Transcript Computational Thermodynamics

Computational Thermodynamics
1
Outline

Theoretical background: thermodynamics of substitional solutions

Introduction to thermodynamic database: element, specie, constitution,
phase, function

Introduction to Pandat software: phase diagram, line/propert and point
calculation

Pandat and database. Writing a database for Cu-Ni system
Theoretical background: thermodynamics
of substitional solutions
By definition, the phase is a homogeneous part of the space.
The phase has the same structure, property and the phase is limited by
phase boundary. Do you agree with this definition?
We can see, that inside the glass
We have 4 different phases:
- Solid phases: ice and straw
- Liquid phase: pepsi-cola
- Gas phase: CO2
But, of course, we can guess, those phases
Are not in equilibrium!
Theoretical background: thermodynamics
of substitional solutions
Let’s re-define a phase:
The phase is a homogeneous part of the space and
the phase is limited by a phase boundary
Theoretical background: thermodynamics
of substitional solutions
A phase diagram is a type of chart
used to show conditions at which
thermodynamically distinct phases
can occur at equilibrium.
Theoretical background: thermodynamics
of substitional solutions
Condition for two phases to be in equilibrium
ìïm aA = m Ab
í a
b
ïîm B = m B
Theoretical background: thermodynamics
of substitional solutions
0
0
0.2
0.4
0.6
0.8
1
-1000
-2000
-3000
-4000
-5000
ΔμAα=ΔμAβ
-6000
-7000
ΔGα
ΔGβ
ΔμBα = ΔμBβ
Theoretical background: thermodynamics
of substitional solutions
ìïm AL = m Ab
í L
ïîm B = m Bb
L
β
ìïm aA = m AL = m Ab
í a
ïîm B = m BL = m Bb
L+β
α+L
α
ìïm aA = m Ab
í a
ïîm B = m Bb
α+β
A
B
Theoretical background: thermodynamics
of substitional solutions
Substitutional solution A-B: atoms A can substitute atoms B and vice versa.
Both phases (FCC and Liquid) are substitional
solutions
Theoretical background: thermodynamics
of substitional solutions
In case of Face Centered Cubic FCC_A1 structure and Cu – Ni alloy,
There are no restrictions and both types of atoms can occupied
any position in crystal structure for whole concentration range.
The Gibbs energy will, in this case, has 3 parts:
FCC _ A1
Cu,Ni
G
= G +G
0
MIX
+G
XS
Theoretical background: thermodynamics
of substitional solutions
FCC _ A1
Cu,Ni
= G +G
FCC _ A1
Cu,Ni
= xCuG
G
G
0
MIX
+G
FCC _ A1
Cu
XS
+ xCuG
FCC _ A1
Cu
+RT (xCu ln xCu + xCu ln xCu ) + G
XS
Theoretical background: thermodynamics
of substitional solutions
FCC _ A1
GCu,Ni
=
FCC _ A1
FCC _ A1
xCuGCu
+ xCuGCu
Superposition of Gibbs energies
of pure elements
+RT (xCu ln xCu + xCu ln xCu ) Gibbs energy mechanical mixing
+G
XS
Excess Gibbs energy
Theoretical background: thermodynamics
of substitional solutions
Redlich-Kister polynominal
G
XS
A,B
= x A xB å L ( x A - xB )
i
i
i
i
L = i A + i B ×T + iC × T × ln (T )
For i=0 and B=C=0 we just have a regular solution xAxBΩ
Value of i depends on thermodynamic properties of a given phase
Theoretical background: thermodynamics
of substitional solutions
Let’s take a look at the Gibbs energy function
Using Excel and the values 0A = 1A = 2A = 1000, 0B = 1B = 2B = 0C = 1C = 2C = 0,
please make a graph of the Gibbs energy (separately for each L and their
superposition) 400
350
300
250
200
150
100
50
0
-50 0
-100
-150
L0
L1
L2
L0+L1+L2
0.5
1
1.5
Introduction to thermodynamic database:
element, specie, constitution, phase, function
The thermodynamic database is a text file with extension TDB
For editing the file one should not use a word processor (i.e.
MS Word) due to invisible information added by the word
processor.
