Thermal Grooving by Surface Diffusion: a Review of Classical Thermo-Kinetics Approach (original) (raw)
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Journal of Materials Science, 2011
A systematic study based on the self-consistent dynamical simulations is presented for the grain boundary thermal grooving problem by strictly following the irreversible thermodynamic theory of surfaces and interfaces with singularities [T. O. Ogurtani, J. Chem. Phys. 124, 144706 (2006)]. This approach furnishes us to have auto-control on the otherwise free-motion of the grain boundary triple junction without presuming any equilibrium dihedral (wetting) angles at the edges. The effects of physicochemical properties and the anisotropic surface diffusivity on the transient grooving behavior, which takes place at the early stage of the scenario, were considered. We analyzed the experimental thermal grooving data reported for tungsten in the literature, and compared them with the carried simulation results. 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.
Variational analysis of thermal grooving kineically governed by surface diffusion
When grain boundaries intersect an aggregate's surface, grooves form due to minimization of interface energy. This surface evolution can be controlled by different atomistic transport processes (Mullins, 1957, Mullins, 1960). A number of theoretical analyses have extended Mullins' seminal work by considering large slopes (Robertson, 1971), anisotropy of interface energies (Zhang, 2004), tilted grain boundaries (Min, 2006), and multi-component diffusion (Klinger 2002).
Journal of Applied Physics, 2008
The variational extremum method is further extended to give the full coverage for the inclined ͑tilted͒ grain-boundary ͑GB͒ configuration with respect to the sidewalls of a bicrystal thin solid film having strong anisotropic specific surface Gibbs free energy associated with the singular directions ͑faceting͒. A set of critical computer simulation experiments is performed on the asymmetrically disposed ͑inclination͒ bicrystal thin metallic films having four-and sixfold anisotropic specific surface Gibbs free energies to demonstrate the various GB-groove root topologies. Special computer runs are also designed using the realistic structural and physicochemical properties to simulate the thermal grooving profile of polycrystalline alumina ͑Lucalox™͒, and tungsten, which undergone heat treatments for 90 and 120 min at 1650 and 1350°C in air and vacuum ͑10 −4 Pa͒, respectively. The simulation profiles almost perfectly agree with the published experimental atomic force microscopy photographs after linewidth matching procedures, and the simulations produced very accurate mean surface ͑mass͒ diffusivities of alumina and tungsten given by D Al 2 O 3 Х 6.45 ϫ 10 −12 m 2 / s and D W Х 5.2ϫ 10 −13 m 2 / s, respectively. These findings are in good agreement with the diffusivities reported in the literature.
Journal of Applied Physics, 2006
A vertical grain boundary intercepting a horizontal free surface forms a groove to reduce the combined surface energy of the system. The groove grows with time and is commonly used for measuring surface diffusion coefficients. This work studies grooving by capillarity-driven surface diffusion with strong surface energy anisotropy and finds that faceted grooves still grow with time t as t 1/4 . However, an anisotropic groove can be smooth if the groove surface does not cross a facet orientation. The groove has the same shape as the corresponding isotropic groove, but the growth rate is reduced by a factor that depends on the degree of anisotropy. This reduction induces an error in the surface diffusion coefficient if the isotropic model is applied to a smooth, but anisotropic groove. We show how to correct for this error.
Grain-boundary grooving by surface diffusion with strong surface energy anisotropy
Acta Materialia, 2003
A vertical grain boundary intercepting a horizontal free surface forms a groove to reduce the combined surface energy of the system. The groove grows with time and is commonly used for measuring surface diffusion coefficients. This work studies grooving by capillarity-driven surface diffusion with strong surface energy anisotropy and finds that faceted grooves still grow with time t as t 1/4 . However, an anisotropic groove can be smooth if the groove surface does not cross a facet orientation. The groove has the same shape as the corresponding isotropic groove, but the growth rate is reduced by a factor that depends on the degree of anisotropy. This reduction induces an error in the surface diffusion coefficient if the isotropic model is applied to a smooth, but anisotropic groove. We show how to correct for this error.
