Anomalous small-angle x-ray scattering (ASAXS) enhances the information that can be gained from SAXS by introducing a chemical, element-specific contrast, which modifies the standard electron density contrast obtained in normal SAXS experiments. This technique has the potential to help understand complex materials better, but its complexity means that it has so far not been used routinely in in-situ experiments. In this paper, we will review ASAXS and its in-situ applications as reported in the literature and present some data from a recent in-situ near-edge SAXS experiment we did at beamline 6.2 at Daresbury.
Alumina-zirconia ceramics are widely used in industry as refractories and as catalyst supports. Nano-structured variants are particularly important as thermal barrier coatings, where careful engineering of the nanoscale structure can increase the mechanical strength significantly, and as bulk catalyst supports with a particularly large surface area. We have also used a nano-scale analogue of a commercial furnace refractory to study corrosion mechanisms in glass melting furnaces along with in-situ NMR of glass melting kinetics.
These nano-ceramics consist of sol-gel prepared alumina and zirconia nanoparticles embedded in a silica-rich sodium silicate glass matrix. The corrosion mechanism is based on leaching of the glass phase followed by mechanical abrasion of the granular zirconia and alumina phases. The resilience of the refractory depends crucially on how well the grains are bonded to the matrix, e.g. by diffusion of Na+ across the grain interfaces and reactive sintering. It also depends on the shape of the particles; oblong particles and whiskers are more likely to withstand the mechanical effect of the contact with the moving batch.
Anomalous scattering is the chemical contrast enhancement that occurs around the absorption edge
of a probe element due to the resonance between scattering and absorption. In a small-angle
scattering experiment dealing with a heterogeneous material, the contrast between the different phases is
usually governed by the difference in electron density. In an idealised material consisting of two types
of particle densely packed within a matrix, the total scattered intensity is due to the
scattering from the interfaces of either particle with the matrix. The intensity is proportional to
the square of the scattering factor (i.e. the electron density difference):|
Near the edge, a complex correction,
is applied to the scattering factor to account for this resonance:
If SAXS experiments are carried out away from the edge (i.e. non-resonant only) and at two energies within the dip of f', then eq. (2) can be solved and the distribution of the labelled phase can be separated. In practice, it is better to use more than three energies because the resonant and cross terms are small and the solution is improved if the system of equations is over-determined.
Usually, all energies are chosen below the actual edge position in order to avoid excessive fluorescence. However, fluorescence can be corrected for if the incoming beam spectrum is known or the scattered intensity tails off to virtually zero in the high-q limit, so that the fluorescence level, which is supposed to be angle independent, can be regarded as the fluorescence contribution.
Fig. 1: Schematic of the three contributions to the scattering contrast near an absorption edge of an element contained in the phase represented by the white spheres. The normal scattering contrast (yellow) combines electron density difference between both white and grey particles and the matrix, the resonant term represents the correlation of scatterers containing the edge element (blue), and the cross term contains correlations between the phases that contain the edge element and those that don't (red).
Fig.2: Resonant correction of the atomic scattering factor near an absorption edge (Zr-K in this case). The real part (f', circles) shows a sharp dip at the edge, while the imaginary part (f", diamonds) increases suddenly.
Most of the previous ASAXS studies do not attempt to make full use of the potential inherent in eq. (2) to separate the cross term, which contains the correlation between the probe and the remaining scatterers, from the self term, which relates to the autocorrelation of the probes themselves, i.e. the pattern that one might expect if the phase containing the probe was in an otherwise perfectly index-matched environment. In order to solve eq. (2), measurements at a great deal more than three energies are required, and in addition to the usual corrections, the data need to be corrected for fluorescence, the width of the beam spectrum, and any chemical shifts of the edge occurring during an in-situ experiment.
