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In the late 1800s, the revelation that light extended beyond visible wavelengths led to the discovery of X-rays by Wilhelm Roentgen. Recognized as high-energy electromagnetic radiation with short wavelengths, X-rays prompted exploration into their interaction with crystals. Max von Laue proposed in 1912 that the periodic arrangement of atoms, ions, or molecules in crystals would cause them to diffract X-rays, a hypothesis confirmed through experiments with copper sulfate and zinc sulfide...
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Synchrotron X-ray Microdiffraction and Fluorescence Imaging of Mineral and Rock Samples
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Published on: June 19, 2018

On the sampling of three-dimensional polycrystalline microstructures for distribution determination.

J Luan1, G Liu, H Wang

  • 1School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing, China.

Journal of Microscopy
|August 4, 2011
PubMed
Summary

Sampling 3D microstructures requires careful consideration to minimize experimental error. A minimum of 800 sampled grains is recommended for accurate distribution analysis, especially when large grains are present.

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Characterization of Ultra-fine Grained and Nanocrystalline Materials Using Transmission Kikuchi Diffraction
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Characterization of Ultra-fine Grained and Nanocrystalline Materials Using Transmission Kikuchi Diffraction

Published on: April 1, 2017

Area of Science:

  • Materials Science
  • Computational Materials Science
  • Microstructure Analysis

Background:

  • Accurate characterization of three-dimensional (3D) microstructures is crucial for understanding material properties.
  • Experimental error in sampling 3D microstructures can significantly impact the reliability of derived characteristic parameters.
  • The Potts Monte Carlo method is a common simulation technique for generating 3D microstructures.

Purpose of the Study:

  • To investigate the impact of sampling strategies on the accuracy of determining characteristic parameters of 3D microstructures.
  • To establish minimum sample sizes required for reliable estimation of grain size and topology distributions.
  • To identify potential sources of error, such as exceptional grain sizes, in microstructure analysis.

Main Methods:

  • Utilized seven single-phase polycrystalline structures simulated using the 400×400×400 Potts Monte Carlo method.
  • Analyzed the effects of varying sample sizes on statistical parameters of grain size and grain face number distributions.
  • Evaluated parameters including mean volume, mean face number, coefficient of variance, skewness, and kurtosis.

Main Results:

  • A minimum of 200 sampled grains ensures <5% relative error for mean grain volume and mean grain face number, and their coefficients of variance.
  • A minimum of 800 sampled grains is necessary for <5% relative error in skewness and kurtosis of grain size and face number distributions.
  • Exceptional grains (e.g., >8x mean volume or >3x mean face number) can lead to abnormal parameter values even with >1000 samples.

Conclusions:

  • The number of sampled grains significantly influences the accuracy of 3D microstructure characterization.
  • Specific statistical parameters require larger sample sizes for reliable determination.
  • The presence of outlier grains necessitates careful consideration in sampling strategies to avoid biased results.