INTERFACE SCIENCE 9, 93–104, 2001 c  2001 Kluwer Academic Publishers. Manufactured in The Netherlands. Stress-Assisted Reaction at a Solid-Fluid Interface J. LIANG AND Z. SUO Mechanical Engineering Department and Princeton Materials Institute, Princeton University, Princeton, NJ 08544, USA suo@princeton.edu Abstract. On the interface between a solid and a fluid, a reaction can occur in which atoms either leave the solid to join the fluid, or leave the fluid to join the solid. If the solid is in addition subject to a mechanical load, two outcomes may be expected. The reaction may proceed uniformly, so that the interface remains flat as the solid recedes or extends. Alternatively, the reaction may cause the interface to roughen and develop sharp cracks, leading to fracture. This paper reviews the current understanding of the subject. The solid-fluid is a thermodynamic system: the solid is in elastic equilibrium with the mechanical load, but not in chemical equilibrium with the fluid. Thermodynamic forces that drive the interfacial reaction include chemical energy difference between the solid and the fluid, elastic energy stored in the solid, and interfacial energy. The reaction is taken to be thermally activated. A kinetic law is adopted in which the stress affects both the activation energy and the driving force of the interface reaction. A linear perturbation analysis identifies the stability condition, which differs substantially from the well known stability condition based on the driving force alone. Large perturbations are examined by assuming that the interface varies as a family of cycloids, from slight waviness to sharp cracks. An analytic elasticity solution is used to compute the stress field in the solid, and a variational method to evolve the shape of the interface. Keywords: interface reaction, interface instability, stress effect, elasticity, kinetics 1. Introduction The question of surface instability of stressed solids arises in many technical situations, including growth of thin films, delayed fracture of optical fibers, and etch- ing of microelectromechanical components. In such a situation, a solid is immersed in a fluid (gas or liq- uid). On the interface between the solid and the fluid, a reaction occurs in which the solid recedes by losing mass to the fluid. If the fluid contains the components of the solid, the solid can also extend by gaining mass from the liquid. For example, when the solid extends by gaining atoms from its own vapor in the surrounding, atoms must diffuse in the vapor, react on the interface, and become part of the solid structure. Either diffusion in the vapor or reaction on the interface may be the rate-limiting step. In this paper, the reaction on the in- terface is taken to be the rate-limiting step. The solid may grow facets when the reaction is anisotropic, or grow pits when the interface is inhomogeneous. These effects are assumed to be negligible in the system to be considered. Ideal examples include pure silica glass and amorphous metals. Mullins [1] considered such an idealized solid, un- der no mechanical load, in contact with its own vapor. The pressure of the vapor is held in equilibrium with the solid when the interface is flat. If the interface is perturbed into a sinusoidal shape, the system deviates from equilibrium: the interfacial energy causes evap- oration at crests, and condensation at troughs. Over time the perturbation amplitude decays, and the inter- face becomes flat. One can also consider a vapor not in equilibrium with the flat solid. Say the pressure of the vapor is held far below the equilibrium value, and the solid evaporates on the entire interface. For a wavy interface, the interfacial energy biases the evaporation rate, so that the solid evaporates faster at crests than at troughs. Over time the perturbation amplitude decays,