Standards for XRD Data Acquisition & Reporting in MIT AMLS Publications

by Tonio Buonassisi (MIT, [email protected]) and Jordan Cox (Characterization.nano, [email protected]), with input from Kangyu Ji & Fang Sheng. Grateful for technical support from Alexander E. Siemenn. Thanks to Kevin Tran for sharing advice and feedback.

Last updated March 2, 2025

I. Why I wrote this Document:

Our lab aims to improve existing materials and discover novel materials for sustainability, faster than the status quo by combining automation, machine learning, simulation, and human domain expertise. For example, one of our research projects might use AI/ML to predict a new material, then robotics to synthesize materials in the lab to confirm the prediction. Some of our experimental campaigns produce dozens to thousands of samples per hour — a very large number to test using traditional XRD.

The purpose of this document, is to guide researchers who aim to use XRD as evidence supporting phase identification of synthesized samples. Our group does not always have a trained crystallographer on board our team, but it does have access to XRD experts at shared-use facilities who can help with sample prep, measurement, and data post-processing. Hence, we should have the humility to admit that it is wise to collaborate with external experts (e.g., at Characterization.nano and other shared-use labs) to make sure we're performing proper sample-prep, measurements, refinements, and reporting. On 7/31/24, three AMLS team members (Kangyu, Fang, and Tonio) had a discussion with Jordan Cox from Characterization.nano, about XRD standards for their upcoming manuscript. From that discussion, Tonio has proposed a set of lab-wide standards for XRD data reporting in publications (journal articles, conference proceedings, posters, theses...). These standards should enable researchers to progress quickly toward publication, while including all necessary information to pass the highest standards of scientific peer review.

II. Overview of XRD and Fitting Methods

There are only three pieces of information one can extract information from in an XRD:

• Intensities (to first order: electron density inside the unit cell, preferred orientation)

• Peak positions (to first order: lattice parameters, lattice symmetry, XRD tool calibration; to second order: strain)

• Widths (to first order: crystallite size; to second order: strain)

If you had two identical crystals and lattice parameters (point groups) but two different sets of atoms, one would have the same peak positions but different peak intensities.

Gold standard: Rietveld refinement: When you do a Rietveld refinement, you're building up a model for what the crystal structure should have been to produce that diffraction pattern and using that model to simulate a hypothetical diffraction pattern. Then, you're testing your structure hypothesis by changing model parameters to improve the goodness of fit between the simulated pattern and the data. Every feature of the diffraction pattern is part of the model — intensities, peak positions, and widths. That's why it's the gold standard. It does come with some assumptions and constraints — the biggest constraint is that you must have a crystal structure as a model, i.e., a close-enough hypothesis of the crystal structure. Just like any fitting method, the closer you are to the right answer, the better the fitting process converges.

Silver standard: Pawley, Le Bail, poly fit...: There are cases when you don't / can't know what the crystal structure is (e.g., a novel compound), but without atomic coordinates Rietveld refinement cannot be performed. To determine the structure of an unknown compound, people first use simplified fitting approaches & models with fewer constraints. These empirically fit the intensities of the data, rather than simulate them, shifting each peak up and down individually to improve the fit. Examples include polynomial fit, Le Bail fit, and Pawley fit. These require a model for the lattice, but not the atoms. In other words, you need to propose a unit cell (like a .cif file without atomic information), and then the model will do its best to adjust unit cell parameters to get the best fit with the data. With the fitted lattice parameters and with knowledge of the composition (e.g., precursor ratios, WDS, XRF, EDX...), one might have enough of a guess of the crystal structure (i.e., atomic positions) to attempt Rietveld refinement again.

Bronze standard #1: thin film measurements: In the case of thin-film measurement, preferred orientation will affect the quality of fit of Rietveld refinement. The peak intensities will not line up with powder specimens if preferred orientation is strong. Therefore, thin-film samples are inadequate to prove the discovery of a new compound. One can shave off the material form the substrate and initiate powder diffraction measurements, following the two paragraphs above. Or, in thin-film form, one can superimpose the peak positions on the data, adjust for strain in the film, and test whether certain known compounds are consistent with the pattern (although this does not prove unique fit).

Bronze standard #2: alloy series, including in thin-film form: Then, there are other cases when one doesn't need to make an explicit point about crystal structure — for example, when scanning a binary series and showing peaks shifting monotonically from A to B. In this case, showing high-quality (e.g., Rietveld) fits for the two end states may be sufficient for making the scientific argument, that the XRD data supports the hypothesis of a solid solution in between A and B end-point compositions. In these cases, one might want to also collect very high-resolution data on individual peaks, and measure their shift.

