==== Front Nat Commun Nat Commun Nature Communications 2041-1723 Nature Publishing Group UK London 20036 10.1038/s41467-020-20036-z Article Split-pulse X-ray photon correlation spectroscopy with seeded X-rays from X-ray laser to study atomic-level dynamics http://orcid.org/0000-0001-8284-751XShinohara Yuya shinoharay@ornl.gov 1 Osaka Taito 2 Inoue Ichiro 2 http://orcid.org/0000-0002-0757-7932Iwashita Takuya 3 Dmowski Wojciech 4 http://orcid.org/0000-0003-1588-4868Ryu Chae Woo 4 Sarathchandran Yadu 5 http://orcid.org/0000-0002-1126-0276Egami Takeshi 145 1 grid.135519.a0000 0004 0446 2659Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 USA 2 RIKEN SPring-8 Center, Sayo, Hyogo, 679-5198 Japan 3 grid.412334.30000 0001 0665 3553Department of Integrated Science and Technology, Oita University, Dannoharu Oita, 870-1192 Japan 4 grid.411461.70000 0001 2315 1184Department of Materials Science and Engineering, The University of Tennessee, Knoxville, TN 37996 USA 5 grid.411461.70000 0001 2315 1184Department of Physics and Astronomy, The University of Tennessee, Knoxville, TN 37996 USA 4 12 2020 4 12 2020 2020 11 621324 5 2020 3 11 2020 © The Author(s) 2020Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.With their brilliance and temporal structure, X-ray free-electron laser can unveil atomic-scale details of ultrafast phenomena. Recent progress in split-and-delay optics (SDO), which produces two X-ray pulses with time-delays, offers bright prospects for observing dynamics at the atomic-scale. However, their insufficient pulse energy has limited its application either to phenomena with longer correlation length or to measurement with a fixed delay-time. Here we show that the combination of the SDO and self-seeding of X-rays increases the pulse energy and makes it possible to observe the atomic-scale dynamics in a timescale of picoseconds. We show that the speckle contrast in scattering from water depends on the delay-time as expected. Our results demonstrate the capability of measurement using the SDO with seeded X-rays for resolving the dynamics in temporal and spatial scales that are not accessible by other techniques, opening opportunities for studying the atomic-level dynamics. Here the authors study atomic scale dynamics in water by using X-ray photon correlation spectroscopy. They use a split-and-delay optics with self-seeding of X-rays to generate pulses of enough energy and controlled time delay between two X-ray pulses. Subject terms Free-electron lasersAtomic and molecular interactions with photonsCharacterization and analytical techniqueshttps://doi.org/10.13039/100006151DOE | SC | Basic Energy Sciences (BES)issue-copyright-statement© The Author(s) 2020 ==== Body Introduction Since the observation of X-ray speckles using coherent X-rays1, scientists have developed a speckle-based technique called X-ray Photon Correlation Spectroscopy (XPCS), where the temporal correlation of speckle patterns is used to extract dynamics of materials at specific correlation lengths2–5. Earlier XPCS studies using synchrotron X-rays primarily focused on determining dynamics on relatively longer length-scales (>10 nm)6–11. Only a few studies have recently been carried out at the atomic-scales, although the timescale is limited to relatively slow dynamics (>10 s)12–14. Extending the timescale of XPCS to picoseconds, which are relevant to studying the atomic-level dynamics in matter such as liquid, has been challenging because of the insufficient intensity of coherent X-rays and the limited frame-rate of detectors (typically < 1 kHz). Meanwhile, recent progress in high-energy-resolution inelastic X-ray and neutron scattering has extended their accessible timescale and its applications15,16. Nevertheless, their timescale and length-scale are not appropriate for probing the atomic-level dynamics in a wide timescale of picoseconds to nanoseconds due to the limitation in energy resolution and intensity. Accordingly, the atomic-level dynamics in liquids, particularly supercooled liquids, remains elusive. The advent of X-ray free-electron lasers (XFELs)17,18, together with recent progress in split-and-delay optics (SDO)19,20, has raised the expectation for bridging the aforementioned gap by extending the timescale of XPCS to picoseconds21. In this timescale, measuring the time-correlation of each speckle is not practical because of the intrinsic limitation