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Physical interpretation of Stephens' phenomenological parameters for anisotropic microstrain broadening in cubic systems.

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Title: Physical interpretation of Stephens' phenomenological parameters for anisotropic microstrain broadening in cubic systems.
Authors: Bhakar, Ashok1,2 (AUTHOR) kashok@rrcat.gov.in, Gupta, Pooja1,2 (AUTHOR), Swami, Mahesh Kumar1,2 (AUTHOR), Rai, Sanjay Kumar1,2 (AUTHOR)
Source: Journal of Applied Crystallography. Aug2026, Vol. 59 Issue 4, p1121-1128. 8p.
Subjects: Cubic crystal system, Dislocation structure, Crystals, Dislocation density
Abstract: Both the Stephens phenomenological model and the modified Williamson–Hall (mWH) plot analysis address the microstrain‐dependent anisotropic peak broadening observed in diffraction patterns. The data analysis strategies of both methods rely on the anisotropic nature of crystalline materials and the quartic form of reflection indices (hkl). Despite these similarities, the results of the two methods are not directly comparable: the Stephens approach is phenomenological, whereas the mWH method is based on the characteristic dislocation parameters for determining microstructural features (size–strain). This study aims to bridge that gap. A simple procedure is proposed to extract microstructural quantities – equivalent to those obtained by the mWH method – using the Stephens phenomenological approach. Furthermore, a microscopic interpretation of Stephens' phenomenological parameters is presented in terms of the nature of dislocations in cubic symmetry. The applicability of this procedure is demonstrated for cubic systems and illustrated with examples. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Applied Crystallography is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 195930088
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  Data: Physical interpretation of Stephens' phenomenological parameters for anisotropic microstrain broadening in cubic systems.
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  Data: <searchLink fieldCode="AR" term="%22Bhakar%2C+Ashok%22">Bhakar, Ashok</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> kashok@rrcat.gov.in</i><br /><searchLink fieldCode="AR" term="%22Gupta%2C+Pooja%22">Gupta, Pooja</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Swami%2C+Mahesh+Kumar%22">Swami, Mahesh Kumar</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Rai%2C+Sanjay+Kumar%22">Rai, Sanjay Kumar</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Crystallography%22">Journal of Applied Crystallography</searchLink>. Aug2026, Vol. 59 Issue 4, p1121-1128. 8p.
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  Data: <searchLink fieldCode="DE" term="%22Cubic+crystal+system%22">Cubic crystal system</searchLink><br /><searchLink fieldCode="DE" term="%22Dislocation+structure%22">Dislocation structure</searchLink><br /><searchLink fieldCode="DE" term="%22Crystals%22">Crystals</searchLink><br /><searchLink fieldCode="DE" term="%22Dislocation+density%22">Dislocation density</searchLink>
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  Data: Both the Stephens phenomenological model and the modified Williamson–Hall (mWH) plot analysis address the microstrain‐dependent anisotropic peak broadening observed in diffraction patterns. The data analysis strategies of both methods rely on the anisotropic nature of crystalline materials and the quartic form of reflection indices (hkl). Despite these similarities, the results of the two methods are not directly comparable: the Stephens approach is phenomenological, whereas the mWH method is based on the characteristic dislocation parameters for determining microstructural features (size–strain). This study aims to bridge that gap. A simple procedure is proposed to extract microstructural quantities – equivalent to those obtained by the mWH method – using the Stephens phenomenological approach. Furthermore, a microscopic interpretation of Stephens' phenomenological parameters is presented in terms of the nature of dislocations in cubic symmetry. The applicability of this procedure is demonstrated for cubic systems and illustrated with examples. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Applied Crystallography is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1107/S1600576726004176
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      – Code: eng
        Text: English
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      – SubjectFull: Cubic crystal system
        Type: general
      – SubjectFull: Dislocation structure
        Type: general
      – SubjectFull: Crystals
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      – SubjectFull: Dislocation density
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      – TitleFull: Physical interpretation of Stephens' phenomenological parameters for anisotropic microstrain broadening in cubic systems.
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            – D: 01
              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
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