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H.K.D.H. Bhadeshia and Sree Harsha Lalam,

Phase Transformations Group,

Department of Materials Science and Metallurgy,

University of Cambridge,

Cambridge, U.K.

Added to MAP: July 1999

To calculate the carbon concentration and the lattice parameter of carbon-enriched austenite, at a specified temperature, after partial transformation to ferrite has occurred. Suitable for high carbon content steels.

Language: | FORTRAN |

Product form: | Source code |

SUBROUTINE MAP_STEEL_PARAM2(AGTX,AGT,AAT,VA,XBAR,XALPHA,XG, & EXG,T,AV,RTEMP) DOUBLE PRECISION AGTX,AGT,AAT,VA,XBAR,XALPHA,XG,EXG,T,AV,RTEMP

This subroutine is used in the analysis of the transformation from austenite to ferrite by program MAP_STEEL_DILAT2. It obtains values for the carbon concentration and the lattice parameter of carbon-enriched austenite, at a temperature T, due to partial transformation of the austenite to ferrite, by solving iteratively equations 5 and 8 in reference 1:

where a_{gT} and a_{g} are the austenite lattice parameters at temperature T before and after carbon enrichment; T_{RT} is room temperature; w_{oc} and w_{c} are the weight fractions of carbon in the austenite before and after enrichment; e_{g} is the thermal expansion coefficient of austenite; C_{c} is the change in the austenite lattice parameter caused by the addition of unit concentration of carbon; w_{ac} is the carbon fraction in the ferrite; V_{a} is the volume fraction of the ferrite; p_{a} and p_{g} are the densities of ferrite and austenite. A value of 3.3Å is used for C_{c} [2]. The densities are calculated from the lattice parameters, where it is assumed that all the atoms are Fe and no corrections are made for the compositional differences between the phases.

This subroutine is a slightly improved version of MAP_STEEL_PARAM; the iteration procedure in this routine continues until the absolute percentage in the calculated lattice parameter is less than 10^{-10}, whereas for MAP_STEEL_PARAM a fractional change of less than 10^{-4} stipulates the convergence criterium.

- H.K.D.H. Bhadeshia, S.A. David, J.M. Vitek, and R.W. Reed, 1991, Materials Science
and Technology,
**7**, 686-698. - D.J. Dyson and B. Holmes, 1970,
*J. Iron Steel Inst.*,**208**, 469.

**AGT**- real- AGT (a
_{gT}) is the austenite lattice parameter at temperature T containing w_{oc}(XBAR) amount of carbon. **AAT**- real- AAT is the ferrite lattice parameter at temperature T.
**VA**- real- VA (V
_{a}) is the volume fraction of ferrite. **XBAR**- real- XBAR (100w
_{oc}) is the initial carbon concentration (wt%). **XALPHA**- real- XALPHA is the concentration of carbon dissolved in ferrite (wt%).
**EXG**- real- EXG (e
_{g}) is the thermal expansion coefficient of austenite (K^{-1}). **T**- real- T is the temperature (°C).
**AV**- real- AV is the Avogadro constant (mol
^{-1}). **RTEMP**- real- RTEMP (T
_{RT}) is room temperature (25 °C).

**AGTX**- real- AGTX (a
_{g}) is the carbon-enriched austenite lattice parameter at temperature T. **XG**- real- XG (100w
_{c}) is the concentration of carbon in enriched austenite (wt%).

Execution of the program is halted and an error flagged if the number of iterations in subroutine MAP_STEEL_PARAM2 exceeds 10^{10}.

No information supplied.

T and RTEMP may be given in either Kelvin or °C, provided that the same units are used for both parameters.

DOUBLE PRECISION AGTX,AGT,AAT,VA,XBAR,XALPHA,XG DOUBLE PRECISION EXG,T,AV,RTEMP C C AV is the Avogadro constant (in 1/(mole) C AV=6.0221367D+23 C WRITE(*,*) 'Input AGT, AAT, VA, EXG:' READ (*,*) AGT,AAT,VA,EXG WRITE(*,*) 'Input XBAR, XALPHA, T:' READ (*,*) XBAR,XALPHA,T RTEMP = 25.0D+00 CALL MAP_STEEL_PARAM2(AGTX,AGT,AAT,VA,XBAR,XALPHA, & XG,EXG,T,AV,RTEMP) WRITE (*,1) AGTX WRITE (*,2) XG STOP 1 FORMAT ('Lattice parameter of carbon-enriched austenite = ', & F8.4,' Angstroms') 2 FORMAT ('Carbon concentration in the austenite = ', & F8.4,' wt%') END

Input AGT, AAT, VA, EXG: 3.6448 2.8808 0.7 3.32E-5 Input XBAR, XALPHA, T: 0.968 0.02 349.0

Lattice parameter of carbon-enriched austenite = 3.7245 Angstroms Carbon concentration in the austenite = 3.3582 wt%

None.

enriched, austenite, ferrite, lattice parameter, carbon, concentration

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