Skip to main content

On Kinetics of Chemical Reaction Fronts in Elastic Solids

  • Chapter
  • First Online:
Surface Effects in Solid Mechanics

Part of the book series: Advanced Structured Materials ((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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

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

    Article  CAS  Google Scholar 

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

    Article  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)

    Article  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)

    Article  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)

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  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)

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  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)

    Article  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)

    Article  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)

    Article  CAS  Google Scholar 

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

    Article  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)

    Article  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)

    Article  Google Scholar 

Download references

Acknowledgments

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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Elena N. Vilchevskaya .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

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

Download citation

Publish with us

Policies and ethics