Materials Algorithms Project
Program Library

Module MAP_Steel_Free_Energy

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.

Conversion to Fortran 90 by S. Cardie
Address as above.

Top | Next

Purpose

A collection of procedures allowing the calculation of free energy change accompanying the transformation from austenite to ferrite of the same chemical composition, and its derivative with respect to the carbon concentration at the T0 boundary. The result incorporates a compensation for Zener ordering effects.

Top | Next | Prev

Specification

MODULE MAP_Steel_Free_Energy
   PRIVATE
   PUBLIC :: MAP_STEEL_FTO1,MAP_STEEL_G91
   CONTAINS

     FUNCTION MAP_STEEL_FTO1(F,H,S,T,W,W1,X)
       USE MAP_Util_Global_Data
       IMPLICIT NONE
       REAL(KIND=real_8_30) ::  MAP_STEEL_FTO1
       REAL(KIND=real_8_30),INTENT(IN)  :: F,H,S,T,W,W1,X
     END FUNCTION MAP_STEEL_FTO1

    FUNCTION MAP_STEEL_G91(F,H,S,T,W,W1,XTO)
      USE MAP_Util_Global_Data
      IMPLICIT NONE
      REAL(KIND=real_8_30),INTENT(IN) :: F,H,S,T,W,W1,XTO
      REAL(KIND=real_8_30) MAP_STEEL_G91
    END FUNCTION MAP_STEEL_G91

    SUBROUTINE ZEN_CALC(T,X,ZENER,ZEN1,ZEN2)
      USE MAP_Util_Global_Data
      IMPLICIT NONE
      REAL(KIND=real_8_30),INTENT(IN)  :: T,X
      REAL(KIND=real_8_30),INTENT(OUT) :: ZENER,ZEN1,ZEN2
    END SUBROUTINE ZEN_CALC

END MODULE MAP_Steel_Free_Energy

Top | Next | Prev

Description

MAP_Steel_Free_Energy contains two public and one private procedures.

The PUBLIC procedures are :

MAP_STEEL_FTO1

Calculates free energy change accompanying the transformation from austenite to ferrite of the same chemical composition.

MAP_STEEL_G91

Calculates the differential of the above with respect to the carbon concentration at the T0 boundary.

The PRIVATE procedure, ZEN_CALC, calculates a Zener ordering term, which describes the ordering of carbon atoms, that leads the body-centered cubic lattice of ferrite becoming body-centered tetragonal; the degree of ordering increases with increasing carbon concentration and descreasing transformation temperature [1]. ZEN_CALC is used by MAP_STEEL_FTO1 and MAP_STEEL_G91.

Top | Next | Prev

References

1. C. Zener, Trans. AIME, 167, (1946), 550.
2. J.C. Fisher, Metals Transactions, 185, (1949), 688-690.
3. H.K.D.H. Bhadeshia and D.V. Edmonds, Acta Metallurgica, 28, (1980), 1265-1273.

Top | Next | Prev

Parameters

Input parameters

1. MAP_STEEL_FTO1 and MAP_STEEL_G91:

   H - real

   Excess partial molar enthalpy of solution of carbon in austenite (J/mol).

   S - real

   Excess partial molar enthalpy of solution of carbon in ferrite (J/mol).

   X - real

   Mole fraction of carbon in ferrite at the T0 boundary.

   T - real

   Absolute temperature.

   W - real

   Carbon-carbon interaction energy in austenite (J/mol).

   W1 - real

   Carbon-carbon interaction energy in ferrite (J/mol).

   F - real

   Free energy change for transformation of austenite to ferrite of the same chemical composition (J).

2. ZEN_CALC:

   T - real

   Absolute temperature.

   X - real

   Mole fraction of carbon in ferrite at the T0 boundary.

Output parameters

MAP_STEEL_FTO1 - real

Free energy change accompanying the transformation from austenite to ferrite of the same chemical composition.

MAP_STEEL_G91 - real

Differential of above.

For ZEN_CALC:

ZENER,ZEN1,ZEN2 - reals

Zener ordering terms. Use depends on context: MAP_STEEL_FTO1 uses ZENER; MAP_STEEL_G91 uses ZEN1 and ZEN2.

Top | Next | Prev

Error Indicators

None.

Top | Next | Prev

Accuracy

No information supplied.

Top | Next | Prev

Further Comments

See the corresponding Fortran 77 procedures, MAP_STEEL_FTO1 and MAP_STEEL_G91.

A value for F could be obtained using, for example, MAP function MAP_STEEL_ENERGY.

Top | Next | Prev

Example

1. Program text

PROGRAM MAP_FTO_TEST
  USE MAP_Util_Global_Data
  USE MAP_Steel_Free_Energy
  IMPLICIT NONE
!
! Variable declarations
!
  REAL(KIND=real_8_30) :: H,S,X,T,W,W1,F,&
                          FTO, G9

    READ(5,*) F,H,S,T,W,W1,X

    FTO = MAP_STEEL_FTO1(F,H,S,T,W,W1,X)

    G9  = MAP_STEEL_G91(F,H,S,T,W,W1,X)

    WRITE(6,1001) FTO
    WRITE(6,1002) G9

  STOP
1001  FORMAT('Free energy change is ',F12.3)
1002  FORMAT('Differential is ',F12.3)

END PROGRAM MAP_FTO_TEST

2. Program data

 -2.8557824601061275E+03
  3.8575000000000000E+04  
 13.4799995422363281
  4.7300000000000000E+02
  8.7324743196967374E+03
  4.8570000000000000E+04
  1.7560130583041827E-02

3. Program results

Free energy change is    -1902.860
Differential is    66529.702

Top | Next | Prev

Auxiliary Routines

MAP_Util_Global_Data

Top | Next | Prev

Keywords

carbon, t0 boundary, ferrite, austenite, free energy change

Top | Next | Prev

Download

Download source code

Top | Prev