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. 2019 Jun 17;377(2147):20180413.
doi: 10.1098/rsta.2018.0413.

The rise of the X-ray atomic pair distribution function method: a series of fortunate events

Simon J L Billinge  1   2
Affiliations

The rise of the X-ray atomic pair distribution function method: a series of fortunate events

Simon J L Billinge. Philos Trans A Math Phys Eng Sci. .

Abstract

The atomic pair distribution function (PDF) technique is a powerful approach to gain quantitative insight into the structure of materials where the structural coherence extends only over a few nanometres. In this paper, I focus on PDF from synchrotron X-rays and describe what is the PDF and where it came from, as well as key moments on the journey that have contributed to its enormous recent growth and expanding impact in materials science today. Synchrotron X-ray sources played a starring role in this story. This article is part of the theme issue 'Fifty years of synchrotron science: achievements and opportunities'.

Keywords: X-ray; pair distribution function; synchrotron.

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Conflict of interest statement

I declare I have no competing interests.

Figures

Figure 1.
Figure 1.
Conventional laboratory powder X-ray diffractometer diffractograms, versus 2θ from (a) a well-crystallized material and (b) a nanomaterial, showing the excessive peak broadening and loss of information in the signal in the case of the nanomaterial. Adapted from [8]. (Online version in colour.)
Figure 2.
Figure 2.
Schematic of the process for obtaining atomic pair distribution functions. Top left: a powder or nanoparticulate sample is placed in an intense beam of X-rays or neutrons and intensity is collected as a function of angle. This results in a ‘raw’ diffraction pattern (lower left) that also contains many effects of the measurement. To the extent possible the signal is corrected for the instrumental aberrations and normalized, resulting in the reduced structure function, F(Q) = Q(S(Q) − 1) (top right), where Q is the momentum transferred during the scattering process. The PDF (bottom right), G(r), is obtained from F(Q) through a Fourier transform relationship shown in the schematic. (Online version in colour.)
Figure 3.
Figure 3.
Raw diffraction data (a) and after dividing by the square of the X-ray atomic form factor and multiplied by Q (b). For many years, the high-Q region in an X-ray experiment was thought to contain little or no information, but the advent of synchrotrons allowed the important weak signals in this region to be measured with good accuracy. As a result, we obtain a signal that contains greatly more information from nanomaterials than in traditional measurements and data treatments. (Online version in colour.)
Figure 4.
Figure 4.
From conventional powder diffraction to the PDF. The patterns on the ((a)(i),(b)(i),(c)(i)) are conventional powder diffraction patterns from three samples, a crystalline material (a), and two nanocrystalline samples (b) and (c). ((a)(ii),(b)(ii),(c)(ii)) The diffraction patterns from the same samples when it is measured and analysed to get the total scattering data suitable for PDF analysis. There is considerably more information in the patterns in the right column. The data in (a) and (b) are shown in figure 1. Adapted from [8]. (Online version in colour.)
Figure 5.
Figure 5.
A schematic of the modelling process. Each unique atom is placed at the origin and larger and larger circles are drawn. Whenever a new atom intersects with the circle, a unit of intensity is added to a histogram at the position r that is the radius of the circle at the intersection point. Thermal motion of materials causes the histogram to broaden into a Gaussians, and so the PDF is well represented by a sum of independent Gaussian functions. Lower right: the blue open symbols are the measured PDF from nickel powder and the red solid line is the PDF calculated from the structure of nickel. The green curve, offset below shows the difference, which in this case is dominated by noise in the measurement. (Online version in colour.)
Figure 6.
Figure 6.
A screenshot from a search from ISI web of science for (X-ray AND PDF) OR (X-ray AND pair distribution function), showing the growth in number of papers referencing the technique. The thick red vertical lines indicate methodological developments, and other external factors, which in the author's view have significantly contributed to the growth of the method. The list of factors is not intended to be exhaustive, but rather illustrational. The factors are discussed in the text. (Online version in colour.)
Figure 7.
Figure 7.
A cartoon drawn by Stacey Morrison and shared with the author by Connie Chidester (now Rajnak) that depicts the deliberations of the Executive Committee of the American Crystallographic Association (ACA) in response for a request to hold a workshop at the 2001 ACA annual meeting. Apparently, at this time, the method was not widely known in the crystallographic community. The workshop was approved. (Online version in colour.)
Figure 8.
Figure 8.
The rapid acquisition PDF (RAPDF) set-up. A beam of high energy X-rays comes from the right, originating from a synchrotron source and hits the powder sample. The scattering is collected in a single-shot on a large area detector that is pushed, close (typically approx. 200 mm) to the sample position. (Online version in colour.)
Figure 9.
Figure 9.
A screenshot of a pdfgui model refinement session illustrating how modern software has facilitated PDF studies. Adapted from the pdfgui manual. (Online version in colour.)
Figure 10.
Figure 10.
PDFs from a nanosized pharmaceutical drug in an aqueous suspension at different concentrations. The blue (black in print) curve is 5 wt%, the green (darker grey in print) curve is 0.6 wt% and the red (light grey in print) curve is 0.25 wt%, which is the actual dose loading. Adapted from [45]. (Online version in colour.)
Figure 11.
Figure 11.
Diffraction tomography from a AAA spiral wound nickel metal hydride rechargable battery (shown on the right). (i) the high-Q scattering, which approximates the signal you would get from an absorption tomography experiment. The other panels show different signals in the diffraction pattern: (ii) the cathode material, (iii) the anode material, (iv) steel, (v) polymer. We have a complete diffraction pattern, and in principle a complete PDF, in each pixel of the image. Adapted from [57]. (Online version in colour.)
See this image and copyright information in PMC

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