PDFmorph Tutorial

Welcome! This will be a quick tutorial to accquaint users with PDFmorph and some of what it can do. For a more detailed tutorial, check out our user manual.

As we described in the README and installation instructions, please make sure that you are familiar with working with your command line terminal before using this application.

Before you’ve started this tutorial, please ensure that you’ve installed all necessary software and dependencies.

Basic PDFmorph Workflow

Open your Terminal or Command Prompt.
If it’s not active already, activate your PDFmorph-equipped conda environment by typing in
conda activate <pdfmorph_env>
If you need to list your available conda environments, run the command conda info --envs or conda env list

Run the pdfmorph --help command and read over the info on that page for a brief overview of some of what we will explore in this tutorial.
Using the mkdir command, create a directory where you’ll store the tutorial PDF files and use the cd command to change into that directory. You can download the tutorial files here. Then, cd into the tutorialData directory.

The files in this dataset were collected by Soham Banerjee at Brookhaven National Laboratory in Upton, New York.

The files are PDF data collected on Iridium Telluride with 20% Rhodium Doping (IrRhTe2) with the first file (01) collected at 10K and the last (44) at 300K. The samples increase in temperature as their numbers increase. The “C” in their names indicates that they have undergone cooling.

Note that these files have the .gr extension, which indicates that they are measured PDFs. The .cgr file extension indicates that a file is a calculated PDF, such as those generated by the PDFgui program.
First, we will run the PDFmorph application without any morphing and only using one PDF. Type the following command into your command line
pdfmorph darkSub_rh20_C_01.gr darkSub_rh20_C_01.gr
This should produce two PDF curves which are congruent, resulting in a flat green line underneath them.
Now, we will see PDFmorph run with two different PDFs and no morphing. Type the following command into your command line
pdfmorph darkSub_rh20_C_01.gr darkSub_rh20_C_44.gr
Without morphing, the difference Rw = 0.407. This indicates that the two PDFs vary drastically.

While running the pdfmorph command, it is important to remember that the first PDF file argument you provide (in this case, darkSub_rh20_C_01.gr) is the PDF which will get morphed, while the second PDF file argument you provide (here, darkSub_rh20_C_44.gr) is the PDF which acts as the model and does not get morphed. Hereinafter, we will refer to the first PDF argument as the “morph” and the second as the “target”, as the PDFmorph display does.
Now, we will start the morphing process, which requires us to provide initial guesses for our scaling factor, Gaussian smear, and stretch, separately. We will start with the scaling factor. Begin by typing the command
pdfmorph --scale=2 -a darkSub_rh20_C_01.gr darkSub_rh20_C_44.gr
Now, the difference Rw = 1.457, a significant increase from our value previously. We must modify our initial value for the scaling factor and do so until we see a reduction in the difference Rw from the unmorphed value. Type
pdfmorph --scale=0.9 -a darkSub_rh20_C_01.gr darkSub_rh20_C_44.gr
The difference Rw is now 0.351, lower than our unmorphed example’s value. To see PDFmorph optimize the scale factor, simply drop -a from the command and type
pdfmorph --scale=0.9 darkSub_rh20_C_01.gr darkSub_rh20_C_44.gr
PDFmorph, given a reasonable initial guess, will use find the optimal value for each morphing feature. Here, we see that PDFmorph displays scale = 0.799025 in the command prompt, meaning that it has found this to be the most optimal value for the scale factor. The difference Rw = 0.330, indicating a better fit than our reasonable initial guess.

It is the choice of the user whether or not to run values before removing -a when analyzing data with PDFmorph. By including it, you allow the possibility to move towards convergence before allowing the program to optimize by removing it; when including it, you may reach a highly optimized value on the first guess or diverge greatly. In this tutorial, we will use it every time to check for convergence.
Now, we will examine the Gaussian smearing factor. We provide an initial guess by typing
pdfmorph --scale=0.8 --smear=0.5 -a darkSub_rh20_C_01.gr darkSub_rh20_C_44.gr
And viewing the results. We’ve tailored our scale factor to be close to the value given by PDFmorph, but see that the difference Rw has increased substantially due to our smear value. One approach, as described above, is to remove the -a from the above command and run it again.

