes the fun bit. In the Constraints tab, select a new constraint and input the above information to match the following screen image. The New Column button allows you to add extra atoms into the new Frac constraint. Note that the 0 0 0 site has a multiplier of 2 for the Ti1 and –2 for the Fe1.
Select the Save button to apply the constraint.
As you have significantly reset the structure, run powpref and genles, then slowly release the atom coordinate, thermals (and Fract for the shared occupancy sites), heavy atoms first, followed by light atoms later. You will notice the occupancies of the two shared sites sum to 1. Fe taken from Fe1 was put into the Fe2 site and visa versa for the titanium. The summed values for the total cell starting composition is still retained.
85

(i.e., there were 0.5 *2 + 0.5 *4 = 3 atoms of Fe in the cell before the start of the refinement. After the refinement, 0.263336*2+0.618332*4=3 atoms of Fe, but in different statistical distribution between the two sites).
This still does not charge balance. You can use the charge balance restraints diagnostically in EXPEDT ( k l s c [RETURN] [RETURN] [RETURN] ) or just to the arithmetic yourself:
+ve charges = +2*2 (Ba1) + +2*4 (Ba2) + +4*2*0.7367 (Ti1) + +3*2*0.2633 (Fe1)
+ +4*4*0.3817 (Ti2) + +3*4*0.6183 =
-ve charge = -2*6 (O1) + -2*12 (O2) =
+33
-36
Sum = 3
Though personal experience is that GSAS tends to make less typographical errors than a human when doing the sums. It can be useful to do both methods of a charge balance check and make sure they both add up. In this case, as shown by the previous section, it looks like the charge imbalance is probably a combination of the Fe sites containing a combination of Fe+3 and Fe+4.
86

Important: It is easy to get inaccurate results from quantitative phase analysis using powder X-ray diffraction, even if the fit looks very good and reasonable.
Thus validation of results (such as XRF analysis, neutron and other appropriate methods) is pretty much mandatory. Refer to the two International Union of
Crystallography (IUCr) Commission on Powder Diffraction (CPD) Quantitative
Analysis Round Robins (QARR) (published in the Journal of Applied
Crystallography but also available via the CPD website - http://www.iucr.org/iucr-top/iucr/cpd.html
)
“Outcomes of the International Union of Crystallography Commission on
Powder Diffraction Round Robin on Quantitative Phase Analysis: samples
1a to 1h”
, I. C. Madsen, N. V. Y. Scarlett, L. M. D. Cranswick and T. Lwin,
J. Appl. Cryst.
(2001) 34 , 409-426
“Outcomes of the International Union of Crystallography Commission on
Powder Diffraction Round Robin on Quantitative Phase Analysis: samples
2, 3, 4, synthetic bauxite, natural granodiorite and pharmaceuticals”
, N. V.
Y. Scarlett, I. C. Madsen, L. M. D. Cranswick, T. Lwin, E. Groleau, G.
Stephenson, M. Aylmore and N. Agron-Olshina, J. Appl. Cryst.
(2002) 35 , 383-
400
In this example, we use IUCr Commission on Powder Diffraction quantitative phase analysis round robin data containing Corundum (Al2O3), Fluorite (CaF2) and Zincite
(ZnO). The diffraction data has been deliberately concatenated, generally meaning that refinement of atomic co-ordinates and thermals should not be performed. In this case, while the unit cell can be refined, you have to obtain reliable atomic coordinate, thermal and occupancy information. If this is not valid for your sample, it can add extra systematic errors to the result.
87

Double click the EXPGUI icon and title of c:\cpdw\quant\1g.exp
).
on the desktop, create a new EXP file (directory
Import the three CIF structure files one after the other by using the Add Phase:
 c:\cpdw\quant\corundum_icsd_10425.cif
(when promped, change spacegroup from R -3 c H to R -3 c)
 c:\cpdw\quant\fluorite_icsd_29008.cif
 c:\cpdw\quant\zincite_icsd_26170.cif
This leads to the following EXPGUI screen where each phase can be selected via its phase number. If there is a Uiso value of zero, this may have reset to a reasonable value as defined by structures in the ICSD.
Also be wary that B values may have been imported and interpreted as Uiso values.
(you can verify this by looking inside the CIF file with a text editor such as notepad)
These need to be reset to Uiso values. The zincite and fluorite structures have Biso values inputted as Uiso values and these need to be reset.
Biso = 8
 2
Uiso : Uiso = Biso/78.96.
So just this formula to convert the Biso to Uiso values.
88

Now add a diffraction pattern ( C:\cpdw\quant\cpd-1g.gsa
) where the Instrument
Parameter file is C:\cpdw\quant\cuka12xrd.prm
. Again reset any bad instrument values (Ratio= 0.5
, IPOLA= 1 , POLA= 0.911
) and change the number of LS cycles to 8.
In the Scale tab, disable the global scale factor and enable the Phase Fractions Scal e parameter.
89

