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We study the time evolution of the two-dimensional kinetic Ising model in finite systems with a non-conserved order parameter, considering nearest-neighbour interactions on the square lattice with periodic and open boundary conditions. Universal data collapse in spin product correlation functions is observed which, when expressed in rescaled units, is valid across the entire time evolution of the system at all length scales, not just within the time regime usually considered in the dynamical scaling hypothesis. Consequently, beyond rapidly decaying finite size effects, the evolution of correlations in small finite systems parallels arbitrarily larger cases, even at large fractions of the size of these finite systems.

Metrology of crystalline defects is crucial for the understanding and development of a wide range of novel materials. Hence there is a huge demand from both academia and the semiconductor industry for extended defect characterisation tools which are simultaneously rapid to use, non-destructive and capable of sampling larger areas on the nanoscale. Electron Channelling Contrast Imaging (ECCI) provides the required capability for various materials through use of scanning electron microscopes [1-3]. While images of extended defects, similar to those observed in plan-view transmission electron microscopy, can be obtained using ECCI (understandably with lower spatial resolution), the uptake of the technique has not been widespread. One of the major challenges limiting the use of ECCI in the wider material science community is challenges associated with characterising low atomic weight, topography-dominated and insulating samples. In the present work, we demonstrate a much wider applicability of ECCI, including for low atomic weight and insulating materials for defect metrology using gaseous secondary electron detectors (GSEDs) [4] in a field emission variable pressure scanning electron microscope. We show the advantage of performing ECCI in the gaseous environment in this case water vapour which plays a dual role in reducing the surface charges as well as acting as an amplification medium, thus providing high signal to noise micrographs. We show example from technologically important semiconductor material such as AlN, a low atomic weight and a wide-band gap material.

Truly nanostructured materials pose a significant spatial resolution challenge to the conventional Electron Backscatter Diffraction (EBSD) characterization technique. Nevertheless, the interaction volume can be reduced by the use of electron transparent samples and the acquisition of electron backscatterlike patterns (EBSP) in transmission mode instead. These transmission Kikuchi diffraction (TKD) patterns are typically acquired by mounting a thin foil, similar to transmission electron microscopy (TEM), and tilting it at a slight angle (20 • -30 • ) from horizontal towards a standard EBSD camera.While TKD has recently gained attention as a high resolution orientation mapping technique [1], indexing of TKD patterns has mostly been performed using the standard EBSD approaches, accounting for the difference in geometry. Only limited work has been done in terms of dynamical TKD pattern simulations. Since it is known from experiments that the sample thickness directly influences the sharpness of the patterns [2] as well as the pattern details, we can expect a transmission model for TKD patterns to show quantitative differences compared to EBSD pattern predictions. We propose the following formulation for the probability that an electron of energy E will leave the foil in the directionk after Rutherford scattering from an individual atom located at a distance z from the exit surface:Here, σ is the Rutherford scattering cross section; E min/max are the minimum and maximum energies considered in the calculation; z is the distance between the scattering site and the sample surface, measured along the exit direction; z 0 (E) is the maximum distance to be considered;λk(E, z) is a weighting function describing the fraction of incident electrons (per unit energy and per unit length) of energy E, originating a distance z from the sample surface and traveling in the directionk.In contrast to the EBSP signal, which provides information about a volume close to the illuminated top surface of the sample, the majority of the electrons contributing to a TKD pattern 'originate' from the bottom region of the sample; they are inelastically scattered inside the sample before reaching the bottom portion of the foil and escaping via a final elastic (Rutherford) scattering event. The formation of these forward scattered escaping electrons is a stochastic process encoded by the functionλk, and determined with a Monte Carlo (MC) trajectory simulation. Fig. 1 shows stereographic projections of the exit electron distribution for a 100 nm Ni foil tilted at 30 • as a function of the exit energy. The exit energy range depends strongly on sample thickness and atomic number, as illustrated in Fig. 2 for Ni and Si; the mean exit energy decreases with increasing sample thickness. This, in turn, must give rise to both broadening and blurring of the Kikuchi bands compared to those observed in an EBSD pattern. This is illustrated in Fig. 3, which shows line profiles across a Kikuchi band, shown on the left, for different sample thicknesses. We will demo...