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Subroutine MAP_STEEL_RRADNED

  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

Calculates the Gibbs-Thompson critical radius for the tip of a needle that leads to zero growth, and the equilibrium concentration at the needle tip.

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Specification

Language:FORTRAN
Product form:Source code

SUBROUTINE MAP_STEEL_RRADNED(RADIUS,RAD,XMAX,XALPHA,XBAR,T,R,
&XMAXR,W,SIG,MOLVOL,CAPCON,EPSI)

DOUBLE PRECISION RADIUS,RAD,XMAX,XALPHA,XBAR,T,R,XMAXR,W,
&SIG,MOLVOL,CAPCON,EPSI

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Description

MAP_STEEL_RRADNED calculates the Gibbs-Thompson critical radius for the tip of a needle that leads to zero growth. It also calculcates the equilibrium concentration at the needle tip, the capillarity constant, and the non-ideality parameter.

The ratio of the actual needle tip radius to the critical radius is calculated using an equation derived by fitting to the graph in Ref [1].

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References

  1. R. Trivedi, Metallurgical Transactions, 1, (1970), 921-927.

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Parameters

Input parameters

SIG - real
SIG is ther interfacial energy (in joules per metre squared, Jm-2).

XBAR - real
XBAR is the mole fraction of carbon in the alloy.

XALPHA - real
XALPHA is the equilibrium mole fraction of carbon in ferrite.

XMAX - real
XMAX is the equilibrium mole fraction of carbon in austenite.

T - real
T is the temperature (in kelvin).

W - real
W is the carbon-carbon interaction energy (in joules per mole, Jmol-1).

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

Output parameters

MOLVOL - real
MOLVOL is the molar volume of ferrite (in cubic metres per mole, m3mol-1).

EPSI - real
EPSI is the non-ideality parameter.

CAPCON - real
CAPCON is the capillarity constant.

RADIUS - real
RADIUS is the critical needle tip radius at which growth stops (in metres).

RAD - real
RAD is the ratio of the actual needle tip radius to the critical radius.

XMAXR - real
XMAXR is the equilibrium concentration at the plate tip, (in mole praction).

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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 RADIUS,RAD,XMAX,XALPHA,XBAR,T,R,XMAXR,W,
&      SIG,MOLVOL,CAPCON,EPSI
       INCLUDE 'map_constants_gas.f'
       READ (5,*) SIG, XBAR, XALPHA
       READ (5,*) XMAX,T,W
       CALL MAP_STEEL_RRADNED(RADIUS,RAD,XMAX,XALPHA,XBAR,T,R,XMAXR,W,
&      SIG,MOLVOL,CAPCON,EPSI)
       WRITE(6,1)SIG,MOLVOL,RADIUS,XMAXR,CAPCON,EPSI
1      FORMAT(' INTERFACIAL ENERGY=',F8.4,' JOULES/METERS SQUARED'
&      ' MOLAR VOLUME OF FERRITE(METERS CUBED PER MOL)=',D15.6
&      ' GIBBS THOMPSON CRITICAL RADIUS(METERS)=',D15.6
&      ' EQUILIBRIUM CONC AT PLATE TIP, MOL FRAC, XMAXR=',D15.6
&      ' CAPILLARITY CONSTANT CAPCON,=',D15.6
&      ' NON-IDEALITY PARAMETER EPSI=',D15.6)
       STOP
       END

2. Program data

None supplied.

3. Program results

None supplied.

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Auxiliary Routines

MAP_STEEL_DCG

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Keywords

Gibbs Thompson, critical radius, equilibrium concentration, austenite, ferrite, tip, needle

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Download

Download source code

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