Run Powpref and Genles . It might be best to exclude the lower angle region where you are no peaks, but an increasing background due to air scatter.
If you excluded a region, run Powpref and Genles again. Then fit the background as before using Powder, Bkgedit .
90

Important: The sample displacement parameter should be the same for all phases with the sample, thus we need to constrain this to refine to an identical value within all the phases. (remembering that this is Bragg-Brentano flat plate geometry data)
Go into the Constraints tab. Select the Profile tab within.
Select Add Constraint , followed by selecting #10 (shft) and continue.
Then select all the (three) phases via the mouse using click and drag. Then Save to create the restraint.
91

Now release the refinement parameters for shft and the unit cell for all the major phases (in this case, all the phases are present in major amounts). Now refine in
Genles.
Now fit the profile. Assuming you are using an appropriate starting profile values from the instrument parameter file, you may find that you only need to release the GW and LY to get a good fit on such a short range of data. If there was evidence of preferred orientation, you would also have to refine preferred orientation parameters for the affected phases.
92

Now refine the background .
The fitting is pretty much done, so go into lstview to obtain the quantitative phase analysis results.
Phase/element fractions for phase no. 1 (Corundum)
Hist Elem: 1 1 PXC
Fraction : 6.16743
Sigmas : 0.356722E-01
Shift/esd: 0.00
Wt. Frac.: 0.33291
Sigmas : 0.128451E-02
Phase/element fractions for phase no. 2 (Fluorite)
Hist Elem: 1 1 PXC
Fraction : 12.0252
Sigmas : 0.474497E-01
Shift/esd: 0.00
Wt. Frac.: 0.33137
Sigmas : 0.874254E-03
Phase/element fractions for phase no. 3 (Zincite)
Hist Elem: 1 1 PXC
Fraction : 23.3777
Sigmas : 0.697861E-01
Shift/esd: 0.00
Wt. Frac.: 0.33572
Sigmas : 0.665731E-03
Phase/element fraction sum(shift/error)**2 : 0.00
This compares with the mixed and XRF values (%):
Corundum Fluorite Zincite
As Mixed
XRF
31.37
31.70
34.42
33.86
34.21
34.01
93

Important: It is very easy to get very inaccurate results form quantitative phase analysis using powder X-ray diffraction, even if the fit looks very good and reasonable. Thus validation of results (such as XRF analysis, neutron, etc) is important do implement, especially in the development stages of working on a new phase system; and as spot checks to ensure nothing untoward has occurred that is throwing the accuracy out.
At present, replacing histogram files is done via the EXPEDT program (the comprehensive GSAS EXP file editor by Bob von Dreele and Allen Larson). Select the EXPEDT ICON from the top left menu.
In EXPGUI, save the current GSAS EXP filename as 1h.exp
.
Then to get to the point where you can replace the histogram, type K P H R 1 (note the descriptors within EXPEDT which explain what these mean while you are doing this). When prompted with Enter raw histogram input file name (<?>,$,QUIT), type the name of the data file: cpd-1h.gsa
and when prompted, confirm this is correct by typing Y . When prompted with Enter POWDER instrument parameter file name (<?>,$,QUIT) , type the name of the GSAS instrument parameter file: cuka12xrd.prm
and when prompted, choose scan number 1
. Don’t bother previewing it. Then type T (Set max 2-Theta or Energy or min TOF), and then / to confirm the maximum angle is acceptable. To exist EXPEDT, type X X X and
[RETURN], the X and [RETURN].
Check the EXP file is OK, especially in the Histogram tab as some of the Instrument parameters may not have been imported correctly. Again, fix up any problems with the Ratio of the wavelengths (0.5). As POLA is set at a value for a curved graphite diffracted beam monochromator based on using the Azaroff function (0.911), IPOLA should be set to 1 to get GSAS to use the Azaroff function. (1). Correct these.
94

Now run powpref followed by Genles which, as the patterns are close to each other, should pretty much complete the refinement.
The fitting is pretty much done, so go into lstview to obtain the quantitative phase analysis results.
Phase/element fractions for phase no. 1
Hist Elem: 1 1 PXC
Fraction : 6.75558
Sigmas : 0.359036E-01
Shift/esd: 0.00
Wt. Frac.: 0.36393
Sigmas : 0.123027E-02
Phase/element fractions for phase no. 2
Hist Elem: 1 1 PXC
Fraction : 12.3218
Sigmas : 0.451448E-01
Shift/esd: 0.00
Wt. Frac.: 0.33887
Sigmas : 0.820825E-03
Phase/element fractions for phase no. 3
Hist Elem: 1 1 PXC
Fraction : 20.7362
Sigmas : 0.625926E-01
Shift/esd: 0.00
Wt. Frac.: 0.29720
Sigmas : 0.630482E-03
This compares with the mixed and XRF values (%):
Corundum Fluorite
As Mixed 35.12
XRF 35.35
34.69
34.26
Zincite
30.19
30.03
95

