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
В работе подробно рассмотрены проблемы использования критерия инкубационного времени в качестве критерия хрупкого разрушения в конечно-элементных расчетах. Приведен ряд примеров численных расчетов задач динамики разрушения с использованием критерия инкубационного времени. Доказана применимость такого подхода для предсказания инициации, развития и остановки динамического разрушения.
In this article, we report on the theoretical analysis of transmission electron microscopy (TEM) images of surface InSb quantum dots (QDs) coherently grown on InAs substrate. A finite element method (FEM) is used to calculate elastic fields and total displacements in a QD and an adjusted region of the substrate. The effects of QD form factor and QD aspect ratio δ on displacements and TEM images are analyzed. A quasilinear dependence of radial displacements on radial coordinate for spherical, elliptical, and truncated spherical QDs is demonstrated. It has been found that the displacement field does not depend on the shape and aspect ratio for QDs with δ > δc1, and the upper part of a QD remains practically undistorted for QDs with δ ≥ δc2. For InSb/InAs heterosystem these critical values are δc1 ≈ 0.13 and δc2 ≈ 0.33. The total displacements are used for computation of TEM diffraction contrast associated with QDs. To achieve this the Howie–Whelan dynamic approach is utilized. Calculated TEM images of heavily strained QDs demonstrate the picture of pseudo‐moiré with a strong dependence of moiré‐like fringe distance Δ on aspect ratio δ. This dependence gives the possibility to determine the aspect ratio and height of QDs from the results of TEM experiments.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.