Variable-resolution fluctuation electron microscopy (VR-FEM) data from measurements on amorphous silicon and PdNiP have been obtained at varying experimental conditions. Measurements have been conducted at identical total electron dose and with an identical electron dose normalized to the respective probe size. STEM probes of different sizes have been created by variation of the semi-convergence angle or by defocus. The results show that defocus yields a reduced normalized variance compared to data from probes created by convergence angle variation. Moreover, the trend of the normalized variance upon probe size variation differs between the two methods. Beam coherence, which affects FEM data, has been analyzed theoretically using geometrical optics on a multi-lens setup and linked to the illumination conditions. Fits to several experimental beam profiles support our geometrical optics theory regarding probe coherence. The normalized variance can be further optimized if one determines the optimal exposure time for the nanobeam diffraction patterns.

Diffuse rings from amorphous materials sit on a steep background resulting in a monotonically decreasing intensity over scattering vector length, frequently with no clear local maximum that could be used to determine the center of the ring. The novelty of the method reported here is that it successful processes such weak patterns. It is based on separating the angular dependence of the positions of the maxima on the azimuthal angle in the measured two-dimensional pattern for a manually preselected peak. Both pattern center and elliptical distortion are simultaneously refined from this angular dependence. Both steps are based on nonlinear least square fitting, using the Levenberg–Marquardt method. It can be successfully applied to any amorphous patterns provided they were recorded with experimental conditions that facilitate dividing them into sectors with acceptable statistics. Patterns with the center shifted to the camera corner (recording a quadrant of a ring) can also be reliably evaluated, keeping precalibrated values of the elliptical distortion fixed during the fit. Finally, the limited number of counts in any pattern is overcome by cumulating many patterns (from equivalent areas) into a single pattern. Eliminating false effects is facilitated by masking out unwanted parts of any recorded pattern from processing.

We compare experimental fluctuation electron microscopy (FEM) speckle data with electron diffraction simulations for thin amorphous carbon and silicon samples. We find that the experimental speckle intensity variance is generally more than an order of magnitude lower than kinematical scattering theory predicts for spatially coherent illumination.

We hypothesize that decoherence, which randomizes the phase relationship between scattered waves, is responsible for the anomaly. Specifically, displacement decoherence can contribute strongly to speckle suppression, particularly at higher beam energies. Displacement decoherence arises when the local structure is rearranged significantly by interactions with the beam during the exposure. Such motions cause diffraction speckle to twinkle, some of it at observable time scales.

We also find that the continuous random network model of amorphous silicon can explain the experimental variance data if displacement decoherence and multiple scattering is included in the modeling. This may resolve the longstanding discrepancy between X-ray and electron diffraction studies of radial distribution functions, and conclusions reached from previous FEM studies.

Decoherence likely affects all quantitative electron imaging and diffraction studies. It likely contributes to the so-called Stobbs factor, where high-resolution atomic-column image intensities are anomalously lower than predicted by a similar factor to that observed here.

Knowledge of the dynamic dimension of materials is an extremely important ingredient for understanding their properties. Neutron scattering is uniquely capable of revealing aspects of the atomic and molecular geometry of motions over a wide range of time scales. To illustrate this fact, we give a number of examples from different areas of materials science. We discuss the diffusion of hydrogen in protonic conductors; the hydration of portland cement; and aspects of the molecular rheology of polymers, emphasizing in particular the effect of branching. All of these experiments have added important basic information to the understanding of the respective systems. With the advent of the new megawatt neutron spallation sources, the role of neutron scattering in revealing the dynamical properties of materials is expected to increase substantially.