Tutorial 7 - Chemical Disorder

Overview

In this tutorial you will model chemical disorder over different length-scales. We will look at two systems, the high-temperature alloy Cu₃Au and the high voltage cathode material LiNi_0.5Mn_1.5O₄ (LNMO). Both systems adopt different structures on the local scale than is apparnet using long-range methods. You will practice entering and constraining crystal structures within the unit cell symmetry. You will also become familiar with running multiple refinements from a single .inp file and outputting values of interest during a refinement.

Acknowledgements

The X-ray PDF data from Cu₃Au for this tutorial was kindly donated by Dr Helen Playford (ISIS Neutron Source), and Mr Lewis Owen (University of Cambridge and relates to the publication L.R. Owen, H.Y. Playford, H.J. Stone and M.G. Tucker, Acta Materialia (2017) 125, 15-26. PDF data was collected at the XPDF (I15-1) beamline at Diamond Light Source and processed with GudrunX.

The neutron PDF data from LNMO was collected at the POWGEN instrument at ORNL. The data was kindly provided by Jue Liu and Katharine Page of ORLN and relates to the publication J. Liu, A. Huq, Z. Moorhead-Rosenberg, A. Manthiram, and K. Page, "Nanoscale Ni/Mn Ordering in the High Voltage Spinel Cathode LiNi_{0. 5}Mn_{1. 5}O₄", Chemistry of Materials (2016) 28(19), 6817-6821.

Required files

Cu3Au_pdf.xy
Ordered_LNMO.xye
LNMO_P4332_icsd70046.cif
Disordered_LNMO.xye
LNMO_Fm-3d_icsd90650.cif

Tutorial instructions

Cu3Au order-disorder alloy - 'Short-to-long-range' (STLR) refinement

The face centred cubic Cu3Au alloy can either form a disordered structure in space group Fm3m with ¼Au and ¾Cu both on (0,0,0), or an ordered structure with Au on (0,0,0) and Cu on (0,½,½) in space group Pm3m. The data Cu3Au_pdf.xy was collected at a temperature where the alloy was starting to order and so is only ordered on the local scale. We will try to fit the data to both ordered and disordered models, and then perform a 'short-to-long-range' (STLR) refinement to simultaneously refine both models.

Use VESTA to create ordered and disordered models of Cu3Au, both with a lattice parameter of 3.78 Å. Export these models to .cif format (File > Export Data...) for use in TOPAS.
Start a fresh PDF refinement using "Cu3Au_pdf.xy" as the filename and in jEdit save the file as 'Cu3Au_ordered.inp'.
Include dQ_damping with a fixed dQ of 0.055.
Import your .cif file from VESTA for the ordered structure (TOPASforPDF > 3. Phase information > 3b. add new phase from CIF > i. Read a .CIF File).
Allow the lattice parameter to refine, but constrained in cubic symmetry.
Replace the beq values with a beq spherical with min r and low r cutoffs.
Run a single step of the refinement in TOPAS to read in the data, then stop the refinement. Look at the PDF data and choose sensible values for rcut and rlo.
In TOPAS, turn on 'Show Cumulative Chi2'
and run the refinement. You should get an Rwp of approximately Rwp 16.2
1. What does the Cumulative Chi2 (χ²) plot tell you?
2. Is the fit better at low-r or high-r?
Save the .inp file as 'Cu3Au_disordered.inp'.
Comment out the ordered structure by putting /* before str and */ after the last site. This is a quick and easy way of commenting out a block of text.
Add the disordered structure to the refinement by importing your .cif file, replacing the beq values with the beq_rcut_rlo_spherical function from your ordered phase, and allow the cubic lattice parameter to refine.
Run the refinement, but reject the result.
There is now a large peak at an r of 0 Å. This is because in the disordered model there are two atoms on the same site, so TOPAS calculates a peak at 0 Å. Fix this by telling TOPAS to ignore everything below an r of 1 Å (TOPASforPDF > 1. PDF data > file preparation > start r value).
Run the refinement. You should get an Rwp of approximately 15.9.
1. Look again at the Cumulative Chi2 (χ²) plot. What does it show now?
2. Which model, ordered or disordered, is more appropriate to use at low-r?
Next will now perform a 'short-to-long-range' refinement using both structures in the same fit, while constraining common parameters for the two phases to be the same. Un-comment the ordered phase by removing /* and */.
Force both lattice parameters to have the same value, and give all atoms the same beq_rcut_rlo_spherical function.
For the phase that fitted the data best at low-r, add local-structure damping (TOPASforPDF > 3. Phase information > sample shape functions > local-structure damping) with a starting radius of 10.
For the other phase, add long-range damping (TOPASforPDF > 3. Phase information > sample shape functions > long-rang damping). This time, rather than refining a separate radius, force the radius to be the same parameter name as used for the local-structure radius,
Run the refinement. You should get an Rwp of approximately 9.4.
1. What is the refined value for the size of the local-structure domain in this material?
2. What does selecting the 'ordered' and 'disordered' phases in TOPAS show you about their contributions to the PDF as a function of r?
3. Uncomment do_errors in your .inp file, re-run the refinement and accept the result. Is the error in the domain size realistic?

