Powder diffraction data beyond the pattern: a practical review

Abstract

We share personal experience in the fields of materials science and high-pressure research, discussing which parameters, in addition to positions of peak maxima and intensities, may be important to control and to document in order to make deposited powder diffraction data reusable, reproducible and replicable. We discuss, in particular, which data can be considered as 'raw' and some challenges of revisiting deposited powder diffraction data. We consider procedures such as identifying ('fingerprinting') a known phase in a sample, solving a bulk crystal structure from powder data, and analyzing the size of coherently scattering domains, lattice strain, the type of defects or preferred orientation of crystallites. The specific case of characterizing a multi-phase multi-grain sample following in situ structural changes during mechanical treatment in a mill or on hydrostatic compression is also examined. We give examples of when revisiting old data adds a new knowledge and comment on the challenges of using deposited data for machine learning.

Keywords: 2D to 1D conversion; FAIR data; high-pressure data; images; in situ mechanochemical studies; materials; metadata; minerals; particle statistics; powder diffraction; raw data.

Figure 1

A sample card from the PDF with powder diffraction data for TiO₂ (anatase). (a) Table with 2θ–d–I–hkl data; (b) a schematic representation of the powder diffraction pattern.

Figure 2

Examples of powder diffraction patterns from (a) a perfect single crystal; (b) a sample with a small number (N_c = 10) of domains with uniform pole distribution; (c) a sample with a large number (N_c = 1000) of domains, again with uniform pole distribution; (d) a sample with N_c = 1000 with anisotropic pole distribution. Reproduced with permission from Binns et al. (2022 ▸) under a Creative Commons Attribution (CC-BY) Licence.

Figure 3

From left to right, a schematic representation of a single-crystal image preserving all 3D information, a 2D powder diffraction image and a powder diffractogram derived from a 2D frame after integration.

Figure 4

The effect of the sample holder size on the 110 reflection in a powder pattern of fructose: blue – 0.3 mm capillary; green – 0.7 mm capillary; red – 0.7 mm capillary with 0.3 mm slits (slits have a wrong offset).

Figure 5

The effect of the fluorescence on similarly collected powder diffraction patterns: green – pattern with fluorescence suppression; red – pattern without fluorescence suppression, including a higher background and non-statistical noise (data taken at the MS beamline, Swiss Light Source).

Figure 6

The diffraction ring coming from the primary beam scattering (A) will be correctly integrated, while that from the diamond-diffracted beam (B) will only contribute to the background. The saturating peak at the center of the B ring has to be masked to avoid an extra strong peak in this position.

Figure 7

Experimental (dots) and theoretical (bold lines) shapes of the same 111 reflection for (a) η-Al₂O₃ and (b) γ-Al₂O₃. In the first case, there are defects lying on a single plane of the {111} family which are bound by the half-dislocation; in the second case, intersecting defects on ( and ) are bounded by the half-dislocations at a dislocation density equal to 20%. Reproduced with permission from Tsybulya & Kryukova (2008 ▸). Copyright (2008) the American Physical Society.

Figure 8

The diffraction patterns collected from the product of the mechanochemical reaction of LiBH₄ with CsBH₄ from two different operando set-ups: in red that described by Friščić et al. (2013 ▸), in blue that by Ban et al. (2017 ▸). In the latter pattern, more features are clearly visible due to the increased resolution and smaller background, but it is also clear that the product is the same.

Figure 9

Changes in the unit-cell parameters (left) and volume (right) of glycinium phosphite collected at a synchrotron (red symbols) and a laboratory (blue symbols) source. Reproduced with permission of the International Union of Crystallography from Bogdanov et al. (2021 ▸).

Figure 10

A ‘cascade plot’ of diffractograms from an operando diffraction study of a ball-milling reaction. The red marks at the top right indicate points in time where the synchrotron top-up happened.

Figure 11

Effect of a wrong calibration on radially integrated peaks, illustrated by an angle-dependent shifted pattern (in red) with respect to the correct values (in green). The errors in the peaks’ positions are non-linear with the angle but of the same order of magnitude as the peaks’ FWHMs. While fingerprinting was correct, the refinement of the patterns was not converging as the peak positions are not simply shifted but affected by a more complex function.

Figure 12

Data from a Mythen detector: the raw data (above) show spurious features, but appropriate correction for flatfield and angular calibration results in the correct pattern (below). The most affected parts of the patterns are encircled. The result of these errors if not corrected would be a noisy, non-statistical background, the presence of spurious features and non-corrected intensities of the peaks, leading to data unusable for structure solution, quantification and even fingerprinting.