The SAXS experiments were carried out at beamline 6.2 at Daresbury. The beamline is equipped with a tunable Si(111) monochromator with horizontal and vertical focussing. The x-ray energy can be adjusted in steps of 1eV, and the upper limit of energies available on the beamline is near 18keV. A one-dimensional Rapid-2 detector was used at a camera length of 4m. The powdered samples were pressed into pellets 13mm in diameter and about 0.25mm thick; these were mounted into a resistance-heated furnace with Mylar windows. In-situ experiments were conducted in a range 250oC to 725oC in steps of 25K. Each temperature step took 17 minutes, comprising a 2min temperature ramp, 3min equilibration time, 5min data acquisition at 18.02keV and 18.05keV (corresponding to the first XANES maximum and minimum post-edge, respectively) and 2min data acquisition at 17.98keV (pre-edge).
The accurate position of the Zr-K absorption edge was determined by scanning the edge before heating
began. For comparison, a thin foil of zirconium metal was also edge-scanned. There is a
chemical shift of about 8eV between the metal reference and the oxide contained in our samples due to the
different electron density in the two materials (chemical shift). In addition, there is also a chemical
shift of about -3eV in the edge position between the raw samples and the heated ones at the end of the
in-situ experiment. From the resonance curve above it is clear that the shift during the
experiment needs to be corrected for, i.e. the x-ray energy has to be adjusted in line with the shift of the
edge to maintain in the same relative position on the resonance curve. This would require frequent and
accurate edge scans at each temperature step. As this was impractical at the time, we resorted to comparing
pre- and post-edge scattering patterns, where the contrast variation is smaller but constant.|
Fig.3: Zr-K edge scans of zirconium foil and zirconia-alumina-silicate mixture. A chemical shift of 8eV arises due to the different electron densities. A further chemical shift of -3eV is observed during the in-situ experiment. The arrows indicate the energies at which in-situ SAXS patterns were recorded.
All scattering patterns are transmission corrected by evaluating the readings of two ion chambers before and after the beam passes through the furnace. At all three energies, fluorescence has to be taken into account since at least part of the beam spectrum is above the absorption edge. To this end, the run-out of the patterns at high q is interpreted as fluorescence-only, and all patterns are shifted vertically to coincide in this limit. The usable q window is therefore in the range from 0.15nm-1 to 4nm-1.
The scattering pattern at 250oC,
which is identical to the room temperature pattern of the raw material, is fairly featureless with a
slope near 2. As the temperature increases, a shoulder emerges in the higher-q range, which is
sufficiently distinct at 350oC to determine a Guinier radius of about 0.6nm. As the
temperature continues to increase, this shoulder grows and shifts gradually to the left. At
the length scale of the scattering object associated with this shoulder has increased to 2.3nm,
and a plateau forms to the left of the slope. As the temperature rises further, the crossover between
slope and plateau moves further to the left, and by 750oC, the Guinier radius becomes so large
that only the sloping section remains to be observed. The exponent of the power law representing the slope
increases from near 2 to 4 as the shoulder appears and then reduces again to a value near 3 as the shoulder
moves towards the low-q end of the accessible q range.|
Fig.4: Scattering patterns at 17.98keV at 250oC, 350oC, and 625oC. The horizontal line indicates the fluorescence level to which all patterns are normalised. Guinier radii are obtained from the shoulder where possible. The three dashed lines in the top right corner indicate slopes of 2, 3, and 4.
|Here we compare the scattering patterns at 375oC just below and just above the Zr-K edge. At this temperature, the shoulder in the pattern is well established and it is straightforward to determine a Guinier radius. From the direct comparison of the two patterns (after adjusting the fluorescence level) it is obvious that the slope on the high-q side is steeper in the pre-edge pattern. On the other hand, there is little difference in the shape of the curves towards the low-q end of the range. The total scattered intensity is lower above the edge due to the fact that the sample as a whole is more absorbing. The difference pattern generally follows the shape of the pre-edge data set except for the area around q ~ 2nm-1, where the two curves approach each other more closely, indicating that the zirconium-bearing phase contributes more strongly in this region.||
Fig.5: Pre- and post-edge scattering patterns (obtained at 17.98keV and 18.02keV, respectively) at 375oC. The difference pattern emphasises those areas where scattering is dominated by the Zr-bearing phase. The vertical dashed line indicates the limit of confidence in the accuracy of the fluorescence correction.