Skip to main content
SpringerLink
Log in

Diffusion in materials with variable temperature: Part I One-dimensional problems

  • Published:
Journal of Materials Science Aims and scope Submit manuscript

Abstract

Solutions for diffusion in non-isothermal conditions are derived by analogy with diffusion in isothermal conditions when diffusivity is constant or time dependent. The effects of heating or cooling rates on the concentration profiles, boundary-layer thickness, and amount of material transferred, are described and can be assessed even when the temperature dependence of diffusivity and/or interfacial concentration is unknown. The effects of the rate of change in temperature on the amount of material transferred can be used also to assess whether this is controlled by diffusion or reaction.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. SESTAK and J. MALEK,Solid State Ionics 63/65 (1993) 245.

    Google Scholar 

  2. N.P. BANSAL, R. H. DOREMUS, A. J. BRUCE and C. T. MOYNIHAN,J. Am. Ceram. Soc. 66 (1983) 233.

    Google Scholar 

  3. D. L. JOHNSON,Phys. Sintering 1 (1969) B1.

    Google Scholar 

  4. I. B. CUTLER,J. Am. Ceram. Soc. 52 (1969) 14.

    Google Scholar 

  5. W. S. YOUNG and I. B. CUTLER,ibid. 53 (1970) 659.

    Google Scholar 

  6. K. BREITKREUTZ and K. HAEDECKE,Powder Metall. Int. 22 (1990) 14.

    Google Scholar 

  7. J. CRANK, “The Mathematics of Diffusion” (Clarendon Press, Oxford, 1975).

    Google Scholar 

  8. G. D. MAHAN,J. Appl. Phys. 54 (1983) 3825.

    Google Scholar 

  9. J. R. FRADE and M. CABLE,J. Am. Ceram. Soc. 77 (1994) 999.

    Google Scholar 

  10. J. R. FRADE,J. Mater. Sci. 32 (1997).

  11. H. S. CARSLAW and J. C. JAEGER, “Conduction of Heat in Solids”, 2nd Edn (Clarendon Press, Oxford, 1959).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Engenharia Ceramica e do Vidro, Universidade de Aveiro, 3800, Aveiro, Portugal

    J. R FRADE

Authors
  1. J. R FRADE
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

FRADE, J.R. Diffusion in materials with variable temperature: Part I One-dimensional problems. Journal of Materials Science 32, 3549–3556 (1997). https://doi.org/10.1023/A:1018657708579

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018657708579

Keywords

Search

Navigation