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E1-1: Equilibrium calculus in Fe-Al-Nb-N-C system - setting up the system

(calculating equilibrium, performing stepped calculations, plotting a pseudobinary phase diagram, evaluating results from equilibrium calculations)

This example was performed on
MatCalc version 5.23 rel 1.037
license: registered user
database: mc_sample_fe.tdb


In this and the following examples, the procedure for the phase equilibrium calculation will be presented. Some practical aspects of the obtained results will be discussed. The basics of the needed MatCalc operations were already discussed in more detail in Tutorials 1-9 - feel free to have a look there.

Problem formulation:

It is desired to predict the properties of the alloy with the following composition:

- 0.1% C
- 0.1% Nb
- 0.1% Al
- 0.005% N
- Fe (remainder)

The question that should be answered are:

- Which are the equilibrum phases in some defined temperature range ?
- Which microstructure (delta-ferrite, austenite, mixed) is expected after solidification of the melt ?
- What is the value of the Ae3 temperature (the lowest temperature at which ferrite is not an equilibrium phase) ? How does the value of the Ae3 temperature change with the alloy composition ?
- What are solubilities of the alloying elements in the iron allotrope phases ?

The answers for this questions will be obtained from the equilibrium calculations. Although in the industrial practice the equilibrium state might be not reached in many cases, it is a useful reference state for any predictions about the features of the system in question.

Regardless of the task which is to be solved, there are some procedures which are to be performed at the start of every project. These are:

1.1 Creation of the MatCalc workspace
1.2 Retrieving the data (thermodynamic, physical, etc...) required for the modelling
1.3 Definition of the system composition
1.4 Calculation of the initial equilibrium

These operations will be performed in this example. At the end, the workspace will be saved and used in the subsequent examples in which the questions will be answered.

1.1 Creation of the MatCalc workspace

The first operation after MatCalc initialisation is always the creation of the workspace. This can be done in the following ways:

- Click on the icon
- Click on 'New' in 'File' menu
- Press 'Ctrl'+'N'

In the window that appears select 'MatCalc workspace' and click 'OK'


1.2 Retrieving the data required for the modelling

For the solution of the given problem, the thermodynamic data required for the modelling must be retrieved from the database. In this example, 'mc_sample_fe.tdb' database will be used which should be included in your MatCalc package. The following operations will be performed:


1.2.1 Open the needed database window

This can be done by clicking on 'Databases' in 'Global' menu (keyboard shortcut 'F5'), selecting 'Thermodynamics' on the left side of the window that appeared on the screen, clicking 'open' button and selecting the database file ('mc_sample_fe.tdb').


1.2.2 Select the elements relevant to the analysed system

The system components ('FE', 'C', 'N', 'AL', 'NB') and the vacancies ('VA') should be selected in the 'Elements' window.

Note: The vacancies describe the vacancies on the interstitial sites!


1.2.3 Select the phases relevant to the analysed system

After selecting the elements, the content of the 'Phases' window changed - the number of phases is limited to the ones in which the selected elements occur. If the user has no previous knowledge on the system, it might be a good idea to select all of the phases. However, in this problem one assumption will be made. It is generally known, that the metal carbides (e.g. cementite) are not equilibrium phase, however, they can be still found in the steels. In order to reproduce this effect, the existence of graphite (which is an equilibrium phase) will be neglected. Therefore, select all phases except of 'GRAPHITE'.


1.2.4 Read the data from the database

After selecting the phases, click on 'Read' button. Subsequently, close the window with 'close' button. Let's have a look on the content of the 'Output', 'Phase details' and 'Phase summary' windows:

- 'Output' window:

opening database 'C:/Programme/MatCalc/database/mc_sample_fe.tdb' ... - OK -
reading thermodynamic data 'C:/Programme/MatCalc/database/mc_sample_fe.tdb' ...
collecting symbols 'C:/Programme/MatCalc/database/mc_sample_fe.tdb' ...
elements: VA AL C FE N NB
phases: LIQUID FCC_A1 BCC_A2 HCP_A3 ALN CEMENTITE M23C6 M7C3 LAVES_PHASE KSI_CARBIDE FE4N ZET
Gibbs: 12 Phases / 1 Composition-Set(s) created
Gibbs: 304 functions linked ...
Gibbs: T = 1273.160000 K, P = 101023.000000 Pa, moles = 1

This informs about the process that was performed. 304 thermodynamic functions which describe 13 phases (12 that were chosen plus 1 created 'composition-set') were read from the database.