Ordered and disordered phases of LNMO, Part 1 - Average structure fitting

The material LiNi_0.5Mn_1.5O₄ (LNMO) is a promising high voltage cathode. Both Ni/Mn ordered and disordered phases can be prepared, depending on the synthesis conditions. First we will look at the ordered structure using neutron PDF data.

Start a fresh PDF refinement using "Ordered_LNMO.xye" as the filename and in jEdit save the file as 'LNMO_ordered.inp'.
Tell TOPAS that this is neutron data (TOPASforPDF > 1. PDF data > neutron data), enter a start r value of 1 Å and an end value of 50 Å.
Include dQ_damping with a fixed dQ of 0.03.
Import the .cif file 'LNMO_P4332_icsd70046.cif' (TOPASforPDF > 3. Phase information > 3b. add new phase from CIF > i. Read a .CIF File) and allow the lattice parameters to refine within cubic symmetry.
Allow the scale factor to refine (TOPASforPDF > 3. Phase information > scale factor).
Use VESTA and the Bilbao Crystallographic Server to refine and constrain the fractional coordinates within the unit cell symmetry. Note that The Mn2/Ni2 sites should be equivalent, so you need to constrain them to have the same position.
This sample of LNMO used an isotopically enriched ⁷Li source to avoid the large absorption cross section of ⁶Li. Change the occupancy type of lithium from 'Li+1' to '7Li'. You don't need to remove charges from the other site types, but the charges are ignored by TOPAS for neutron data as they are not relevant.
Allow the amount of disorder on the two Ni/Mn sites to refine. There are three times as many of the Ni2/Mn2 sites as there are Mn1/Ni1 sites (Wyckoff positions 12d and 4b respectively), so for each amount of Mn which goes to site 1, a third of this value needs to be removed from site 2.
Replace beq 0.4 with a beq_spherical peak shape (no cutoffs are required for this phase). Constrain the Li, Mn/Ni and O sites to have the same values for beqlo and beqhi, and refine a single beqradius for all of them.
Run the refinement and inspect the .out file.
1. What is the amount of Ni/Mn site mixing that is refined?
2. What do the refined displacement (beq) parameters tell you about the relative motions of the different atom types?
Turn on do_errors and repeat the refinement.
1. Are the refined values statistically meaningful?

Next we will look at the disordered polymorph of LNMO, again using neutron data.

Start a fresh PDF refinement using "Disordered_LNMO.xye" as the filename and in jEdit save the file as 'LNMO_disordered.inp'.
Tell TOPAS that this is neutron data, enter a start r value of 1 Å and an end value of 50 Å.
Include dQ_damping with a fixed dQ of 0.03.
Import the .cif file 'LNMO_Fm-3d_icsd90650.cif' and allow the lattice parameters to refine within cubic symmetry and allow the scale factor to refine.
Add a suitable phase name (TOPASforPDF > 3. Phase information > phase name).
Use VESTA and the Bilbao Crystallographic Server to refine and constrain the fractional coordinates within the unit cell symmetry.
Change the lithium atom type to 7Li.
Replace the beq values with the beq_spherical values you refined for the ordered LNMO phase.
Run the refinement and inspect the results.
1. What does the fit to the PDF tell you about what is happening in this disordered material?
Turn on do_errors and repeat the refinement.
1. Are there any parameters which do not refine properly? Why could that be?
2. What can you conclude about the local structure of the disordered phase?

Ordered and disordered phases of LNMO, Part 2 - Box-car refinements

As with case of Cu3Au, it seems likely that the local structure of the disordered LNMO phase properly resembles the ordered phase. Here we will explore how the well the average structure fits the observed PDF data using a 'box-car' refinement, where sequential portions of the PDF data are fitted. This part of the tutorial will make use of ways of making TOPAS automatically run multiple times and output the results that you are most interested in.