Important: It is very easy to get very inaccurate results form quantitative phase analysis using powder X-ray diffraction, even if the fit looks very good and reasonable. Thus validation of results (such as XRF analysis, neutron and other appropriate methods) is pretty much mandatory. Refer to the two International
Union of Crystallography (IUCr) Commission on Powder Diffraction (CPD)
Quantitative Analysis Round Robins (QARR) (published in the Journal of
Applied Crystallography but also available via the CPD website - http://www.iucr.org/iucr-top/iucr/cpd.html
)
“Outcomes of the International Union of Crystallography Commission on
Powder Diffraction Round Robin on Quantitative Phase Analysis: samples
1a to 1h”
, I. C. Madsen, N. V. Y. Scarlett, L. M. D. Cranswick and T. Lwin,
J. Appl. Cryst.
(2001) 34 , 409-426
“Outcomes of the International Union of Crystallography Commission on
Powder Diffraction Round Robin on Quantitative Phase Analysis: samples
2, 3, 4, synthetic bauxite, natural granodiorite and pharmaceuticals” , N. V.
Y. Scarlett, I. C. Madsen, L. M. D. Cranswick, T. Lwin, E. Groleau, G.
Stephenson, M. Aylmore and N. Agron-Olshina, J. Appl. Cryst.
(2002) 35 , 383-
400
In this example, we use neutron powder data collected on a corundum crucible containing cubic Y2O3. The aim here was to check that the corundum crucible being used for a specialised insitu neutron diffraction experiment would also work as an internal standard to follow the formation of crystalline and amorphous material.
Corundum Crucible : 2.211g 83.0 %
Y2O3 : 0.453g 17.0 %
Double click the EXPGUI icon on the desktop, create a new EXP file (directory and title of c:\cpdw\preferred_orientation\crucible.exp
) .
Import the two CIF structure files one after the other by using the Add Phase:
 c:\cpdw\preferred_orientation\corundum_icsd_10425.cif
(when promped, change spacegroup from R -3 c H to R -3 c) Change the UISO values from 0 to 0.01.
 c:\cpdw\quant\y2o3_icsd_26190.cif ( ignore the EXGUI warning that I a –3 is likely incorrect) Change the UISO values from 0 to 0.01.
This leads to the following EXPGUI screen where each phase can be selected via its phase number. If there is a Uiso value of zero, this may have reset to a reasonable value as defined by structures in the ICSD (for inorganics, often a “starting” UISO value of 0.01 is used. As this is neutron powder diffraction data, thermals/UISO can be refined in cases which would not be possible with X-ray powder diffraction data.
96

Also be wary that B values may have been imported and interpreted as Uiso values.
(you can verify this by looking inside the CIF file with a text editor such as notepad) If
Biso’s are present, they need to be reset to Uiso values using the formula:
Biso =
8
 2
Uiso : Uiso = Biso/78.96
.
Now add a diffraction pattern ( C:\cpdw\quant\cructs.gsa
) where the Instrument
Parameter file is C:\cpdw\quant\c2_1_3A.prm
. Reset any bad instrument values.
Though in this example, the instrument parameter has no false information within it.
In the Scale tab, disable the global scale factor and enable the Phase Fractions Scal e parameter.
97

In LS Controls , set the number of cycles to 9 . Run Powpref and Genles and check the initial fit with Live Plot. You can specify that phase names be displayed in the legend by Options, Configure Tickmarks, Label by Name .
Even though the background looks very simple, out of habit, fit the background as before using Powder, Bkgedit .
98

As this is capillary neutron data, it is usual to refine the Zero offset (not the sample displacement as this only makes sense for Flat Plate diffractometer data). Refine the
Zero Offset and the Unit Cell for the two phases.
Now fit the profile and refine the atomic positions and thermals/UISO’s. This would not normally be possible so easily with X-ray powder diffraction data.. Assuming you are using an appropriate starting profile values from the instrument parameter file, you may find that you only need to release the GW and LY to get a good fit on such a short range of data. As this is neutron data, the heavy atoms and light atoms have similar scattering factors and the atomic can be released at the same time. Also refine the background .
99

You will see from the above screen image that some reflections are not fitting well with the corundum. Be careful that this could mean we have incorrect structural information, the refined parameters are in a strange false minima, or the data is flawed, or suffering preferred orientation. (For some people, if the data has preferred orientation, this means the data is flawed and you should try a type of sample preparation and data collection that eliminates the preferred orientation: e.g., spray drying sample preparation of the powder) . All this should be checked.
Zoom up in LivePlot and do CONTROL left mouse click near the HKL lines of the affected . This will display the affected HKLs.
While a number of HKLs can be investigated, it looks like preferred orientation involving the 006 direction. In this example, we will use the March-Dollase correction options within GSAS. Go into the MD Pref Orient tab and put 0 0 6 for corundum
( Phase 1 ) and set ratio to refine .
100

