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Subroutine MAP_STEEL_SCHEIL

  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.

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Provenance of Source Code

K. Ichikawa (Nippon Steel Corporation) and 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

To estimate the concentration profiles by solidification-induced
segregation, based on classical Scheil theory.

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Specification

SUBROUTINE MAP_STEEL_SCHEIL(CC,CSI,CMN,CNI,CMO,CCR,CV,
& R,C,I,IN)

DOUBLE PRECISION C(7),CC,CSI,CMN,CNI,CMO,CCR,CV,R

INTEGER I,IN

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Description

The Scheil equation gives:-

CS(X) = k0(X)C0(X)(1 - fS)[k0(X)-1]

where:-

CS(X) is the concentration of alloy element X in solid phase (in weight
percent).

C0(X) is the initial concentration of X in the alloy (in weight percent).

k0(X) is the equilibrium partition coefficient of alloy element X, where
k0(X) = CS(X) / Cl(X).

Cl(X) is the concentration of alloy element X in liquid phase (in weight
percent).

fS is the fraction solidified.

If the fraction solidified fS is divided by a positive integer n, each
segment of the fraction represents a fraction of 1/n of the final solid.
Therefore the midpoint of the nth section can be represented as:-

fS = (i/n) - [1/(2n)]

where i = 1, 2, 3, ..., n
After substituting for fS, CS(X) can be calculated for the ith segment from
:-

CS(X) = k0(X)C0(X)/[1 - {(i/n) - (1/(2n))}][k0(X)-1]

where the equilibrium distribution coefficient k0(X) of the alloy element X
may be calculated using the subroutine MAP_STEEL_EDC.

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References

1. E. Scheil, Z. Metallkunde, 34, (1942), 70-72.

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Parameters

Input parameters

CC - real
     CC is the carbon concentration (in weight percent).

CSI - real
     CSI is the silicon concentration (in weight percent).

CMN - real
     CMN is the manganese concentration (in weight percent).

CNI - real
     CNI is the nickel concentration (in weight percent).

CMO - real
     CMO is the molybdenum concentration (in weight percent).

CCR - real
     CCR is the chromium concentration (in weight percent).

CV - real
     CV is the vanadium concentration (in weight percent).

R - real
     R is the universal gas constant (in joules per mole per kelvin,
     Jmol-1K-1).

I - integer
     I is the ordinal number of the segment.

IN - integer
     IN is the number of segments.

Output parameters

C - real array of dimension 7.
     C(1) is the weight percent of carbon in the ith segment.
     C(2) is the weight percent of silicon in the ith segment.
     C(3) is the weight percent of manganese in the ith segment.
     C(4) is the weight percent of nickel in the ith segment.
     C(5) is the weight percent of molybdenum in the ith segment.
     C(6) is the weight percent of chromium in the ith segment.
     C(7) is the weight percent of vanadium in the ith segment.

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Error Indicators

None.

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Accuracy

No information supplied.

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Further Comments

None.

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Example

1. Program text

       DOUBLE PRECISION CC,CSI,CMN,CNI,CMO,CCR,CV
       DOUBLE PRECISION R,C(7)
       INTEGER I,IN
       INCLUDE 'map_constants_gas.f'
       READ (5,*) CC,CSI,CMN,CNI,CMO,CCR,CV
       READ(5,*) I,IN
       CALL MAP_STEEL_SCHEIL(CC,CSI,CMN,CNI,CMO,CCR,CV,
&      R,C,I,IN)
       WRITE (6,*) (C(I),I=1,7)
       STOP
       END

2. Program data

 0.04  0.35   1.0   1.96   0.35   0.38   0.01
10   100

3. Program results

4.0000000000000D-02   0.25555426222485   0.76736120867397   0.94123971424815   0.18206130345040   0.31925041575708   7.7665238384234D-03

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Auxiliary Routines

MAP_STEEL_EDC

Keywords

Scheil equation, solidification-induced segregation

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

Contact Information :-

Harry Bhadeshia / hkdb@cus.cam.ac.uk
Hugh Davies / rhd@newton.npl.co.uk
Web site admin. / map@cam.ac.uk

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