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Subroutine MAP_STEEL_ALLL

  1. Provenance of code.
  2. Purpose of code.
  3. Specification.
  4. Description of subroutine's operation.
  5. References.
  6. Parameter descriptions.
  7. Error indicators.
  8. Accuracy estimate.
  9. Any additional information.
  10. Example of code
  11. Auxiliary subroutines required.
  12. Keywords.
  13. Download source code.
  14. Links.

Provenance of Source Code

H.K.D.H. Bhadeshia,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

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Purpose

MAP_STEEL_ALLL estimates the one-dimensional parabolic thickening rate constant for diffusion-controlled growth.

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Specification

Language:FORTRAN
Product form:Source code

SUBROUTINE MAP_STEEL_ALLL(XGAG, XBAR, XAGA, DIFF, ALPHA, GES)

DOUBLE PRECISION XGAG, XBAR, XAGA, DIFF, ALPHA, GES

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Description

When the diffusion coefficients do not depend on concentration, there is an implicit relation [1-4] for the one-dimensional diffusion-controlled thickening rate constant alpha1 as follows:

[Eqn 1]

where f1 is a fractional supersaturation given by :-

[Eqn 2]

c1 is the average concentration in the alloy,
c1{gamma alpha} is the concentration in gamma which is in equilibrium with alpha and c1{alpha gamma} is the concentration in alpha which is in equilibrium with gamma.

The thickness q as a function of time t is then given by :-

[Eqn 3]

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References

  1. H.K.D.H. Bhadeshia, Progress in Materials Science, 29, (1985), 321-386.
  2. C. Zener, Journal of Applied Physics, 20, (1949), 950.
  3. C.A. Dubé, Ph.D. Thesis, Carnegie Institute of Technology, U.S.A (1948).
  4. C. Atkinson, Acta Metallurgica, 15, (1967), 1207.

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Parameters

Input parameters

XGAG - real
XGAG is the mole fraction of solute in gamma which is in equilibrium with alpha.

XBAR - real
XBAR is the mole fraction of solute in the alloy as a whole.

XAGA - real
XAGA is the mole fraction of solute in alpha which is in equilibrium with gamma.

DIFF - real
DIFF is the diffusion coefficient in the parent phase (in cm2s-1).

GES - real
GES is an estimate of ALPHA1/(2*sqrt DIFF), typically 0.51466.

Output parameters

ALPHA - real
ALPHA is the one-dimensional parabolic thickening rate constant (in cms-0.5).

DUM1 - real
DUM1 is a measure of the accuracy of the result.

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Error Indicators

None.

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Accuracy

DUM1 should be much smaller than ALPHA, and can be taken to be an indication of the accuracy. Ideally, DUM1 should be zero.

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Further Comments

Care must be exercised when applied to multicomponent steels, since the theory is valid for the diffusion of just one species [1]. However, can be applied to paraequilibrium transformation in multicomponent steels.

The method does not allow for soft-impingement, i.e. the concentration in the matrix far away from the moving interface remains constant at c.

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Example

9.1 Program text

       DOUBLE PRECISION XGAG, XBAR, XAGA, DIFF, ALPHA, DUM1, GES
       READ(5,*) XGAG, XBAR, XAGA, DIFF, GES
       CALL MAP_STEEL_ALLL(XGAG, XBAR, XAGA, DIFF, ALPHA, GES, DUM1)
       WRITE (6,*) ALPHA, DUM1
       STOP
       END

9.2 Program data

0.0181   0.0092   0.5911D-03   0.6453D-08   740.0   0.51466

9.3 Program results

0.71395D-04   0.00000D+00

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Auxiliary Routines

Utility Subroutines:
MAP_UTIL_ANALY
MAP_UTIL_DAERF

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Keywords

parabolic thickening

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Download

Download source code

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