Fluctuation X-ray Microscopy (FXM) studies at the 2-ID-B beamline at the Advanced Photon Source (APS)
Fluctuation x-ray microsocopy is the x-ray analog of the FEM technique in the transmission electron microscope (TEM). Unlike the the TEM, acquiring full sample images under given scattering conditions (called tilted dark field imaging in the TEM) is difficult, because suitable lens systems are not yet available. However, the focused probe mode is available, using either pinholes or zone plates to generate the probe at the sample. The pinholes can generate (unfocused) probes as small as ~ 1µm on the sample provided the pinhole is very close to the sample. Zone plates can generate probes smaller than 100 nm. In order to optimize the zone plate performance, we use soft x-rays of wavelength ~0.7 nm at the 2-ID-B beamline at the APS, Argonne National Laboratory.
As a proof-of-principle, a number of test samples were studied. One interesting system comprised latex spheres that are suspended in aqueous water/alcohol and allowed to dry on thin SiN membranes. Depending on the drying rate, the sample could be polycrystalline (long range order resulting from a slow drying rate), to amorphous (short range order resulting from a rapid drying rate). Typical sphere diameters were 0.25 µm. The image below shows scanning electron micrographs of the surfaces of three such thin films. (By thin, we mean 10 – 30 µm thick.) The surfaces of the films are deceptive. It seems that during drying, surface tension acts to order and smooth the outer layer of the assembly. When the film is cracked to allow views into the interior, the inner layers exhibit much less regularity, resembling the fast-dry material shown on the right.
Experiments are conducted by focusing the probe onto the sample, and collecting the diffraction pattern. The sample is moved to another (usually neighboring) point, and a new diffraction pattern is collected from the new sample point. This is continued until a rectilinear sample grid is collected, usually around 60 x 60 points. For a nominal probe size D, the scan steps are arranged to be ~ D/2 for optimal sampling. The diffraction data set is then processed to extract the mean diffraction pattern and the normalized variance of the diffraction pattern.
Data for four different pinhole sizes are shown in the figure on the right. Within each of the four images, the mean diffraction pattern is shown on the left, and the corresponding normalized variance is mirrored on the right. This sample has some crystalline regularity, as evidenced by the appearance of spots in the normalized variance data (right halves). However, there is no clear sign of this regularity in the mean diffraction data, except perhaps for the 10 µm probe. the normalized variance is maximum for the 1.6 µm and 5.5 µm probes, strongly suggesting that the characteristic length scale of order is within this range. This particular data set represents the variable resolution mode of fluctuation microscopy.
The smooth circular rings that appear in this data are due to the spherical form factor for scattering from a sphere. The spheres in this sample are monodisperse (same diameter to within about ±1%), and so the ringing is strong. Strictly speaking, the ringing should not be appearing in the normalized varaince data (right halves) since the normalaization procedure is intended to remove all dependencies on the form factor. The ringing persists because of shot noise in the data, which introduces an additive term to the variance that is proportional to the mean intensity. Properly correcting for such additional noise artifacts removes most of the ringing.
Experiments are currently underway at the 2-ID-B beamline to study pore disorder in mesoporous amorphous-silica films. These experiments do not study the atomic scale disorder in the silica (FEM is better-suited to such length scales), but instead study the pore disorder at longer length scales (3 nm and larger).
It is hoped that the FXM technique will become sufficiently refined that we can address much more difficult nanosclae self-assemblies. One promising challenge is explore the synthesis of zeolitic materials. At what stage in the synthesis process do the ordered nuclei appear? And, at what nucleus size does the growth stage occur. Although the length scales of this problem, ~1-5 nm, are short for soft x-rays, the ability of x-rays to penetrate the synthesis apparatus is invaluable.