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On Kinetics of Chemical Reaction Fronts in Elastic Solids

Part of the Advanced Structured Materials book series (STRUCTMAT,volume 30)

Abstract

A chemical reaction front where an oxidation reaction is localized is considered as an internal surface dividing two solid deformable constituents. The reaction is sustained and controlled by the diffusion of the gas constituent through the oxide layer. The transformation strains produced by the chemical reaction lead to internal stresses which in turn affect the chemical reactions front kinetics. Analitical solution of axially-symmetric mechano-chemistry problems in a case of small strain approach are obtained. We examine how stress state affects the reaction front kinetics and demonstrate reaction locking effects due to internal stresses. We also study how the reaction rate depends on the chemical reaction front curvature.

Keywords

  • Reaction Front
  • Cylindrical Hole
  • Oxide Layer Thickness
  • Solid Constituent
  • Critical Layer Thickness

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Deal, E., Grove, A.S.: General relationship for the thermal oxidation of silicon. J. Appl. Phys. 36, 3770–3778 (1965)

    CrossRef  CAS  Google Scholar 

  2. Epstein, M., Maugin, G.A.: Thermomechanics of volumetric growth in uniform bodies. Int. J. Plast. 16, 951–978 (2000)

    CrossRef  Google Scholar 

  3. Freidin, A.B.: On chemical reaction fronts in nonlinear elastic solids. In: Indeitsev, D.A., Krivtsov, A.M. (eds.) Proceedings of XXXVI International Summer School-Conference APM’ 2009, pp. 231–237. Institute for problems in, mechanical Engineering, St.Petersburg (2009)

    Google Scholar 

  4. Glansdorff, P., Prigogine, I.: Thermodynamic theory of structure, stability and fluctuations. Wiley, New York (1971)

    Google Scholar 

  5. Guillou, A., Ogden, R.W.: Growth in soft biological tissue and residual stress development. In: Holzapfel, G.A., Ogden, R.W. (eds.) Mechanics of Biological Tissue. Springer, Heidelberg (2006)

    Google Scholar 

  6. Gusev, E., Lu, H., Gustafsson, T., Garfunkel, E.: Growth mechanism of thin silicon oxide films on \(Si(100)\) studied by medium-energy ion scattering. Phys. Rev. B52, 1759–1775 (1995)

    Google Scholar 

  7. Kelly, S.T., Clemens, B.M.: Moving interface hydride formation in multilayered metal thin films. J. Appl. Phys. 108(1), 013521 (2010)

    CrossRef  Google Scholar 

  8. Kikkinides, E.S.: Design and optimization of hydrogen storage units using advanced solid materials: General mathematical framework and recent developments. Comput. Chem. Eng. 35, 1923–1936 (2011)

    CrossRef  CAS  Google Scholar 

  9. Klisch, S.M., VanDyke, T.J.: A theory of volumetric growth for compressible elastic biological materials. Math. Mech. Solids 6, 551–575 (2001)

    CrossRef  Google Scholar 

  10. Knowles, J.K.: On the dissipation associated with equilibrium shocks in finite elasticity. J. Elast. 9, 131–158 (1979)

    CrossRef  Google Scholar 

  11. Larche, F., Cahn, J.W.: A linear theory of thermochemical equilibrium of solids under stress. Acta Metall. 21, 1051–1063 (1973)

    CrossRef  CAS  Google Scholar 

  12. Larche, F., Cahn, J.W.: A nonlinear theory of thermochemical equilibrium of solids under stress. Acta Metall. 26, 53–60 (1978)

    CrossRef  CAS  Google Scholar 

  13. Larche, F., Cahn, J.W.: Thermochemical equilibrium of multiphase solids under stress. Acta Metall. 26, 1579–1589 (1978)

    CrossRef  CAS  Google Scholar 

  14. Larche, F., Cahn, J.W.: The effect of self-stress on diffusion in solids. Acta Metall. 30, 1835–1845 (1982)

    CrossRef  Google Scholar 

  15. Lee, E.H.: Elastic-plastic deformation at finite strains. ASME J. Appl. Mech. 36, 1–8 (1969)

    CrossRef  Google Scholar 

  16. Lubarda, V.A.: Constitutive theories based on the multiplicative decomposition of deformation gradient: Thermoelasticity, elastoplasticity, and biomechanics. Appl. Mech. Rev. 57(2), 95–108 (2004)

    CrossRef  Google Scholar 

  17. Muhlstein, C.L., Stach, E.A., Ritchie, R.O.: A reaction-layer mechanism for the delayed failure of micron-scale polycrystalline silicon structural films subjected to high-cycle fatigue loading. J. Acta Mater. 50, 3579–3595 (2002)

    CrossRef  CAS  Google Scholar 

  18. Rosencher, E., Straboni, A., Rigo, S., Amsel, G.: An \(^{18}{\rm {O}}\) study of the thermal oxidation of silicon in oxygen. Appl. Phys. Lett. 34, 254–257 (1979)

    CrossRef  CAS  Google Scholar 

  19. Taber, L.A.: Biomechanics of growth, remodeling and morphogenesis. ASME Appl. Mech. Rev. 48, 487–545 (1995)

    CrossRef  Google Scholar 

  20. Trimaille, I., Rigo, S.: Use of \(^{18}{\rm {O}}\) isotopic labeling to study the thermal dry oxidation of silicon as a function of temperature and pressure. Appl. Surf. Sci. 39, 65–80 (1989)

    CrossRef  CAS  Google Scholar 

  21. Wu, C.H.: The role of Eshelby stress in composition-generated and stress-assisted diffusion. J. Mech. Phys. Solids 49, 1771–1794 (2001)

    CrossRef  Google Scholar 

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Acknowledgments

This work was supported by Russian Foundation for Basic Research (Grant 10-01-00670), Sandia National Laboratories and RAS Programs for Fundamental Research.

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Correspondence to Elena N. Vilchevskaya .

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Vilchevskaya, E.N., Freidin, A.B. (2013). On Kinetics of Chemical Reaction Fronts in Elastic Solids. In: Altenbach, H., Morozov, N. (eds) Surface Effects in Solid Mechanics. Advanced Structured Materials, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35783-1_14

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