III. Gold Standard: Powder XRD + Rietveld Refinement

When to apply: Whenever possible, and certainly when we state in our publication that we have "discovered a novel material."

Step 1: Sample prep: Use agate mortar and pestle to grind the sample. Insert the resulting powder into a microcapillary. Consult with staff from Characterization.nano with Tonio in cc- regarding choice of hardware & consumables. Details to be aligned include how to ensure acceptable particle sizes before packing into a microcapillary (specific process depends on the material).

Step 2: Powder XRD measurement: Once powder is packed into a microcapillary, measure in transmission mode.¹ Ideally, measure with specimen rotating during measurement.²

Step 3: Report Rietveld Refinement values in the text: Several values should be reported in the main text, so a crystallographer can judge whether the Rietveld refinement fit was properly performed.

• space group, space group number, and lattice parameters.

• R_exp tells you about data quality and degree of overfitting. One hopes for R_exp around 2--3% or lower. In a sense, this is a metric for the quality of the workflow; those wishing to implement a "kaizen" mentality can track it over time and see how it improves.

• R_wp is ideally 10--20%. An explanation is needed if larger

• R_p is ideally 10--20%. An explanation needed if larger.

• GOF ideally as close to 1 as possible. Values approaching 2 indicate data-quality issues.

Step 4: Plotting data and providing raw data as a supplementary file:

• XRD data should show both the individual data points (e.g., circles) and the Rietveld refinement fit (thin line).

• Plot the residual and/or normalized residual ∆/σ below the XRD pattern. The residual (∆) is the data minus the refinement, or observed minus calculated. For the normalized residual, ∆ is divided by the standard deviation (σ) associated with the experimental data at each 2θ value. One should aim for ∆ < 15% of max peak height, and ∆/σ values <<1 . Achieving these depends on the user (you) achieving both high data quality (sample prep, measurement acquisition) and high fitting quality.

• How to calculate σ: For a single measurement, $σ = \sqrt{I}$, where $I$ is the total XRD detector counts (signal strength) at each 2θ value. For multiple measurements, $σ = \sqrt{I\frac{\sum_{}^{}{(I_{i} - \overline{I})}^{2}}{N - 1}}$, assuming sample does not degrade.

• Nice-to-have: representation of atomic structure (e.g., using Crystalmaker)

• Optional: Plot the peak positions (2θ values) and relative peak heights according to the structure file, as narrow lines.

Example of excellent gold-standard XRD reporting:

A team led by Schoop and Palgrave wanted to determine if one of the experimental XRD patterns reported in the A-Lab paper better fit with a simple candidate material (SnO₂) or a more complex one (SnSbPb₂O_6.5). The team plotted the peak positions for two candidate structures (blue and red), together with the residual plotted both in absolute (cyan) and normalized (black) scales, following the procedure in the previous page. Please take a look at Figure 4 in their paper http://doi.org/10.1103/PRXEnergy.3.011002.

IV. Silver Standard: Pawley refinement for reporting novel compounds

We can't always meet this gold standard for early-stage materials (e.g., novel compounds), because a crystal structure file (with point group and atomic coordinates & occupancies) does not exist. I'd like to discuss acceptable and unacceptable practices in this context.

Use case #1 is determining the space group of a novel compound, when you have a guess about the crystal structure. Pawley refinement (or Le Bail, or poly fit) fit the intensities of the peaks to determine the structure factors. (You don't specifically fit the positions or occupancies of individual atoms — the fits are atom-agnostic.)

Sample prep is the same as Part I.

Several values should be reported in the main text, so a crystallographer can judge whether the Pawley or Le Bail refinement fit was properly performed:

• Any structural parameters that were assumed at the beginning of the fit (space group and space-group number).

• lattice parameters coming from the fit (refinement)

• R_exp (ideally 2--3% or lower)

• R_wp (ideally 10--20%; explanation is needed if larger)

• R_p (ideally 10--20%; explanation needed if larger)

• Poly or Le Bail fits have slightly better R factors than Rietveld (because they're more empirical, less constraints, more degrees of freedom)

• GOF ideally as close to 1 as possible. (values approaching 2 indicate data-quality issues.)

Plotting data and providing raw data as a supplementary file:

• XRD data should show both the individual data points (e.g., circles) and the refinement fit (thin line).