- 'Phase details':

#### /LIQUID/ moles: 1, gm: -59188,7 (0), sff: 1
Phasestatus: entered - active
FE +9,82608e-001 C +9,12975e-003 NB +8,26210e-003 AL +1,96522e-010
N +1,96522e-010

#### /FCC_A1/ moles: 1, gm: -62257,5 (0), sff: 0,990879
Phasestatus: entered - active
FE +9,90875e-001 C +9,12099e-003 NB +4,20300e-006 N +9,81666e-011
AL +4,99861e-014

#### /FCC_A1#01/ moles: 1, gm: -111291 (0), sff: 0,502513
Phasestatus: entered - active
NB +5,02507e-001 C +4,97487e-001 FE +5,92179e-006 N +4,26595e-010
AL +1,18436e-011

#### /BCC_A2/ moles: 1, gm: -61574,9 (0), sff: 0,981868
Phasestatus: entered - active
FE +9,81864e-001 C +1,81323e-002 NB +4,16478e-006 N +2,92729e-010
AL +2,47658e-014

#### /HCP_A3/ moles: 1, gm: -59762,7 (0), sff: 0,993175
Phasestatus: entered - active
FE +9,80805e-001 NB +1,23704e-002 C +6,82487e-003 AL +1,96161e-010
N +4,89694e-011

#### /CEMENTITE/ moles: 1, gm: -52390,8 (0), sff: 0,25
Phasestatus: entered - active
FE +7,49997e-001 C +2,50000e-001 NB +3,18127e-006 N +1,34534e-009
AL +5,67520e-014

#### /ALN/ moles: 0, gm: -184222 (0), sff: 0,5
Phasestatus: entered - active
AL +5,00000e-001 N +5,00000e-001

#### /M23C6/ moles: 0, gm: -53695,2 (0), sff: 0,0344828
Phasestatus: entered - active
FE +7,93103e-001 C +2,06897e-001

#### /M7C3/ moles: 0, gm: -48033 (0), sff: 0,1
Phasestatus: entered - active
FE +7,00000e-001 C +3,00000e-001

#### /LAVES_PHASE/ moles: 0, gm: -82045,6 (0), sff: 0,333333
Phasestatus: entered - active
FE +6,66665e-001 NB +3,33335e-001

#### /KSI_CARBIDE/ moles: 0, gm: -41486,3 (0), sff: 0,25
Phasestatus: entered - active
FE +7,50000e-001 C +2,50000e-001

#### /FE4N/ moles: 0, gm: -48935,2 (0), sff: 0,2
Phasestatus: entered - active
FE +8,00000e-001 C +2,00000e-001 N +8,61017e-010

#### /ZET/ moles: 0, gm: -65540 (0), sff: 0,499705
Phasestatus: entered - active
FE +4,99705e-001 NB +4,99705e-001 N +5,90519e-004

### inactive ###

This gives information about the phase compositions, though it is quite meaningless now, as no equilibrium calculation was performed yet. Comparing the phases in the list with the ones listed in the 'Output' window (the list of loaded phases), it can be found that 'FCC_A1#01' is the phase which was created by the system.

- 'Phase summary'

LIQUID
FCC_A1
FCC_A1#01
BCC_A2
HCP_A3
CEMENTITE *
ALN
M23C6
M7C3
LAVES_PHASE
KSI_CARBIDE
FE4N
ZET

act
act
act
act
act
act
act
act
act
act
act
act
act

1,00000e+000
1,00000e+000

1,00000e+000
1,00000e+000

1,00000e+000
1,00000e+000
0,00000e+000
0,00000e+000
0,00000e+000
0,00000e+000
0,00000e+000
0,00000e+000
0,00000e+000

dfm: +5,91887e+004
dfm: +6,22575e+004
dfm: +1,11291e+005
dfm: +6,15749e+004
dfm: +5,97627e+004
dfm: +5,23908e+004
dfm: +1,84222e+005
dfm: +5,36952e+004
dfm: +4,80330e+004
dfm: +8,20456e+004
dfm: +4,14863e+004
dfm: +4,89352e+004
dfm: +6,55400e+004

### inactive ###

This is the short version of the list given in the 'Phase details' window.

1.3 Definition of the system composition

1.3.1 Open the window in which system composition is defined by clicking on 'Composition' in 'Global' menu (keyboard shortcut 'F7').

1.3.2 Select iron as reference element (select 'FE' and click on 'Set reference element')

1.3.3 Select 'weight percent' as a unit in which the composition will be expressed

1.3.4 Enter the composition for every element ('0.1' for C, Al and Nb; '0.005' for N) - either select the relevant element and click on 'Change (F2)' button or simply click on the number that needs to be changed.

