A Transfer Function for Relating Mean 2D Cross-Section Measurements to Mean 3D Particle Sizes

Gerlt, A. R. C.; Picard, R. S.; Saurber, A. E.; Criner, Amanda Keck; Semiatin, S. L.; Payton, E.J.

doi:10.1007/s11661-018-4808-8

Cited by 15 publications

(9 citation statements)

References 15 publications

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“…In prior work, the authors have demonstrated that the errors introduced by applying this equation to lognormal distributions of either spherical particles or tetrakaidecahedra often exceeds 50 pct in application. [5,10] Furthermore, traditional stereological transfer functions only provide an estimate of a mean value, with no quantification of the shape, skew, or variance of the size distribution.…”

Section: Introductionmentioning

confidence: 99%

Non-linear Transfer Functions for Accurately Estimating 3D Particle Size, Distribution, and Expected Error from 2D Cross Sections of a Lognormal Distribution of Spherical Particles

Gerlt

Criner

Semiatin

et al. 2020

Metall Mater Trans A

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Accurately estimating the mean size of features within an opaque material using only 2D observations is a common requirement in the materials and medical communities. Attempting to employ numerical methods to obtain an accurate estimate of the full 3D size distribution, which is often important for calculating structure-dependent material properties, is substantially more challenging. This paper circumvents the error propagation issues observed with classical numerical approaches, such as those formulated by Saltikov, Johnson, and Schwartz, through comparison of two calculation methods: (i) the direct simulation of synthetic particles and (ii) inversion of the conventional Saltikov analysis. Each method was used to generate dispersions whose 3D particle diameters followed lognormal distributions of varying shape parameters; the mean and variance were then predicted for 2D cross-sectional measurements. Parameters from both the 2D and 3D distributions were analytically coupled to produce a set of equations for accurately transforming cross-sectional observations into estimates of the full 3D distributions. Accuracy of the 2D-to-3D transformation is, for the first time, characterized as a function of the population size and measurement resolution. Specifically, included figures allow for rapid conversion from 2D to 3D metrics with the corresponding margin of error. The Inverse Saltikov method is shown to provide superior transformation accuracy for the idealized cases of lognormally distributed and randomly dispersed spherical particles when compared to either the Direct Simulation method or classical numerical approaches.

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Section: Introductionmentioning

confidence: 99%

Non-linear Transfer Functions for Accurately Estimating 3D Particle Size, Distribution, and Expected Error from 2D Cross Sections of a Lognormal Distribution of Spherical Particles

Gerlt

Criner

Semiatin

et al. 2020

Metall Mater Trans A

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“…Now however, computational simulations of particle dispersions and grain size distributions can be used to test these equations, as was done recently by the authors . During our investigation, a discrepancy was observed between simulation results and Equation .…”

Section: Introductionmentioning

confidence: 81%

On the grain size proportionality constants calculated in M.I. Mendelson's “Average Grain Size in Polycrystalline Ceramics”

et al. 2018

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In 1969, M.I. Mendelson published a paper in the Journal of the American Ceramic Society that introduced a proportionality constant of 1.558 for estimating the average 3D grain size from the mean 2D lineal intercept under the assumption of lognormally distributed grains. Recent simulations by the authors revealed that the lognormal parameterization in the original work actually calculates the median grain size instead of the mean. The relationship between the mean caliper diameter and mean lineal intercept was found to be 1.60 when using common parameterizations. In addition, it is demonstrated through simulations that the correct proportionality constant can range from 1.776 to below unity depending on a material's grain size dispersion, such that 1.60 should only be used as a crude approximation. K E Y W O R D Scharacterization, grain size distribution microstructure, particle size distribution, simulations, stereology

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“…Also shown is the particle size distribution found by analysing SEM images of MALI in PMMA composites. This was carried out using MATLAB image processing function regionprops and making corrections to account for the 2D projection of a slice through a 3D geometry, with the assumption of spherical particles with a log normal distribution of sizes 31,32 . The deviation of the right side tail is due to the difficulty of properly characterizing it from a relatively small sample set of values from what is a widely dispersed population 32 .…”

Section: B Particle Size Analysismentioning

confidence: 99%

“…This was carried out using MATLAB image processing function regionprops and making corrections to account for the 2D projection of a slice through a 3D geometry, with the assumption of spherical particles with a log normal distribution of sizes 31,32 . The deviation of the right side tail is due to the difficulty of properly characterizing it from a relatively small sample set of values from what is a widely dispersed population 32 . To extract the electrical properties, room temperature complex impedance, Z* plots were fitted with a single RC element to extract the bulk conductivity ( ) and relative permittivity of MALI and gave values of and , respectively.…”

Section: B Particle Size Analysismentioning

confidence: 99%

Predicting the energy storage density in poly(methyl methacrylate)/methyl ammonium lead iodide composites

Kennedy

Sinclair

Reaney

et al. 2019

Journal of Applied Physics

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A Transfer Function for Relating Mean 2D Cross-Section Measurements to Mean 3D Particle Sizes

Cited by 15 publications

References 15 publications

Non-linear Transfer Functions for Accurately Estimating 3D Particle Size, Distribution, and Expected Error from 2D Cross Sections of a Lognormal Distribution of Spherical Particles

Non-linear Transfer Functions for Accurately Estimating 3D Particle Size, Distribution, and Expected Error from 2D Cross Sections of a Lognormal Distribution of Spherical Particles

On the grain size proportionality constants calculated in M.I. Mendelson's “Average Grain Size in Polycrystalline Ceramics”

Predicting the energy storage density in poly(methyl methacrylate)/methyl ammonium lead iodide composites

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