Figure 13

Effect on the counting statistics over the detector of appropriate masking of non-Poissonian and multiple pixels. The distribution of the variance over the mean counts per pixel, measured pixel by pixel for 256 images of silicone oil. Masks 0, 1 and 2 correspond, respectively, to masking only the pixels flagged by DECTRIS, masking also the rebinned pixels between sub-modules and detector edges, and masking also pixels with high σ/ (typically damaged pixels) as well as dilating by 1 pixel the regions around each masked pixel. The percentages of pixels masked in each case were 8.6%, 15.4% and 15.8%, respectively. The blue lines are a Gaussian fit to the final (mask 2) data and the difference curve. Inset: the same data on a semi-log scale. Reproduced with permission from Vaughan et al. (2025 ▸) under a Creative Commons Attribution (CC-BY) Licence.

Figure 14

Examples of a 2D powder diffraction pattern collected for a powder sample in a diamond anvil cell in situ at a synchrotron source using a 2D pixel detector, with the reflections from diamonds and ruby calibrant (points) overlaying the diffraction pattern from a powder sample (rings): (a) before masking, (b) after partial masking, (c) after 2D → 1D integration without masking (red) and after masking (green). The major differences between the masked and non-masked 1D patterns are circled. The background was not subtracted, but one plot was shifted vertically with respect to another.

Figure 15

(a) A typical raw high-pressure (10 GPa) X-ray powder diffraction pattern (San Carlos olivine) collected during laser heating to 2000 K. The shadow on the right-hand side is caused by the downstream laser heating optics. The broad smooth partial rings on the right side stem from X-ray scattering on the laser mirror. Both artifacts need to be masked out for data reduction and analysis. (b) Integrated diffraction pattern with and without masking of laser heating artifacts. Reproduced with permission under a Creative Commons Attribution (CC-BY) Licence from Stan et al. (2018 ▸).

Figure 16

Examples of a 2D powder diffraction pattern collected with a laboratory diffractometer, when the beam size is so large that the beam hits also the metal gasket. One can see the reflections from diamonds, ruby calibrant (points) and steel gasket (bold thick rings shown by red arrows) overlaying very weak rings originating from the poorly scattering powder sample (shown by blue arrows): (a) before masking, (b) after masking. The red mask is unambiguously justified. At least some of the point reflections of low intensity that were preliminarily masked (green) are located at rings and could potentially belong to a new phase that crystallizes under high-pressure conditions in the DAC. Therefore, their masking is not unambiguously justified; the origin of these reflections deserves further investigation.

Figure 17

Two powder diffraction patterns (unmasked) collected from the same phase in a DAC at a laboratory source (left) and at a synchrotron source (right). Comparing the primary 2D patterns makes it possible to see that the phase studied in the laboratory is in fact the same as that studied later at the synchrotron source (sample rings in the left photograph are shown by blue arrows). The pattern on the left is the same as was shown in Fig. 16 ▸. Note that masking of the gasket rings (shown by red arrows) was no longer necessary for data collected at the synchrotron source, but masking of a few point reflections originating from diamond would still be needed. One can also see from the comparison that one of the gasket broad bold rings in fact overlaps with two rings from the sample that became accessible in a synchrotron experiment. Data courtesy of Dr N. Tumanov.

Figure 18

(a) A single crystal of sulfathiazole polymorph III after having transformed completely into polymorph I. The pseudomorph preserves the initial shape. There is no evidence of melting. The visible cracks appeared during the polymorphic transition. (b) A diffraction pattern of the pseudomorph shown in (a). [The plot is from the Boldyreva research group archive. Data used for this plot were discussed by Drebushchak et al. (2008 ▸).]

Figure 19

A sample of HgI₂ uniaxially squeezed between DAC culets, with stress increased from the left to right photographs. The color changes in HgI₂ mark phase III (to 0.4 GPa), phase IV (to 1.3 GPa), phase VI (to 7.6 GPa) and phase VII at the center of the right photograph. Reproduced with permission of the International Union of Crystallography from Katrusiak (2008 ▸); data from Hostettler & Schwarzenbach (2005 ▸).

Figure 20

A series of photographs of a sample of l-alanine immersed in a methanol–ethanol–water mixture in a DAC, showing a sequence of transformations on decompression from 5 GPa to ambient pressure. Top: the sample as viewed in an optical microscope. First a single crystal of l-alanine, then polycrystalline phase 1 (a solvate) and phase 2 (a polymorph of l-alanine) formed on desolvation of phase 1 on decompression. Bottom: powder diffraction patterns collected from different parts of the sample in the left photographs (already converted from the 2D to 1D format with background eliminated). Reproduced with permission of the International Union of Crystallography from Tumanov et al. (2010 ▸).

Figure 21

Top: a fragment of the 2D pattern collected from a powder sample of l-serine III in a DAC at a synchrotron experiment with some unidentified peaks. Bottom: the same pattern after being converted to a 1D format (the peaks that could not be assigned to l-serine III are marked ‘?’). Lower figure reproduced from Boldyreva et al. (2006 ▸) with permission from Elsevier.

Figure 22

Relative contents of four polymorphs of l-serine at various pressures depending on the pressure-increase rate. Figure prepared using data published by Fisch et al. (2015a ▸).