Modelling of ternary phase diagrams
Assadour Margarian
phase diagrams? Or even the construction of ternary phase diagrams
from binary phase diagrams.
Cheers
--
Assadour Margarian Tel: 61 - 2 - 413 7409
Magnetic Materials Resarch Fax: 61 - 2 - 413 7383
CSIRO Division of Applied Physics email: as...@dap.CSIRO.au
PO Box 218, Lindfield NSW 2070,Australia
ara...@maple.circa.ufl.edu
/Does anyone know of a textbook that discusses the modelling of ternary
/phase diagrams? Or even the construction of ternary phase diagrams
/from binary phase diagrams.
/
/Cheers
/
/--
/Assadour Margarian Tel: 61 - 2 - 413 7409
/Magnetic Materials Resarch Fax: 61 - 2 - 413 7383
/CSIRO Division of Applied Physics email: as...@dap.CSIRO.au
/PO Box 218, Lindfield NSW 2070,Australia
Yes, the book we use for our phase diagrams class here class here (by Rhines)
is incredible. Unfortunately, it's out of print.
-jason
IMPurdy
> Does anyone know of a textbook that discusses the modelling of ternary
> phase diagrams? Or even the construction of ternary phase diagrams
> from binary phase diagrams.
....
> Assadour Margarian Tel: 61 - 2 - 413 7409
Dunno about the modelling, but here are some good refs for construction of
phase diagrams:
Porter and Easterlings book: Phase Transformations of Metals and Alloys
and there is also a good book by Prince (don't recall the title). Its old
and out of print, but very good. Discusses phase diagrams in detail.
Another text, by Tamas and Pal even has 3-D pictures of ternary and
higher-order systems. The book comes with a pair of 3-D glasses.
Chad M. Miller
>(Assadour Margarian) wrote:
>
>> Does anyone know of a textbook that discusses the modelling of ternary
>> phase diagrams? Or even the construction of ternary phase diagrams
>> from binary phase diagrams.
>....
>> Assadour Margarian Tel: 61 - 2 - 413 7409
A good journal to look at for phase diagram modelling (calculating) is
"CALPHAD". It isn't a textbook but I've found it helpful.
Chad
--
___________________________________________________________________________
Chad M. Miller -- cmmi...@iastate.edu
Metallurgy, Iowa State University
__________________________________________________________________________
Del Cotter
G-...@mct.anl.gov (IMPurdy) writes:
[ternary phase equilibria recommendations]
>Porter and Easterlings book: Phase Transformations of Metals and Alloys
Seconded.
>and there is also a good book by Prince (don't recall the title).
>It's old and out of print, but very good.
>Discusses phase diagrams in detail.
'Alloy Phase Equilibria', Elsevier (1966?). Seconded.
Shame it's out of print, but since Prince was our first year phase
equilibrium lecturer, we got a neatly photocopied edition :-)
>Another text, by Tamas and Pal even has 3-D pictures of ternary and
>higher-order systems. The book comes with a pair of 3-D glasses.
K00L!
--
',',',',',',',' Del Cotter mt9...@brunel.ac.uk
',', ,'
',', ,' How come Alexander Abian gets
',' more followups than I do?
Steve Marschman
>
>Does anyone know of a textbook that discusses the modelling of ternary
>phase diagrams? Or even the construction of ternary phase diagrams
>from binary phase diagrams.
>
University of Montreal, Montreal, Quebec, Canada, H3C 3A7. He can build a phase
diagram from thermodynamic data (binaries and ternaries). He and others at UM
and Argonne National Laboratory in Chicago, IL have been working on modeling
systems for years.
Good luck.
Steve
Lars Hoglund
For those interested in phase diagram modelling.
(more information can be retrieved from the anonymous ftp server
lunix.met.kth.se)
Software Description Form November 1993
Thermo-Calc system
Copyright: 1993, Foundation of Computational Thermodynamics
Site: Department of Material Science, KTH, S-100 44 Stockholm, Sweden
Contact persons: Bo Sundman or Bo Jansson
Tel +46 8 790 9140; Fax +46 8 100 411; E-mail t...@met.kth.se
General
Thermo-Calc is a software package for equilibrium and phase diagram
calculations. It can be applied to any thermodynamic system in the
fields of chemistry, metallurgy, material science, alloy development,
geochemistry, semiconductors etc. depending on the kind of database it
is connected to. It can also be used as a subroutine package in
application programs, for example in transformation or process
simulations. The first version of Thermo-Calc was released in 1981.
There has been an update almost every year and the most recent,
version J, was released in November 1993. The first description of
Thermo-Calc was published 1985 [85Sun]. A recent publication about
Thermo-Calc can be found in [93Jan].
