Dislocation density measurement in cold rolled metals using XRD and TEM

A. XRD-Based Dislocation Density Measurement

  1. Collect the diffraction pattern of the cold-rolled metal sample.
  2. Choose a relevant diffraction peak (e.g., a strong, well-resolved peak) for analysis.
  3. Determine Peak Broadening
  4. Measure the peak’s full width at half maximum (FWHM), denoted as β.
  5. Use appropriate XRD analysis software (e.g., X’Pert HighScore, Jade, or similar).
  6. Subtract Instrumental Broadening
  7. Obtain the instrumental FWHM from a strain-free standard sample.
  8. Subtract this instrumental contribution from β to isolate broadening due to lattice imperfections.
  9. Calculate the crystallite size using the Scherrer’s formula.
  10. Calculate the dislocation density from the average crystallite size.
  11. Perform the above steps on different peaks to verify consistency.
  12. Average the resulting dislocation density values for a representative result.


Figure 1: X-ray diffractogram for cold rolled metals and computation of dislocation density.

B. TEM-Based Dislocation Density Measurement

  1. Prepare TEM Sample → Create a thin foil (using techniques like mechanical polishing and ion milling) so electrons can transmit through the sample.
  2. Acquire TEM Micrographs
  3. Use bright-field or diffraction-contrast TEM imaging to observe dislocations.
  4. Adjust imaging conditions (voltage, focus, etc.) to clearly see dislocation lines.
  5. Measure Dislocations in Images
  6. Use image analysis software (e.g., ImageJ) to measure either:
    a) The total length of dislocation lines (Lₐ).
    b) The number of discrete dislocation segments (N).
  7. Determine Foil Thickness
  8. Measure or estimate the sample thickness (t) using methods such as convergent beam electron diffraction (CBED) or thickness fringes.
  9. Calculate Dislocation Density
  10. Repeat for Multiple Regions
  11. Collect images from different regions of the sample to ensure statistical validity.
  12. Average the dislocation densities from all micrographs for a final representative value.


Figure 2: TEM nanograph for cold rolled metal showing dislocations.