A thin gold film under annealing on a silica substrate can develop “fingers” at the perimeter of the film. The perimeter retracts to leave behind longer fingers, which eventually pinch off to reduce the surface energy of the system. New fingers then form at the film edge and the process continues until the entire film disintegrates. To maintain the structure integrity of annealed thin films, this fingering instability must be understood. The retraction of a straight film edge via capillarity-driven surface diffusion has been analyzed in two dimensions by Wong et al.[Acta Mater. 48, 1719 (2000)]. They found that a retracting film is thickened at the edge followed by a valley before the film thickness becomes uniform. We study the three-dimensional linear stability of this two-dimensional film profile and find one unstable mode of perturbation. The growth rate of the perturbation is determined as a function of the wavelength of the perturbation and the speed of the receding edge. The results show that a str...

Fingering instability of a retracting solid film edge

Grain-boundary grooving by surface diffusion with strong surface energy anisotropy

Pure forsterite bicrystals were produced by direct bonding of highly polished single crystal plates. We fabricated a series of synthetic grain boundaries with tilt axis a and tilt angles ranging from 9.9 to 21.5°. Transmission Electron Microscope (TEM) investigations show low-angle grain boundaries with arrays of c-dislocations for all misorientations with tilt angles up to 21.5°. Low-angle grain boundary structures were fully developed at annealing temperatures <400°C and no structural changes were observed in the grain boundary region after further annealing at 1650°C.

Synthetic [100] tilt grain boundaries in forsterite: 9.9 to 21.5°

We study the coupled surface and grain boundary motion in bi- and tricrystals in three-space dimensions, building on previous work by the authors on the simplified two-dimensional case. The motion of the interfaces, which in this paper are presented by two-dimensional hypersurfaces, is described by two types of normal velocities: motion by mean curvature and motion by surface diffusion. Three hypersurfaces meet at triple-junction lines, where junction conditions need to hold. Similarly, boundary conditions are prescribed where an interface meets an external boundary, and these conditions naturally give rise to contact angles. We present a variational formulation of the flows, which leads to a fully practical finite-element approximation that exhibits excellent mesh properties, with no mesh smoothing or remeshing required in practice. For the introduced parametric finite-element approximation we show well posedness and, in general, unconditional stability, i.e. there is no restriction on the chosen time-step size. Moreover, the induced discrete equations are linear and easy to solve. A generalisation to anisotropic surface energies is straightforward. Several numerical results in two- and three-space dimensions are presented, including simulations for thermal grooving and sintering. Three-dimensional simulations featuring quadruple junction points, non-standard boundary contact angles and fully anisotropic surface energies are also presented.

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Finite Element Approximation of Coupled Surface and Grain Boundary Motion with Applications to Thermal Grooving and Sintering

Grain-boundary migration controls grain growth, which is important in material processing and synthesis. When a vertical grain boundary ends at a horizontal free surface, a groove forms at the tip to reduce the combined grain-boundary and surface energies. The groove affects the migration of the grain boundary, and its effect must be understood. This work studies grain-boundary grooving by capillarity-driven surface diffusion with asymmetric and strongly anisotropic surface energies. The surface energies are described by the delta-function facet model that holds for temperatures above the roughening temperature of the bicrystal. Since the asymmetric anisotropy does not introduce a length scale, the asymmetric groove still grows with time t as t1∕4. Thus, the nonlinear partial differential equation that governs grooving is reduced by a self-similar transformation to an ordinary differential equation, which is then solved numerically by shooting methods. We vary systematically the crystallographic orientations of the bicrystal and the normalized grain-boundary energy. We find that the self-similar groove profile is faceted and asymmetric for most bicrystals. However, a few asymmetric bicrystals can also yield smooth and symmetric grooves. Some bicrystals may even form ridges instead of grooves. We also find that the asymmetric surface energies tilt the grain-boundary tip sideways, which induces the grain boundary to migrate. We show that anisotropic groove profiles measured in SrTiO3 and Ni can be well fitted by our model.

Grain-boundary grooving by surface diffusion with asymmetric and strongly anisotropic surface energies

Coupled grooving and migration of inclined grain boundaries: Regime II

Self-similar growth of a compound layer in thin-film binary diffusion couples

The diffusion controlled growth of a compound phase AnB between two thin films of material A and B is studied with the nonlinear Kirkendall effect included. This growth process is important in electronic materials processing and in synthesis of high-temperature materials using multilayer films. Previous models of the growth rate do not solve the diffusion equation, and thus do not fully utilize the predictive capability. This paper describes a self-similar transformation that reduces the nonlinear, time-dependent diffusion equation with two free boundaries into a nonlinear ordinary differential equation, which is solved numerically by a shooting method. It is found that the intrinsic diffusion coefficients of A and B in AnB can be determined from the positions of the interfaces without using the concentration profile. This provides a simpler method for measuring intrinsic diffusion coefficients. An asymptotic solution valid for small concentration gradients is derived and agrees with the numerical results.

The techniques of enhancing tubeside heat transfer have been studied extensively. However, the reports of research concerned with the combination of two different techniques, termed compound enhancement are very limited in the literature. In this paper, the experimental results of compound enhancement of tubeside heat transfer with combination of spirally corrugated tubes and twisted-tape inserts are presented. The test facility for the experiments and the experimental method are described. The experiments are conducted for the spirally corrugated tubes and the twisted-tape inserts respectively, and for the combination of spirally corrugated tubes with the twisted-tape inserts. Experiments are performed with air in the fully developmental turbulent region (Re&#61;10<sup>4</sup>-10<sup>5</sup>). Large volumes of experimental data are presented in the paper. Empirical correlations are developed in the form of convenient use for heat exchanger application. Performance evaluation are given for spirally corrugated tubes and twisted-tape inserts, and for the combination of spirally corrugated tubes with twisted-tape inserts. 

An experimental study on the compound enhancement of tubeside heat transfer with air flow

The diffusion controlled growth of a compound phase AnB between two thin films of material A and B is studied with the nonlinear Kirkendall effect included. Previous models of the growth rate do not solve the diffusion equation, and thus do not fully utilize the predictive capability. This paper describes a self-similar transformation that reduces the nonlinear, time-dependent diffusion equation with two free boundaries into a nonlinear ordinary differential equation, which is solved numerically by a shooting method. It is found that the intrinsic diffusion coefficients of A and B in AnB can be determined from the positions of the interfaces without using the concentration profile. This provides a simpler method for measuring intrinsic diffusion coefficients.

Huifang Zhang

Papers

Coupled grooving and migration of inclined grain boundaries: Regime II

Self-similar growth of a compound layer in thin-film binary diffusion couples

Self-similar growth of a compound layer in thin-film binary diffusion couples

An experimental study on the compound enhancement of tubeside heat transfer with air flow

A Self-Similar Solution for the Growth Rate of a Compound Layer in Thin-Film Binary Diffusion Couples