Grain boundary networks and shape preferred orientation –: A fresh angle on pattern quantification with GBPaQ

Johanna Heeb*, David Healy, Nicholas E. Timms, Enrique Gomez-Rivas

*Corresponding author for this work

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A quantitative understanding of grain shape preferred orientation (SPO) and grain boundary networks as fundamental characteristics of rocks and other crystalline solids is of major interest in geology and material science. Grain boundary networks contain useful information on the deformation history of polycrystalline aggregates, and their diagenetic and metamorphic histories. SPO can have a major impact on material characteristics such as permeability, acoustic velocity and mechanical strength, and on reaction surfaces. The objective of this study is to present a semi-automated toolbox of MATLAB™ scripts, named Grain Boundary Pattern Quantification (GBPaQ), that incorporate different methods for grain boundary pattern quantification for their application to, for example, seismic wave attenuation estimation. GBPaQ uses grain boundary statistics and calculates radial scan line intercepts. In this paper, GBPaQ is tested on two example grain boundary patterns, a granular texture and a foam texture with equant grains, which have been digitally stretched (deformed) to analyse their SPO evolution. The results show that a combination of grain ellipse, grain boundary segment orientation, and grain boundary segment intercept density rose diagrams provide a complete, detailed quantification of grain boundary pattern anisotropy. Grain boundary segment intercept (GBSI) analysis using GBPaQ yields a new grain boundary network parameter – the minimum intensity of grain boundary intercepts (Imin) – which follows a power law relationship with the average axial ratio of grain-fitted ellipses (r) during SPO development. We propose that Imin can be used for the quantitative analysis of SPO strength as a useful tool to assess the deformation history of polycrystalline aggregates. Further studies involving a broader range of different patterns and strain histories are necessary to fully investigate the potential of Imin versus r diagrams.

Original languageEnglish
Article number105311
JournalComputers and Geosciences
Early online date14 Feb 2023
Publication statusPublished - May 2023

Bibliographical note

Funding Information:
The author acknowledges support from an Aberdeen-Curtin Alliance International Postgraduate Scholarship and a Curtin Publication Grant. The author thanks Chris Elders for supervision throughout this project, the PhD thesis examiners Thomas Blenkinsop, Steve Reddy, Mark Jessell, and Ian Alsop for their contributions to this work, the two referees, who gave valuable input for this publication, and Isabel Zutterkirch for helpful discussions. David Healy acknowledges funding from the UKRI NERC grant NE/T007826/1 . Enrique Gomez-Rivas acknowledges the “Ramón y Cajal” fellowship RYC2018-026335-I , funded by the Spanish Ministry of Science and Innovation (MCIN) / State Research Agency of Spain (AEI) / European Regional Development Fund (ERDF) / 10.13039/501100011033 , the DGICYT research project PID2020-585 118999GB-I00 , funded by the Spanish Ministry of Science and Innovation (MCIN) / State Research Agency of Spain (AEI) / 10.13039/501100011033 , and the Grup Consolidat de Recerca “Geologia Sedimentària” ( 2021 SGR-Cat 00349 ), funded by the Catalan Council ..

Publisher Copyright:
© 2023 The Authors

Data Availability Statement

The source code is available on GitHub. A link can be found in the 'Computer code availability' section of the publication.

Computer code availability
Name of code: GBPaQ.

Developer: David Healy, Johanna Heeb, Nicholas E. Timms, Enrique Gómez-Rivas E-Mail:

Year first available: 2021.

Software required: MATLAB 2020

Program language: MATLAB.

Program size: 767 MB.

Source code:


  • GBPaQ toolbox
  • Grain boundary pattern symmetry
  • Intercept-based quantification
  • Shape preferred orientation
  • Strain evolution


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