Proposal of simplified modified Williamson-Hall equation

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


Williamson-Hall (WH) plots are characterized by irregular arrangement of data due to the elastic anisotropy in each {hkl} plane. In order to correct the effect of elastic anisotropy, Ungár developed a unique methodology using the contrast factor C, so called the modified Williamson-Hall (mWH) method. When X-ray with the wave length λ was used for diffraction analysis and diffraction angle θ and integral breadth β was obtained in each diffraction peak, the following mWH equation is constructed as functions of the parameter K (= 2sinθ/λ) and ΔK (= βcosθ/λ). K K C OK2C Here, the parameter α is dependent on the crystallite size. The parameter φ and O are constants but the O-value is much smaller than the φ-value. In the mWH plots in 60% cold rolled ferrite (Fe-0.0056%C), ultra low carbon martensite (Fe-18%Ni) and 20% cold rolled austenite (SUS316L), it was confirmed that the value of OK2C is negligibly small. As a result, the following simplified equation is applicable for the analysis by mWH method.

Original languageEnglish
Pages (from-to)2354-2356
Number of pages3
Journalisij international
Issue number12
Publication statusPublished - Dec 2018

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Metals and Alloys
  • Materials Chemistry


Dive into the research topics of 'Proposal of simplified modified Williamson-Hall equation'. Together they form a unique fingerprint.

Cite this