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Program MAP_STEEL_MO2C

  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

Nobuhiro FUJITA and 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

To calculate the kinetics of the diffusion-controlled precipitation of carbides (taking capillarity effects into account), with particular reference to the carbides in secondary hardening steels (Fe-Mo-C steel). It is assumed that the first carbide to form is cementite.

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Specification

This is a self-contained program.
Language:FORTRAN
Product form:Source code

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Description

The program reads thermodynamic data (e.g. from MTDATA or Thermocalc) from a pre-established database. It then calculates the evolution of volume fraction and particle size with time for up to 4 carbides forming simultaneously.

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References

  1. N. Fujita and H. K. D. H. Bhadeshia, 'Precipitation of Molybdenum Carbide in Steel: Multicomponent-Diffusion & Multicomponent Capillarity', Materials Science and Technology, 1998, in press.
  2. J. D. Robson and H. K. D. H. Bhadeshia, 'Simultaneous Kinetics in Power Plant Steels: Part 1 - Kinetic Theory', Materials Science and Technology, 13 (8) 631-639 1997.
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Parameters

Input parameters

TK - double precision
Temperature in K.

DG - double precision array of size 4
Driving force for formation of carbides 1-4.

XB - double precision array of size 4
Mean composition of species 1-4 (mole fraction).

XC - double precision array of size 4x4
Equilibrium composition of species 1-4 in carbides 1-4 (mole fraction).

XA - double precision array of size 4x4
Composition of species 1-4 matrix in equilibrium with carbides 1-4 (mole fraction).

CXB - double precision array of size 4
Mean carbon composition of species 1-4 (mole fraction).

CXC - double precision array of size 4x4
Equilibrium carbon composition of species 1-4 in carbides 1-4 (mole fraction).

CXA - double precision array of size 4x4
Carbon composition of species 1-4 matrix in equilibrium with carbides 1-4 (mole fraction).

VMAX - double precision array of size 4
Maximum volume fraction of carbides 1-4.

SFEN - double precision array of size 4
Interfacial energy for nuclei of carbides 1-4 (Jm-2).

NAD - double precision array of size 4
Nucleation site density factor for carbides 1-4.

CTYPE - double precision array of size 4
             Morphology for carbides 1-4.
1 = Needle shaped
2 = Spherical

DS - double precision array of size 4
Species assumed to be controlling growth for phase 1-4.

CC - double precision
Mean carbon concentration (wt%).

GTHI - double precision
              Thickness of cementite on boundaries (m).

THI - double precision
Thickness of cementite within grain (m).

DR - double precision array of size 4
The ratio of cementite density between on boundaries and with in grains.

Output parameters

T - double precision
Time in seconds.
VE - double precision array of size 4
Volume fraction of carbides 1-4.

SZEX - double precision array of size 4x the number of time steps
The particle size for carbides 1-4.
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Error Indicators

None.

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Accuracy

No information supplied.

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Further Comments

The program is set to read the input data from an ASCII text file 'datain.d' and to write the results to file 'dataout.d'. An sample version of 'datain.d' is provided.

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Example

An example for cementite and Mo2C precipitating in a ternary Fe-2wt%Mo-0.1wt%C steel.

1. Program text

       Complete program

2. Program data

0
0.0D0
1.0D0
0.0D0
1.0D0
0.18623d-1
0.0D0
0.0D0
0.18623d-1
0.0114
0.061498
0.010433
0.00514
0.25
0.000493
0.2481
1d-6
1.0D0
1.0D0
0.150d-1  
0.150d-1
-1.29d2
0.150d-1
0.0114
0.582579
0.001192
0.00514
0.33
0.000493
50
923
0.11
0.9
5D-8
2D-8