Modularity
Thermo-Calc consists of modules for the various tasks the user may be
interested to perform. There is one module, called TDB, for the
selection of database and data. Another module, called GES, is used
for listing thermodynamic data or interactive manipulation and
entering of such data. The most important module for equilibrium
calculation is called POLY. A useful facility in Thermo-Calc is the
PARROT module for assessment of experimental data in terms of
thermodynamic models. There is also a module called TAB for tabulation
of data for substances or chemical reactions. The user may also
develop and add modules of his own.
With Thermo-Calc one may simulate processes where the time-dependence
can be ignored, for example by stepwise calculation of a sequence of
equilibria with transfer of heat and matter between the equilibria.
This "reactor concept" has been inspired by the work of Gunnar
Eriksson [78Eri] and implemented as a generic reactor module in
Thermo-Calc. This is available in source code and the user may tailor
it for his specific process. Another example of a transformation
simulation which do not require kinetic data is the Scheil-Gulliver
solidification scheme which can be performed in the POLY-3 module.
User interface
Each module is interactive and the user has a menu of commands to
select from. A command is usually a whole sentence and that makes it
easy to understand what it does. When a module is expecting input from
the user it will write a prompt. In order to minimize the typing
required by the user all commands can be abbreviated. In most cases a
command needs some additional information in order to be executed and
the user is then asked questions. In most cases the program will
suggest a default value which is taken as answer if the user just
presses the RETURN key. An experienced user who knows what questions
the command will ask can type the answers after the command on the
same line. This minimizes the amount of unnecessary output from the
program.
All modules have a user's guide in the documentation set and these
manuals can also be obtain as on-line help by use of the "help" and
"information" commands or by giving a question mark "?" as answer to a
question one does not understand.
Equilibrium calculations
The current version of the equilibrium module is POLY-3 developed by
Bo Jansson [84Jan]. It has a very powerful and general set of commands
to specify almost any kind of equilibrium or phase diagram
calculation. Each condition necessary for the calculation is set
separately and examples of conditions are:
o value of the temperature or the enthalpy (or entropy);
o value of the pressure or the volume;
o activities or chemical potentials of components;
o overall composition in total number of moles or mass or in mole or mass fractions;
o specifying some or all stable phases, e.g. the stable eutectoid temperature in
Fe-C can be calculated by specifying that the Fcc, Bcc and Cementite phases
must be stable;
o the composition of a stable phase;
o general functions of state variables, e.g. the congruent melting point of
Pyrrhotite in the binary Fe-S system can be calculated directly by giving
X(Liquid,S)-X(Pyrrhotite,S)=0 as one of the conditions.
By combining various types of conditions the user can directly
calculate many types of equilibria that he would only find by trial
and error by using other software for equilibrium calculations. This
means that the user can calculate directly how the "input" to a
process should be in order to obtain the desired "output" rather than
forcing the user to change the "input" manually and calculate several
times. It is a unique feature in POLY-3, not available in most other
software for thermodynamic calculations, that conditions on individual
phases like the composition of a phase or its enthalpy can be set.
In POLY-3 the user also can define functions of state variables and
use these as conditions or for plotting the final results. The user is
thus not limited to a set of predefined diagrams but can combine
conditions as he wishes for generating a diagram. In particular the
user may calculate the derivative of any state variable with respect
to a condition using the dot "." notation. A simple example of using
this is the heat capacity which is the function "H.T". Another example
in a nitrogen alloyed stainless steel is the function "X(Fcc,N).T" (in
both calculations the temperature must have been set as a condition).
The function gives how much the solubility of N in Fcc will change
with a small change of the temperature.
Diagrams and graphics
Any condition in POLY-3 can be used as axis variable and one may step
in the axis variable and calculate how any other quantity depends on
the axis variable. In the post processor one may select any number of
quantities to be plotted on the axis and an example of this in a
multicomponent system is how the amounts of the stable phases vary
with temperature. Another example is how the carbon activity varies
with the composition.
One may also set two conditions as axis variables and the program will
then calculate lines where the number of stable phases changes. This
is usually called a phase diagram. Due to the generality of
Thermo-Calc all types of phase diagrams can be calculated in almost
the same way. Examples of phase diagrams are binary T-x diagrams,
ternary isothermal sections, multicomponent isoplets, predominance
area diagrams. With Thermo-Calc one may calculate many types of
diagrams that noone has thought of before.
