Materials Algorithms Project
Program Library

Subroutine MAP_STEEL_NUC

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

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 calculate the heterogeneous nucleation rate per unit area for allotriomorphic ferrite nucleating at austenite grain boundaries.

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Specification

  SUBROUTINE MAP_STEEL_NUC(SITE, GSTAR, KTEMP, GV, BI, BIFACE, BIEDGE,
& BICORN, SIGMA, LINEAL, HH, BOLTZ, AV)

  DOUBLE PRECISION SITE, GSTAR, KTEMP, GV, BI, BIFACE, BIEDGE, BICORN,
& SIGMA, LINEAL, HH, BOLTZ, AV

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Description

The nucleation rate per unit area is determined at three different sites on the grain boundary - grain faces, edges and corners - using classical nucleation theory:

I_b = [(K₁^f)/a²][kT/h]exp[{-(K₂^f)}G^* + Q}/kT]

Site factors K₁^f (affecting the number of each site) and shape factors K₂^f (affecting the interfacial energy of each type of site) for the three sites are incorporated. The overall grain boundary nucleation rate is obtained by summing the three rates for the individual sites.

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References

1. R.C. Reed and H.K.D.H. Bhadeshia, Mat. Sci. Tech., 8, (May 1992), 421-435.
2. J.W. Christian, The theory of phase transformations in metal and alloys, Part 1, 2nd ed., Pergamon, Oxford, 1965.

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Parameters

Input parameters

SITE - real

SITE is the fraction of active grain boundary sites for nucleation.

GSTAR - real

GSTAR is the activation energy for grain boundary nucleation (in joules).

KTEMP - real

KTEMP is the temperature (in kelvin).

GV - real

GV is the free energy change per unit volume for nucleation (in joules per cubic metre, Jm^-3).

SIGMA - real

SIGMA is the austenite matrix/ferrite nucleus interfacial energy per unit area (in joules per square metre, Jm^-2).

LINEAL - real

LINEAL is the mean lineal intercept austenite grain size (in microns).

HH - real

HH is Planck's constant (in Js).

BOLTZ - real

BOLTZ is Boltzmann's constant (in JK^-1).

AV - real

AV is the Avogadro constant (in mol^-1).

Output parameters

BI - real

BI is the overall grain boundary nucleation rate per unit area (m^-2 s^-1).

BIFACE - real

BIFACE is the grain boundary nucleation rate per unit area on grain faces (m^-2s^-1).

BIEDGE - real

BIEDGE is the grain boundary nucleation rate per unit area on grain edges (m^-2s^-1).

BICORN - real

BICORN is the grain boundary nucleation rate per unit area on grain corners (m^-2s^-1).

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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 SITE,GSTAR,KTEMP,GV,BI,BIFACE,BIEDGE
       DOUBLE PRECISION BICORN,SIGMA,LINEAL,HH,BOLTZ,AV
       INCLUDE 'map_constants_planck.f'
       INCLUDE 'map_constants_boltz.f'
       INCLUDE 'map_constants_av.f'
       READ (5,*) SITE,GSTAR,KTEMP
       READ (5,*) GV,SIGMA,LINEAL
       CALL MAP_STEEL_NUC(SITE,GSTAR,KTEMP,GV,BI,BIFACE,BIEDGE,
      & BICORN,SIGMA,LINEAL,HH,BOLTZ,AV)
       WRITE (6,*) BI,BIFACE,BIEDGE,BICORN
       STOP
       END

2. Program data

 1.0D-09    1.045D-19   975
-3.497D+07  0.05         62.5

3. Program results

0.1479D+15   0.1479D+15   0.2702D+10   0.214D+05

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Auxiliary Routines

None.

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Keywords

allotriomorphic ferrite, nucleation, austenite, grain boundary, nucleation rate

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Download

Download source code

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