Before refining the preferred orientation, run LSTVIEW and check the state of the quantitative analysis.
Corundum: 81.9% (0.2)
Y2O3: 18.0% (0.5)
Now run Powpref and Genles.
This seems to fix up most of the mis-fitting of the data.
Everything that looks reasonable to do has been done. Run LSTVIEW and check the result of the quantitative analysis.
Corundum: 81.8% (0.1)
Y2O3: 18.1% (0.4)
This compared with the weighed values:
Corundum Crucible : 2.211g 83.0 %
Y2O3 : 0.453g 17.0 %
It seems that the preferred orientation correction does not affect the quantitative analysis significant, which is nice. It can be good to keep track of how the quantitative analysis results change as a function of the parameters that are being varied. If some parameters cause the result of interest (in this case quantitative phase analysis) to vary quite considerably, then extra effort should be put into seeing if the parameters are going to reasonable values. With X-ray data, often refining thermal parameters with inadequate data can cause the quantitative analysis to become very inaccurate. In that case, trying to fix the values based on literature values can be a decent thing to try.
Cross validating the results with XRF/Chemical analysis can also be very useful to ensure the results are physically reasonable.
101

This example should be tried after you are quite comfortable with doing single phase refinements. This is a multiphase refinement with respect to both X-ray and neutron data. It involves some manual indexing of peaks, so having some idea of basic crystallography is a good idea. It illustrates the concept of scattering contrast and the sometimes great difference between X-ray and neutron diffraction. It also illustrates the sensitivity of neutron radiation to light atoms. I skip some steps, assuming you know how to do them, and in some cases refer to other examples - so don’t do this one first.
The standard phase diagrams for Ti and Zr consist of hexagonally close-packed
(

) and body centred cubic (

) phase. In addition to this, a third phase is seen at high pressure in these metals, and certain alloys. This phase is known as the wphase. This phase is seen a non-quenchable displacive phase in elemental Zr, but can be retained in small amounts in alloys.
Create a new EXP file and read in the X-ray data file <Ti0.67Zr0.33X.gsa> and the associated parameter file.
Double click the EXPGUI icon on the desktop, and the "Select an experiment file to read" dialog will be displayed. Browse to: c:\cpdw\fourier directory, type in
“TiZrO” and click
READ followed, when prompted, by Create to create a new EXP file. Put in the extra title information as required.
When prompted for a title enter: “Ti-Zr (O) alloy”
Using the CIF files, import three phases corresponding to
 
and

See example (SECTION 5: Importing a Cif structure file and determining the polarisation of the X-ray beam using Y
2
O
3
) for the process. Note that these are for elemental Ti.
Phase Lattice Parameters Zr

P6
3
/mmc a (Å)
Ti
3.2331 2.95111 c (Å)

Im-3m a (Å)
5.1480 4.68433
3.568 3.3112
102


P6/mmm a (Å) c (Å)
4.6
2.8
Your CIFs are for elemental Ti. They need adjustment to take into account the effect of alloying on lattice parameter and the presence of the alloying atom
(Zr). i) Given that the nominal composition of the material is Ti
2
Zr, adjust the cell parameters accordingly to get what you might think would be reasonable starting values. (Assume Vegard’s
Law for ideal solid solutions for

and

For

, you will have to assume the values for Ti or we may guess that they should be a little larger for the alloy.) ii) You should add in the extra atoms into all three phases, corresponding to Zr. You can assume that

and

phases are solid solutions, so to begin with you can put in the nominal composition of Ti
2
Zr as the atomic fraction (i.e. Ti 0.67 Zr 0.33).
For the case of

, it is known that Zr strongly prefers the 0, 0, 0 site and Ti strongly prefers the 2/3, 1/3, 1/2 site. Examine the multiplicities of the two sites in the P6/mmm cell. Can you accommodate full atomic ordering simply? Again: examine the relative proportion of Ti and Zr in the nominal composition, and compare it to the ratio of the site multiplicities. Ask yourself, are you feeling lucky, punk? iii) Add constraints that tie the alloyed atoms together. You need to think here. Are the x,y,z atom sites in these lattice fixed (i.e., are they special equivalent positions). All of x,y,z , or perhaps just x ? You need to consult the International Tables for
Crystallography, or you could experiment by doing a refinement at some point. (Looking up the International Tables is the way to go.). At the very least you need to constrain the atoms on the same site to have the same UISO . You should also probably constrain the site occupancies so that if Ti increases on one site,
Zr decreases, keeping it fully occupied. [See SECTION 10
Importing a structure using a GSAS macro file, and using occupancy constraints and charge balance restraints]
Your constraints should look something like:
103

You should also check and if necessary correct the values of x , y , z and the
UISO so that they are the same across both atoms. You can do the same process to make a solid solution for the