The easiest way to edit the database is to use Notepad or
other simple editor (personally, I like to use the Edit Plus)
Introduction to thermodynamic database:
element, specie, constitution, phase, function
Format of the database:
- Information about elements
- Information about species (if applicable)
- Functions
- Parameters
Introduction to thermodynamic database:
element, specie, constitution, phase, function
Se-Te database (part)
Introduction to thermodynamic database:
element, specie, constitution, phase, function
$ comment line
$ Database file written 2010-10-28
$ From database: User data 2010.10.28
ELEMENT /- ELECTRON_GAS
0.0000E+00 0.0000E+00 0.0000E+00!
ELEMENT VA VACUUM
0.0000E+00 0.0000E+00 0.0000E+00!
ELEMENT SE HEXAGONAL_A8
7.8960E+01 5.5145E+03 4.1966E+01!
ELEMENT TE HEXAGONAL_A8
1.2760E+02 6.1212E+03 4.9497E+01!
Atomic mass
ELEMENT SYMBOL Crystal structure SER
Enthalpy and entropy difference
between 0 and 298.15 K for the
element in
SI units. If they are unknown, the
values can be set to zero.
ELEMENT [element name]*2 [ref. state]*24 [mass] [H298] [S298] !
Introduction to thermodynamic database:
element, specie, constitution, phase, function
H298 and S298 - the enthalpy and entropy difference between
0 and 298.15 K for the element in SI units.
All these information (reference state, H298 and S298) precisely
define the so-called SER (Stable Element Reference State).
Introduction to thermodynamic database:
element, specie, constitution, phase, function
SPECIES [species name]*24 [stoichiometric formula] !
This keyword defines species in the data structure. Every species name (maximum 24
characters) must be unique. The species are built from the already defined set of
elements in the stoichiometric formula. The stoichiometric formula is written with a
simplified chemical notation, in which the chemical elements should always be given in
UPPER-cases and in any preferred order, and their stoichiometric coefficients can be
written in either real numerical factor or integer digits. It is important that the
numerical factor of 1 cannot be left out.
SPECIES AL2O3 AL2O3 !
SPECIES Silica SI1O2 !
SPECIES NaSb_6OH NA1SB1O6H6 !
SPECIES FE+2 FE/+2 !
SPECIES SB-3 SB/-3 !
SPECIES AlCl2/3 AL.33333CL.666667 !
Introduction to thermodynamic database:
element, specie, constitution, phase, function
FUNCTION [function name]*8 [lowest temp. limit]
[expression 1]; [upper temp. limit 2] Y
[expression 2]; [upper temp. limit 1] Y
[expression 3]; [upper temp. limit 2] Y
.......... ; ..... Y
[expression n-1]; [upper temp. limit n-1] Y
[expression n]; [upper temp. limit n] N {Ref. Index} !
Introduction to thermodynamic database:
element, specie, constitution, phase, function
TYPE_DEFINITION % SEQ *!
DEFINE_SYSTEM_DEFAULT ELEMENT 2 !
DEFAULT_COMMAND DEF_SYS_ELEMENT VA /- !
PHASE HEXAGONAL_A8 % 1 1.0 !
CONSTITUENT HEXAGONAL_A8 :SE,TE : !
PARAMETER G(HEXAGONAL_A8,SE;0) 2.98150E+02 +GHSERSE#; 1.00000E+03 N
REF0 !
PARAMETER G(HEXAGONAL_A8,TE;0) 2.98150E+02 +GHSERTE#; 1.60000E+03 N
REF0 !
PARAMETER G(HEXAGONAL_A8,SE,TE;0) 2.98150E+02 -9.9498291E+02
+2.7357836E+00*T;
1.60000E+03 N REF0 !
Introduction to thermodynamic database:
element, specie, constitution, phase, function
TYPE_DEFINITION [data-type code]*1 [secondary keyword with
parameters] !
This keyword couples phases to an action performed by the TDB module
when the TDB command GET_DATA is executed. The available secondary
keywords and associated parameters in syntax for TYPE_DEFINITION are:
SEQ [filename]
RND# [filename]
GES [valid GES command with parameters]
POLY [valid POLY command with parameters]
TDB [valid TDB command with parameters]
IF [conditional statement] THEN [keyword with parameters]
AFTER [valid GES command with parameters]
Introduction to thermodynamic database:
element, specie, constitution, phase, function
The secondary keyword SEQ specifies a sequential file that stores
parameters belonging to the phases using the associated data type code
(which is defined by this TYPE_DEFINTION keyword). A special case
where the filename is given as an asterisk, *, implies that the database
definition file also acts as a sequential data storage file. This case makes
it possible to have a single file for a small database, which is especially
suited for personal databases.
