MTDATA – Phase Diagram Software from the National Physical Laboratory









MTDATA Demonstration : Iron Based Alloys


  1. Introduction
  2. The Fe-Cr system
  3. The Fe-Cr-Ti system
  4. MULTIPHASE calculations
  1. Sigma phase embrittlement
  2. A titanium-stabilised stainless steel
  3. Non-equilibrium phenomena


Calculated phase equilibria have been used to assist in a wide range of problems arising from the development and use of high-temperature alloys. Examples include solidification/melting behaviour relevant to the segregation of impurities during continuous casting, optimisation of compositions of prototype heat-resisting steels, and solid state reactions involving the precipitation of embrittling phases, for example the sigma phase.

The Fe-Cr system

Using MTDATA it is possible to model fcc-bcc transformations (the gamma loop) in iron-based alloys. Here the replotted partial phase diagram for the Fe-Cr system, together with experimental data, is shown. The full phase diagram calculated at the "compute" command has been omitted.

WHICH MODULE ? binary define system 'Fe,Cr' source sgte_sol output 'fecr' !
sgte_sol        - SGTE Solution Database 3.01 - 19/7/93

BINARY OPTION ? step t 1100 1700 10 ! compute !
BINARY OPTION ? abscissa limits 0 0.2 !
BINARY OPTION ? replot experimental_file 'fecr.exp' !

The Fe-Cr-Ti system

Combination with data for the iron-titanium and chromium-titanium binary systems allows through TERNARY and its REPLOT command the calculation of the iron-rich corner of the iron-chromium-titanium system. The complete isothermal section calculated at the "compute" command has been omitted.

WHICH MODULE ? ternary
TERNARY OPTION ? define system 'Fe,Cr,Ti' source sgte_sol !
sgte_sol        - SGTE Solution Database 3.01 - 19/7/93

TERNARY OPTION ? set t 1300 ! compute !
TERNARY OPTION ? set n(1) 0.85 n(2) 0.10 n(3) 0.05 !
TERNARY OPTION ? replot magnification 5 5 !

MULTIPHASE calculations

Titanium markedly reduces the composition range over which the fcc phase is stable in comparison with chromium. Using MULTIPHASE the amounts of the fcc and bcc phases present in a ternary alloy of composition 10 mol % Cr, 0.5 mol % Ti, balance Fe, are mapped as a function of temperature in the following diagram.

WHICH MODULE ? multiphase
MULTIPHASE OPTION ? define datafile !
MULTIPHASE OPTION ? set n(1) 0.895 n(2) 0.10 n(3) 0.005 !
MULTIPHASE OPTION ? step t 1000 1500 5 !
MULTIPHASE OPTION ? compute print graphics !
MULTIPHASE OPTION ? ordinate n phase !

The previous diagram simulates the effect of moving through the gamma loop in temperature with respect to a fixed composition, and for this particular alloy the material is not completely austenitic at any temperature. A series of calculations in which the composition of a six-component steel was varied to produce optimum properties has led to the successful development of two prototype stainless steels.

Sigma phase embrittlement

For the previous calculated phase equilibria the solution phases, for example, liquid, fcc and bcc, have been treated using the Redlich-Kister/Muggianu model for non-ideal mixing. For these relatively simple metallic solutions this widely used model is of proven reliability. However, for systems in which there is very strong interaction between the components, or for intermetallic compounds which exhibit a range of homogeneity, it is necessary to treat the components as mixing on separate sublattices.

A case in point is that of the embrittling sigma phase, here treated using the sublattice model developed by Hillert and Staffansson in 1968.

The embrittlement of heat-resisting alloys due to precipitation of sigma phase is well known and has been extensively studied. A full understanding relies on a knowledge of the phase equilibria. However, as with light-metal alloys the available information is primarily limited to the simpler ternary sub-systems, and accurate data are sparse for temperatures below about 900 K.

The next example shows the calculated iron-chromium phase diagram utilising the sublattice model for the sigma phase.

BINARY OPTION ? define datafile 'fecr.mpi' !
BINARY OPTION ? classify miscibility(bcc) 1 !
BINARY OPTION ? step t 500 2500 10 ! compute !

The Gibbs energies of formation of the sigma phase, and those of the other phases in this binary system can be calculated as a function of composition using the Module GPLOT.