on the temporal resolution of X-ray detectors as well as the repetition rate of the XFELs. This limitation is overcome by a split-and-delay approach21,22, which uses two X-ray pulses that are generated from a single XFEL pulse. The accessible timescale is determined by the ability to generate two pulses separated in time Δt. The contrast β(Q, Δt) at momentum transfer Q in the sum of speckle scattering patterns from a sequence of two separate X-ray pulses is analyzed to extract the information on dynamics by the Speckle Visibility Spectroscopy (SVS)23,24, utilizing the relationship between β(Q, Δt) and the intermediate scattering function, f(Q, Δt)20,22,25–27. Recently, SVS using X-ray pulses with variable pulse duration has been demonstrated for the femtoseconds dynamics in supercooled water without using SDOs28, and accelerator-based double X-ray pulse generations29,30 are also accomplished; however, their pulse duration or time delay is restricted either to a limited range of orders of femtosecond or to discrete steps of hundreds of picoseconds. Alternatively, in an SDO system, a single XFEL pulse is divided into two pulses by a beam splitter, and a delay time between the pulses is controlled by their path length difference. Hard X-ray SDO systems have hitherto been developed19,31–34, and a few experimental results using the SDO have been reported20,35. However, their application was still limited to a longer length-scale (>1 nm) and the study of atomic-level dynamics at sub-nm scale using X-ray SVS (XSVS) with an SDO has not been reported because of the insufficient pulse energy of X-rays. Here, we report the XSVS result utilizing the SDO combined with the self-seeded X-rays36 at SPring-8 Angstrom Compact free-electron Laser (SACLA)18. The self-seeding of X-rays36–38 generates narrow-band X-rays and thus can provide higher X-ray intensity after passing through the SDOs. The increase in the X-ray pulse energy at the sample position enables the application of XSVS at high Q (>1 Å−1), which is relevant to the study of atomic-level dynamics. Results Statistics of self-seeded X-rays after the SDO The XSVS experiment was carried out using the setup shown in Fig. 1. A reflection self-seeding36 at a photon energy of 10 keV was employed. Each X-ray pulse was then split into two sub-pulses using a wavefront-division SDO, making use of Si(220) crystals31. The delay time Δt between the sub-pulses was controlled by the path length difference between the variable-delay branch and the fixed-delay branch. We changed Δt between 0 and 2 ps, although the accessible range of Δt is much longer31. The pulse energy of the variable-delay branch (Idelayed) and the fixed-delay branch (Ifixed) were monitored by the beam intensity monitors, which were installed in the split-delay optics system39. The exit beams were overlapped and focused to a size of 0.7 µm (H) and 0.9 µm (V) at the sample position with X-ray mirrors40.Fig. 1 Experimental setting of XPCS using split-and-delay optics and reflection self-seeding at BL3, SACLA18. The seed pulse was produced by monochromatizing the SASE from the upstream undulator segments. Then the seed was amplified in the downstream undulators. The details are described in ref. 36. The amplified X-ray pulse was split into two sub-pulses using the SDO31. The sub-pulses with a delay time Δt are focused by mirrors40 and hit the water jet. Scattered X-rays were recorded by the MPCCDs42. Figure 2a shows the histogram of X-ray pulse energy at the sample position, Itot = Idelayed + Ifixed. The dashed line is a fit to the experimental data using a gamma density-distribution function41: 1 PItot=MItotMexp−MItot/ItotItotM−1Γ(M), where Γ(M) is the gamma function, 〈Itot〉 represents the average X-ray pulse energy over shots, and M is the number of modes. Our analysis yields 〈Itot〉 = 7.7 μJ and M = 2.24, which is close to the values at the Linac Coherent Light Source (USA) using 8 keV X-rays (M = 2.35)35. The energy bandwidth of single-shot self-seeded X-ray (~2 eV in FWHM) improved the throughput of the SDO system, compared to the case using only self-amplified spontaneous emission (SASE), where the averaged bandwidth is ~30 eV and 〈Itot〉 = 0.38 µJ31. This significant improvement facilitates the XSVS at high Q, where the probabilities of multiple photons per pixel events can be too low to conduct the XSVS. The split ratio, R = Ifixed/(Ifixed + Idelayed), was distributed shot-by-shot, and 13% of the total events satisfy the condition of the ratio of 0.475 < R < 0.525 (Fig. 2b). This distribution originated from shot-to-shot variations in the profile and position of the incident X-ray beam.Fig. 2 Statistics of self-seeded XFEL pulses after split-and-delay optics. a A pulse energy distribution at sample position for 280,815 shots (red bar). The dashed line represents the best fit to a gamma distribution. b A histogram of the split ratio R for 340,732 shots. The solid line represents the best fit to a Gaussian distribution for the average = 0.48 and the standard deviation = 0.15. c Time-courses of X-ray beam position of two sub-pulses at the sample position, X and Y, and their relative position, ∆X and ∆Y. ∆X (or ∆Y) were calculated by subtracting X (or Y) of the variable-delay branch (blue) from X (or Y) of the fixed-delay branch (red). d The histograms of X, Y, ∆X, and ∆Y. The position of two X-ray pulses was shifted in the Y direction to distinguish them. In our experiment, a continuous stream of water with a flow rate of 0.7 mL/min was irradiated by the X-rays. The diameter of the water stream was 50 µm, much larger than the variation in the beam position at the sample during the experiment, as shown in Fig. 2c, d. The time-courses of the X-ray beam position clarify that the absolute position of the X-ray beam on the sample, X and Y, drifted ~ 2 µm in 3 h. However, the relative position between two sub-pulses, ∆X and ∆Y, remained stable enough to assume that the two sub-pulses overlapped with each other on the sample. This high stability of the SDO system is a crucial factor for carrying out the XSVS experiment successfully. The scattering from the sample was recorded by three multi-port charge-coupled devices (MPCCDs)42 located 1 m downstream of the sample to cover Q-ranges shown in Fig. 3. The speckle size is estimated to be around 0.18 mm, which is larger than the pixel size of the MPCCDs, 50 µm.Fig. 3 X-ray scattering from water. a Single split-pulse scattering pattern in a 100 × 100 pixel region of interest at around Q = 2.0 Å−1 with Itot = 3.3 µJ and Δt = 0.0 ps. The vertical and horizontal directions correspond to Q-direction and the azimuthal direction, respectively. b Histogram of the charge (in units of analog-to-digital units (ADU)) per shot in a 1024 × 512 pixel region. The blue solid line is the average histogram of the 287,982 raw images, and the red dashed line is after the droplet algorithm has been applied. The single-photon event corresponds to 595 ADU. c The number of photons at each pixel per shot obtained by averaging 35,899 shots with Δt = 0.0 ps and 〈Itot〉 = 7.9 µJ. (red lines). The area around Q = 2.0 Å−1 was covered by a single MPCCD and that around Q = 3.0 Å−1 was covered by a dual MPCCD42. The solid black line is the estimation of X-ray elastic scattering using the result of high-energy X-ray diffraction intensity profile47, the thickness of the sample, the X-ray energy, the size of a pixel, and the average number of X-ray photons for a single shot. The dashed line is × 0.64 of the solid line. X-ray scattering of water using the SDO and seeded X-rays Figure 3a shows an example of raw CCD images taken around Q = 2 Å−1 with Itot = 3.3 µJ. Because of the low-scattering cross-section of water, the signal produced by photons is sparsely distributed. Figure 3c shows a one-dimensional scattering intensity profile, which was averaged over 35,899 shots, the averaged pulse energy of which was 7.9 µJ. A droplet algorithm43–46 was employed to convert raw data into the digitized X-ray photon images (see “Methods”). The number of photons at each pixel per shot was 0.64 times the estimated value that was calculated using the result of high-energy X-ray diffraction47. This discrepancy could originate from the limited alignment accuracy, ~20 µm, of the sample position relative to the X-ray beam, hence a smaller irradiated volume. The result shows that the observed X-ray intensities predominantly represent scattering from the water. We now discuss the sample heating induced by the first sub-pulse. Because of the high-pulse energy, the sample temperature may have risen before the second sub-pulse hit the sample. Using the sample thickness, X-ray pulse energy, the specific heat of water, and the transmission of water at 10 keV, the temperature rise can be estimated