Abstract. We consider a stress-assist chemical reaction front propagation implying the reaction like silicon oxidation. We assume that the chemical reaction is localized at the reaction front that divides two solid constituents. The reaction is sustained and controlled by the diffusion of the gas constituent through the oxide. We determine a transformation strain tensor produced by the chemical reaction in dependence on the reaction parameters. Then we derive an expression of the entropy production due to the reaction front propagation and, as a result, obtain the formula of the chemical affinity tensor. The normal component of the chemical affinity tensor acts as a configurational force that drives the propagating reaction front. Then we introduce the notion of the equilibrium gas constituent concentration as the concentration at which the chemical affinity is zero. We formulate a kinetic relationship for the reaction front velocity in terms of current gas concentration at the reaction front and the equilibrium concentration that depends on stresses at the front. We obtain analytical solutions of simplest axially symmetric problems of mechanochemistry considering chemical reactions around a hole as a simplest stress concentrator and the oxidation of a cylinder. We demonstrate the reaction locking effects due to internal stresses and examine how stress state affects the reaction front kinetics. IntroductionThe influence of mechanical loading on chemical reaction kinetics remains to be of significant interest for both fundamental and applied engineering science. Chemo-mechanical problems have received a new attention in recent years due to miniaturization of structure elements. For example, fracture processes in micron-scale parts of MEMS made of polycrystalline silicon thin films involve sequential oxidation of polysilicon and environmentally-assisted crack growth inside an oxide layer. In turn, the kinetics of the oxide growth is determined by mechanical stresses produced by the crack. The catastrophic failure happens when the crack reaches the reaction front. Thus, major events which determine the life time of MEMS are related with coupling between stresses and chemical reactions (see details in [1,2]). Reactions similar to the silicon oxidation also take place in the process of metal hydride formation used in hydrogen storage applications (see e.g. [3]). Many models of silicon oxidation arise to pioneering papers by Deal and Grove [4], see for example a recent paper [3]. However neither external loading nor internal stresses were taken into account in these works. One of the first attempts to obtain an expression of the chemical potential in a multicomponent solid under stress was made by Larche and Cahn [5][6][7][8]. They considered diffusing solids and showed that the chemical potential depends on the trace of the stress tensor. This result was further developed in
We consider a stress-assist chemical reaction front propagation in a deformable solid undergoing a localized chemical reaction between solid and gas constituents. The reaction is sustained by the diffusion of the gas constituent through the transformed solid material. We introduce a chemical transformations strain tensor that relates two reference configurations of solid constituents. Then mass, momentum and energy balances are written down for the open system considered and the expression of the entropy production due to the reaction front propagation in a solid with arbitrary constitutive equations is derived. As a result, the expression of the chemical affinity tensor is obtained. Kinetic equation for the chemical reactions front propagation is formulated in a form of the dependence of the front velocity on normal components of the chemical affinity tensor. The locking effect — blocking the reaction by stresses is demonstrated. Finally the kinetic equation for the bulk chemical reaction is derived in a form of the dependence of the reaction rate on the first invariant of the chemical affinity tensor.
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