Grain boundary grooving by surface diffusion: an analytic nonlinear model for a symmetric groove

1995 ◽  
Vol 450 (1940) ◽  
pp. 569-587 ◽  
Keyword(s):  
Grain Boundary ◽  
Surface Diffusion ◽  
Nonlinear Evolution Equation ◽  
Nonlinear Boundary ◽  
Nonlinear Evolution ◽  
Surface Profile ◽  
Boundary Groove ◽  
Constant Slope ◽  
Limiting Case ◽  
Integrable Nonlinear Evolution Equation

The fourth-order nonlinear boundary-value problem for the evolution of a single symmetric grain-boundary groove by surface diffusion is modelled analytically. A solution is achieved by partitioning the surface into subintervals delimited by lines of constant slope. Within each subinterval, the advance of the surface is described by an integrable nonlinear evolution equation. The model is capable of incorporating the actual nonlinearity arbitrarily closely. The surface profile is determined for various values of the central groove slope including the limiting case of a groove which has a root that is vertical. Such a solution exists only because of the nonlinearity.

The Effect of Grain Boundaries on Surface Diffusion Mediated-Planarization of Polycrystalline Cu Films

1995 ◽  
Vol 389 ◽  
Author(s):  
R.A. Brain ◽  
D.S. Gardner ◽  
D.B. Fraser ◽  
H.A. Atwater
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Surface Diffusion ◽  
Cross Sections ◽  
Boundary Surface ◽  
Surface Profile ◽  
Transmission Electron Micrograph ◽  
Cu Films ◽  
Transmission Electron

ABSTRACTIn situ, ultrahigh vacuum anneals were performed to induce Cu reflow at 500°C following deposition of Cu films and a Ta barrier layer on 1 μm wide by 1 μm deep trenches. Transmission electron micrograph cross-sections show profiles which suggest that grain boundaries and surface energy anisotropy significantly affect reflow. The extent of reflow is dependent on the structure of grain boundary-surface intersections, and the surface profile consists of regions of low curvature within grains and with sharp discontinuities in curvature at grain boundaries, a structure that inhibits surface diffusion. We present results showing how the surface diffusion mediated reflow varies with grain boundary groove angle and position, and compare these results with finite-element simulations that model surface diffusion-driven reflow.

Grain boundary grooving by surface diffusion in SrTiO3 bicrystal

1999 ◽  
Vol 14 (6) ◽  
pp. 2548-2553 ◽  
Author(s):  
Minxian Jin ◽  
Eriko Shimada ◽  
Yasuro Ikuma
Keyword(s):  
Diffusion Coefficient ◽  
Grain Boundary ◽  
Surface Diffusion ◽  
Diffusion Coefficients ◽  
Present Experiment ◽  
Titanium Atom ◽  
Boundary Groove ◽  
Surface Diffusion Coefficient ◽  
Atomic Force ◽  
Different Temperatures

High-purity SrTiO3 bicrystal sample (the angle between two [001] directions is 24°) was used in the present experiment to develop a thermal grain boundary groove along the bicrystal grain boundary at different temperatures (1150–1400 °C) and times (15–6720 min) in air. An atomic force microscope (AFM) was used to observe the surface morphological change in the annealed bicrystal sample in order to measure the width W and depth h of the developed grain boundary groove. It was found that the log W–log t (at 1150–1400 °C) and the log h°log t (at 1400 °C) relationships are approximately linear, having slopes of approximately 1/4. Using Mullins' formulas, the surface diffusion coefficients of SrTiO3 at different temperatures were calculated. Finally, the surface diffusion coefficient determined in the present experiment appears to correspond to the titanium atom, which has the lowest diffusivity in SrTiO3.

scholarly journals Hydrodynamic scaling limit of continuum solid-on-solid model

2006 ◽  
Vol 2006 ◽  
pp. 1-37 ◽  
Author(s):  
Anamaria Savu
Keyword(s):  
Surface Diffusion ◽  
Nonlinear Evolution Equation ◽  
Nearest Neighbor ◽  
Complex Dynamics ◽  
Nonlinear Evolution ◽  
Scaling Limit ◽  
Solid Model ◽  
Neighbor Interaction ◽  
Hydrodynamic Scaling ◽  
The Continuum

A fourth-order nonlinear evolution equation is derived from a microscopic model for surface diffusion, namely, the continuum solid-on-solid model. We use the method developed by Varadhan for the computation of the hydrodynamic scaling limit of nongradient models. What distinguishes our model from other models discussed so far is the presence of two conservation laws for the dynamics in a nonperiodic box and the complex dynamics that is not nearest-neighbor interaction. Along the way, a few steps have to be adapted to our new context. As a byproduct of our main result, we also derive the hydrodynamic scaling limit of a perturbation of the continuum solid-on-solid model, a model that incorporates both surface diffusion and surface electromigration.

scholarly journals SHAPE OF GRAIN BOUNDARY GROOVE ONPURE ICE SURFACE

Anales AFA ◽  
2021 ◽  
Vol 31 (4) ◽  
pp. 112-116
Author(s):  
C. L. Di Prinzio ◽  
◽  
D. Stoler ◽  
P. I. Achával ◽  
G. Aguirre Varela ◽  
...  
Keyword(s):  
Free Surface ◽  
Grain Boundary ◽  
Surface Diffusion ◽  
Boundary Groove ◽  
Gaseous Diffusion ◽  
Dry Air ◽  
Ice Surface ◽  
Regular Time ◽  
Matter Transport ◽  
Time Periods

In this work we studied the evolution of the groove that forms the grain boundary (BG) when it emerges to a free surface, in the presence of different processes of matter transport. By using a confocal microscope, the shape of the grain edge groove was obtained in an ice sample with orientation< 1010 >/50◦ at −5◦C ; after keeping it 3 h in an environment with dry air. The shapes and depths of the grain boundary groove obtained experimentally, at regular time periods, were satisfactorily fitted considering a process of transport of matter developed by Srinivasan and Trivedi. In this model the transport of matter is mainly ruled by gaseous diffusion and not by surface diffusion.

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