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Phase Transformations Group,

Department of Materials Science and Metallurgy,

University of Cambridge,

Cambridge, U.K.

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

Language: | FORTRAN |

Product form: | Source code |

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

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

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:

where f_{1} is a fractional supersaturation given by :-

__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.

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

- H.K.D.H. Bhadeshia, Progress in Materials Science,
__29__, (1985), 321-386. - C. Zener, Journal of Applied Physics,
__20__, (1949), 950. - C.A. Dubé, Ph.D. Thesis, Carnegie Institute of Technology, U.S.A (1948).
- C. Atkinson, Acta Metallurgica,
__15__, (1967), 1207.

**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
cm
^{2}s^{-1}). **GES**- real- GES is an estimate of ALPHA1/(2*sqrt DIFF), typically 0.51466.

**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.

None.

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

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, 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

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

0.71395D-04 0.00000D+00

**Utility Subroutines**:

MAP_UTIL_ANALY

MAP_UTIL_DAERF

parabolic thickening

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