to be several hundred Kelvin, depending on Ifixed. To evaluate the possible heating effect, we binned our data based on Ifixed and Δt and then analyzed the scattering intensity around Q = 2 Å−1 (Fig. 4a). When the delay time is zero or small (<0.2 ps), the intensity profiles remain the same regardless of Ifixed. However, with a longer delay time and higher Ifixed, the peak shift to high Q is observed as shown in Fig. 4b. Using the temperature dependence of peak position47, we estimated the amount of temperature rise ∆T, as shown in Fig. 4c. Note that the observed scattering intensity profile is the sum of the two scattering intensity profiles, the one from the fixed-delay branch at t = 0 and the other from the variable delayed branch at t = Δt. Thus, the actual temperature rise can be twice as large as ∆T shown in Fig. 4c. The result shows that there exists a heating effect only after Δt = 0.5 ps with Ifixed < 3 µJ, but is much smaller than the simple estimation. On the other hand, ∆T at 1.0 ps and 2.0 ps shows similar values regardless of Ifixed. X-rays first excite electrons, and the electronic energy is transferred to molecular motion (phonons). The Δt-dependence suggests that the heat dissipation through phonons comes into effect after 1 ps, which calls for further experiments and simulations.Fig. 4 Dependence of scattering intensity profiles on the pulse energy of the fixed-delay branch. a Normalized scattering intensity around Q = 2 Å−1. The delay time between two sub-pulses Δt is shown at the top of the panels. The pulse energy of the fixed-delay branch Ifixed is shown on the right. The profiles are vertically shifted for the sake of clarity. The dashed lines show the peak position when Δt  = 0 and 1 µJ < Ifixed < 2 µJ. b Dependence of the peak position Qp on Ifixed. Δt is shown as the legend. c Estimated values of the temperature rise due to the sub-pulse from the fixed-delay branch. The error bars were determined by the standard deviation of the fitting of the peak position. Speckle contrast analysis From the statistics of observed photons, the visibility of the X-ray speckle pattern at a specific Q was calculated. Following the previous studies20,27,28,35,43, we assume that the probability for observing k photons at a single-pixel is described by a negative binomial distribution with the average number of photons per pixel, μ, when the number of scattered photons is low41: 2 Pk∣μ,Ms=Γ(k+Ms)ΓMsk!MsMs+μkμMs+μMs. Here, Ms is the number of modes in observed scattering images and is related to β such that β = 1/Ms20,22,43. After we binned our data based on Ifixed as in the last section, we determined the value of β by using the log-likelihood ratio statistic of this distribution as demonstrated in earlier studies20, as shown in Fig. 5. At Q = 2 Å−1 with Ifixed < 3 µJ, as the delay time increased, the visibility of speckle reduces, reflecting the dynamics of the sample. At delay-times longer than Δt = 1.0 ps, the values of β agree with that of the baseline value that was determined by the uncorrelated beams without spatial overlap. The decrease in the contrast is comparable to those calculated from the result of inelastic X-ray scattering (IXS) of water as shown in Fig. 548,49. Here, the result of IXS was vertically shifted and scaled using the baseline value and the XSVS result at Δt = 0. Although the heating effect by the first sub-pulse may affect the dynamics at Δt > 0.5 ps even with Ifixed < 3 µJ, the agreement between the contrast decrease and the IXS result suggests that the data points up to, at least, 0.2 ps with Ifixed < 3 µJ are reliable. This is the first time that the dependence of the speckle contrast on the delay time was measured using an SDO system. On the other hand, the dependence of β(Q = 2 Å−1, Δt) on Ifixed shows no clear decaying behavior for Ifixed > 7 µJ because of the heating effect discussed above. Besides, we could not find a clear decaying behavior at Q = 3 Å−1 or higher even with Ifixed < 3 µJ (Supplementary Fig. S1), presumably due to the smaller number of photons and the additional decoherence at a higher Q, which will be addressed in a future study.Fig. 5 X-ray speckle contrast obtained by maximum-likelihood estimation. At Q = 2.00 ± 0.06 Å−1 with (circles) Ifixed < 3 µJ, (squares) 3 µJ < Ifixed < 5 µJ, (triangles) 5 µJ < Ifixed < 7 µJ, and (crosses) Ifixed > 7 µJ. (diamonds). The solid line