-phase (phase 2).
Your

-phase should look something like this:
Your

-phase should look like this:
104

Add in the X-ray data contained in the file Ti0.67Zr0.33X.gsa and the X-ray parameter file Yttria-Ultima-1deg-PG.prm. (This process is given in SECTION
2 An Easy start: refining the structure of corundum (

-Al
2
O
3
) powder using diffraction data collected on a neutron powder diffraction system.)
By running POWPREF , determine which of these phases is likely present.
Use Expgui/liveplot and select the tickmarks from each phase to show. The peaks are broad in this diffraction pattern due to the nature of the material.
Hints: Which phase can the lowest peak only come from?
In this example our lattice parameters are clearly wrong (yours may differ).
What is the index of the lowest peak? Use expgui/liveplot to pick off its index.
Do this by touching the “h” key in the vicinity of the lowest yellow line.
105

As we know that the lowest peak is 100  , we can determine a better starting value for a  .
From your observation that the calculated value of 2

100  is bigger than that observed, what do you have to do to the model value of a  to get it to respond to reality?
Hint : remember the Bragg equation:

=2 d sin

. Given sin
  
(for small

), for a fixed

does increasing d (for 100, it is proportional to a ) increase or decrease sin

,

and 2

?
To work out a new value of a go to Options/Show Cursor Position in
Liveplot . Read off the centre of the observed peak and deduce a  . Remember this is hexagonal so d
100
= a cos30º. You should find a value of a  in the vicinity of 4.80 Å.
Put a value in the scale factor for the refinement and fix it. A value that roughly scales the peaks to the observed intensity is fine at this stage.
106

You can run GENLES
There are four peaks in the range 36-40º 2
 and there are three distinct bands and four calculated peaks in that region from just

We may be able to get away with using only

and
 which we already know is in there, even if it
“should not be” at ambient P , T

, as those two phases appear to generate enough peaks in this area of 2

.
107

Note that the first peak is likely 100  so is easy to adjust a  a little to get a better fit. This process of matching observed peaks to calculated peaks from models is called indexing peaks. It’s not unreasonable to assume our lattice parameters for a are close to the real values, so we can probably assign those observed peaks that are near calculated positions for

to

. Our biggest remaining error is probably c  , as we are still assuming the value from

Ti
. Find out the hkl of the two

peaks in this region. Any with a non-zero component of l is likely to be the one that shifts the most. You need to adjust this peak so it lies under the peaks near 36.5º, by varying c  alone.
When you’ve done this, you should have something like this:
Let’s take  out of the equation
Run Powpref . Where once there was a single “scale factor” and three “phase fractions”, there are now only the single “scale factor” and two “phase fractions”. Now you can do a standard Rietveld refinement on this.
108

In essence, both “phase fractions” and the “scale factor” are scale factors. As you only have 2 phases you need only two of them. The best practice is to leave the “scale factor” fixed, and vary the two “phase fractions”
Slowly release the lattice parameters and the UISO of each atom. You probably want to exclude the pattern below 18º 2 
You will need to refine the profile parameters. You probably want to constrain both phases to have the same profile parameters, at least to begin with.
109

Select all three phases (I know we’re only using two) and hit Save
You can refine U, V, W, Y, S/L and H/L [the latter two one at a time] and shift .
What happens when you refine the fractional occupancy ( FRAC ) of the atoms in phase 1 and 3. Why may this happen?
You should fairly rapidly get a fit that easily looks as good or better than this:
110

So we can pretty much explain all the peaks with a mixture of

and
 alloys, with some systematic differences. Perhaps we could ascribe them to preferred orientation?
Repeat the same steps you used to add in the X-ray data, this time adding in the file ti2zr.gsa and the parameter file c2neutron.prm
. Now we have to be very careful to tie together the two datasets correctly. First note that the new dataset automatically includes beta (phase 2).
Kill that phase. Next go to scaling. Notice that the scale and phase fractions look like this
111

Compare that to the values for histogram one (to do this select the row 1 XC…. in the left window above). The ratio of the two values of FRAC are proportional to the ratio of the number of unit cells of both phases. Since this will be the same ratio in both datasets, you should copy the values you have refined in your X-ray refinement (Histogram 1) into the neutron dataset
(Histogram 2). Now you need to add a linear constraint to ensure that if one dataset is forcing a change in the value of one of these parameters, it will do the same in the other.
In the version of EXPGUI above, this is not supported (maybe it is now), so you have to use EXPEDT . To the prompts you receive enter Y L O S
Now enter K [i.e. pretend you are German and spell constraint with a K ]
Then I [for Insert]
And then 1 1:2 1 [which you can means constrain the value of the phase fraction for phase 1 [the first “ 1 ”] across both histograms [ 1:2 ] to be the same
[the last 1 –here this means if the value of the parameter changes in one histogram by a given amount, apply the same change to the other]. You need to hit “Enter” or “Return” twice to terminate the is constraint.
112