Note: The warnings that the Terminal/Command Prompt displays are largely numerical in nature and do not indicate a physically irrelevant guess. These are somewhat superficial and in most cases can be ignored.

We see that this has had hardly any effect on our PDF. To see an effect, we restrict the rmin and rmax values to reflect relevant data range by typing
pdfmorph --scale=0.8 --smear=0.5 --rmin=1.5 --rmax=30 darkSub_rh20_C_01.gr darkSub_rh20_C_44.gr
Now, we see that the difference Rw = 0.204 and that the optimized smear=-0.084138.

We restricted the r values because some of the Gaussian smear effects are only visible in a fixed r range. We chose this r range by noting where most of our relevant data was that was not exponentially decayed by instrumental shortcomings.
We are getting closer to an acceptably close fit to our data!
Finally, we will examine the stretch factor. Provide an intial guess by typing
pdfmorph --scale=0.8 --smear=-0.08 --stretch=0.5 --rmin=1.5 --rmax=30 -a darkSub_rh20_C_01.gr darkSub_rh20_C_44.gr
And noting that the difference has increased. Before continuing, see if you can see which direction (higher or lower) our initial estimate for the stretch factor needs to go and then removing the -a to check optimized value!

If you cannot, type
pdfmorph --scale=0.8 --smear=-0.08 --stretch=0.005 --rmin=1.5 --rmax=30 -a darkSub_rh20_C_01.gr darkSub_rh20_C_44.gr
to observe decreased difference and then remove -a to see the optimized --stretch=0.001762. We have now reached the optimal fit for our PDF!
Now, try it on your own! If you have personally collected or otherwise readily available PDF data, try this process to see if you can morph your PDFs to one another. Many of the parameters provided in this tutorial are unique to it, so be cautious about your choices and made sure that they remain physically relevant.

Enjoy the software!

Extra Tutorials

PDFmorph has some more functionalities not showcased in the basic workflow above (see pdfmorph –help for an overview of these functionalities). Tutorials for these additional functionalities are included below. Additional files for these tutorials can be downloaded here.

Performing Multiple Morphs

It may be useful to morph a PDF against multiple targets: for example, you may want to morph a PDF against multiple PDFs measured at various temepratures to determine whether a phase change has occured. PDFmorph currently allows users to morph a PDF against all files in a selected directory and plot resulting \(R_w\) values from each morph.

Within the additionalData directory, cd into the morphMultiple directory. Inside, you will find multiple PDFs of \(SrFe_2As_2\) measured at various temperatures. These PDFs are from “Atomic Pair Distribution Function Analysis: A primer”.
Let us start by getting the Rw of SrFe2As2_150K.gr compared to all other files in the directory. Run
```
pdfmorph SrFe2As2_150K.gr . --multiple
```
The multiple tag indicates we are comparing PDF file (first input) against all PDFs in a directory (second input). Our choice of file was SeFe2As2_150K.gr and directory was the cwd, which should be morphMultiple.
After running this, we get chart of Rw values for each target file. However, this chart can be a bit confusing to interpret. To get a more understandable plot, run
```
pdfmorph SrFe2As2_150K.gr . --multiple --sort-by=temperature
```
This plots the Rw against the temperature parameter value provided at the top of each file. Parameters are entries of the form <parameter_name> = <parameter_value> and are located above the r versus gr table in each PDF file.
Between 192K and 198K, the Rw has a sharp increase, indicating that we may have a phase change. To confirm, let us now apply morphs onto SrFe2As2_150K.gr with all other files in morphMultiple as targets
```
pdfmorph --scale=1 --stretch=0 SrFe2As2_150K.gr . --multiple --sort-by=temperature
```
Note that we are not applying a smear since it takes a long time to apply and does not significantly change the Rw values in this example.
We should now see a sharper increase in Rw between 192K and 198K.
Go back to the terminal to see optimized morphing parameters from each morph.
On the morph with SrFe2As2_192K.gr as target, scale = 0.972085 and stretch = 0.000508 and with SrFe2As2_198K.gr as target, scale = 0.970276 and stretch = 0.000510. These are very similar, meaning that thermal lattice expansion (accounted for by stretch) is not occurring. This, coupled with the fact that the Rw significantly increases suggests a phase change in this temperature regime. (In fact, \(SrFe_2As_2\) does transition from orthorhombic at lower temperature to tetragonal at higher temperature!)

