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Subroutine MAP_STEEL_GB_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.

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 planar grain boundary using classical nucleation theory.

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Specification

Language:FORTRAN
Product form:Source code

SUBROUTINE MAP_STEEL_GB_POTENCY(GBGMAX1VOL,GMAX1VOL,
& UFAFENERGY,FAFENERGY,AGBENERGY,GBAEB,AEBHOMOG,
& GBFRACHOMAEB)

IMPLICIT NONE
DOUBLE PRECISION GBGMAX1VOL, GMAX1VOL, UFAFENERGY, FAFENERGY,
& AGBENERGY, GBAEB, AEBHOMOG, GBFRACHOMAEB,
& PI, GBRC, GBBETA, GBFUNCBETA, TESTY, GBSIGMA,
& GBFUNCSIGMA, GBVSEG, GBVC3, GBASEG, GBAC2,
& GBAC4, GBAF, NUCSTRAIN1VOL

PARAMETER (PI=3.141592654)

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Description

The activation energy barrier to nucleation on a planar grain boundary is calculated using classical nucleation theory. The nucleus of the product phase is assumed to exhibit a low-energy facet with one of the adjacent parent grains.

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References

  1. S.J. Jones, PhD. thesis, University of Cambridge, 1996
  2. W.C. Johnson, "Influence of Crystallography on Aspects of Solid-solid Nucleation Theory", Met. Trans., 6A, (1975) 911-919.
  3. J.W. Christian, "The Theory of Phase Transformations in Metals and Alloys", Part 1, 2nd ed., Permagon, Oxford, (1965).

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Parameters

Input parameters

GBGMAX1VOL - real
GBGMAX1VOL is the maximum possible thermodynamic driving force for nucleation local to the boundary, per unit volume (Jm-3).

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

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).

AGBENERGY - real
AGBENERGY is the interfacial energy per unit area at the boundary between two grains of the parent phase (Jm-2).

Output parameters

GBAEB - real
GBAEB is the activation energy barrier to nucleation at the planar boundary (J).

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

GBFRACHOMAEB - real
GBFRACHOMAEB is the ratio between GBAEB and AEBHOMOG. This is the effective 'shape' factor for nucleation at the planar boundary.

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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 TESTY is greater than unity 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

       IMPLICIT DOUBLE PRECISION(A-H,K-Z), INTEGER(I-J)
       READ(*,*) GBGMAX1VOL,GMAX1VOL,UFAFENERGY,
      & FAFENERGY,AGBENERGY
       CALL MAP_STEEL_GB_POTENCY(GBGMAX1VOL,GMAX1VOL,
      & UFAFENERGY,FAFENERGY,AGBENERGY,GBAEB,AEBHOMOG,
      & GBFRACHOMAEB)
       WRITE(*,10) GBAEB,AEBHOMOG,GBFRACHOMAEB
10     FORMAT (E10.3,1X,E10.3,1X,E10.3)
       STOP
       END

2. Program data

-0.260E7 -0.260E7 0.500E-1 0.363E-1 0.708E-1

3. Program results

0.199E-16 0.310E-15 0.643E-1

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Auxiliary Routines

None.

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Keywords

activation, energy, barrier, nucleation, classical, planar, boundary, substrate, facet, coherent, heterogeneous, homogeneous

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Download

Download source code

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

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