             Materials Algorithms Project
             FORTRAN Library

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Subroutine MAP_STEEL_INC_POTENCY

  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

S.J. Jones* and H.K.D.H. Bhadeshia,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

*Dr S.J. Jones is now with Ford Motor Co. (UK) Ltd.

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Purpose

To calculate the heterogeneous activation energy barrier to nucleation on a
spherical substrate such as an inclusion using classical nucleation theory.

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Specification

SUBROUTINE MAP_INC_POTENCY(INCGMAX1VOL,GMAX1VOL,
&RI,UFAFENERGY,FAFENERGY,FIENERGY,AIENERGY,AEB,
&AEBHOMOG,FRACHOMAEB)

DOUBLE PRECISION INCGMAX1VOL,GMAX1VOL,RI,UFAFENERGY,
&FAFENERGY,FIENERGY,AIENERGY,AEB,AEBHOMOG,FRACHOMAEB

DOUBLE PRECISION PI,RC,TESTIT,PHI,SEPN,PSI,THETA,BETA,
&FUNCTHETA,FUNCPSI,FUNCBETA,VS,VC1,VC2,VC3,XHGT,YHGT,AS,
&AC1,AC2,AC4,AF

PARAMETER (PI=3.141592654)

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Description

Barritte [2] developed a model for the activation energy barrier to
nucleation on a spherical substrate by assuming that the 'wetting' angle is
fixed at 90. This new model removes this assumption.

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References

  1. S.J. Jones, PhD. thesis, University of Cambridge, (1996).
  2. G.S. Barritte, "The microstructure of weld metals in low alloy steels",
     PhD. thesis, University of Cambridge, (1982).
  3. R.A. Ricks, G.S. Barritte and P.R. Howell, "Influence of second phase
     particles on diffusional transformations in steels", Solid State Phase
     Transformations, Proc. Metall. Society of AIME, Pittsburgh, (1981).

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Parameters

Input parameters

INCGMAX1VOL - real
     INCGMAX1VOL is the maximum possible thermodynamic driving force for
     nucleation local to the spherical substrate, per unit volume (Jm-3).

GMAX1VOL - real
     GMAX1VOL is the maximum possible thermodynamic driving force for
     nucleation remote from the spherical substrate, per unit volume (Jm-3).

RI - real
     RI is the radius of the spherical substrate(m).

UFAFENERGY - real
     UFAFENERGY is the interfacial energy per unit area at a disordered
     boundary between the product and the parent phases (Jm-2 ).

FAFENERGY - real
     FAFENERGY is the interfacial energy per unit area at a facetted
     (coherent) boundary between the product and the parent phases (Jm-2 ).

FIENERGY - real
     FIENERGY is the interfacial energy per unit area between the product
     phase and the spherical substrate (Jm-2 ).

AIENERGY - real
     AIENERGY is the interfacial energy per unit area between the parent
     phase and the spherical substrate (Jm-2 ).

Output parameters

AEB - real
     AEB is the activation energy barrier to nucleation at the spherical
     substrate (J).

AEBHOMOG - real
     AEBHOMOG is the activation energy barrier to homogeneous nucleation
     remote from the spherical substrate (J).

FRACHOMAEB - real
     FRACHOMAEB is the ratio between AEB and AEBHOMOG. This is the effective
     'shape' factor for nucleation on the spherical substrate.

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Error Indicators

  1. If FAFENERGY is greater than UFAFENERGY then an error is reported and
     the program execution is stopped.
  2. If the absolute value of TESTIT is greater than unity then an error is
     reported and the program execution is stopped.
  3. If YHGT is greater than XHGT then an error is reported and the program
     execution is stopped.

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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 GMAX1VOL,RI,UFAFENERGY,FAFENERGY,
     &FIENERGY,AIENERGY,AEB,AEBHOMOG,FRACHOMAEB,INCGMAX1VOL
      READ(*,*) INCGMAX1VOL,GMAX1VOL,RI,UFAFENERGY,FAFENERGY,
     &FIENERGY,AIENERGY
C
       CALL MAP_STEEL_INC_POTENCY(INCGMAX1VOL,GMAX1VOL,RI,UFAFENERGY,
     &FAFENERGY,FIENERGY,AIENERGY,AEB,AEBHOMOG,FRACHOMAEB)
C
       WRITE(*,10) AEB,AEBHOMOG,FRACHOMAEB
10     FORMAT(E10.3,1X,E10.3,1X,E10.3)
       STOP
       END

2. Program data

-0.260E7 -0.260E7 0.270E-6 0.500E-1 0.363E-1 0.463E-1 0.623E-1

3. Program results

0.814E-16 0.310E-15 0.263E0

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Auxiliary Routines

None.

Keywords

activation, energy, barrier, nucleation, classical, spherical, substrate,
inclusion, heterogeneous, homogeneous

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

MAP Website administration / map@msm.cam.ac.uk

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