MAP_STEEL_ALLL estimates the one-dimensional parabolic thickening rate constant for diffusion-controlled growth.
Language: | FORTRAN |
Product form: | Source code |
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 f1 is a fractional supersaturation given by :-
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 :-
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
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