The Thermodynamic Factors for the Cation Diffusion in a P-Type Oxide AO Doped with a Monovalent Impurity

  • Francesco Gesmundo
Part of the NATO ASI Series book series (NSSB, volume 129)


The thermodynamic factors for the cation diffusion in a p-type semiconducting oxide of a divalent metal containing a monovalent impurity are evaluated by means of thermodynamic considerations, assuming that the defect structure of the base oxide is known. It is shown that these parameters are not only functions of the oxygen activity and of the dopant concentration, but depend also strongly on the ratio between the gradients of these two variables. Limiting expressions corresponding to the presence of only one gradient are obtained and evaluated approximately for very small or large impurity concentrations. It is found in particular that under constant oxygen activity the two thermodynamic factors are always close to one but change in opposite directions with the impurity concentration. On the contrary, under constant impurity concentration the thermodynamic factors are both very large and decrease as the oxygen activity increases. A general relationship between the two thermodynamic factors is obtained by means of the Gibbs-Duhem equation applied to the relevant ternary system. Finally, the theoretical equations are used to calculate the thermodynamic factors in NiO doped with a monovalent impurity at 1000°C, using a detailed model to represent its defect structure.


Mixed Oxide Oxygen Activity Impurity Concentration Electron Hole Thermodynamic Factor 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. G. Shewmon, “Diffusion in Solids,” Diffusion in Solids, New York (1963).Google Scholar
  2. 2.
    J. R. Manning, Theory of Diffusion, in:“Diffusion,”, H. I. Aaronson, ed., American Society for Metals, Metals Park, Ohio (1973).Google Scholar
  3. 3.
    A. D. Le Claire, Diffusion, in:“Treatise on Solid State Chemistry,” N. B. Hannay, ed., Plenum Press, New York (1976).Google Scholar
  4. 4.
    H. Schmalzried, “Solid State Reactions,” Academic Press, New York (1974).Google Scholar
  5. 5.
    G. J. Yurek and H. Schmalzried, Ber. der Bunsenges. Phys. Chem. 78:1379 (1974).Google Scholar
  6. 6.
    G. J. Yurek and H. Schmalzried, Ber. der Bunsenges. Phys. Chem. 79:225 (1975).Google Scholar
  7. 7.
    W. K. Chen and N. L. Peterson, J. Phys. Chem. Solids 34:1093 (1973).ADSCrossRefGoogle Scholar
  8. 8.
    F. Gesmundo, J. Phys. Chem. Solids 44:819 (1983).ADSCrossRefGoogle Scholar
  9. 9.
    F. A. Kroger, “The Chemistry of Imperfect Crystals,” Vol. II, North-Holland, Amsterdam (1973).Google Scholar
  10. 10.
    F. Gesmundo, J. Phys. Chem. Solids, in press.Google Scholar
  11. 11.
    C. Wagner, Corros. Sci. 9:91 (1969).CrossRefGoogle Scholar
  12. 12.
    F. Gesmundo, Oxid. Met., submitted for publication.Google Scholar
  13. 13.
    C. M. Osburn and R. W. Vest, J. Phys. Chem. Solids 32:1343 (1971).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1985

Authors and Affiliations

  • Francesco Gesmundo
    • 1
  1. 1.Istituto di Chimica Fisica Applicata dei MaterialiGenovaItaly

Personalised recommendations