Nanoparticle Shape Effects

A nanoparticle’s finite size and shape can affect the shape of its PDF. We can use PDFmorph to morph a bulk material PDF to simulate these shape effects. Currently, the supported nanoparticle shapes include: spheres and spheroids.

Within the additionalData directory, cd into the morphShape subdirectory. Inside, you will find a sample Ni bulk material PDF Ni_bulk.gr. This PDF is from “Atomic Pair Distribution Function Analysis: A primer”. There are also multiple .cgr files with calculated Ni nanoparticle PDFs.
Let us apply various shape effect morphs on the bulk material to reproduce these calculated PDFs.
- Spherical Shape
  
  The Ni_nano_sphere.cgr file contains a generated spherical nanoparticle with unknown radius. First, let us plot Ni_blk.gr against Ni_nano_sphere.cgr
  
  pdfmorph Ni_bulk.gr Ni_nano_sphere.cgr
  
  Despite the two being the same material, the Rw is quite large. To reduce the Rw, we will apply spherical shape effects onto the PDF. However, in order to do so, we first need the radius of the spherical nanoparticle.
  
  To get the radius, we can first observe a plot of Ni_nano_sphere.cgr
  
  pdfmorph Ni_nano_sphere.cgr Ni_nano_sphere.cgr
  
  Nanoparticles tend to have broader peaks at r-values larger than the particle size, corresponding to the much weaker correlations between molecules. On our plot, beyond r=22.5, peaks are too broad to be visible, indicating our particle size to be about 22.4. The approximate radius of a sphere would be half of that, or 11.2.
  
  Now, we are ready to perform a morph applying spherical effects. To do so, we use the --radius parameter
  
  pdfmorph Ni_bulk.gr Ni_nano_sphere.cgr --radius=11.2 -a
  
  We can see that the Rw value has significantly decreased from before. Run without the -a tag to refine
  
  pdfmorph Ni_bulk.gr Ni_nano_sphere.cgr --radius=11.2
  
  After refining, we see the actual radius of the nanoparticle was closer to 12.
- Spheroidal Shape
  
  The Ni_nano_spheroid.cgr file contains a calculated spheroidal Ni nanoparticle. Again, we can begin by plotting the bulk material against our nanoparticle
  
  pdfmorph Ni_bulk.gr Ni_nano_spheroid.cgr
  
  Inside the Ni_nano_spheroid.cgr file, we are given that the equatorial radius is 12 and polar radius is 6. This is enough information to define our spheroid. To apply spheroid shape effects onto our bulk, run
  
  pdfmorph Ni_bulk.gr Ni_nano_spheroid.cgr --radius=12 --pradius=6 -a
  
  Note that the equitorial radius corresponds to the --radius parameter and polar radius to --pradius.
  
  Remove the -a tag to refine.

There is also support for morphing from a nanoparticle to a bulk. When applying the inverse morphs, it is recommended to set --rmax=psize where psize is the longest diameter of the nanoparticle.

Bug Reports

Please enjoy using our software! If you come accross any bugs in the application, please report them to diffpy-users@googlegroups.com.