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Determination of dihedral angle distributions in polycrystals: Application to {itα} + {itβ} brass

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Abstract

A method is described to determine the distribution of dihedral angles of a given type in a polycrystalline aggregate from the measured distribution of angles in random sections. Each of the two angular distributions (2D and 3D) is divided inton classes and the probabilityp ik that a dihedral angle in the 3D classk originates an angle in the 2D classi is calculated. Ann ×n matrixP = (p) is then introduced to relate the two distributions. The 9 × 9 matricesP andP - 1 corresponding to intervals of 20 deg are given in the paper. The method is applied to the determination of the distributions of dihedral angles atααβ andαββ triple lines in aα + β brass, submitted to a long annealing treatment at 620 °C. Using the average angles and the standard deviations of the distributions, the relative values of the interfacial tensionsact, ββ, and αβ were calculated. It was found that γαα ≃γ ββ ≃ 14γαβ.

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Authors and Affiliations

  1. Department of Materials Engineering, Institute Superior Técnico-Universidade Técnica de Lisboa, 1000, Lisboa, Portugal

    M. A. Fortes (Professor and Head of Department) & A. C. Ferro (Assistant)

Authors
  1. M. A. Fortes
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  2. A. C. Ferro
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Fortes, M.A., Ferro, A.C. Determination of dihedral angle distributions in polycrystals: Application to {itα} + {itβ} brass. Metall Trans A 19, 1147–1151 (1988). https://doi.org/10.1007/BF02662574

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  • DOI: https://doi.org/10.1007/BF02662574

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