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H.K.D.H. Bhadeshia,

Phase Transformations Group,

Department of Materials Science and Metallurgy,

University of Cambridge,

Cambridge, U.K.

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.

Language: | FORTRAN |

Product form: | Source code |

SUBROUTINE MAP_STEEL_RRAD(RADIUS, XMAX, XALPHA, XBAR, T, R, XMAXR,

& W, SIG, MOLVOL, CAPCON, EPSI)

DOUBLE PRECISION RADIUS, XMAX, XALPHA, XBAR, T, R, XMAXR, W, SIG,

& MOLVOL, CAPCON, EPSI

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/m^{2}),
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 :-

- H.K.D.H. Bhadeshia, Materials Science and Technology,
__1__, (1985), 497-504. - J.W. Christian, Theory of Transformations in Metals and Alloys, Part 1, Pergamon Press, 2nd edition, p180.

**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
^{-1}K^{-1}).

**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, m
^{3}mol^{-1}). **CAPCON**- real- CAPCON is the capillarity constant Gamma.
**EPSI**- real- EPSI is the non-ideality parameter.

None.

No information supplied.

None.

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

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

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

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

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