Grooving of a grain boundary by evaporation–condensation below the roughening transition

The development of surface grooves at grain boundaries that intersect a planar surface is analyzed for the case that the evolution occurs below the thermodynamic roughening transition by evaporation–condensation processes. The dynamics are described by a nonlinear partial differential equation that...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of applied physics 2005-06, Vol.97 (11)
Hauptverfasser: Stone, H. A., Aziz, M. J., Margetis, D.
Format: Artikel
Sprache:eng
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:The development of surface grooves at grain boundaries that intersect a planar surface is analyzed for the case that the evolution occurs below the thermodynamic roughening transition by evaporation–condensation processes. The dynamics are described by a nonlinear partial differential equation that has a similarity solution, so the resulting groove profile is described by a nonlinear ordinary differential equation. An approximate analytical solution to the nonlinear problem is obtained and is in excellent agreement with the numerical solution. The depth and width of the groove varies as t1∕2, where t is time, analogous to the classical results valid above the thermodynamic roughening temperature. In addition, the approximate analytical solution provides an explicit relation between the groove width and the dihedral angle, and is in sufficiently good agreement with the numerical results as to make such numerical solutions unnecessary for this problem. The results demonstrate explicitly how the groove shape depends on the functional form of the slope-dependent surface mobility.
ISSN:0021-8979
1089-7550
DOI:10.1063/1.1922583