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Subroutine MAP_STEEL_PROGC

  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 effective diffusivity of carbon in austenite.

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Specification

Language:FORTRAN
Product form:Source code

SUBROUTINE MAP_STEEL_PROGC(VMAX, T, XMAX, W, XBAR, HH,
& BOLTZ, R, PI, ANS)

DOUBLE PRECISION VMAX, T, XMAX, W, XBAR, HH, BOLTZ, R, PI, ANS

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Description

MAP_STEEL_PROGC calculates the effective diffusivity of carbon in austenite, taking account of the concentration dependence of this diffusivity. The concentration dependence uses the theory in [1], and is accounted for by evaluating the weighted average diffusion coefficient D for the range of carbon concentrations from that of the bulk alloy to the equilibrium austenite composition at the temperature concerned i.e.:

Equation

The effect due to substitutional alloying elements on the activity and interaction energy of carbon in austenite is calculated according to the theory in [2].

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References

  1. R.H. Siller and R.B. McLellen, Trans. Metallurgical Society of the American Institute of Mech. Engineers, 245, (1969), 697-700.
  2. J.R. Lacher, Proc. Camb. Phil. Soc. Math. Phys. Sci., 33, (1937), 518.
  3. R.H. Fowler and E.A. Guggenhiem, Statistical Thermodynamics, Cambridge University Press, New York, 1939.

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Parameters

Input parameters

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

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

W - real
W is the carbon-carbon interaction energy in austenite.

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

HH - real
HH is Planck's constant.

BOLTZ - real
BOLTZ is Boltzmann's constant.

R - real
R is the gas constant.

PI - real
PI is pi.

Output parameters

ANS - real
ANS is the weighted average diffusion coefficient of carbon in austenite (in cm2s-1).

VMAX - real
VMAX is the speed of diffusion of carbon in austenite.

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Error Indicators

None.

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Accuracy

See [1] for details.

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Further Comments

None.

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Example

1. Program text

       DOUBLE PRECISION T, XMAX, W, XBAR, VMAX, HH, BOLTZ, R, ANS
       INCLUDE 'map_constants_planck.f'
       INCLUDE 'map_constants_gas.f'
       INCLUDE 'map_constants_boltz.f'
       READ (5,*) T, W, XMAX, XBAR
       CALL MAP_STEEL_PROGC(VMAX, T, XMAX, W, XBAR, HH, BOLTZ, R, PI, ANS)
       WRITE (6,10) VMAX
10     FORMAT('The speed of diffusion of carbon in austenite = ',D13.5)
       WRITE (6,20) ANS
20     FORMAT('Weighted average diffusion coefficient = ',D13.5)
       STOP
       END

2. Program data

961.15   8352.3   0.03023   0.0062

3. Program results

Weighted average diffusion coefficient = 0.32954D-08

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Auxiliary Routines

Subroutines:
MAP_STEEL_RRAD
MAP_STEEL_VEL4

Functions:
MAP_STEEL_CG
MAP_STEEL_DCG
MAP_STEEL_XALPH

Utility Subroutines:
MAP_UTIL_TRAPE

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Keywords

diffusion, carbon, diffusivity, austenite

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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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