[MAP Logo]

Materials Algorithms Project
Program Library


  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 and Sree Harsha Lalam,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

Added to MAP: July 1999.

Top | Next


To calculate the volume fraction of the amount transformed from austenite to ferrite, during cooling, from a measure of the length change. Suitable for high carbon content steels.

Top | Next | Prev


Product form:Source code

Complete program.

Top | Next | Prev


Austenite and ferrite are two different allotropes of iron, with face-centered and body-centered cubic structure respectively. The transformation of austenite to ferrite is therefore accompanied by a change in density, and causes the external dimensions of a piece of solid austenite/ferrite to change (dilatation). These changes can be measured, enabling the transformation itself to be monitored as it progresses, using a dilatometer.

The program MAP_STEEL_DILAT2 calculates the volume fraction of transformed austenite to ferrite from the measured dilatations. The ferrite lattice parameter is obtained for the given solute concentrations by subroutine MAP_STEEL_FERR. An iterative procedure is used to calculate the volume fraction of ferrite. For a given volume fraction, subroutine MAP_STEEL_PARAM2 evaluates the lattice parameter and carbon content of the austenite [1,2]. The expected density change of the material, as calculated from the lattice parameters and volume fractions of the two components, is then compared with the measured dilatation using subroutine MAP_STEEL_FPARAM, which gives a measure of the error in the calculated dilation. The derivative of the dilatation error with respect to the volume fraction is then calculated and used to find a new value for the volume fraction. The size of the change made with each iteration is modified by the parameter SENS in the main program, and is currently set to 0.1.

This method of iteration is an improvement on the method used by MAP_STEEL_DILAT, and allows data from steels with high carbon content (greater 0.5wt%) and low dilatation to be successfully analysed. Subroutine MAP_STEEL_PARAM2 is a slightly improved version of MAP_STEEL_PARAM, called by MAP_STEEL_DILAT; 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.

Sample input and output data files (LENGTH.DAT and OUT.DAT) are provided with the program.

Top | Next | Prev


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

Top | Next | Prev


Input parameters

Name Type Description
IDATA integer Number of L,T pairs to be read in.
XBAR real Carbon concentration (weight percent).
SI real Silicon concentration (wt%).
MN real Manganese concentration (wt%).
NI real Nickel concentration (wt%).
MO real Molybdenum concentration (wt%).
CR real Chromium concentration (wt%).
VAN real Vanadium concentration (wt%).
XALPHA real Amount of carbon trapped in ferrite (wt%). This can be calculated using MAP_STEEL_XALPH.
EXA real Linear expansion coefficient of ferrite (K-1).
EXG real Linear expansion coefficient of austenite (K-1).
IPARAM integer Set IPARAM to 1 if the user wishes the program to read in values for the ferrite and the pure austenite lattice parameters (GG0 and PP). Otherwise if IPARAM to 0, PP is calculated using subroutine MAP_STEEL_FERR and GG0 is set to 3.573x10-10m.
GG0 real Lattice parameter for pure austenite at room temperature (metres).
PP real Lattice parameter for the ferrite in the steel at room temperature (metres).
L real array of
dimension IDATA
Fractional change in length, as measured by the dilatometer.
T real array of
dimension IDATA
Temperature (°C).
TIME real array of
dimension IDATA
Time since start of transformation (incubation time) (seconds).

The input parameters are read in by the program from a file called LENGTH.DAT and should be arranged as follows:

PP  GG0 
L(1)  T(1)  TIME(1)
L(2)  T(2)  TIME(2)
L(3)  T(3)  TIME(3)  etc.

Line 3 (PP and GG0) should only be included if IPARAM is not set to 0.

Output parameters

Name Column label Description
T Ctemp Temperature (°C).
L Del-L Fractional change in length.
TIME Time(s) Incubation time (seconds).
VA V-alpha Volume fraction of ferrite.
XG Xg-wt% Carbon concentration in carbon-enriched austenite (wt%).
XGM Xg-Mfrc Mole fraction of carbon in carbon-enriched austenite.
AAT AAT Ang Ferrite lattice parameter (Å) at temperature T.
AGT AGT Ang Lattice parameter (Å) of austenite containing the initial amount of carbon (XBAR) at temperature T.
AGTX AGTX Ang Lattice parameter (Å) of the carbon enriched austenite (containing XG amount of carbon) at temperature T.
AA AA Ferrite lattice parameter at 298K.

The program writes all the output to the file OUT.DAT.

Top | Next | Prev

Error Indicators

Execution of the program is halted and an error flagged if the number of iterations in subroutine MAP_STEEL_PARAM2 exceeds 1010 or if the number of iterations in the main program exceeds 104.

Top | Next | Prev


No information supplied.

Top | Next | Prev

Further Comments

The program will fail if the input data includes negative values for the dilatation.

See also program MAP_UTIL_READLEN.

Top | Next | Prev


1. Program text

Complete program.

2. Program data


3. Program results

See file: OUT.DAT

Top | Next | Prev

Auxiliary Routines




Top | Next | Prev


dilatometer, austenite, ferrite, transformation, volume fraction

Top | Next | Prev


Download source code

Top | Prev

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

MAP Website administration / map@msm.cam.ac.uk

Top | Index | MAP Homepage Valid HTML 3.2!