In POLY-3 there is a postprocessor which allows the user to select
axis variables to be used in the plot. They may be different from
those used in the calculation but a user must be aware of the fact
that some combinations of axis variables may not be sensible. Only
two-dimensional plots can be generated but scaling and size can be set
interactively. Many different types of graphical devices are supported
for example X-windows, Tektronix 4010, 4107 and 4125, HPGL,
HP-Laserjet, Regis and PostScript. On PC and PS/2 systems there is
also support for EGA, VGA etc.
Thermo-Calc uses a public domain graphics software, DIGLIB, developed
at Lawrence Livermore in USA.
Thermodynamic models
In the Gibbs Energy System (GES module) the thermodynamic data needed
for the calculations are stored. Normally these data are read from a
database but the user can interactively list or amend the data. A
large number of models for the composition dependence have been
implemented in GES and the most important ones are
o The regular model with binary Redlich-Kister parameters and composition
dependent ternary parameters according to Hillert [80Hil];
o The compound energy model with up to 10 sublattices and Redlich-Kister
and ternary interaction parameters on all sublattices [81Sun1];
o Molecules, associates and ions can be constituents in any sublattice;
o The two-sublattice ionic liquid model [85Hil];
o The associate model [79Jor];
o The Kapoor-Frohberg-Gaye cell model for liquid oxides [84Gay];
o The CVM tetrahedron model [51Kik, 90Sun1];
o The Inden model for magnetic ordering [75Ind];
o The Pitzer model for aqueous solutions including the Debye-Huckel term.
Many of the models listed above are actually special cases of the
generalized compound energy model [86And]. Of course each phase can be
described with a different model. A review of most of the models
implemented in Thermo-Calc can be found in [90Sun2].
All parameters in the models can be temperature and pressure dependent
and the logarithmic and exponential function can be used in the
temperature and pressure functions.
Algorithms and data structures
The equilibrium calculation method used in the POLY modules is a
minimization of the integral Gibbs energy using a Lagrangian
multiplier method for the constraints. This is the same method used by
almost all other software for equilibrium calculations. But in
Thermo-Calc the minimization algorithm has been implemented in a more
general way, using analythically calculated second derivatives
[84Jan], which allows non-linear constraints and this makes it
possible for the user to set conditions in a more flexable way.
This generalization is possible because the GES module provides
subroutines for the calculation of analytical first and second
derivatives of the integral Gibbs energy with respect to temperature,
pressure and the constitution of all phases [81Sun2]. The use of first
and second of derivatives are necessary for the non-linear constraints
and they also speed up convergence and increase the stability of the
calculation.
The calculation of thermodynamic equilibrium is an iterative process
and it is necessary to supply some start varlues for the compositions
of the phases in the system. This has earlier been a quite complicated
but from version F of Thermo-Calc the automatic start values generated
from the databases will almost always work.
In the GES module the thermodynamic data are stored in a list
structure with records and pointers [81Sun2]. Compared to a
traditional linear storage in arrays, the list structure has the great
advantage that the expression for the integral Gibbs energy of the
model used is described by the actual storage of the parameters. This
makes it possible to store data for many different models in a way
that saves memory and is efficient for calculations. The use of list
structures is employed in the other modules also.
Thermo-Calc is written in Fortran 77 and consists of more than 50000
lines of code divided in more than 500 subroutines. It has been
implemented on a number of different hardware and operating systems. A
small number of the subroutines are machine dependent and has to be
rewritten for different computers and operating systems.
Availability
Thermo-Calc is available on-line on TCP/IP, the X.25 network or modem
from KTH, Sweden or as a package (in slightly variable forms) on for
example the following computers and operating systems:
o VAX/VMS, VAX/Ultrix and DEC/Ultrix
o DEC-Alpha/VMS or OSF
o SUN SPARC/SunOS, SUN 3/SunOS, SUN/Solaris
o HP-9000/800, HP-UX
o IBM RS/6000, AIX
o IBM PC or IBM PS/2 or compatible (MS-DOS and Windows)
o Sillicon Graphics
The IBM PC and PS/2 versions require at least 4 Mbyte of memory and
a 486 or a 386 with a math coprocessor. Thermo-Calc version J can also
be used together with MS-Windows on PC.
Other versions, especially on various UNIX dialects, are available on
request. A "benchmark calculation" on some computers is given below.
The benchmark is an isopleth calculation of Fe-13%Cr-C between 0-2% C
and 800 to 1800 K. Start point at 1% C and 1200 K, no direction. Only
phases which can be stable are included.
On PC several frequences and three different fortran compilers have been
tested, Salford on MS-DOS, Microsoft on OS/2 and Lahey on both MS-DOS
and OS/2.
