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Nanometre-sized particles are of considerable current interest because of their special size-dependent physical properties. Debye±Scherrer diffraction patterns are often used to characterize samples, as well as to probe the structure of nanoparticles. Unfortunately, the well known`Scherrer formula' is unreliable at estimating particle size, because the assumption of an underlying crystal structure (translational symmetry) is often invalid. A simple approach is presented here which takes the Fourier transform of a Debye±Scherrer diffraction pattern. The method works well on noisy data and when only a narrow range of scattering angles is available.

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Soil biota have important effects on crop productivity, but can be difficult to study in situ. Laser ablation tomography (LAT) is a novel method that allows for rapid, three-dimensional quantitative and qualitative analysis of root anatomy, providing new opportunities to investigate interactions between roots and edaphic organisms. LAT was used for analysis of maize roots colonized by arbuscular mycorrhizal fungi, maize roots herbivorized by western corn rootworm, barley roots parasitized by cereal cyst nematode, and common bean roots damaged by Fusarium. UV excitation of root tissues affected by edaphic organisms resulted in differential autofluorescence emission, facilitating the classification of tissues and anatomical features. Samples were spatially resolved in three dimensions, enabling quantification of the volume and distribution of fungal colonization, western corn rootworm damage, nematode feeding sites, tissue compromised by Fusarium, and as well as root anatomical phenotypes. Owing to its capability for high-throughput sample imaging, LAT serves as an excellent tool to conduct large, quantitative screens to characterize genetic control of root anatomy and interactions with edaphic organisms. Additionally, this technology improves interpretation of root–organism interactions in relatively large, opaque root segments, providing opportunities for novel research investigating the effects of root anatomical phenes on associations with edaphic organisms.

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