Grain boundary grooving in bi-crystal thin films induced by surface drift-diffusion driven by capillary forces and applied uniaxial tensile stresses

Abstract

Grain boundary (GB) grooving, induced by surface drift-diffusion and driven by the combined actions of capillary forces and applied uniaxial tensile stresses, is investigated in bi-crystal thin films using self-consistent dynamical computer simulations. A physico-mathematical model, based on the irreversible thermodynamics treatment of surfaces and interfaces with singularities allowed auto-control of the otherwise free-motion of the triple junction at the intersection of the grooving surface and the GB, without having any a priori assumption on the equilibrium dihedral angles. In the present theory, the generalised driving forces for stress-induced surface drift-diffusion arise not only from the usual elastic strain energy density (ESED), but also much stronger elastic dipole tensor interactions (EDTI) between the applied stress field and the mobile atomic species situated at the surface layer and in the GB regions. Accelerated groove-deepening kinetics shows that the surface drift-diffusion enhanced by the applied uniaxial tensile stresses through EDTI is dominant over the GB flux leakage at the triple junction. At high uniaxial stress levels (≥500 MPa for a 100-nm thick copper film), a sequential time-frame for micro-crack nucleation and growth is recorded just before specimen failure took place. These non-equilibrium thermokinetics discoveries (kinetics and energetics) contradict or at least do not support the hypothesis of the steady-state diffusive GB micro-crack formation and propagation due to ‘constant’ flux drainage through GB enhanced by tensile stresses acting normal to it.

Keywords:

• surfaces
• grain boundary interfaces
• non-equilibrium phenomena
• numerical modelling
• thin-film mechanics
• diffusion
• surface thermodynamics
• shape evolution

Acknowledgements

The authors wish to thank Professors William D. Nix of Stanford University, Macit Özenbaş of METU and Salim Çıracı of Bilkent University for their encouraging interest in the initiation of this extensive research program at METU. This work was partially supported by the Turkish Scientific and Technological Research Council, TUBITAK, through a research Grant No. 107M011.