Mesoscopic nonequilibrium thermodynamics treatment of the grain boundary thermal grooving induced by the anisotropic surface drift diffusion

Akyıldız, Öncü; Ören, Ersin Emre; Oǧurtani, Tarik Ömer

doi:10.1007/s10853-011-5567-8

Cited by 6 publications

(6 citation statements)

References 34 publications

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“…This linear regime assumes a Hull-Rimmer-type growth rate proportional to the applied stress, app , at low stress intensities, but shows a nonlinear stress dependence for high stress levels, where the growth rate becomes proportional to app 1/2 . (2) The stress-affected rupture times compared to thermal grooving, which was also studied very recently using a similar set up as given here [38], show that there are drastic reductions by factors of about 25 and 900 for those test modules subjected to the uniaxial tensile stresses in the range 10 MPa and 1.5 GPa, respectively. Philosophical Magazine 825 tip stress is monitored at each time-step, and the nose-like diffusive microcrack formation is detected at the groove tip for high stresses just before the failure of the test module.…”

Section: Discussionsupporting

confidence: 54%

“…(8) On the other hand, as expected a priori the situation is completely different in the short-living transient regime and is rather stretched in the transition stage, where the time exponent depends on applied uniaxial tensile stresses. The transition regime, which has a rather long lifetime, sufficient to be observed experimentally [54], in general appears to be important in interpreting experimental results, as clearly demonstrated by Akyildiz et al [38] for thermal grain boundary grooving data reported for tungsten [54], especially with low triple junctions mobilities, where the metastable stationary or the linear time-dependent regime is hardly achieved.…”

Section: Discussionmentioning

confidence: 60%

“…The elastic dipole tensor interaction parameter is taken as Figure 2b shows that the final normalised rupture time for the film agglomeration eventually reduces to " t f ¼ 1.1 compared to that of thermal grooving experiment [38] " t f ¼ 27.5 presented in Figure 3. This indicates that the applied uniaxial tensile stress drastically increases the rate of groove deepening and, thereby, reduces the rupture time by a factor of 25, which is much higher than that suggested by Genin et al [9], who reported that the groove is 1.5 times as deep as it would have been with capillarity alone.…”

Section: Resultsmentioning

confidence: 99%

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

Akyıldız¹,

Ören²,

Oǧurtani³

2012

Philosophical Magazine

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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.

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Section: Discussionsupporting

confidence: 54%

Section: Discussionmentioning

confidence: 60%

Section: Resultsmentioning

confidence: 99%

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

Akyıldız¹,

Ören²,

Oǧurtani³

2012

Philosophical Magazine

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“…Previously, asymmetric formations at the grain boundaries due to anisotropic diffusivity and/or surface energy in the form of facets or slits were reported [24][25][26][27][28]. The simulation results presented here showed that the asymmetry in driving force for surface diffusion with respect to a grain boundary due to external loadings might also cause an asymmetric groove profile evolution.…”

Section: Resultsmentioning

confidence: 48%

Influence of displacement constraints to the surface reconstruction of stressed bicrystal thin films

Akyıldız

2020

Mater. Res. Express

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In this work, surface morphology evolution of bicrystal thin films under the combined action of grain boundary and surface diffusion is investigated by considering different mechanical constraints. 2D surface topographies of thin films, that are (a) freestanding, (b) strongly bonded to its substrate and (c) strongly bonded to its substrate and one of sidewalls, are simulated using a numerical implementation of an irreversible thermo-kinetics model. Relationships which give the groove depth as a function of time are obtained. Results show that mechanical loading conditions are effective in determining the morphology and kinetics of grooving. For the three scenarios that had been investigated, it was found that the groove depth evolves linearly with different tip velocities under the same level of uniaxial tension. In freestanding films groove tip evolves faster; i.e. as the film gets constrained from its substrate and/or one of its sidewalls, the tip velocity slows down. It was also observed that high triple junction mobilities at low levels of applied stress hinder the effects of displacement constraints to groove shape, even in the case of asymmetric stress distributions inside the film. On the other hand, low triple junction mobilities at moderate applied stresses allow formation of asymmetric grain boundary grooves due to the induced asymmetry in the driving force for surface diffusion with respect to the grain boundary.

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“…Growth exponents for depth values as high as 0.4 are possible in this model, whereas Mullins' model predicts an exponent of 0.25 for both the width and depth of the groove. Later Akyildiz et al [26], analyzed the experimental thermal grooving data reported by these authors, and compared them with their simulation results based on a mesoscopic nonequilibrium thermodynamics treatment. This investigation showed that the observed changes in the dihedral angles are strictly connected to the transient behavior of the simulated global system, and manifest themselves at the early stage of the thermal grooving phenomenon, which is completely overlooked by Mullins' based approach.…”

Section: Surface Energy Anisotropymentioning

confidence: 99%

Thermal Grooving by Surface Diffusion: a Review of Classical Thermo-Kinetics Approach

Akyıldız

Oǧurtani

2017

Hittite J. Sci. Eng.

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P olycrystalline materials are composed of tiny perfect crystalline regions (grains) in between internal interfaces called grain boundaries. Grain boundaries and the external interfaces (i.e. free surfaces which separate the material from the environment) determine the morphology of the material at a major extent. A material may change its morphology through interface motion if a driving force exists. An important special case, which is the focus of this review, is the grain boundary grooving. Wherever a grain boundary intersects a free surface and whenever the topographic variation associated with the atomic motion is favored by total free energy dissipation, the surface grooves. Grooving can occur via several mass transport mechanisms, such as surface diffusion, bulk diffusion, and evaporation and condensation. Surface diffusion dominates for temperatures far below the melting temperature, and for grooves less than 10 micron in size [1]. If the surface evolution is driven solely by the total excess free energies associated with the interfaces the resulting force for motion is conventionally called a capillary force,

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Mesoscopic nonequilibrium thermodynamics treatment of the grain boundary thermal grooving induced by the anisotropic surface drift diffusion

Cited by 6 publications

References 34 publications

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

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

Influence of displacement constraints to the surface reconstruction of stressed bicrystal thin films

Thermal Grooving by Surface Diffusion: a Review of Classical Thermo-Kinetics Approach

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