1.3.5 Close the window ('OK' button)

1.4 Calculation of the initial equilibrium

A calculation of the initial equilibrium is required for a successful start of any simulation.

1.4.1 Setting start values

The first thing to be done is to adjust the total amount of the atoms in the system to 1 mole - this is the boundary condition used by MatCalc. As it can be seen in 'Phase summary' window, this condition is not fulfilled yet, as there are six phases with amount of 1 mole). The adjustment is done by selecting 'Set start values' in 'Calc' menu (keyboard shortcut 'Ctrl'+'Shift'+'F'). When this is done, the system is set to contain only one mole of 'FCC_A1' phase while the amount of the others is zero moles.

1.4.2 Equilibrium calculation

Now the initial equilibrium can be calculated by clicking on 'Equilibrium' in 'Calc' menu (keyboard shortcut 'Ctrl'+'E', icon on the toolbar). Leave the default temperature (1000°C) and pressure (101023 Pa) and click on 'Go' button.

The following information will be displayed in the windows:

- 'Output'

iter: 44, time used: 0,09 s
T: 1000 C (1273,16 K), GibbsEnergy: -62686,151 J
- OK -

This informs that the calculation was performed without any problems ('OK' message) and shows the value of the Gibbs energy of the system for this conditions (composition, temperature and pressure).

- 'Phase summary'

FCC_A1 *
FCC_A1#01
ALN
act
act
act
9,98626e-001
1,02757e-003
3,46235e-004
dfm: +0,00000e+000
dfm: +0,00000e+000
dfm: +0,00000e+000

### inactive ###
BCC_A2
HCP_A3
LIQUID
LAVES_PHASE
M23C6
CEMENTITE
FE4N
M7C3
KSI_CARBIDE
ZET


- OK -
- OK -
- OK -

- OK -
- OK -
- OK -
- OK -
- OK -
- OK -
- OK -


0,00000e+000

0,00000e+000
0,00000e+000
0,00000e+000
0,00000e+000
0,00000e+000
0,00000e+000
0,00000e+000
0,00000e+000
0,00000e+000


dfm: -8,06671e+001
dfm: -3,28891e+003
dfm: -3,69990e+003
dfm: -5,40138e+003
dfm: -7,24432e+003
dfm: -8,24759e+003
dfm: -1,19930e+004
dfm: -1,22647e+004
dfm: -1,91561e+004
dfm: -4,19320e+004

 

This window gives information about equilibrium phases present in the system and their amounts expressed in moles, first (FCC_A1, FCC_A1#01 and ALN). Below the line with '### inactive ###' message are data about all phases which are unstable, along with their driving forces.

- 'Phase details'

#### /FCC_A1/ moles: 0,998626, gm: -62591,7 (-62591,7), sff: 0,99584
Phasestatus: entered - active
FE +9,93879e-001 C +4,13983e-003 AL +1,89009e-003 NB +7,16128e-005
N +1,97480e-005

#### /FCC_A1#01/ moles: 0,00102757, gm: -113509 (-113509), sff: 0,512982
Phasestatus: entered - active
NB +5,12784e-001 C +4,81540e-001 N +5,47740e-003 FE +1,97887e-004
AL +2,56470e-007

#### /ALN/ moles: 0,000346235, gm: -184222 (-363151), sff: 0,5
Phasestatus: entered - active
AL +5,00000e-001 N +5,00000e-001

### inactive ###

#### /BCC_A2/ moles: 0, gm: -62695,8 (-62695,8), sff: 0,999589
Phasestatus: entered - not active (dfm=-80,67)
FE +9,96382e-001 AL +3,11501e-003 C +4,06868e-004 NB +9,18694e-005
N +4,10648e-006

...

Here, a detailed data on the composition minimising Gibbs energy for every phase is given. The unit in which these compositions are expressed can be adjusted in 'options' window.

As it can be seen from this calculation, at 1000°C the system consists dominantely of austenite (Fe-fcc) phase which solves the most part of the alloying elements. What cannot be solved is present in the two other phases: AlN (Al and N only) and NbC (containing Nb and C mainly with some traces of Fe, Al and N).

1.5 Save the workspace

It is very useful to save the workspace after the initial equilibrium was calculated, as it is conveinent to use it as a starting point for the various calculations. To save your data either click on 'Save' in 'File' menu (keyboard shortcut 'Ctrl'+'S') or just click on icon. Type the name for the file and click on 'Save'.

Try it out …