DEC VAX uVAX-II ;VMS ;1529 s
DEC VAX 4000VLC ;VMS ; 216 s
DEC DEC DS3100 ;Ultrix ; 106 s
DEC AXP 3000/400 ;OpenVMS ; 14 s
SUN SLC ;SunOS ; 166 s
SUN ELC ;SunOS ; 92 s
SUN SS-2 ;SunOS ; 76 s
SUN SS-10/41 ;Solaris ; 31 s
HP 720 ;HP-UX ; 34 s
IBM RS/6000 320 ;AIX ; 55 s
PS/2 M70 386/387 25 MHz ;DOS/Salford 2.71 ; 466 s
PC/AT 486, 33 MHz, 64kb cache ;DOS/Salford 2.71 ; 119 s
PC/AT 486, 66 MHz, 256kb cache ;DOS/Salford 2.71 ; 67 s
Assessment
A separate program, called Thermo-Optimizer, is included in most
Thermo-Calc distributions. Thermo-Optimizer includes the PARROT module
[84Jan] which is used for assessing experimental data on the
thermochemistry and phase diagram in terms of parameters of a
thermodynamic model. These parameters can later be incorporated in a
database for Thermo-Calc.
The Thermo-Optimizer can be used for other purposes than fitting model
parameters as it is actually an overlayed minimization procedure. Thus
one may calculate para-equilibrium or equilibria where the properties
of the phases depend on eachother using the Thermo-Optimizer.
Databases
Thermo-Calc must be connected to databases with thermochemical data.
There are a number of such databases available, mainly for special
applications like the Fe-base database for steels, the IRSID database
for metallurgical slags, a database for Si-Al-O-N systems, the Saxena
database for geochemistry etc. A user can also have his own databases.
The Scientific Group Thermodata Europe (SGTE) has a long term aim to
develop a validated and generally applicable thermodynamical database
[86Ans]. At present this database consists of carefully checked and
consistent data for about 3000 compounds and 2000 gas species in a
substance database and about 250 assessed alloys and other solutions
in a solution database. A special publication of all unary data of
this database is available [91Din]. There is separate a documentation
page for the most important databases that can be used with
Thermo-Calc.
The development of databases is a major scientific task connected with
the use of thermodynamic software. It is a responsibility for all who
work in this field to make all efforts to provide the users with
reliable and high quality databases for many different applications.
Documentation and courses
The documentation set to the Thermo-Calc system consists of two
volumes with approximately 700 pages. The volume includes the user's
guides and the second gives about twenty examples of applications. The
examples gives the full interaction between the user and the program
showing how to calculate many different types of equilibria and
diagrams.
A programmers guide is also available on request. This describes all
subroutines in the METLIB utility package for the user interface, list
manipulation etc. It also describes the subroutines in GES and the
most important routines in POLY-3.
There are two-day courses for new users of Thermo-Calc arranged
several times every year at KTH. Recent years courses have alse been
arranged in France, USA, England, Japan and Australia. Special courses
can be arranged on request.
Revision history
The first release of the Thermo-Calc system was in 1981 including the
TDB, GES-4 and POLY-1 modules. In GES-4 the compound energy model
(then called the sublattice model) was supported but with elements as
constituents only. The POLY-1 module was intended for alloy phase
diagram calculations and did not allow calculation of for example a
gas phase.
In 1986 Thermo-Calc version C was released with a new GES-5 module
including a large number of new models, for example the gas phase, the
two-sublattice ionic liquid model and the associated model. The first
version of POLY-3 which could handle single equilibria calculations
for these new (as well as the old) models was also included. In the
Thermo-Calc versions released later a large number of bugs have been
corrected, some new models in GES-5 and the step and map features of
the POLY-3 module have been added as well as a new post-processor. The
TDB module has also been improved in order to handle large databases
and simplify start value problems. The Thermo-Optimizer with the
PARROT module has been included since 1986.
The modifications of POLY-3 needed for the Scheil-Gulliver
solidification simulation were added 1989 and the reactor module was
added 1990.
Future
A new user interface, based on X-windows, is currently developed and
will make it possible for "occational" users to take advantage of the
powerful features of Thermo-Calc [93Sun]. This also includes a
graphical user interface to the reactor module. A number of smaller
packages for PC will also be developed for specific applications like
phase fraction plots etc. The facilities offered by a thermodynamic
database system will soon be as indispensable a tool for materials and
process development as an electron microscope.
Thermo-Calc is limited to equilibrium calculations and will always
be. For transformations there is a separate software project, the
DICTRA program [90And], which uses Thermo-Calc together with kinetic data
to simulate solidification and other processes.