Open your 'LNMO_ordered.out' file from Part 1 and save it as 'LNMO_disordered_boxcar.inp'.
Edit the xdd filename to "Disordered_LNMO.xye".
Comment out do_errors , run one cycle of the refinement, and accept the result. This will delete C_matrix_normalized from your file and any reported errors.
1. In TOPAS, inspect how well the ordered structure matches the disordered data. What do you notice?
Add the following lines to the top of the file:
prm !start_X_boxcar 1 prm !range_X_boxcar 5 prm !step_X_boxcar 1 num_runs 90
start_X_boxcar, range_X_boxcar and step_X_boxcar are parameters we will use to define the lowest r value to fit, the r range of the boxcar to fit, and the step between each of the fits, respectively. num_runs tells TOPAS to run through the same .inp file multiple times and can be used to set up batches of refinements.
Where you previously defined the start_X value, replace it with the following lines:
start_X =start_X_boxcar + Run_Number step_X_boxcar; finish_X =Get(start_X) + range_X_boxcar; prm mid_X = (Get(start_X)+Get(finish_X))/2;
This will calculate the start_X and finish_X values for each of the individual refinements. A parameter mid_X is also defined, which will be used when outputting the data in a form which is easily to plot. The parameter Run_Number returns the current run number (starting from zero) and can be used in combination with num_runs.
When using num_runs, TOPAS will not automatically save .out files. In order for us to see the results of interest, we can tell TOPAS to write selected parameters to a file. Add the following code to the bottom of your .inp file:
out "boxcar_occMn.xy" append Out(mid_X, "\n%V") Out(occMn, "\t%V") out "boxcar_aLP.xy" append Out(mid_X, "\n%V") Out(Get(a), "\t%V")
This will generate two files, each with two columns of data in it. The first column is the middle r value of each boxcar, which will make it easier to plot the data, and is written with the line Out(mid_X, "\n%V"). The code "\n%V" tells TOPAS to output a new line (\n) and then insert the value of mid_X as a value (%V).
There are lots of other ways of formatting values written to TOPAS output files, such as %4.8f to write a float with different column spacings and precision, and %e to write in scientific format. If in doubt, just use %V.
For "boxcar_occMn.xy", the second column is the parameter occMn which is the amount of Mn/Ni site disorder, and is written with the line Out(occMn, "\t%V") which tells TOPAS to write a tab spacing (\t) following by the value. The For "boxcar_aLP.xy", the second column is the a lattice parameter; note that here you need to use Get(a) to return the parameter value. The use of the keyword append tells TOPAS to add the results to the end of the file; this is necessary when using num_runs (otherwise it will create a new file at the start of each refinement cycle), but remember if you run the .inp file multiple times it will keep appending new data to the end of the previous file. If you want a fresh file, either give it a new filename, or delete the file before re-running the refinement.
Add a third output file for the r_wp value of the refinement.
Run the refinement in TOPAS and watch how it works. It will take a little over a minute to complete the refinement.
In TOPAS, click Load Scan files:
and select boxcar_occMn.xy (you will need to select 'X-Y data files'). On the least squares plot on TOPAS, click the right-hand mouse button and select 'Yobs normalise' to show the data on a more useful scale.
1. What does this the variation of occMn with r tell you about the local structure of disordered LNMO?
2. How consistent is the a lattice parameter as a function of r?
Experiment with some different boxcar ranges, but remember to change the output filenames.
1. Can you achieve a consistent looking plot of occMn as a function of r?

Ordered and disordered phases of LNMO, Part 3 - STLR refinement

We will now try the same approach of a short-to-long-range refinement for LNMO as we did for Cu3Au to see how the result compares with the results from the box-car method.

Open your 'LNMO_disordered.out' file from Part 1 and save it as 'LNMO_disordered_stlr.inp'.
Copy the structure from your 'LNMO_ordered.out' as a second phase in 'LNMO_disordered_stlr.inp'.
Constrain both lattice parameters to be the same.
Make sure that the beq_spherical parameters are suitably constrained as the same values across the two phases.
Constrain the scale factors to be the same for both phases.
Add long-range damping to the disordered phase and local-structure damping to the ordered phase. Constrain the same radius to be refined across both phases.
Run the refinement and look at the results.
1. How does the refined local sphere radius compare with the range of long range ordering observed from the boxcar refinement?
2. Can you improve the fit by allowing some thermal parameters to vary between the local- and long-range structures?
3. What are the relative benefits of STLR and box-car refinements?

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