3. Program results

        Time/s      Vol.F.(Cem.)   Mo2C Vol.F.   Mo2C Max.Size/m 
     0.10000D+03    0.18623D-01    0.12689D-09    0.41117D-08
     0.15000D+03    0.18623D-01    0.49499D-09    0.61235D-08
     0.20000D+03    0.18623D-01    0.13401D-08    0.81058D-08
     0.25000D+03    0.18623D-01    0.29375D-08    0.10058D-07
     0.30000D+03    0.18623D-01    0.56070D-08    0.11981D-07
     0.35000D+03    0.18623D-01    0.97042D-08    0.13875D-07
     0.40000D+03    0.18623D-01    0.15612D-07    0.15738D-07
     0.45000D+03    0.18623D-01    0.23733D-07    0.17571D-07
     0.50000D+03    0.18623D-01    0.34481D-07    0.19374D-07
     0.55000D+03    0.18623D-01    0.48276D-07    0.21147D-07
     0.60000D+03    0.18623D-01    0.65536D-07    0.22890D-07
     0.65000D+03    0.18623D-01    0.86671D-07    0.24602D-07
     0.70000D+03    0.18623D-01    0.11208D-06    0.26284D-07
     0.75000D+03    0.18623D-01    0.14214D-06    0.27935D-07
     0.80000D+03    0.18623D-01    0.17720D-06    0.29555D-07
     0.85000D+03    0.18623D-01    0.21760D-06    0.31145D-07
     0.90000D+03    0.18623D-01    0.26363D-06    0.32704D-07
     0.95000D+03    0.18623D-01    0.31559D-06    0.34232D-07
     0.10000D+04    0.18623D-01    0.37429D-06    0.35744D-07
     0.10500D+04    0.18623D-01    0.44018D-06    0.37240D-07
     0.11000D+04    0.18623D-01    0.51367D-06    0.38720D-07
     0.11500D+04    0.18623D-01    0.59519D-06    0.40184D-07
     0.12000D+04    0.18623D-01    0.68513D-06    0.41632D-07
     0.12500D+04    0.18623D-01    0.78388D-06    0.43063D-07
     0.13000D+04    0.18623D-01    0.89181D-06    0.44479D-07
     0.13500D+04    0.18623D-01    0.10093D-05    0.45878D-07
     0.14000D+04    0.18623D-01    0.11366D-05    0.47261D-07
     0.14500D+04    0.18623D-01    0.12741D-05    0.48628D-07
     0.15000D+04    0.18623D-01    0.14221D-05    0.49979D-07
     0.15500D+04    0.18623D-01    0.15808D-05    0.51313D-07
     0.16000D+04    0.18623D-01    0.17506D-05    0.52631D-07
     0.16500D+04    0.18623D-01    0.19315D-05    0.53932D-07
     0.20500D+04    0.18623D-01    0.38009D-05    0.63757D-07
     0.26000D+04    0.18623D-01    0.76084D-05    0.75582D-07
     0.32500D+04    0.18623D-01    0.14102D-04    0.87807D-07
     0.40500D+04    0.18623D-01    0.26060D-04    0.10179D-06
     0.51000D+04    0.18623D-01    0.50134D-04    0.11895D-06
     0.64000D+04    0.18623D-01    0.98992D-04    0.13963D-06
     0.80000D+04    0.18623D-01    0.20007D-03    0.16459D-06
     0.10050D+05    0.18623D-01    0.41993D-03    0.19565D-06
     0.12650D+05    0.18594D-01    0.88711D-03    0.23315D-06
     0.15900D+05    0.18383D-01    0.18181D-02    0.27660D-06
     0.20050D+05    0.17502D-01    0.35586D-02    0.32586D-06
     0.25200D+05    0.14879D-01    0.62906D-02    0.37594D-06
     0.31700D+05    0.88666D-02    0.97735D-02    0.42109D-06
     0.39900D+05    0.00000D+00    0.12033D-01    0.44464D-06
     0.50200D+05    0.00000D+00    0.12632D-01    0.45037D-06
     0.63150D+05    0.00000D+00    0.13115D-01    0.45486D-06
     0.79500D+05    0.00000D+00    0.13500D-01    0.45835D-06
     0.10005D+06    0.00000D+00    0.13803D-01    0.46105D-06
     0.12595D+06    0.00000D+00    0.14040D-01    0.46313D-06
     0.15855D+06    0.00000D+00    0.14225D-01    0.46475D-06
     0.19960D+06    0.00000D+00    0.14370D-01    0.46600D-06
     0.25125D+06    0.00000D+00    0.14483D-01    0.46697D-06
     0.31630D+06    0.00000D+00    0.14572D-01    0.46773D-06
     0.39820D+06    0.00000D+00    0.14641D-01    0.46832D-06
     0.50125D+06    0.00000D+00    0.14695D-01    0.46878D-06
     0.63105D+06    0.00000D+00    0.14738D-01    0.46914D-06
     0.79440D+06    0.00000D+00    0.14772D-01    0.46942D-06
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Auxiliary Routines

The subroutines called by this program are :-

CONST
GROWTH
LINEARGROWTH
PARABOLGROWTH
SIZE
NURATE
DIFCO
USER
LINECALC

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Keywords

simultaneous precipiateion reactions, capillarity, secondary hardening steel

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Download

Download source code

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