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Reciprocal space imaging of ionic correlations in intercalation compounds

An Author Correction to this article was published on 30 October 2019

This article has been updated


The intercalation of alkali ions into layered materials has played an essential role in battery technology since the development of the first lithium-ion electrodes. Coulomb repulsion between the intercalants leads to ordering of the intercalant sublattice, which hinders ionic diffusion and impacts battery performance. While conventional diffraction can identify the long-range order that can occur at discrete intercalant concentrations during the charging cycle, it cannot determine short-range order at other concentrations that also disrupt ionic mobility. In this Article, we show that the use of real-space transforms of single-crystal diffuse scattering, measured with high-energy synchrotron X-rays, allows a model-independent measurement of the temperature dependence of the length scale of ionic correlations along each of the crystallographic axes in sodium-intercalated V2O5. The techniques described here provide a new way of probing the evolution of structural ordering in crystalline materials.

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Fig. 1: The monoclinic structure of Na0.45V2O5 (space group C2/m), with a = 15.34 Å, b = 3.61 Å, c = 10.04 Å and β = 109.6° at 100 K, derived from the Crystallographic Information File of ref. 32.
Fig. 2: Diffuse scattering and ΔPDF from Na0.45V2O5.
Fig. 3: A comparison of the real-space model of sodium ions in the x = 0 plane with the ΔPDF peak intensities at 50 K, from which the model is derived.
Fig. 4
Fig. 5: The results of fitting the ΔPDF peak intensities to a decaying exponential as a function of temperature along the three crystallographic axes.

Data availability

Files containing the datasets used in this Article are available for download from the Materials Data Facility43 ( as NeXus files stored in the HDF5 format44. The files for each measured temperature contain S(Q), ΔPDF and, at three temperatures, the total PDF results. The data can be plotted using the Python package NeXpy (

Change history

  • 30 October 2019

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.


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This work was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division and Scientific User Facilities Division. X-ray experiments were performed at APS, which is supported by the Office of Basic Energy Sciences under contract no. DE-AC02-06CH11357, and CHESS, which is supported by the NSF and NIH/NIGMS via NSF award DMR-1332208. Computational developments were supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the US Department of Energy, Office of Science, and the National Nuclear Security Administration. We thank D. Robinson and X. Zhang for technical support during the experiments, A. Rettie for performing the EDX analysis, T. Weber and A. Simonov for discussions about the ΔPDF technique, B. Campbell for help with the formalism of transforming the data to reciprocal space and P. Zapol and C. Haley for discussions about interpreting the results. Crystal structure images were generated using CrystalMaker, CrystalMaker Software Ltd,

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Samples were prepared by J.T.V. and prepared for measurement by M.J.K. The experiments were devised by M.J.K., S.R. and R.O. The X-ray experiments were performed by M.J.K., S.R., J.P.C.R., J.M.W. and R.O. The data were analysed by M.J.K., R.O., J.M.W. and G.J., using software written by G.J., M.J.K., R.O. and J.M.W. The manuscript and Supplementary information were written by R.O. with input from all the authors.

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Correspondence to Raymond Osborn.

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Supplementary methods, Figs. 1–15, notes and references.

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Krogstad, M.J., Rosenkranz, S., Wozniak, J.M. et al. Reciprocal space imaging of ionic correlations in intercalation compounds. Nat. Mater. 19, 63–68 (2020).

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