Acknowledgement
The development of Thermo-Calc have been inspired by Prof. Mats
Hillert from his early recognition of the importance of thermodynamic
calculations [70Hil]. His constant advice and support has been
essential for the success of this work. The Swedish Board for
Technical Development has given generous support for the development
of both software and databases in Thermo-Calc.
The development of Thermo-Calc would not have been possible without
the interaction with a growing community of users. Sandvik Steel AB in
Sweden was the first large user and a close cooperation with Dr Larry
Kaufman, the originator of the "Calphad" technique [70Kau], has
provided many suggestions and improvements. New groups of users from
universities and industry are constantly added and they are both a
testing ground for ideas and a source of suggestions for improvements.
Currently more than 150 universities and industries all over the world
has a Thermo-Calc license.
References
51Kik: R Kikuchi, Phys Rev 81, 1951, p 998
70Hil: M Hillert, in "Phase Transformations", ASM Metals Park, Ohio, 1970
70Kau: L Kaufman and H Bernstein, "Computer Calculation of Phase Diagrams",
Acad Press, NY USA, 1970
75Ind: G Inden, Z Metallkde, Vol 66, 1975, p 725
78Eri: G Eriksson and T Johansson, Scand J of Met, Vol 7, 1978, p 264
79Jor: A S Jordan, in "Calculations of Phase Diagrams and Thermochemistry
of Alloy Phases", Eds Y A Chang and J F Smith, TMS-AIME, 1979, p 100
80Hil: M Hillert, Calphad, 1980, p 1
81Sun1: B Sundman and J Ågren, J Phys Chem Solids, Vol 42, 1981, p 297
81Sun2: B Sundman, Thesis, Royal Institute of Technology, Stockholm, Sweden
84Gay:, H Gaye and J Welfringer, 2nd Int Symp on "Metallurgical Slags and fluxes",
Warrendale, P A, Met Soc of AIME, Eds H A Fine and D R Gaskell, 1984, p 357
84Jan: B Jansson, Thesis, Royal Institute of Technology, Stockholm, Sweden
85Hil: M Hillert, B Jansson, B Sundman and J Ågren, Metall Trans A, 16A,
1985, p 261
85Sun: B Sundman, B Jansson and J-O Andersson, Calphad, 1985, p 153
86Ans: I Ansara and B Sundman, in "Computer Handeling and Dissemination
of Data", Ed P S Glaser, Elsevier Science Publ, CODATA, 1986, p 154
86And: J-O Andersson, A Fernandez Guillermet, M Hillert, B Jansson and
B Sundman, Acta Met, Vol 34, 1986, p 437
90And: J-O Andersson, L Höglund, B Jönsson and J Ågren, in "Fundamentals
and Applications of Ternary Diffusion", Ed G R Purdy, Pergamon Press,
NY USA, 1990, p 153
90Sun1: B Sundman and T Mohri, Z Metallkde, Vol 81, 1990, p 251
90Sun2: B Sundman, Anales de Fisica, Serie B, Vol 86, 1990, p 69
91Din: A Dinsdale, Calphad, Vol 15, 1991, p 317
93Jan: B Jansson, M Schalin, M Selleby and B Sundman, in "Computer Software
in Chemical and Extractive Metallurgy", Eds C W Bale and G A Irons,
The Met Soc of CIM, Quebec, 1993, p 57.
93Sun: B Sundman, B Jansson and M Schalin, J Phase Equil, 1993, p?
Competitors
Several packages for equilibrium calculations with databases are
available. The applicability and quality may vary and it is up to the
user to find the package that suits his needs best. The list below is
not complete.
ChemSage: GTT, Kaiserstrasse 100, D-52134 Herzogenrath 3, Germany
FACT: CRCT, Ecole Polytechnique, PO Box 6079, Station A,
Montreal, Quebec, Canada H3C 3A7
HSC: Outokumpu Research Oy, PO Box 60, FIN-28101 Pori, Finland
MTDATA: Division of Materials Metrology, NPL, Teddington,
Middlesex TW11 0LW, UK
Thermo-Calc: Division of Computational Thermodynamics,
Department of Materials Science and Engineering, KTH, S-100 44 Stockholm, Sweden
Thermodata: Thermodata, Domaine Universitaire de Grenoble,
BP 66, F-38402 Saint Martin d'Heres, Cedex, France
AESOP69
Assadour,
The person you want to contact is Larry Kaufman. He has published a ton of
articles on the modelling of phase diagrams. Also look up issues of The
Bulletin of Alloy Phase Diagrams; this journal was the source of much work in
phase diagrams from about 1980 to the late 80's and was published by the the US
government's National Bureau of Standards(now called NIST).
Good Luck
AESOP69