Then I again and 3 1:2 1 means insert the same constraint for Phase 3. After hitting “Enter” twice, hit “L” [for List] and you should see:
LEQV PSFR 1 1,1:2 1.0000
LEQV PSFR 2 3,1:2 1.0000
You can exit EXPEDT by hitting X <CR> multiple times.
Make sure you “ Load New ” when EXPGUI takes over again.
Now you still have the arbitrary value of “Scale” in the neutron dataset, currently at 1.00, and your fixed value associated with the X-ray refinement (in the file I am using it was left at 50). How do you handle this?
You need one more scale factor, to account for the fact that a different number of X-ray photons or neutrons are scattered in both patterns (i.e. different exposure times, sample sizes, scattering efficiencies). So you should turn on the value of scale in either the X-ray or the neutron histogram. I will choose the neutron histogram. I would do a refinement with only this parameter on to begin with. Then you can turn on the phase fractions in both histograms , so that the situation should look something like.
You should also ensure that the Damping factors are all the same for the constrained parameters (Phase Fraction 1 and 3 in Histogram 1 and 2). You also need to trim the neutron dataset. Cut off below 15 degrees, and cut off above ca
83 degrees. I assume that you know how to do this by now.
When you being to refine, it may be best to turn off all the parameters associated with the atoms, the lattice parameters, and the peak shape of the Xrays and just let the neutron scale factor settle in. You can turn on the lattice parameters, and you can also refine the zero parameter for the neutron data, and the wavelength (both of which are at nominal values in the parameter file: note neutron wavelengths are always determined by calibrations with a std and are subject to error, whereas X-ray anode wavelengths are fixed, so you should always leave an X-ray wavelength constant).
You may see something like this:
113

Quelle horreur! How can this be? Look at the atomic scattering factors and lengths of Ti and Zr.
Element X-ray atomic scattering factor (Z) Neutron scattering length (fm)
Ti 22 -3.37
Zr
O
40
8
7.16
5.08
So the values of FRAC for the atomic occupancies are poorly determined by Xray alone: the X-ray pattern can fit with a composition that clearly gives a terrible fit to the neutron pattern. Ti and Zr can yield radically different scattering contrast in the case of the

-phase, and also are coupled strongly to the scale/phase fractions for the solid solutions. You will frequently find in refinements that FRAC (change in atomic scattering amplitude) is correlated strongly to SCALE and PHASE FRACTION (changes in scattering intensity from crystalline phase) and even to UISO (which reduces scattering into Bragg peaks at high angles).
Turn back on the FRAC and UISO flags ( F and U ) in phase 1 and 3. Now look at the two fits. They should appear something like
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This is much better, but still has problems. You should set up constraints on the neutron profile parameters GU GV GW LY and asym , and you will be able to fit the shape better. They should look something like after you have finished. (Note I am leaving some steps for you to figure out here).
But try as you may, you will find that the systematic differences in intensities cannot be fixed. Take a look in liveplot and decide which phase has the misfitting lines in the neutron pattern:

