Nanofocused x-ray photon correlation spectroscopy

Here, we demonstrate an experimental proof of concept for nanofocused x-ray photon correlation spectroscopy, a technique sensitive to nanoscale fluctuations present in a broad range of systems. The experiment, performed at the NanoMAX beamline at MAX IV, uses a novel event-based x-ray detector to capture nanoparticle structural dynamics with microsecond resolution. By varying the nanobeam size from $\sigma =88$ nm to $\sigma =2.5\mu \mathrm{m}$, we quantify the effect of the nanofocus on the small-angle scattering lineshape and on the diffusion coefficients obtained from nano-XPCS. We observe that the use of nanobeams leads to a multifold increase in speckle contrast, which greatly improves the experimental signal-to-noise ratio, quantified from the two-time intensity correlation functions. We conclude that it is possible to account for influence of the high beam divergence on the lineshape and measured dynamics by including a convolution with the nanobeam profile in the model.

Figure 1

(a) An illustration of the experimental scheme: The beam is focused using nanofocusing Kirkpatrick-Baez (KB) mirrors on the sample, consisting of nanoparticle suspensions in capillaries. The scattering data are recorded with the Tristan detector, reaching readout rates down to $1\mu \mathrm{s}$. The direct beam is blocked by a beamblocker, indicated by the dark region in the center of the detector. (b) The angularly integrated small-angle x-ray scattering (SAXS) intensity for silica nanoparticles in pure water measured with beam size $\sigma =88$ nm. Open circles denote experimental data while the lines refer to the model with the convolution of the beam profile (solid line) and without the convolution (dashed line) for particles with radius $R=48$ nm.

Figure 2

(a) Intensity autocorrelation ($g_2$) functions at different $Q$ for silica nanoparticles in pure water measured at the beam focus ($\sigma =88$ nm). The inset shows the $Q$ dependence of the average relaxation times $\tau$ obtained from fits of the $g_2$ functions to Eq. (3). The solid line denotes a fit to a model that incorporates a convolution with the divergent beam profile, while the dashed line represents the model in absence of the convolution. (b) $g_2$ functions for silica nanoparticles in DMSO-water solution measured at different beam sizes ($Q=0.067{\mathrm{nm}}^{-1}$). (c) The $Q$ dependence of the average relaxation times $\tau$ obtained from fits of the $g_2$ functions in panel (b) to Eq. (3). (d) Speckle contrast $\beta$ versus beam size $\sigma$. The experimental $\beta$ values from silica nanoparticles in water (open black circle) and DMSO-water (black circles), extracted from the fits to the $g_2$ functions ($Q=0.067{\mathrm{nm}}^{-1}$) are compared with an analytical estimate (dashed line).

Figure 3

(a) Two-time correlation (TTC) functions at $Q=0.066{\mathrm{nm}}^{-1}$ for silica nanoparticles in water at the beam focus ($\sigma =88$ nm) averaged over an acquisition time (top) $t_a=0.01$ s and (bottom) $t_a=1$ s. (b) The average correlation function ($g_2$) obtained by averaging the antidiagonals of the TTC for various acquisition times $t_a$. The shaded areas denote the noise level. (c) Signal-to-noise ratio (SNR) of TTCs as a function of acquisition time. The experimental SNR (black dots) agrees with the analytical estimate (blue dashed line).