represents the contrast measured when there was no overlap between two sub-pulses. The uncertainty was calculated using the second derivative of the log-likelihood based on the approach in ref. 20, and the uncertainty for the solid line is represented by the shade. The dashed line represents the decaying behavior48,49, which are estimated by the result of inelastic X-ray scattering where their amplitude was set by the XSVS result at Δt  = 0. Discussion The estimated values of Ms depend on (1) the dynamics of the sample to be obtained, (2) the splitting ratio R, (3) the initial contrast, (4) the contrast reduction due to the experimental setting, and (5) the degree of decoherence between the two split pulses20,22. In this letter, we did not include the data with |R − 0.5| > 0.025 to reduce the uncertainty with respect to (2). We can reasonably assume that the sample thickness involved in the scattering was constant because the shot-by-shot positional fluctuations of X-rays were small (Fig. 2c). Then, the effects of (3) and (4) can be expressed in terms of β, which was estimated to be β0 = 0.23 ± 0.02 at Q = 2 Å−1 by measuring the contrast with a single pulse using only the fixed-delay branch by blocking the variable-delay branch. This value is consistent with the baseline value because the baseline should be β0/220. Meanwhile, the result for dual pulses was β(Q, Δt  = 0) = 0.155 ± 0.023, smaller than β0. This contrast reduction can be reasonably explained by the degree of decoherence between the sub-pulses. The angular mismatch parallel to the detector plane between the sub-pulses50, 0.15 mrad, creates the positional difference between two speckles ~ 0.15 mm on the detector plane, thereby reducing the contrast from 0.23 to ~0.15 ~ β(Q, Δt = 0). Note that the angular mismatch perpendicular to the detector plane can be ignored. The perpendicular component of the mismatch is written as −kiη sin 2θ sin φ + kiO(η2), where ki, η, 2θ, and φ are the magnitude of the wavevector, the angular mismatch, the scattering angle, and the azimuthal angle of the scattering, respectively. In our case, φ = 0 and thus the perpendicular component is kiO(η2), hence it is negligibly small. Shot-to-shot incomplete geometrical overlap of the sub-pulses could reduce the contrast20. The relative positional fluctuations were inherently random as shown in the lower rows of Fig. 2c and cannot be monitored simultaneously during the X-ray SVS measurement. Including these effects in analyses to provide reasonable estimates of decoherence using more sophisticated approaches such as hierarchical models51 warrants future studies. The use of hierarchical models will also allow us to include the data with different R for the estimation, thereby significantly increasing the statistics. This will make it possible to extract meaningful information at higher Q and could facilitate the evaluation of femtoseconds to nanoseconds dynamics at the atomic scale. The current results indicate that with Ifixed > 3 µJ the XSVS results of water in this Q-range are not reliable because of the sample heating. This does not mean that the increase in the X-ray pulse energy by the self-seeding was unnecessary. The number of shots with 1 < Ifixed < 3 µJ was ~ 65% of the total number of shots. Thus, most of the data were within the range where the heating effect has little effect at a timescale shorter than 0.5 ps. On the other hand, with Ifixed < 1 µJ meaningful estimations of β were not obtained because almost all the photon-counting event is not a multi-photon event but a single-photon event. Without the seeded X-rays, 〈Itot〉 = 0.38 µJ31, and it was impossible to carry out the XSVS at the atomic scale. Our results demonstrate the capability of XSVS measurement using the SDO with seeded X-rays as well as the advantages and necessity of the self-seeded X-rays in the XSVS at high Q. Methods Self-seeded X-rays We used an 8-GeV electron beam with a charge of 130 pC and ~10 fs duration for reflection self-seeding36 using a Si(220) microchannel-cut crystal monochromator at SPring-8 Angstrom Compact free-electron Laser (SACLA)18. Eight undulator segments were used to generate the SASE with average pulse energy of 80 µJ, and a channel-cut crystal monochromator was used to select a 10 keV radiation with a bandwidth of 0.6 eV (FWHM). The X-ray was used as a seed, which was amplified by the 13 downstream undulator