Introduction to thermodynamic database:
element, specie, constitution, phase, function
DEFINE_SYSTEM_DEFAULT [keyword] {G-ref. type index} ! Thermocalc software!
This keyword sets the default value to ELEMENT or SPECIES in the TDB command
DEFINE_SYSTEM. For a substance database, it might be appropriate to have ELEMENT
as default value whereas a large solution database can benefit from having SPECIES as
default value. A proper default value is beneficial for a beginner, but an advanced user
will probably use the TDB commands DEFINE_ELEMENT and DEFINE_SPECIES to
override the default value.
{G-ref. type index} is an integer indicating the reference state type for an element
when entering and listing data in the GES module. The following lists legal numbers and
their corresponding meaning (the reference state type for an element):
1 ⇒ symbol: G
2 ⇒ symbol: H298
3 ⇒ symbol: H0
Introduction to thermodynamic database:
element, specie, constitution, phase, function
DEFAULT_COMMAND [secondary keyword and parameters] ! Thermocalc software
The keyword specifies commands to be executed by the TDB module at database
initialization. The syntax of the available commands is currently not the same as the
user available TDB commands but the actions are similar. The available secondary
keywords and parameters in syntax for DEFAULT_COMMAND are,
DEFINE_SYSTEM_ELEMENT [element names]
DEFINE_SYSTEM_SPECIES [species names]
DEFINE_SYSTEM_CONSTITUENT [phase] [sublattice] [species]
REJECT_SYSTEM_ELEMENT [element names]
REJECT_SYSTEM_SPECIES [species names]
REJECT_SYSTEM_CONSTITUENT [phase] [sublattice] [species]
REJECT_PHASE [phase names]
RESTORE_PHASE [phase names]
Introduction to thermodynamic database:
element, specie, constitution, phase, function
PHASE [phase name]*24 [data-type code]*8 [numb. subl.] [sites in subl. 1] [sites in
subl. 2] etc... {auxiliary text string} !
This keyword defines a phase and its properties (except for what species are allowed to enter it and for its
thermodynamic parameters).
The data-type code consists of 1 to 8 characters where each character must stand for
connecting to a specific database file
The data entries [numb. subl.] [sites in subl. 1] [sites in subl. 2] etc... specify the total
number of sublattices (always as an integer digit) and the sites (i.e., stoichiometric
coefficients) of each of the sublattices (given in either integer digits or real numerical
factors) for the phase.
Optionally, an auxiliary text string (maximum 78 characters) may be given after the last
[sites in sublattice #] but before the exclamation mark “!”; see examples below. This
string will show up in connection with the phase name in some listings within the TDB
module.
Introduction to thermodynamic database:
element, specie, constitution, phase, function
PHASE GAS:G % 1 1.0 !
PHASE LIQUID:L %ZCDQ 2 1.0 1.0
> Metallic liquid solution, modelled by CEF Model. !
PHASE IONIC-LIQ:Y %ZCDQ 2 1.0 1.0
> Ionic liquid solution, modelled by Ionic Two-Sublattice Model. !
PHASE SPINEL:I %ZA 4 1 2 2 4
> Complex Spinel Solution, by CEF model with ionic constraints. !
PHASE M23C6 % 3 20.0 3.0 6.0 !
PHASE FCC_A1 %&A 2 1 1
> Disordered FCC phase; also as MX carbides/nitrides. !
PHASE FCC_L10 %&AX 3 0.75 0.25 1
> Ordered FCC phase, modelled by 2-Sublattice Model for Ordering. !
PHASE FCC_L12:F %&AX 5 0.25 0.25 0.25 0.25 1.0
> Ordered FCC phase, modelled by 4-Sublattice Model for Ordering. !
PHASE AQUEOUS:A %HIJMR 1 1.0
> Aqueous Solution: using the Complete Revised HKF Model. !
