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Determination of the Nitrogen Diffusion Coefficient in Steels with Non-isothermal Experiments

  • Jordan S. Georgiev EMAIL logo und Ljubomir A. Anestiev EMAIL logo
Veröffentlicht/Copyright: 16. Dezember 2021
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International Journal of Materials Research
Aus der Zeitschrift International Journal of Materials Research Band 89 Heft 6

Abstract

A non-isothermal method for the determination of the gas diffusivity in metals and alloys is proposed. The method allows to determine the temperature dependence of the gas diffusion coefficient in a wide temperature range with a limited number of experiments. The results obtained with this method (for the diffusivity of nitrogen in steels), agree favourably with the diffusion data obtained with other experimental techniques. Hence, the proposed method leads to reliable results and can be successfully used in further studies.

Abstract

Hiermit wird eine nichtisotherme Methode zur Bestimmung von Gasdiffusionskoeffizienten in Metallen vorgestellt, mit deren Hilfe die Temperaturabhängigkeit des Koeffizienten in einem weiten Temperaturbereich über eine geringe Zahl von Experimenten bestimmt werden kann.

Die auf diese Weise erhaltenen Ergebnisse über die Diffusion von Stickstoff in Stählen stimmen sehr gut mit den Daten, welche bis jetzt anhand anderer experimenteller Techniken ermittelt worden sind, überein.

Es ist festzustellen, daß die vorgestellte Methode zuverlässig genug ist, um zu weiteren Untersuchungen zur Bestimmung des Gasdiffusionskoeffizienten in Metallen herangezogen werden zu können.

J.S. Georgiev, L.A. Anestiev Institute of Metal Science, Bulgarian Academy of Sciences 67 Shipchenski Prohod, Str.1574 Sofia, Bulgaria

  1. The authors are grateful to the Volkswagen Stiftung for the financial support of the present research. We also wish to thank Prof. J. Sietsma (Delft University, Netherlands) and Dr. K. Russew (IMS, Sofia) for the kindly given FORTRAN-version of the Nelder-Mead simplex algorithm.

Literature

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Appendix

Error analysis

Let us consider Eq. (9) taking into account, that the values of Tm, I and α are measured with definite accuracy ∆Tm, ∆I and ∆α. Therefore, instead Tm, I and α, the values of these quantities substituted into Eq. (9) are Tm = Tm ± ΔTm, I = I ± ΔI and α = α ± Δα (Note that our analysis assumes ΔTm/Tm ≪ 1, ΔI/I ≪ 1 and Δα/α ≪ 1:

(A1) ln(αl2(1±Δαα)(1±2Δll)RTm2(1±2ΔTmTm))=ln(D0π2)−ERTm(1±ΔTmTm)

Rearranging the members of the left and the right hand side of the Eq. (A1) it is obtained:

(A2) ln(αlRTm2)+ln[ (1±Δαα)(1±2Δll)(1±2ΔTmTm) ]=ln(D0π2E)−ERTm(1±ΔTmTm)

In the above equation it is accounted for that the errors of the measurements has a cumulative effect on the final result. That is why, in the second and the fourth members of Eq. (A2) instead (∓) appears (±) operation. Taking into account this circumstance and that for x ≪ 1 – ln(1 ± x)≈ ±x, the above equation yields:

(A3) ln(αl2RTm2)=ln(D0π2E)−ERTm±Δ

Here Δ=Δαα+2Δll+ERTm(1+2ΔTmTm) is the error accumulated during the experimental measurements.

Finally the above equation can be rewritten as follows:

(A4) ln(D0!π2E)=ln(D0exp⁡(±Δ)π2E)−ERTm=ln(D0!π2E)−ERTm

where D′0=D0exp⁡(±Δ) is the actual value for D0 determined from the experiment. Note the strong dependence (exponential!) of D'0 on the accumulated error ∆. Taking into account that the latter is a function not only of the small quantities ΔTm, ΔI and Δα but also of E and Tm a conclusion may be drawn that D0 is determined in this method with considerable uncertainty. This is especially true for high activation energies E and low Tm. This result explains why the value of D0 for the ON3 iron determined with the aid of the present method, correlate so favourably with these obtained by other methods. In this case E is relatively small (see Table 1). The observed discrepancy between the values of D0 for the 1.4306 (DIN) steel obtained by the different methods discussed here is due to the relatively large values of E for this steel.

Received: 1997-11-06
Published Online: 2021-12-16

© 1998 Carl Hanser Verlag, München

Artikel in diesem Heft

  1. Frontmatter
  2. Aufsätze
  3. Study of the Transitions AuCu I → AuCu II → Disorder by Differential Scanning Calorimetry
  4. Critical Data and Vapor Pressures for Aluminium and Copper
  5. Study of Al1–xTixB2 Particles Extracted from Al–Ti–B Alloys
  6. Experimental Investigation and Thermodynamic Modeling of the Ni–Ti–C System
  7. Erratum
  8. Determination of the Nitrogen Diffusion Coefficient in Steels with Non-isothermal Experiments
  9. Microstructures and Hot Tensile Properties of Pressure-diecast and Gravity-cast Commercial Zinc-based Alloys
  10. Development of Annealing Textures in Al–Mg Alloys
  11. Hot Deformation and Microstructural Evolution in an α2/O Titanium Aluminide Alloy Ti-25Al-15Nb
  12. Microhardness of Structure Units in the Ternary Ti-rich Ti–Si–Al Alloys
  13. Metallurgical Factors Affecting Impact Toughness of Eutectic Al-Si Casting Alloy
  14. Mitteilungen der Deutschen Gesellschaft für Materialkunde e.V.
  15. Personen
  16. Buchbesprechungen
https://doi.org/10.3139/ijmr-1998-0076

Artikel in diesem Heft

  1. Frontmatter
  2. Aufsätze
  3. Study of the Transitions AuCu I → AuCu II → Disorder by Differential Scanning Calorimetry
  4. Critical Data and Vapor Pressures for Aluminium and Copper
  5. Study of Al1–xTixB2 Particles Extracted from Al–Ti–B Alloys
  6. Experimental Investigation and Thermodynamic Modeling of the Ni–Ti–C System
  7. Erratum
  8. Determination of the Nitrogen Diffusion Coefficient in Steels with Non-isothermal Experiments
  9. Microstructures and Hot Tensile Properties of Pressure-diecast and Gravity-cast Commercial Zinc-based Alloys
  10. Development of Annealing Textures in Al–Mg Alloys
  11. Hot Deformation and Microstructural Evolution in an α2/O Titanium Aluminide Alloy Ti-25Al-15Nb
  12. Microhardness of Structure Units in the Ternary Ti-rich Ti–Si–Al Alloys
  13. Metallurgical Factors Affecting Impact Toughness of Eutectic Al-Si Casting Alloy
  14. Mitteilungen der Deutschen Gesellschaft für Materialkunde e.V.
  15. Personen
  16. Buchbesprechungen
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