segments. Split-and-delay optics A wavefront-division SDO using Si(220) crystals was used to split a single pulse into two sub-pulses with a delay time31. The SDO system was installed 70 m downstream from the last undulator segment. Shot-to-shot noninvasive diagnostics of pulse energies for both branches were made using inline diagnostic modules. After propagating through the SDO, the pulse width of X-ray was ~8 fs, which was similar to that of SASE (6–8 fs). Experimental setting The experiment was carried out at BL3, SACLA (Japan). The exit beams from the SDO system were focused on a sample position with a focusing mirror system and hit a water jet. The diameter of the water jet was 50 μm, and the water temperature was 22°C. A CCD was located 0.3 m downstream of the sample for monitoring the overall beam intensity and position in shot-by-shot. Each pulse energy of the sub-pulses was monitored by the intensity monitors39 in the SDO system. The time-courses of the X-ray beam position at the sample position were separately measured by installing another CCD with a magnification system at the sample position. Scattering from the water was recorded using three MPCCDs with a pixel size of 50 µm. The distance between the sample and the detector was 1 m. In this experimental setting, the speckle size on the detector plane is estimated to be 0.18 mm. As suggested by a recent study, an SDO with wavefront division has an intrinsic reduction of speckle contrast due to the difference in the speckle position on the detector plane50. In the current setting, the angular difference between two sub-pulses was expected to be 0.15 mrad, leading to the differences in the speckle positions between two sub-pulses ~0.15 mm on the detector plane, which corresponds to 83% of the speckle size. This angular mismatch would lead to a 74% decrease in speckle contrast. Because the contrast with a single pulse from the fixed-delay branch was 0.23 and that with uncorrelated beam was 0.12, the decreased contrast would be (0.23 – 0.12) × 0.26 + 0.12 = 0.15, which is consistent with the measured values at Δt = 0 ps. Data reduction In a CCD image, the electron charge cloud produced by an X-ray photon spreads over several pixels over the detector. A single 10 keV X-ray photon produces ~590 analog-to-digital units (ADU) on average, but the signal on a pixel is widely distributed due to the charge sharing between neighboring pixels, as shown in the solid line in Fig. 3b. We convert the raw data into the digitized X-ray photon images by using a droplet algorithm43–45. The histogram of the signal in a droplet in units of ADU is shown as the dashed line in Fig. 3b. Then, we carried out the photon assignment following a procedure labeled as Greedy Guess46. As discussed in great detail in ref. 46, the photon assignment process involves systematic errors but shows a linear response to contrast changes. In this work, we measured the baseline of the contrast, β0/2, by shifting the beam position such that the two sub-pulses do not overlap with each other. β0 was separately estimated by blocking the variable-delay branch. Then, the measured contrast was compared with these values without further calibration. Supplementary information Supplementary Information Peer review information Nature Communications thanks Christian Bressler Fivos Perakis and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available. Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Supplementary information Supplementary information is available for this paper at 10.1038/s41467-020-20036-z. Acknowledgements X-ray scattering work by Y. Shinohara, W.D., C.W.R., and T.E. was supported by U.S. Department of Energy, Office of Science, Office of Basic Energy Science, Division of Materials Sciences and Engineering. Work by T.O. was supported by JSPS KAKENHI (Grant No. 18K18307) and work by I.I. was supported by JSPS KAKENHI (Grant No. 19K20604). The experiments at SACLA were carried out under the approval of JASRI (Proposal Nos. 2018B8041, 2019A8043, and 2019B8011). Author contributions Y. Shinohara, T.O., I.I., and T.E. conceived the project. T.O. and I.I. prepared the SDO and self-seeding of X-rays. Y. Shinohara, T.I., W.D., C.W.R., and Y. Sarathchandran carried out the experiments with support by T.O. and I.I. Y. Shinohara analyzed the experimental data. Y. Shinohara, T.O., I.I., and T.E. wrote the paper. All