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Subroutine MAP_STEEL_ALL3

  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

S.V. Parker,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

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Purpose

MAP_STEEL_ALL3 estimates the three-dimensional parabolic thickening rate constant for diffusion-controlled growth.

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Specification

Language:FORTRAN
Product form:Source code

SUBROUTINE MAP_STEEL_ALL3(XGAG,XBAR,XAGA,DIFF,ALPHA3)

DOUBLE PRECISION OMEGA,DUM3,DER3,DX3,ALPHA3,GES3

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Description

Solution of the diffusion equations for three-dimensional growth (spheres) involving local equilibrium at the gamma/alpha interface in Fe-C alloys leads to an expression for the three-dimensional rate constant, alpha3 [1-3]:

[Eqn 1]

where f1 is a fractional supersaturation given by :-

[Eqn 2]
In this case :-
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.

It is assumed that the diffusion coefficients do not depend on concentration and capillarity effects can be neglected.

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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. F.C. Frank, Proc. Royal Society, A201, (1950), 586.

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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 carbon in the alloy.

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

DIFF - real
DIFF is the diffusion coefficient of carbon in gamma.

GES3 - real
GES3 is an estimate of ALPHA3(2*sqrt{DIFF}), typically 0.51466.

Output parameters

ALPHA3 - real
ALPHA3 is the three-dimensional parabolic thickening rate constant for growth.

DUM3 - real
DUM3 is a measure of the accuracy of the result.

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Error Indicators

None.

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Accuracy

DUM3 should be much smaller than ALPHA3, and can be taken to be an indication of the accuracy. Ideally, DUM3 should be zero.

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Further Comments

This routine is MAP_STEEL_ALLL but modified for 3-D growth.

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

1. Program text

       DOUBLE PRECISION XGAG, XBAR, XAGA, DIFF, ALPHA3, DUM3, GES3
       READ(5,*) XGAG, XBAR, XAGA, DIFF
       CALL MAP_STEEL_ALL3(XGAG, XBAR, XAGA, DIFF, ALPHA3, DUM3)
       WRITE (6,*) ALPHA3, DUM3
       STOP
       END

2. Program data

0.03015   6.661D-04   0.01104   4.512D-09

3. Program results

1.993D-04   -3.108D-08

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Auxiliary Routines

MAP_UTIL_DAERFC may be needed to replace the DERF calls in the subroutine.

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Keywords

parabolic thickening rate constant, diffusion-controlled growth

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Download

Download source code

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MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.

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