Measurement of probability distributions for internal stresses in dislocated crystals

Research output: Contribution to journalArticlepeer-review


  • Angus J. Wilkinson
  • Edmund Tarleton
  • Arantxa Vilalta-Clemente
  • Jun Jiang
  • T. Benjamin Britton

Colleges, School and Institutes

External organisations

  • University of Oxford
  • Imperial College London


Here, we analyse residual stress distributions obtained from various crystal systems using high resolution electron backscatter diffraction (EBSD) measurements. Histograms showing stress probability distributions exhibit tails extending to very high stress levels. We demonstrate that these extreme stress values are consistent with the functional form that should be expected for dislocated crystals. Analysis initially developed by Groma and co-workers for X-ray line profile analysis and based on the so-called "restricted second moment of the probability distribution" can be used to estimate the total dislocation density. The generality of the results are illustrated by application to three quite different systems, namely, face centred cubic Cu deformed in uniaxial tension, a body centred cubic steel deformed to larger strain by cold rolling, and hexagonal InAlN layers grown on misfitting sapphire and silicon carbide substrates.


Original languageEnglish
Article number181907
JournalApplied Physics Letters
Issue number18
Publication statusPublished - 3 Nov 2014

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