Improvement of ultra-small-angle XPCS with the Extremely Brilliant Source

The technical performance of ultra-small-angle X-ray photon correlation spectroscopy with the ESRF Extremely Brilliant Source is presented. The brighter X-ray source together with advanced pixel array detectors enable investigations of faster dynamics in relatively dilute suspensions by this method.

(FWHM = 2 2 ln(2)σ B ) can be determined from the fit.In order to determine the beam size at sample position, several beam images are taken close to the sample position, and extrapolated to the sample position.Because of the focusing, the beam size variation is not linear far away from the sample position.The beam size as a function of sample-to-detector distance is described in (Narayanan et al., 2022).

Theoretical speckle contrast calculations
The speckle contrast (β) is a sample-independent quantity (Abernathy et al., 1998) defined by the experimental parameters such as the coherence of the incident X-ray beam and the resolution of speckles on the detector.Following the ideas in (Sandy et al., 1999;Lumma et al., 2000;Möller et al., 2019), under certain assumptions that are met in this experimental setup, the contrast can be factorized.y is the axis of the beam, x is the horizontal axis perpendicular to the beam and z the vertical axis.
On the z−axis [β z (V z , ζ)] and on the xy−plane [β xy (q, V x , V y , ξ, λ, ∆E/E)], these factors compare the illuminated volume to the coherence length.[β q (q, S y , V x , λ, ∆E/E)] express the contrast of the speckles tilted by the scattering angle (θ) (Hruszkewycz et al., 2012).The last two factors are due to limited angular resolution of the detector, IUCr macros version 2.1.6:2014/01/16 The expressions used for the theoretical speckle contrast calculation are: The integrals are evaluated numerically using the nquad function in NumPy suite.
The beamline parameters used to compute the theoretical speckle contrast are provided in Table 1

Standard deviation and χ 4
A common quantity to quantify the steady-state in molecular dynamics simulations is χ 4 (τ, q) that is defined as: (Dasgupta et al., 1991;Glotzer et al., 2000) χ 4 (τ, q) = g 2 tt (q, τ, t) t − ⟨g tt (q, τ, t) which is the variance of g tt (q, τ, t) normalized by the square of experimental speckle contrast.However, β is usually lower than 1 in XPCS, and cannot be determined directly from the data without fitting due to the limited frame rate (the plateau of the autocorrelation function at short lag time might not be accessible).Thus, it is difficult to predict β and thus to measure χ 4 accurately in an online data reduction pipeline (Conrad et al., 2015).Instead, the standard deviation (σ) is computed, which does not make any assumption at the processing time, and it is related to Figure 2 shows the pixel intensity distribution at q =1 × 10 −2 nm −1 for the same acquisition as the one presented in Fig. 8 of the main text.At this q, the shape of the distribution for the orange is a Poisson-Gamma function.No crenelation pattern is visible and the relative count of even numbers is much closer to 50%.Compared to Fig. 8(a) in the main text, the contrast recovered the expected value at this q.
IUCr macros version 2.1.6:2014/01/16 10 2 10 1 q(nm 1 )  Figure 3 shows the unsubstracted SAXS profile from the silica colloidal suspension used to measure the impact of high count rate on the intensity statistics and apparent speckle contrast.Even if the minimum of the form factor is about one decade above the background, this still leads to a contrast reduction as shown in the main text.
This reduction can be expressed in terms of the relative intensity of the background to the sample scattered intensity.

Rheo-XPCS
For the shear cessation experiment, the geometry used was composed of two concentric quartz capillaries, and the X-ray beam traversed just below the rotor.the capillary Couette cell mounted on the beamline.This cell has been described in (Narayanan et al., 2020).(right) Photo of the shear cell on the beamline.

Fig. 1 .
Fig. 1.Direct beam profile at (a) 1 m from the sample position, (b) 31 m from the sample position.The dark image has been subtracted and the colormap is in logarithmic scale.Dashed lines represent fits using Gaussian profiles.

Figure 1
Figure1shows the typical profile of the direct beam, in coherence mode for the parameters described in the main manuscript.The profiles have been measured at 1 m and 31 m from the sample position.The profiles from vertical and horizontal slices show a Gaussian shape, and the beam size in terms of full width at half maximum Fig. 2. Histogram of pixel intensities at q =1 × 10 −2 nm −1 for the same acquisition as in Fig. 8.

Fig. 3 .
Fig.3.Unsubtracted SAXS profile from the dilute suspension of 600 nm sized silica particles and the corresponding background.
Figure 4(left) shows a scheme of the setup used in the experiment and (right) displays a photo of IUCr macros version 2.1.6:2014/01/16 Fig. 4. (left) Scheme of the capillary shear cell used in the shear cessation experiment.(right)Photo of the shear cell on the beamline.

Table 1 .
Main beamline parameters in coherent scattering mode used for the calculation of theoretical speckle contrast values.