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The solvent-fixed coordinate system applied to two-phase diffusion coatings resulting from a constant surface flux of solute

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Abstract

The explicit finite difference form of the diffusion equation has been used to describe a two-phase binary diffusion problem which includes a constant surface flux boundary condition, a concentration-dependent diffusion coefficient, and dimensional change due to both additions of material and nonideal solution behavior. The ξγ coordinate system, containing an equal number of mols of the substrate component per increment, has been employed to simplify the mathematical form of the diffusion equation. At the two-phase interface a Lagrangian extrapolation has been employed in conjunction with the finite difference equations to determine solute concentration and flux as well as interface movement. Results of sample calculations for the α and β phases formed when a constant flux of aluminum is admitted to a copper surface at 850°C are presented graphically. Results include concentration profiles, surface concentration as a function of time, and movement of theα-β interface for a flat plate and for a cylinder. This treatment is applicable to any two-phase binary system wherein the arrival rate of solute atoms at the solvent surface, either by ionic transport in high-temperature electrodiffusion cells or from the vapor phase, is equal to the diffusion rate into the surface.

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References

  1. R. L. Benedetti and D. L. Creighton:Met. Trans., 1970, vol. 1, pp. 3383–87.

    CAS  Google Scholar 

  2. B. J. Chao and J. C. Chato:Advanced Heat Transfer, pp. 306–11, University of Illinois, Urbana, 1967.

    Google Scholar 

  3. W. Jost:Diffusion in Solids, Liquids and Gases, pp. 69–72, Academic Press, N.Y., 1960.

    Google Scholar 

  4. L. S. Castleman:Nucl. Sci. and Eng., 1958, vol. 4, pp. 209–26.

    CAS  Google Scholar 

  5. D. D. Van Horn:Trans. ASM, 1959, vol. 51, pp. 185–98.

    Google Scholar 

  6. C. Atkinson:Acta Met., 1968, vol. 16, pp. 1019–22.

    Article  Google Scholar 

  7. A. G. Guy, V. Leroy, and T. B. Lindemer:Trans. ASM, 1966, vol. 59, pp. 517–34.

    CAS  Google Scholar 

  8. W. D. Murray and F. Landis:Trans. ASME Series C, 1959, vol. 81, pp. 106–12.

    CAS  Google Scholar 

  9. M. Hansen:Constitution of Binary Alloys, 2nd ed., p. 85, McGraw-Hill Book Company, NX, 1958.

    Google Scholar 

  10. O. D. Sherby and M. T. Simnad:Trans. ASM, 1961, vol. 54, pp. 227–40.

    CAS  Google Scholar 

  11. J. Crank:The Mathematics of Diffusion, pp. 58, 74, Oxford University Press, Oxford, England, 1956.

    Google Scholar 

  12. H. W. Carslaw and J. C. Jaeger:Conduction of Heat in Solids, pp. 75, 203, Oxford University Press, Oxford, England, 1947.

    Google Scholar 

  13. R. A. Tanzilli and R. W. Heckel:Trans. TMS-AIME, 1968, vol. 242, pp. 2313–31.

    CAS  Google Scholar 

  14. J. Crank and P. Nicolson:Proc. of Cambridge Phil Society, 1947, vol. 43, pp. 50–64.

    Article  Google Scholar 

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Authors and Affiliations

  1. Mechanical and Aerospace Engineering, University of Missouri-Columbia, 65201, Columbia, MO

    Donald L. Creighton (Associate Professor)

  2. Power Burst Facility, Systems Engineering Branch, E.G. and G., Idaho National Engineering Laboratory, Idaho Falls, ID

    Robert L. Benedetti (Branch Manager)

Authors
  1. Donald L. Creighton
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  2. Robert L. Benedetti
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Creighton, D.L., Benedetti, R.L. The solvent-fixed coordinate system applied to two-phase diffusion coatings resulting from a constant surface flux of solute. Metall Trans A 8, 1721–1726 (1977). https://doi.org/10.1007/BF02646875

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  • DOI: https://doi.org/10.1007/BF02646875

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