Morphological instability of pores and tubules

Abstract

We present a linear stability analysis of a uniaxially stressed, hollow cylindrical tubule, where the mass transport mechanism is surface diffusion driven by surface curvature-and elastic-energy. We find that there are always two distinct eigenmodes for any choice of wavenumbers, applied stress, and geometry. We also find that applied stress has a destabilizing effect, increasing the range of unstable wavenumbers. For any choice of applied stress and geometry, the most dangerous mode is axisymmetric, and can be either sinuous or varicose depending on choices of geometry and applied stress. The case of a cylindrical pore in a stressed infinite solid emerges as a limiting case.

Morphological instability of two stressed spherical shells

“…Introducing axial and radial sinusoidal fluctuations onto the surface of the cylinder, the conditions of its stability have been characterized (Suo and Wang, 1994;Colin et al, 1997;Wang and Suo, 1997). The case of non-axi-symmetric instability has been also recently investigated (Kirill et al, 1999;Kirill et al, 2002). The analytical study of the linear stability of the surface of solids has been completed by numerical simulations of the evolution of the roughness in the non-linear regime in the case of planar and axi-symmetrical geometries (Chiu and Gao, 1993;Yang and Srolovitz, 1993;Kassner and Misbah, 1994;Spencer and Meiron, 1994;Suo and Wang, 1994;Wang and Suo, 1997).…”

Morphological Instability of a Transversally Isotropic Solid Cylinder Under Stress

“…The time evolution equation by surface diffusion of the lateral surface can be written as [1,5,6,8,17] dr Dy;QfSn " 2 ( , «el (2) with t the time, the surface Laplacian, Ds the surface diffusivity, n the atomic volume, SQ the number of atoms per unit area on the solid surface, k the Boltzmann's constant, and T the absolute temperature. The stress relaxation a,y with respect to the initial stress state < r® .…”

“…The stress relaxation a,y with respect to the initial stress state < r® . before the surface fluctuations develop has been determined to the first order in 5 [2,[4][5][6][7][8], The mean curvature k and the elastic energy density sei = l / 2 (<r?. + er,■,)(<•?.…”

“…Likewise, the effect of stress on the development of nonaxisymmetrical modes leading to helical surfaces has been characterized [6,7]. For pores and tubules, it has been found that the most dangerous modes are the axisymmetrical sinuous or varicose modes, depending on the geometry and applied stress [8]. The effect of surface stress on the surface per turbation evolution by surface diffusion has been also character ized in the case of a misfit-strained cylindrical core-shell nanowire [9], Likewise, the case of a spherical pore in a matrix under stress has been discussed [10-12].…”

Application of Onsager's variational principle to the dynamics of a solid toroidal island on a substrate

“…In addition, solid-state dewetting involves the motion of contact lines. Recently, morphological evolution in three phase systems with contact lines has attracted significant attention in many different research communities, e.g., Rayleigh instability in the presence of substrates [16][17][18][19][20][21], wetting/dewetting in batteries [22,23], heterogeneous nucleation at walls [24,25]. As illustrated in Fig.…”