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  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.

Added to MAP (corrected version): July 1999.

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To calculate the volume fraction of the amount transformed from austenite to ferrite, during cooling, from a measure of the length change.

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Product form:Source code

Complete program.

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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_DILAT calculates the volume fraction of transformed austenite to ferrite from the measured dilatations. Subroutine MAP_STEEL_PARAM is used to obtain a value of the lattice parameter of austenite, taking into account the concentrations of all alloying additions [1,2]. Newton's iteration procedure is utilised to refine the accuracy of the results. The calculations are performed for several different values of the ferrite lattice parameter at 298K. Sample input and output data files (LENGTH.DAT and OUT.DAT) are provided with the program.

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  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.

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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 (in K-1).
EXG real Linear expansion coefficient of austenite (in K-1).
L real array of
dimension IDATA
Fractional change in length, as measured by the dilatometer.
T real array of
dimension IDATA
Temperature (°C).

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

L(1)  T(1)
L(2)  T(2)
L(3)  T(3) etc.

Only the first two columns of data (L and T) in the data file are read by the program. Any subsequent columns are ignored.

Output parameters

Name Column label Description
T CTEMP Temperature (°C).
L Del-L Fractional change in length.
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.

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Error Indicators


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No information supplied.

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Further Comments

This program is suitable for use only on data from steels containing an initial carbon concentration of less than about 0.5 wt%. MAP_STEEL_DILAT2 is a modified version of the program, which can analyse data from steels with higher carbon concentrations.

See also program MAP_UTIL_READLEN.

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1. Program text

Complete program.

2. Program data


3. Program results

See file: OUT.DAT

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Auxiliary Routines




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dilatometer, austenite, ferrite, transformation, volume fraction

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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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