Materials Algorithms Project
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Subroutine MAP_STEEL_RRAD

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 zero growth of a ferrite plate in austenite at a given temperature and the equilibrium concentration at the plate tip.

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Specification

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Description

If the equilibrium carbon concentration of austenite is x^{[gamma alpha]}, and a ferrite plate has a radius of curvature of rho at its tip, then the austenite concentration in local equilibrium with this tip (taking account of the Gibbs-Thompson effect) is x_rho, where:-

where sigma is the alpha/gamma interfacial energy (J/m²), f is the activity coefficient of austenite, V_mol is the molar volume of ferrite and gamma, the capillarity constant, is :-

The critical radius at which the growth of the plate is zero is reached when x_rhoc = x, i.e. when :-

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References

1. H.K.D.H. Bhadeshia, Materials Science and Technology, 1, (1985), 497-504.
2. J.W. Christian, Theory of Transformations in Metals and Alloys, Part 1, Pergamon Press, 2nd edition, p180.

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Parameters

Input parameters

XMAX - real

XMAX is the equilibrium mole fraction of carbon in austenite x^{[gamma alpha]}.

XALPHA - real

XALPHA is the equilibrium mole fraction of carbon in ferrite x^{[alpha gamma]}.

XBAR - real

XBAR is the mole fraction of carbon in the alloy x.

T - real

T is the absolute temperature T (in kelvin, K).

W - real

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

SIG - real

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

R - real

R is the gas constant (in Jmol^-1K^-1).

Output parameters

RADIUS - real

RADIUS is the Gibbs Thompson critical radius for zero growth rho_c (in metres).

XMAXR - real

XMAXR is the equilibrium concentration at the plate tip x_rho (mole fraction).

MOLVOL - real

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

CAPCON - real

CAPCON is the capillarity constant Gamma.

EPSI - real

EPSI is the non-ideality parameter.

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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, XMAX, XALPHA, XBAR, T, R, XMAXR, W,
&      SIG, MOLVOL, CAPCON, EPSI
       INCLUDE 'map_constants_gas.f'
       READ (5,*) XMAX, XALPHA, XBAR
       READ (5,*) T, W, SIG
       CALL MAP_STEEL_RRAD(RADIUS, XMAX, XALPHA, XBAR, T, R, XMAXR, W,
&      SIG, MOLVOL, CAPCON, EPSI)
       WRITE (6,10) RADIUS, XMAXR, MOLVOL, CAPCON, EPSI
10     FORMAT('Gibbs Thompson critical radius = ',D13.5,' metres'
&      'Equilibrium concentration at plate tip = ',D13.5
&      'Molar volume of ferrite = ',D13.5,' cubic metres per mole'
&      'Capillarity constant = ',D13.5
&      'Non-ideality parameter = ',D13.5)
       STOP
       END

2. Program data

  0.51111D-01    0.74501D-03   0.13738D-01
901.15        8352.3           0.2

3. Program results

Gibbs Thompson critical radius =   0.30652D-08 metres
Equilibrium concentration at plate tip =   0.45787D-01
Molar volume of ferrite =   0.72412D-05 cubic metres per mole
Capillarity constant =  -0.22413D-08
Non-ideality parameter =   0.16247D+01

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Auxiliary Routines

MAP_STEEL_DCG

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Keywords

Gibbs Thompson, critical radius, equilibrium concentration, capillarity constant, non-ideality parameter, ferrite, austenite, tip, plate

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Download

Download source code

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