or

? Given that both the

and
 peaks fit well in the X-ray case, it implies some other error in the model that is detectable with neutrons but not readily so by X-rays.
Lets try a difference Fourier map to see if there is an atom missing somehow
(not clear how if this is an alloy!).
Run EXPEDT . Answer Y F and 3 to the first three questions. Select a difference map ( DELF
). You don’t need individual step sizes, and give a value of 0.1
or 0.2
to the fixed step size, and just answer “ 0 1 ” to min and max values of x , y and z . Run POWPREF GENLES and then FOURIER (via
Graphs/Fourier) through EXPGUI .
Then run VRSTPLOT . Answer “ 3 ” for phase. Type “ U ” to get unit cell outline, and “
A
” for atoms and in this answer “
U
” for all atoms in unit cell, sequence number 1:4 [we have four atoms] , and “
0 1
” to how far along each of x , y and z axes. Exit the atom selection menu with “ X ” and then “ W ” to write the .wrl
file. You can pick any colour you like as the background. “ Q
” to quit.
You should find a file with the extension .wrl. With a little bit of luck, you should find Internet explorer can load the virtual reality
You need to have a virtual reality viewer such as COSMO installed
( http://ovrt.nist.gov/cosmo/downloads/cosmo_win95nt_eng.exe
).
If you get it going you should be able to generate a difference Fourier map such as these. This should give you any locations inside the unit cell where scattering amplitude is missing. What do you see:
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Clearly an atom is missing at ½ ½ 0. If you check the
International Tables for
Crystallography you will see that the other locations of intensity are all part of the same special equivalent position. If you sketch out the structure you would find that this coincides with an octahedral interstice. Typical octahedral interstice species are O, C and N, and we know that the starting material was oxidized. So let’s try putting an O in that position in the 
-phase, and let the fractional occupancy refine [warning, you may need to turn off other parameters first]. I’m skipping the details: you should be able to figure out how to do this by now.
Doing so yields fits like:
Now both fit OK, or at least they are great improvements. You should observe that the fit to the X-ray pattern has barely changed at all with the addition of this O atom. Why? Because the scattering is dominated by Zr (Z=40), and Ti
(Z= 22), with little input from O (Z=8). You can see one or two weak peaks in the neutron spectrum. These are from the V can in which the sample is contained: usually these are so weak they can be ignored, but here they are relatively strong. That is because the mean scattering length of the “Ti
2
Zr” sample is close to zero <b>=(2/3*(-3.37) + 1/3*7.16 = 0.14fm). So the average scattering from the disordered alloy is very weak, but contrast from Ti/Zr site ordering is incredibly strong, if it exists. Even weak scattering from V (b=-
0.38fm) shows up strongly.
Add V as another phase, imported from the V.cif
file. Make sure that it is
ONLY included in the neutron refinement [X-rays experiments are not done in
V!]. As this is highly textured metal and we only want to “eat” the intensity from it in the fit, we can model it as a Le Bail fit
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The neutron fit should now explain all the peaks. You can play with the parameters as far as you like to improve it. What you have discovered is a nonstoichiometric oxide called Ti
2
ZrO, which is the free oxide that forms from reaction of ZrO
2
+Ti, and probably also from Zr(O) in which O is in solid solution. We’ll leave the refinement at this stage.
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This involves a reasonable knowledge of crystallography. I assume you now have familiarity with EXPGUI
. If you don’t have, or don’t want, this kind of knowledge, this is not the example to follow: certainly not the first one to do.
You may need to refer to the International Tables for Crystallography. I jump several steps that I assume you know by now.
This involves the study of deuterated ammonium perrhenate at 20 K. At this temperature the ammonium ion is orientationally ordered in the lattice. From Xray powder diffraction it is impossible to tell the orientation. With neutrons D stands out very strongly. We know from X-ray spectra that the structure is
I4
1
/a , a =6 Å, c
=12Å. We know that N sits at ½ ¾ 1/8 and Re lies on 0 ¼ 1/8 and O lies near .2 3/8 .05. We know nothing about D. We will model it as a rigid body (RB).
First setup a new EXP file.
Add the phase
The International Tables for this space group are shown below for later reference. Not there are two choice of origin. GSAS will always choose the one with the centre of symmetry at the origin, which in this case is choice 2.
118

119

Add New Atoms
120

Note we created 4 deuterium atoms with default positions: it doesn’t matter what values they have, as you will see when you insert the RB in a moment.
Add in the data:
Now so far as a RB is concerned, it is just a set of vectors in Cartesians defined about an origin (the geometric centre is chosen as the centre). Vectors have a direction and a magnitude. Define a unit vector along [111], [-1-11], [1-1-1] [-
11-1]. A unit vector has magnitude of unity, so each component along x,y,z is
1/sqrt(3)=0.57735 so vector components would be [0.57735,0.57735,0.57735] etc…. Then in order for that unit vector to map onto a real length, we only need multiply unity by the known bond lenth. For N-H it is known to be ca. 1.03Å.
Therefore we define the RB in EXPEDT reached via EXPGUI/EXPEDT
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Type L to list the monster that you have created
Currently this is an abstract concept, consisting of unit vectors defining a tetrahedron, a magnitude (1.03 Å) representing the N-H bond length, but it has not been linked to the atoms in your model. So next, we insert the rigid body definition into the atom list at atom 1 (N) which sites at the origin (0,0,0).
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NOTE: We need to put in the position of N here again at 0.5 .75 .125.
Whatever you write here overwrites what you have originally written in your atom list so be careful: the atom list is just a slave to the RB constraint.
Therefore type I 1 1 as so and copy the following
If you type X twice and then re-enter the RB menu in EXPEDT with B you will see the new positions for the atoms of the ND
4
molecular cation that have been defined by your RB shape that has been inserted with zero rotation about
X, Y and Z .
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As we set all the rotations to 0 when inserting the RB into the atom menu, the orientation of the RB is given by the following matrix (see the GSAS technical manual for full mathematical description):
L reduces to a diagonal matrix containing a,b,c. X’ contains the positions of the atoms of the RB in Cartesians (we applied no rotation on insertion). Our initial orientation of R1(X) = R2(Y) = R3(Z) = 0 is “arbitrary”. We next need to
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refine both the orientation of the molecular cation, and the tilt of the inorganic sublattice.
Now we need to think.
NOTE: GSAS is pretty smart, but we all have our limitations. So if you turn on the translations TX , TY and TZ it will not let them move: you can test this and verify it a little later! However, it is not quite so smart when it comes to rotations. So if you were to set R1(X) , R2(Y) and R3(Z) to refine, they would all refine to non-zero values. But this would rotate the molecule into orientations about the -4-axis that would generate multiple distorted copies. So for rotations you have to be even smarter than GSAS! What rotations allow something that lies in a mirror plane to remain in a mirror plane? Rotations about the normal to that plane. So the only rotation you can allow is R3(Z) , rotation about the z -axis of the tetragonal crystal.
But look at the stoichiometry. With our general definition of all the angles between an ammonium ion, on the particular site symmetry in this space group, multiple copies appear. Therefore adjust the fractional occupancy. Why is this?
Because both N (and Re) lie on a -4 axis about (001) [you can check this quickly by going into EXPEDT and typing L A L] – unfortunately EXPGUI doesn’t copy this, or you can look at the
International Table for
Crystallography above. That means anything placed about it is copied 4 times, including any D atom. See below where I have done just that:
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Refine the lattice parameters and W of the Gaussian lineshape.
Go back into the RB menu in EXPEDT and when entering and using C 1 1 (to change the first (only) copy of the first (only) RB) and then turn on the rotation about Z as a free parameter (using V ). Think about the action of a -4 axis. Why is this the only possible choice? Each unique parameter has a unique parameter number in the RB menu. Damp the RB parameters to 90% damping as shown below.
126

