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Phase Transformations Group,

Department of Materials Science and Metallurgy,

University of Cambridge,

Cambridge, U.K.

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

Language: | FORTRAN |

Product form: | Source code |

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

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

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]:

where f1 is a fractional supersaturation given by :-

- In this case :-
__c__1 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.

- H.K.D.H. Bhadeshia, Progress in Materials Science,
__29__, (1985), 321-386. - C. Zener, Journal of Applied Physics,
__20__, (1949), 950. - F.C. Frank, Proc. Royal Society,
__A201__, (1950), 586.

**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.

**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.

None.

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

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.

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

0.03015 6.661D-04 0.01104 4.512D-09

1.993D-04 -3.108D-08

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

parabolic thickening rate constant, diffusion-controlled growth

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