• Plot the residual and/or normalized residual ∆/σ below the XRD pattern. The residual (∆) is the data minus the refinement, or observed minus calculated. For the normalized residual, ∆ is divided by the standard deviation (σ) associated with the experimental data at each 2θ value. One should aim for ∆ < 15% of max peak height, and ∆/σ values <<1 . Achieving these depends on the user (you) achieving both high data quality (sample prep, measurement acquisition) and high fitting quality.

• How to calculate σ: For a single measurement, $σ = \sqrt{I}$, where $I$ is the total XRD detector counts (signal strength) at each 2θ value. For multiple measurements, $σ = \sqrt{I\frac{\sum_{}^{}{(I_{i} - \overline{I})}^{2}}{N - 1}}$, assuming sample does not degrade.

• Nice-to-have: representation of atomic structure (e.g., using Crystalmaker)

• Optional: Plot the peak positions (2θ values) and relative peak heights according to the assumed structure file after fitting, as narrow lines.

Example of excellent silver-standard XRD reporting:

Example: In 2016, a team led by Fengxia Wei, Tony Cheetham and colleagues wanted to figure out if Pb²⁺ (in lead-halide perovskite) could be replaced with a +1 and +3 charged B-site cation pair. They reported the first double perovskite structure, (MA)₂KBiCl₆ .³ Shijing Sun was a co-author on this paper. During her "Campaign 1.0" in our lab⁴, she discovered Cs₂AgSbBr₆, later confirmed in a follow-up study with Fengxia Wei and Anthony Cheetham.⁵ The overall development of the field of double perovskites is shared in a nice perspective.⁶

Fengxia and colleagues preferred a Pawley fit, which refines peak positions and intensities based solely on lattice parameters (not a crystallographic model like Rietveld reinfement, which requires atomic positions / fractional coordinates, atomic displacement parameters, partial occupancies, bond lengths / angles). See the Supporting Information file of Wei's paper http://doi.org/10.1039/c9cc01134j.

V. Bronze Standard #1: Fitting thin-film samples

If we make a thin-film sample and want to determine its structure, we must bear in mind that preferred orientation and strain in the film compromise our ability to perform Rietveld refinement, so other strategies are needed. We can shave off the film, grind it into a powder, and proceed with the Silver or Gold standards above. Or, we can proceed with a film measurement.

With modest preferred orientation and strain in the film, one can attempt Rietveld or Pawley/Le Bail/poly fits. Often, this doesn't work.

In those cases, one can perform high-resolution XRD (HRXRD), which is similar to the other empirical methods and includes a description of the preferred orientation. Fits can be performed around single peaks or the entire spectrum, but the HRXRD fit will only apply to the peaks that have the specified orientation. One can still plot the peak positions from structure files with the data. This can work for compounds that might only have a handful of possible structures, and the diffraction patterns are distinct enough. One example is Robert Hoye's work discovering methylammonium bismuth iodide. But often, the differences between spectra are too small, especially when preferred orientation leads to missing peaks and strain shifts peak positions. One example is the difficulty distinguishing between the 0D and 2D phases of cesium bismuth iodide and cesium bismuth bromide.

VI. Bronze Standard #2: Fitting for compositional gradients

Let's say we want to estimate the % of A and B in a composition gradient. We perform XRD on deposited films with strong preferred orientation (from our high-throughput robotic tool). We have high confidence in our end compositions.

In this case, we'll want to get good fits for our end compositions A and B — either thin-film form (following the Bronze Standard #1 above) or scraping off the powders (following Gold or Silver Standards). Then, for the intermediate compositions between A and B, taking high-resolution (in 2θ) measurements around specific peaks, 2θ ranges, or the entire spectrum is most helpful in measuring small peak shifts. Peak shifts due to changes in lattice parameters are more pronounced at higher 2θ angles, hence it's important to collect data out to high angles, and track the 2θ positions of those peaks during the compositional gradient A to B.

Footnotes

1. In transmission mode, one doesn't need to worry about irradiated volume, because amount of sample doing the scattering is always the same. This contrasts to packing powder into a well and measuring in reflectance mode, where the incoming and outgoing X-ray beam penetration depth (information depth) may vary depending on material density and excitation energy. ↩

2. Rotating the specimen during measurement further reduces the chance for preferred orientation to affect the measurement. ↩

3. https://pubs.rsc.org/en/content/articlelanding/2016/mh/c6mh00053c ; open access: https://arxiv.org/pdf/1603.00537 ↩

4. https://doi.org/10.1016/j.joule.2019.05.014 ↩

5. https://doi.org/10.1039/C9CC01134J ↩

6. https://doi.org/10.1039/D4MH90029D ↩