Introduction to thermodynamic database:
element, specie, constitution, phase, function
Legal GES phase-type codes are (Thermocalc software):
G ⇒ Bit set for a gaseous mixture phase.
A ⇒ Bit set for an aqueous solution phase.
Y ⇒ Bit set for an ionic liquid solution phase (that is specially treated by the Ionic TwoSublattice Liquid Model).
L ⇒ Bit set for a liquid solution phase [but not A (aqueous) or Y (ionic liquid)].
I ⇒ Bit set for a phase with charged species [but not G (gaseous), A (aqueous) or Y
(ionic liquid)].
F ⇒ Bit set for an ordered FCC or HCP solution phase with 4 substitutional sublattices
(additionally, such a phase can also have an interstitial sublattice).
B ⇒ Bit set for an ordered BCC solution phase with 4 substitutional sublattices
(additionally, such a phase can also have an interstitial sublattice).
Introduction to thermodynamic database:
element, specie, constitution, phase, function
CONSTITUENT [phase name]*24 [constituent description]*2000 !
This keyword (and the ADD_CONSTITUENT keyword for large solution phase) defines
the phase-constitution as a list of constituents (for a substitutional phase with no
sublattice) or of constituent arrays (for a sublattice phase).
Introduction to thermodynamic database:
element, specie, constitution, phase, function
PARAMETER [GES parameter name] [lowest temp. limit]
[expression 1]; [upper temp. limit 1] Y
[expression 2]; [upper temp. limit 2] Y
[expression 3]; [upper temp. limit 2] Y
.......... ; ..... Y
[expression n-1]; [upper temp. limit n-1] Y
[expression n]; [upper temp. limit n] N {Ref. Index} !
GES parameters
G Standard energy parameter (Gibbs energy of formation);
L Excess energy parameter (Gibbs energy of interaction);
TC Curie temperature for magnetic ordering;
BMAGN or BM Bohr magneton number for magnetic ordering
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Program Files->Computherm->Pandat 2012 Demo->Pandat 2012 Examples->
PanPhaseDiagram->Line
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Right-click on a database
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Point calculation
Line calculation
Phase diagram calculation
Let’ start from phase
diagram calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Edit
Select
Pan mode
Line/Arrow
Legend
Zoom
Label
Text
Introduction to Pandat software: phase diagram,
line/property and point calculation
Double click
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
After that we have to deal with tables.
However, a new version, Pandat 2013, has a new menu: Property
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
Lets calculate activity of components in liquid phase
Introduction to Pandat software: phase diagram,
line/property and point calculation
Introduction to Pandat software: phase diagram,
line/property and point calculation
It doesn’t look good, does it?
Introduction to Pandat software: phase diagram,
line/property and point calculation
As you see, we calculated activity
of all phases. We have to delete
everything what we don’t need
Pandat and database. Writing a database for CuNi system
Pandat and database. Writing a database
for Cu-Ni system
Pandat and database. Writing a database
for Cu-Ni system
Pandat and database. Writing a database
for Cu-Ni system
Pandat and database. Writing a database
for Cu-Ni system
Right-click on database
Pandat and database. Writing a database
for Cu-Ni system
How many phases do we
have in Cu-Ni system?
How many phases do we
have in the TDB file?
Let’s delete everything what
we don’t need!
Pandat and database. Writing a database
for Cu-Ni system
Pandat and database. Writing a database
for Cu-Ni system
Don’t forget to save the changes!
Pandat and database. Writing a database
for Cu-Ni system
Gibbs energies of pure elements. We need to add interaction
parameters (excess Gibbs energy)
Pandat and database. Writing a database
for Cu-Ni system
Where are the parameters?
Pandat and database. Writing a database
for Cu-Ni system
Let’s calculate a phase diagram, activities of Cu and Ni in FCC (500K) and Liquid
(1500K), enthalpy of mixing in Liquid (1400K) in respect (with reference state)
to Liquid and FCC (2 pictures)
Pandat and database. Writing a database
for Cu-Ni system
Phase diagram
Activities at 500K
Enthalpy at 1400K, ref. state liquid
Activities at 1500K
Enthalpy at 1400K, ref. state FCC
Homework
Homework
Base on the paper, prepare a TDB file for Te-Se system