Grain boundary grooving in thin films revisited: The role of interface diffusion
Acta Materialia, 2014
Thin nickel (Ni) films were grown on c-plane-oriented sapphire substrates by electron-beam deposition. The as-deposited films exhibited a mazed bicrystal microstructure consisting of interwoven grains of two twinned orientations. Annealing of the specimens at 700°C resulted in the thickening of the Ni film. At the same time a mass deficit in the surface regions near grain boundary thermal grooves was observed. The shape of the observed grooves was very different from that predicted by the classical Mullins model. We developed a model of thermal grooving with simultaneous film thickening due to Ni diffusion along the Ni-sapphire interphase boundary, which agreed well with the experimental results. These findings demonstrate that self-diffusion of metal atoms along the metal-ceramic interface plays an important role in mass transport in thin films. Some implications of fast interphase boundary diffusion for the thermal stability of thin films are discussed.
Journal of Applied Physics, 2011
The morphological evolution kinetics of a bicrystal thin film induced by anisotropic surface drift diffusion and driven by the applied electrostatic field is investigated via self consistent dynamical computer simulations. The physico-mathematical model, which is based upon the irreversible thermodynamic treatment of surfaces and interfaces with singularities [T. O. Ogurtani, J. Chem. Phys. 124, 144706 (2006)], provided us with auto-control on the otherwise free-motion of the triple junction at the intersection of the grooving surface and the grain boundary, without having any a priori assumption on the equilibrium dihedral angles. The destruction of the symmetry of the freshly formed grain boundary grooves under the anisotropic surface diffusion driven by the concurrent action of the capillarity and electromigration is observed. After prolonged exposure times the applied electric field above the well defined threshold level modifies Mullins' familiar stationary state time law as, t 1=4 , and causes the premature termination of the groove penetration because of the current crowding at the tips of counteracting grain boundary-grooves initiated on both sides of the test modulus. That finding indicates that the electromigration plays the same role as a healing agent [T. O. Ogurtani, J. Appl. Phys. 106, 053503 (2009)] in arresting the thermal grooving, thereby avoiding the premature interconnect failure as in the case of surface roughening and crack initiation caused by compressive stress gradients. The role of the electromigration and wetting parameter on the ridge/slit formations are thoroughly investigated in this study and the prerequisite conditions are also identified. V
Journal of Crystal Growth, 2009
The variational non-equilibrium thermodynamic method is further extended to give full coverage for the tilted grain-boundary (GB) configuration with respect to the sidewalls of a bicrystal thin solid film having strong anisotropic specific surface Gibbs free energy associated with the singular directions (faceting, vicinal planes). A set of critical computer simulation experiments supported by the generalized longitudinal force diagrams is performed on the asymmetrically disposed (inclination) bicrystal thin metallic films having four-and six-fold anisotropic specific surface Gibbs free energy to demonstrate the various GB-groove root topologies caused by the grain-boundary grooving under the surface drift-diffusion driven by the capillarity forces (thermal grooving). In the computer simulations, the strongly anisotropic surface-specific Gibbs free energy associated with the cusp regions is represented by the modified cycloid-curtate function (MCCF) as a basis (generator) for the Dirac delta distribution function on the Wulff construction, which involves not only the Wulff surface roughness (WSR) parameter (anisotropy constant) but also the Wulff surface topography (WST) index (shape parameter) that may be used as a metric for the temperature roughening phenomenon. A special computer run is also designed using the realistic structural and physicochemical properties in order to simulate the thermal groove profiles of cube-textured pure nickel tape {Ni-99.99 wt%} annealed four hours in vacuum at 800 1C, and observed by the atomic force microcopy (AFM). The experimental line width fitting procedure applied to the simulation profile subjected to the self-similarity transformation, which resulted in almost perfect replication of the experimental digitized AFM photography, has yielded a mean surface (mass) diffusivity of nickel about 5.7 Â 10 À13 m 2 /s (800 1C), which is in excellent quantitative agreement with the diffusivity relationship at TX1300 K reported in the literature on relatively contaminated surfaces, and obtained by high-precision profilometry measurements of the decay of capillary modes associated with the wide surface scratches.