Ultimate small-angle resolution for probing large Bragg spacings
Ultra-small-angle X-ray scattering (USAXS) is complementary to conventional small-angle X-ray scattering (SAXS). By sacrificing intensity in favor of resolution, in a USAXS experiment the small-angle resolution is strongly pushed to the ultimate limits. This enables to characterize larger particles and to probe larger Bragg spacings, in the range of hundreds of nanometers. By combining USAXS, SAXS, WAXS and ultimately PDF data, multi-level (hierarchical) structures can be analyzed on different length scales.
A classical USAXS setup proposed by Bonse and Hart (ref. 1) uses multiple reflections from high-quality single crystals (in a non-dispersive arrangement) for beam collimation and as receiving optics. Such a setup, even though being very compact, can give a very good resolution.
Here we will show how the Empyrean instrument can easily be configured for USAXS experiments with a Bonse-Hart type of setup and demonstrate the good performance. The setup makes use of standard high-resolution optical components that are also used for the characterization of epitaxial layers.
Basis of the USAXS setup on the Empyrean platform is the high-resolution theta-theta goniometer (smallest step size 0.0001 °2theta) with its PreFIX interfaces. A Cu X-ray tube in the line focus orientation is mounted on the theta arm. For the shaping and monochromatization of the incident beam a 4xGe(220) Bartels monochromator is used. The multiple reflections from the high-quality crystals result in a very narrow (rocking curve width < 14 arc sec) and highly collimated beam, in which the tails are very effectively suppressed.
Different types of sample stages can be used: a multipurpose SAXS/WAXS stage, a capillary spinner, or a reflection-transmission spinner with an optional sample changer. A 3-bounce Ge(220) channel-cut analyzer crystal is mounted on the 2theta arm of the goniometer, and used as receiving optics. It has a very narrow angular acceptance of 12 arc sec and thus contributes to the overall angular resolution of the USAXS setup. As to the detector, the PIXcel3D, PIXcel1D, X'Celerator or MiniProp counter can be used. The low intrinsic noise of these detectors greatly contributes to the high signal-to-background ratio that can be achieved. The goniometer not only enables a horizontal USAXS setup, but also a vertical setup with the X-ray tube on top and the detector at the bottom.
While the beam in this setup is highly collimated and narrow in the equatorial direction, it is much elongated and divergent in the axial direction. This results in data 'smearing' which must be taken into account when analyzing the data.
A Bonse-Hart type of experimental setup for USAXS measurements on the Empyrean platform is described. Key elements are high-resolution X-ray optical modules, PreFIX interfaces, a high-resolution goniometer and a low-noise detector. The setup is compact and mechanically very stable. A smallest scattering angle of 0.005 °2θ, corresponding to a maximum Bragg spacing of 1.7 µm, can thus be achieved.
Figure 1. Examples of experimental setups for USAXS measurements
USAXS measurements are done with the incident beam angle (omega) fixed at 0 deg when using a horizontal setup, or at 90 deg in case of a vertical setup. The detector, together with the analyzer crystal, is moved around the sample in a 2θ scan. Using the detector as a point detector (0D mode), scattering data are collected sequentially at the different angular positions. Depending on the sample characteristics, the step size is chosen typically between 0.0005 and 0.0050 °2θ.
Each measurement contains the direct beam profile as a reference. A sample measurement is usually complemented by a corresponding background measurement. Measurement times typically range between 30 min and several hours, depending on the sample type. Figure 2 shows a typical direct beam profile without any sample inserted. It is characterized by a very small width (FWHM below 0.0040 °2θ), a steep intensity decay without long tails, and a wide intensity dynamic range (up to seven orders of magnitude). These are key performance characteristics of a USAXS setup.
Figure 2. Typical direct beam profile, displayed on a logarithmic intensity scale
To verify the performance of the USAXS setup, measurements were done on various aqueous dispersions of silica particles, with diameters in the range of several hundreds of nanometers and very narrow size distributions. In all samples the particle concentration was 5 wt%. The dispersions were filled in disposable quartz capillaries of 1 mm diameter. With the sample having the largest particles (diameter 1.5 µm), sedimentation was encountered, even when using a capillary spinner. Therefore, in that case USAXS data were measured from the sediment, using a vertical experimental setup.
In the examples shown in Figure 3, symmetrical 2θ scans around the direct beam were used, to include both negative and positive scattering angles. As expected for spherical particles having a very narrow size distribution, several distinct, symmetrical fringes in the scattering curves could be readily resolved. The very narrow spacing between these fringes decreases with increasing particle size. Bell-shaped scattering curves are observed around the direct beam, which is characteristic for particle systems with no (or small) interparticle interaction (Guinier's law). In case of the sedimented particles (D = 1550 nm) effects of interparticle interaction (structure factor) are seen at the smallest angles.
In all these measurements the first significant data point is just below 0.005 °2θ, corresponding to a smallest scattering vector qmin of 0.00036 Å-1 and a Bragg spacing dmax of 1750 nm. This demonstrates the excellent resolution of the experimental setup.
Figure 3. USAXS data from large silica particles. Black arrow: direct beam. Blue arrow: first significant data point at approx. 0.0050 °
High-quality USAXS data can be obtained on the Empyrean platform. The small-angle resolution is about ten times higher as compared to what can be achieved with a conventional SAXS setup.