authors reviewed and discussed analysis and the paper. Data availability Data supporting the findings of this study are available within the article and the supplementary materials, and additional data are available from the corresponding authors upon reasonable request. Code availability The codes supporting the findings of this study are available from the corresponding authors upon reasonable request. Competing interests The authors declare no competing interests. ==== Refs References 1. Sutton M Observation of speckle by diffraction with coherent X-rays Nature 1991 352 608 610 10.1038/352608a0 2. Stephenson GB Robert A Grübel G Revealing the atomic dance Nat. Mater. 2009 8 702 703 10.1038/nmat2521 19701213 3. Madsen, A., Fluerasu, A. & Ruta, B. Structural dynamics of materials probed by X-ray photon correlation spectroscopy. in Synchrotron Light Sources and Free-Electron Lasers (eds Jaeschke, E. J., Khan, S., Schneider, J. R. & Hastings, J. B.) 1617–1641 (Springer, 2016). 4. Sutton M A review of X-ray intensity fluctuation spectroscopy C. R. Phys. 2008 9 657 667 10.1016/j.crhy.2007.04.008 5. Grübel G Zontone F Correlation spectroscopy with coherent X-rays J. Alloy. Compd. 2004 362 3 11 10.1016/S0925-8388(03)00555-3 6. Dierker SB Pindak R Fleming RM Robinson IK Berman L X-ray photon correlation spectroscopy study of Brownian motion of gold colloids in glycerol Phys. Rev. Lett. 1995 75 449 452 10.1103/PhysRevLett.75.449 10060024 7. Thurn-Albrecht T Photon correlation spectroscopy of colloidal palladium using a coherent X-Ray beam Phys. Rev. Lett. 1996 77 5437 5440 10.1103/PhysRevLett.77.5437 10062803 8. Mochrie SGJ Dynamics of block copolymer micelles revealed by X-ray intensity fluctuation spectroscopy Phys. Rev. Lett. 1997 78 1275 1278 10.1103/PhysRevLett.78.1275 9. Falus P Borthwick MA Mochrie SGJ Fluctuation dynamics of block copolymer vesicles Phys. Rev. Lett. 2005 94 016105 10.1103/PhysRevLett.94.016105 15698103 10. Caronna C Chushkin Y Madsen A Cupane A Dynamics of nanoparticles in a supercooled liquid Phys. Rev. Lett. 2008 100 055702 10.1103/PhysRevLett.100.055702 18352390 11. Shinohara Y Kishimoto H Yagi N Amemiya Y Microscopic observation of aging of silica particles in unvulcanized rubber Macromolecules 2010 43 9480 9487 10.1021/ma102095b 12. Leitner M Sepiol B Stadler L-M Pfau B Vogl G Atomic diffusion studied with coherent X-rays Nat. Mater. 2009 8 717 720 10.1038/nmat2506 19633660 13. Ruta B Atomic-scale relaxation dynamics and aging in a metallic glass probed by X-ray photon correlation spectroscopy Phys. Rev. Lett. 2012 109 165701 10.1103/PhysRevLett.109.165701 23215091 14. Ruta B Revealing the fast atomic motion of network glasses Nat. Commun. 2014 5 3939 10.1038/ncomms4939 24835825 15. Baron, A. Q. R. High-resolution inelastic X-ray scattering I: context, spectrometers, samples, and superconductors. in Synchrotron Light Sources and Free-Electron Lasers (eds Jaeschke, E. J., Khan, S., Schneider, J. R. & Hastings, J. B.) 1643–1719 (Springer International Publishing, 2016). 16. Stone MB A comparison of four direct geometry time-of-flight spectrometers at the spallation neutron source Rev. Sci. Instrum. 2014 85 045113 10.1063/1.4870050 24784665 17. Emma P First lasing and operation of an ångstrom-wavelength free-electron laser Nat. Photon 2010 4 641 647 10.1038/nphoton.2010.176 18. Ishikawa T A compact X-ray free-electron laser emitting in the sub-ångström region Nat. Photon 2012 6 540 544 10.1038/nphoton.2012.141 19. Osaka T Wavelength-tunable split-and-delay optical system for hard X-ray free-electron lasers Opt. Express 2016 24 9187 10.1364/OE.24.009187 27137535 20. Roseker W Towards ultrafast dynamics with split-pulse X-ray photon correlation spectroscopy at free electron laser sources Nat. Commun. 2018 9 1704 10.1038/s41467-018-04178-9 29703980 21. Grübel G Stephenson GB Gutt C Sinn H Tschentscher TH XPCS at the European X-ray free electron laser facility Nucl. Instrum. Meth. Phys. Res. B 2007 262 357 367 10.1016/j.nimb.2007.05.015 22. Gutt C Measuring temporal speckle correlations at ultrafast X-ray sources Opt. Express 2009 17 55 10.1364/OE.17.000055 19129872 23. Dixon PK Durian DJ Speckle Visibility spectroscopy and variable granular fluidization Phys. Rev. Lett. 2003 90 184302 10.1103/PhysRevLett.90.184302 12786009 24. Bandyopadhyay R Gittings AS Suh SS Dixon PK Durian DJ Speckle-visibility spectroscopy: a tool to study time-varying dynamics Rev. Sci. Instrum. 