An improved model of break-up of dislocation dipoles into loops: Application to sapphire (α-Al2O3)

doi:10.1016/0001-6160(82)90229-2

Acta Metallurgica

Volume 30, Issue 2, February 1982, Pages 491-498

https://doi.org/10.1016/0001-6160(82)90229-2 Get rights and content

Abstract

Edge dislocation dipoles formed during basal glide in sapphire break up into loops by a series of processes involving self-climb. The energetics of the break-up are analysed by approximating fluctuations in dipole width as piece-wise straight dislocation segments and by determining the changes in interaction energy and self energy. Small amplitude fluctuations are energetically favorable only if the wavelength. λ, is much greater than the dipole width, a. This implies that nucleation must occur at dipole ends or by the accumulation of pre-existing jogs. Large amplitude fluctuations leading to loop formation are found to be energetically favorable only if λ > 3.7a. The kinetics of dipole break-up are also considered and the dominant wavelength is shown to be ~ 5.4a, in approximate agreement with experiment.

Résumé

Les dipôles de dislocation coins formés au cours du glissement basai dans le saphir se divisent en boucles par l'intermédiaire d'une série de mécanismes mettant en jeu l'auto-montée. Nous avons analysé l'énergie de cette division en approximant les fluctuations de la largeur du dipôle par des segments de dislocation rectilignes et en déterminant les variations d'énergie d'intéraction et d'énergie propre. Les fluctuations de faible amplitude ne sont énergétiquement favorables que si la longueur d'onde λ est nettement plus grande que la largeur a du dipôle. Ceci implique que la germination doit se produire aux extrémités du dipôle ou par l'accumulation de crans préexistants. Les fluctuations de grande amplitude conduisant à la formation de boucles ne sont énergétiquement favorables que si λ > 3,7 a. Nous étudions aussi la cinétique de la division des dipôles et nous montrons que la longueur d'onde dominante est ~ 5,4 a, en assez bon accord avec les résultats expérimentaux.

Zusammenfassung

Stufenversetzungsdipole, die in Saphir während der Basisgleitung gebildet werden, können sich mit mehreren Schritten in Reihen von Versetzungsringen umwandeln. Die energetischen Aspekte dieses ‘Aufbrechens’ werden hier analysiert, indem die Fluktuationen in der Dipolweite mit stückweise geraden Versetzungssegmenten angenähert und die Änderung in Selbst- und Wechselwirkungsenergie bestimmt werden. Kleine Amplitudenfluktuationen sind energetisch nur begünstigt, wenn die Wellenlänge λ viel gröβer ist als die Dipolweite a. Das heiβt, daβ die Keimbildung an Dipolenden oder durch Zusammenlagerung vorhandener Versetzungssprünge beginnen muβ. Groβe zum Dipolaufbrechen führende Amplitudenfluktuationen sind energetisch nur begünstigt, wenn λ > 3,7a ist. Die Kinetik des Dipolaufbrechens wird ebenso untersucht. Es wird gezeigt, daβ in diesem Fall die dominierende Wellenlänge ~5,4a ist. Dieses Ergebnis stimmt näherungsweise mit dem Experiment überein.

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^†: Present address: Department of Metallurgy and Mining Engineering University of Illinois, Urbana, IL 61820 U.S.A.

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An improved model of break-up of dislocation dipoles into loops: Application to sapphire (α-Al2O3)

Abstract

Résumé

Zusammenfassung

Acta metall.

Acta metall.

Acta metall.

J. Am. Ceram. Soc.

J. appl. Phys.

An improved model of break-up of dislocation dipoles into loops: Application to sapphire (α-Al₂O₃)