3D particle size distributions from 2D observations: stereology for natural applications (original) (raw)
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Theory of the Stereological Analysis of Spheroid Size Distribution – Validation of the Equations
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Often experimentalists study colloidal suspensions that are nominally monodisperse. In reality these samples have a polydispersity of 4-10%. At the level of an individual particle, the consequences of this polydispersity are unknown as it is difficult to measure an individual particle size from microscopy. We propose a general method to estimate individual particle radii within a moderately concentrated colloidal suspension observed with confocal microscopy. We confirm the validity of our method by numerical simulations of four major systems: random close packing, colloidal gels, nominally monodisperse dense samples, and nominally binary dense samples. We then apply our method to experimental data, and demonstrate the utility of this method with results from four case studies. In the first, we demonstrate that we can recover the full particle size distribution in situ. In the second, we show that accounting for particle size leads to more accurate structural information in a random close packed sample. In the third, we show that crystal nucleation occurs in locally monodisperse regions. In the fourth, we show that particle mobility in a dense sample is correlated to the local volume fraction.
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A simple mathematical expression with four variable parameters is introduced for the purpose of generating two-dimensional polygonally symmetric shapes. The motivation of the implementation of this expression is to improve the methods of characterization of particle shapes and sizes. Previous methods include the purely size classification, which does not carry information about the shape, and the orthogonal polynomial method, which involves too many parameters and therefore is too complicated. It is demonstrated that the simple equation introduced here is capable of simulating many shapes such as quasi-spherical particles and near-exact polygons. Values of the parameters for generating near-exact polygons are included. A sample of simulated particles is generated by this equation with a predetermined distribution of parameters to show the diversity of the shapes and sizes of particles represented by the equation. Since each parameter has a clear physical meaning (a, amplitude parameter; b, width parameter; c, center size parameter; and n, polygonality parameter), it may be possible to explain the physical processes involved by examining the distributions of each parameter.
Acta Materialia, 2003
The composition distribution in a chemically nonuniform system may be described as a set of scalar fields X k (x, y, z), one for each component k, where X k is the atom fraction of component k. For each component statistical information about this spatial distribution may be obtained by combining a sampling of microprobe line traces with stereological analysis. This analysis yields the volume weighted concentration distribution function, f v (X k), where f v (X k)dX k is the fraction of the volume of the system that has compositions in the range X k to X k + dX k , and S v (X k), the area per unit volume of structure of the isocomposition contour at each composition. The harmonic mean of the distribution of concentration gradients over each isocomposition contour can be computed from this information. The methodology also can be applied to the analysis of the distribution of any scalar property that is nonuniform in a structure.
Journal of Quantitative Spectroscopy and Radiative Transfer, 2012
Scattered intensity measurement is a commonly used method for determining the size of small particles. However, it requires calibration and is subject to errors due to changes in incident irradiance or detector sensitivity. Analysis of two-dimensional scattering patterns offers an alternative approach. We test morphological image processing operations on patterns from a diverse range of particles with rough surfaces and/or complex structure, including mineral dust, spores, pollen, ice analogs and sphere clusters from 4 to 88 mm in size. It is found that the median surface area of intensity peaks is the most robust measure, and it is inversely proportional to particle size. The trend holds well for most particle types, as long as substantial roughness or complexity is present. One important application of this technique is the sizing of atmospheric particles, such as ice crystals.