A tangent-plane marker-particle method for the computation of three-dimensional solid surfaces evolving by surface diffusion on a substrate

We introduce a marker-particle method for the computation of three-dimensional solid surface morphologies evolving by surface diffusion. The method does not use gridding of surfaces or numerical differentiation, and applies to surfaces with finite slopes and overhangs. We demonstrate the method by computing the evolution of perturbed cylindrical wires on a substrate. We show that computed growth rates at early times agree with those predicted by the linear stability analysis. Furthermore, when the marker particles are redistributed periodically to maintain even spacing, the method can follow breakup of the wire.     

Stability of plane-parallel vibrational flow in a two-layer system

The stability of the interface separating two immiscible incompressible fluids of different densities and viscosities is considered in the case of fluids filling a cavity which performs horizontal harmonic oscillations. There exists a simple basic state which corresponds to the unperturbed interface and plane-parallel unsteady counter flows; the properties of this state are examined. A linear stability problem for the interface is formulated and solved for both (a) inviscid and (b) viscous fluids. A transformation is found which reduces the linear stability problem under the inviscid approximation to the Mathieu equation. The parametric resonant regions of instability associated with the intensification of capillary-gravity waves at the interface are examined and the results are compared to those found in the viscous case in a fully numerical investigation.     

Numerical Simulation of Grain-Boundary Grooving by Level Set Method

A numerical investigation of grain-boundary grooving by means of a level set method is carried out. An idealized polycrystalline interconnect which consists of grains separated by parallel grain boundaries aligned normal to the average orientation of the surface is considered. Initially, the surface diffusion is the only physical mechanism assumed. The surface diffusion is driven by surface-curvature gradients, while a fixed surface slope and zero atomic flux are assumed at the groove root. The corresponding mathematical system is an initial boundary value problem for a two-dimensional equation of Hamilton–Jacobi type. The results obtained are in good agreement with both Mullins analytical “small-slope” solution of the linearized problem (W. W. Mullins, 1957, j. Appl. Phys. 28, 333) (for the case of an isolated grain boundary) and with the solution for a periodic array of grain boundaries (S. A. Hackney, 1988, Scripta Metall. 22, 1731). Incorporation of an electric field changes the problem to one of electromigration. Preliminary results of electromigration drift velocity simulations in copper lines are presented and discussed.     

Stability of a fluid interface under tangential vibrations

The stability of the interface between two immiscible fluids of different density which occupy a plane horizontal layer performing harmonic horizontal oscillations is considered. Within the framework of the ideal fluid model a transformation reducing the problem of small plane perturbations to the Mathieu equation is found. Resonance instability domains associated with the formation of capillary-gravitational waves are investigated. A model which takes into account dissipation processes due to the presence of viscous friction is constructed. The role of the viscous dissipation in suppressing resonance instability is discussed. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 25–31, May–June, 1998. The work was carried out with partial support from the Russian Foundation for Basic Research (project No. 95-01-00386).     

Spin dynamics in solid dilute paramagnets

The free-induction decay signals for the two-spin clusters, the “matrix,” and the entire spin system as a whole are calculated for a real dipole-dipole interaction on the basis of a method for the cluster expansion of correlation functions previously developed by the authors. The intracluster interactions, which generate a discrete spectrum, are taken into account exactly, and the interactions outside the clusters are taken into account on the basis of the Anderson-Weiss-Kubo (AWK) theory of phase relaxation. The corresponding shape functions of the resonance line are calculated. Before the clusters are separated, an AWK analysis in the limit of slow fluctuations of the local fields is in satisfactory agreement with the exact results obtained in the Anderson model of dipolar interactions, but a similar analysis for realistic fluctuation rates and Dt?1 leads to a significant qualitative difference: exp(?Dt) transforms into $\exp ( - \sqrt {D_1 t} )$ . After the clusters are separated, this difference is obliterated. The free-induction decay is almost exponential up to Dt～10, and nonexponential behavior of the long-time asymptote appears sooner. This finding is not altered significantly when the analysis is complicated by raising the maximum rank of the clusters to 3 or more.