Leave EXPEDT and go back to the atom menu. Turn on the X flag for all atoms (including N) constrained by the RB.
NOTE: If you had turned on the atom X flags in the atom list but did not turn on the RB rotation parameters, nothing would change. However, if you turn on the RB rotation parameters, but not the atom X flags you will get error messages from GSAS.
Run GENLES .
127

Turn on the U flag for ND
4
in the atom list.
We will use TLS tensors (a way of defining rigid body motion in terms of translations [T], librations [L] (mean-sq rotations) and screw [S] (helical) motions). This is part of the RB menu.
Follow the following instructions upon entering the RB menu in EXPEDT :
128

Note that by giving the parameter number 2 to T11 and T22 we are constraining changes in the values of T11 to be equivalent to those in T22 . Exit
EXPEDT . How do we know the constraints to make and how many parameters to use? See
129

Run GENLES . By now the fit should be pretty good:
Go back into the RB menu in EXPEDT and turn on the librational components subject to the same symmetry constraints for this site symmetry (L11=L22):
130

Exit and run GENLES
You could go back and try the allowed screw components too if you like, but I did not here. Are they stable to refine? If so are they large. I will continue only doing T and L.
You can also make the inorganic thermal motion anisotropic via XFORM
Atoms. Your refinement should look something like:
131

So far the magnitude of the RB is fixed, but we can refine the N-D bond length.
Note this is not a property of a copy of an RB that has been inserted in the menu (accessed via C 1 1 ), but is in the definition of the abstract geometry of the RB (accessed by E 1 for edit the definition of the first (only) RB type). You can give this a distinct parameter number:
132

Go back and turn on GU GV GY LY and asym and refine with GENLES again:
NOTE: UISO on Re is negative. It is a heavy metal so should not move as much as D. In addition we have not accounted for the absorption of Re, which is an effective absorber. It is small and negative, so that’s OK and we only are interested in demonstrating the RB part in this refinement. We could correct for this (if we wished) by calculating the absorption and putting the value in
EXPEDT L O A and then changing the value with C .
Looking at the output file under EXPGUI/LSTVIEW we see the rigid body output in terms of rotation of the ammonium ion about Z and rigid body motion of the body split up into the translational components of motion, which are nearly isotopic, but the librational component is quite anisotropic with the larger component being about the z -axis, which is also the axis about which the degree of freedom of rotation exists.
133

Is this stable enough to not require any constraints. Go back into the RB menu and at the place you would normally type C 1 1 , type D 1 1 (for delete) and confirm your choice. Also E 1 and turn off using V the refinement of the magnitude of the RB by placing that parameter number to 0. Go back to the atom menu. Delete all but one D atom using XFORM and then set that occupancy to 1
Refine with GENLES . Look at the LST file:
Yup, it’s pretty stable, as the bond length is still good, and the D-N-D bond lengths are still near the ideal tetrahedral values of 109.5º. The fit should not have changed much.
134

Congratulations.You’ve done a simple RB refinement using TLS tensors.
Further details of RBs are in:
 the GSAS technical manual ( http://www.ccp14.ac.uk/ccp/ccp14/ftpmirror/gsas/public/gsas/manual/GSASManual.pdf
)
 the Fireside Guide to Rigid Bodies ( http://www.ccp14.ac.uk/ccp/webmirrors/ian-swainson/fireside_fuide_to_rigid_bodies.pdf
) and

A Practical Guide to Creating Rigid Bodies for GSAS http://www.ccp14.ac.uk/solution/gsas/A_Practical_Guide_to_Creating_
Rigid_Bodies_in_GSAS.pdf
135


136