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Related Concept Videos

X-ray Crystallography02:18

X-ray Crystallography

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The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
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Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring...
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Principal Stresses in a Beam01:11

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In prismatic beams subject to arbitrary transverse loading, It is essential to analyze the interaction between shear forces and bending moments in order to understand stress distribution and ensure structural integrity. The highest normal or bending stress occurs at the outer fibers of the beam, decreasing linearly to zero at the neutral axis. In contrast, shear stress peaks at the neutral axis and diminishes toward the outer surfaces.
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Principal Moments of Area01:14

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In mechanics, the product of inertia and moments of inertia of area help to calculate the stability and performance of various structures and components. The coordinate transformation relations are used to calculate the moments and products of inertia for an area about the inclined axes. Further, the moments and products of inertia with respect to the principal axes can be determined using the moments and products of inertia about the inclined axes.
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Principal Stresses01:24

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The graphical depiction of normal and shearing stress equations is represented by a circle, demonstrating the interplay between these stresses under different angular conditions. The center of this circle C, located on the vertical axis, represents the average normal stress, while its radius shows the range of stress variations. At points A and B, where the circle intersects the horizontal axis, the maximum and minimum normal stresses are observed, occurring without shearing stress. These...
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A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
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When analyzing two planes intersecting at right angles under the influence of shearing, tensile, and compressive stresses, it is essential to identify principal planes, maximum shearing stress, and principal stresses. To find the principal planes, apply a formula that equates them to twice the shearing stress divided by the difference between tensile and compressive stresses.
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Related Experiment Video

Updated: Feb 13, 2026

Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon
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Evaluating X-Ray Microanalysis Phase Maps Using Principal Component Analysis.

Ben Buse1, Stuart Kearns1

  • 1School of Earth Sciences,University of Bristol,Wills Memorial Building,Queen's Road,Bristol BS81RJ,Avon,UK.

Microscopy and Microanalysis : the Official Journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada
|March 22, 2018
PubMed
Summary
This summary is machine-generated.

Principal component analysis offers advanced methods for evaluating automated phase maps, improving data quality assessment beyond traditional techniques. These new approaches enhance the characterization of complex geological samples and material science applications.

Keywords:
K-means clusteringelectron probe microanalysiselemental mapsphase mappingscanning electron microscopy

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Area of Science:

  • Materials Science
  • Geology
  • Analytical Chemistry

Background:

  • Automated phase mapping is crucial for sample characterization.
  • Current data quality evaluation methods (BSE image overlay, composition averages) have significant limitations.

Purpose of the Study:

  • To introduce novel principal component analysis (PCA) based methods for evaluating automated phase map quality.
  • To address limitations of existing evaluation techniques in materials and geological analysis.

Main Methods:

  • Utilized PCA to create RGB composite images of principal components representing chemical variation.
  • Developed PCA maps for individual phases to assess intra-phase chemical heterogeneity.
  • Applied K-means clustering and K-nearest neighbor for phase classification.

Main Results:

  • PCA-based RGB composite images provide a superior reference for phase map comparison compared to BSE images.
  • PCA maps reveal chemical zoning and heterogeneity within phases, aiding in identification of unclassified phases and analytical artifacts.
  • Demonstrated effectiveness on a complex geological sample.

Conclusions:

  • PCA offers powerful, sensitive methods for automated phase map evaluation.
  • These methods improve the reliability and interpretability of phase mapping in complex samples.
  • Highlights the importance of robust data quality assessment in automated analysis.