2005 76 093110 10.1063/1.2037987 25. Inoue I Shinohara Y Watanabe A Amemiya Y Effect of shot noise on X-ray speckle visibility spectroscopy Opt. Express 2012 20 26878 10.1364/OE.20.026878 23187541 26. Li L Photon statistics and speckle visibility spectroscopy with partially coherent X-rays J. Synchrotron Rad. 2014 21 1288 1295 10.1107/S1600577514015847 27. Verwohlt J Low dose X-ray speckle visibility spectroscopy reveals nanoscale dynamics in radiation sensitive ionic liquids Phys. Rev. Lett. 2018 120 168001 10.1103/PhysRevLett.120.168001 29756927 28. Perakis F Coherent X-rays reveal the influence of cage effects on ultrafast water dynamics Nat. Commun. 2018 9 1917 10.1038/s41467-018-04330-5 29765052 29. Hara T Two-colour hard X-ray free-electron laser with wide tunability Nat. Commun. 2013 4 2919 10.1038/ncomms3919 24301682 30. Marinelli A High-intensity double-pulse X-ray free-electron laser Nat. Commun. 2015 6 6369 10.1038/ncomms7369 25744344 31. Hirano T Performance of a hard X-ray split-and-delay optical system with a wavefront division J. Synchrotron Rad. 2018 25 20 25 10.1107/S1600577517014023 32. Sakamoto J Design of a prototype split-and-delay unit for XFEL pulses, and their evaluation by synchrotron radiation X-rays J. Synchrotron Rad. 2017 24 95 102 10.1107/S1600577516017744 33. Roseker W Performance of a picosecond x-ray delay line unit at 8.39 keV Opt. Lett. 2009 34 1768 10.1364/OL.34.001768 19529697 34. Roseker W Development of a hard X-ray delay line for X-ray photon correlation spectroscopy and jitter-free pump–probe experiments at X-ray free-electron laser sources J. Synchrotron Rad. 2011 18 481 491 10.1107/S0909049511004511 35. Roseker W Double-pulse speckle contrast correlations with near Fourier transform limited free-electron laser light using hard X-ray split-and-delay Sci. Rep. 2020 10 5054 10.1038/s41598-020-61926-y 32193442 36. Inoue I Generation of narrow-band X-ray free-electron laser via reflection self-seeding Nat. Photon 2019 13 319 322 10.1038/s41566-019-0365-y 37. Emma C Experimental demonstration of fresh bunch self-seeding in an X-ray free electron laser Appl. Phys. Lett. 2017 110 154101 10.1063/1.4980092 38. Amann J Demonstration of self-seeding in a hard-X-ray free-electron laser Nat. Photon 2012 6 693 698 10.1038/nphoton.2012.180 39. Tono K Single-shot beam-position monitor for X-ray free electron laser Rev. Sci. Instrum. 2011 82 023108 10.1063/1.3549133 21361574 40. Yumoto H Focusing of X-ray free-electron laser pulses with reflective optics Nat. Photon 2013 7 43 47 10.1038/nphoton.2012.306 41. Goodman, J. W. Statistical Optics (John Wiley & Sons, 1984). 42. Kameshima T Development of an X-ray pixel detector with multi-port charge-coupled device for X-ray free-electron laser experiments Rev. Sci. Instrum. 2014 85 033110 10.1063/1.4867668 24689567 43. Hruszkewycz SO High contrast X-ray speckle from atomic-scale order in liquids and glasses Phys. Rev. Lett. 2012 109 185502 10.1103/PhysRevLett.109.185502 23215295 44. Chushkin Y Caronna C Madsen A A novel event correlation scheme for X-ray photon correlation spectroscopy J. Appl. Cryst. 2012 45 807 813 10.1107/S0021889812023321 45. Livet F Using direct illumination CCDs as high-resolution area detectors for X-ray scattering Nucl. Instrum. Meth. Phys. Res. Sec. A 2000 451 596 609 10.1016/S0168-9002(00)00333-8 46. Sun Y Montana-Lopez J Fuoss P Sutton M Zhu D Accurate contrast determination for X-ray speckle visibility spectroscopy J. Synchrotron Rad. 2020 27 999 1007 10.1107/S1600577520006773 47. Skinner LB Benchmark oxygen-oxygen pair-distribution function of ambient water from X-ray diffraction measurements with a wide Q -range J. Chem. Phys. 2013 138 074506 10.1063/1.4790861 23445023 48. Shinohara Y Viscosity and real-space molecular motion of water: observation with inelastic X-ray scattering Phys. Rev. E 2018 98 022604 10.1103/PhysRevE.98.022604 30253607 49. Iwashita T Seeing real-space dynamics of liquid water through inelastic X-ray scattering Sci. Adv. 2017 3 e1603079 10.1126/sciadv.1603079 29291242 50. Sun Y Realizing split-pulse X-ray photon correlation spectroscopy to measure ultrafast dynamics in complex matter Phys. Rev. Res. 2020 2 023099 10.1103/PhysRevResearch.2.023099 51. Gelman A Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper) Bayesian Anal. 2006 1 515 534 10.1214/06-BA117A