GPLOT OPTION ? define datafile 'fecr.mpi' !
GPLOT OPTION ? set t 1000 !
GPLOT OPTION ? classify reference bcc ! compute !
GPLOT OPTION ? plot go

Unlike the conventional solutions, liquid, fcc and bcc, which are modelled over the entire composition range, the sigma phase is modelled over a limited composition range. The sigma phase has a unit cell with 30 atoms. Due to the site occupation on the sublattices involved in this treatment Gibbs energies of the sigma phase run from 8/30 or 26.6 mol % Fe to 26/30 or 86.6 mol % Fe.

A key sub-system in relation to the development of stainless steels and the potential embrittlement by the sigma phase is the chromium-iron-nickel system. The following example shows a calculated isothermal section for this system at 1273 K, validated by the superimposed experimental tie-line data. Again, only the replotted diagram is shown.

WHICH MODULE ? ternary
TERNARY OPTION ? define system 'Fe,Cr,Ni' source sgte_sol output 'fecrni' !
sgte_sol        - SGTE Solution Database 3.01 - 19/7/93

TERNARY OPTION ? set t 1273 ! compute !
TERNARY OPTION ? replot experimental_file 'fecrni.exp' !

The sigma phase appears in this ternary system below about 1200 K, although it is not stable in the binary chromium-iron system at temperatures above 1100 K. The following example shows the calculated phase equilibria for 1000 K, delineating the composition range over which the sigma phase is stable.

TERNARY OPTION ? set t 1000 !
TERNARY OPTION ? compute !

A titanium-stabilised stainless steel

Phase equilibria for a six-component system follow. The composition in wt % is 0.08 C, 18 Cr, 10 Ni, 1 Si, 0.4 Ti, balance Fe and it approximates to a type 321 titanium-stabilised stainless steel.

ACCESS OPTION ? define system 'C,Cr,Fe,Ni,Si,Ti' sou sgte_sol out 'steel' !
sgte_sol        - SGTE Solution Database 3.01 - 19/7/93

WHICH MODULE ? multiphase
MULTIPHASE OPTION ? define datafile "steel.mpi" !
MULTIPHASE OPTION ? set temperature 600 1500 10 !
MULTIPHASE OPTION ? set w 1 w(1) 8E-4 w(2) 0.18 w(4) 0.1 w(5) 0.01 w(6) 0.004 !
MULTIPHASE OPTION ? compute print graphics !
MULTIPHASE OPTION ? ordinate mass phase ! plot go

Due to the small amounts of carbides present, particularly the M23C6 phase, the facility within MULTIPHASE to plot using a logarithmic ordinate is of great advantage. The following diagram quantifies in a convenient manner the proportions of the various phases present and indicates the temperatures at which this particular alloy is sigma prone.

MULTIPHASE OPTION ? ordinate log_scale yes ! plot go

Non-equilibrium phenomena

MTDATA, and in particular the MULTIPHASE Module, provides equilibrium thermodynamics and phase equilibrium calculations. However it is possible to investigate non-equilibrium phenomena using the APPLICATION interface. This programming interface allows the MTDATA computational tools to be used directly from a user's own FORTRAN code.

The cooling of a liquid may be investigated using the Scheil application to allow a certain fraction to solidify which is then removed from further consideration. This has the effect of changing the liquid composition and subsequent liquid-solid equilibria. In this way it is possible to simulate the effect of progressive crystallisation of a melt on the composition of the remaining liquid and solid phases formed.

The following examples show the calculated mass and composition of the liquid phase of an iron-chromium-nickel alloy as a function of temperature during solidification.

WHICH MODULE ? application
APPLICATION OPTION ? define datafile 'fecrni.mpi' !
APPLICATION OPTION ? set w(1) 0.74 w(2) 0.18 w(3) 0.08 !
enter percent solid: 10
enter number of liquid phase: 1
enter number of termination phase: 2
enter termination percent loss of liquid: 99.9
enter maximum number of steps: 200
enter <Min, max, tolerance> for temperature/K: 1700 1800 0.1
APPLICATION OPTION ? ordinate mass phase(liquid) !
APPLICATION OPTION ? abscissa temperature system ! plot go
APPLICATION OPTION ? ordinate w_(WEIGHT FRACTION) substance(liquid) ! plot go

The above examples of phase equilibria illustrate just a few applications of MTDATA in relation to iron-based alloy systems. Utilisation of the various databases within MTDATA allows the calculation of phase equilibria for a huge range of commercially important alloys. The areas cover alloy development, energy conversion, extractive metallurgy, crystal growth, joining (solders, welding, brazing), waste processing and recycling, and materials handling and compatibility. The benefits include cost and time saving, process prediction, improved control of processes and pollution and corrosion control.