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E2: Equilibrium calculus in Fe-Al-Nb-N-C 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 example, the procedure for the phase equilibrium calculation will be presented. The results will be summarised in form of the pseudobinary phase diagram. 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.

Step 1: Create a MatCalc workspace and setup the system

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

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


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

- open the window in which system composition is defined by clicking on 'Composition' in 'Global' menu (keyboard shortcut 'F7').
- select iron as reference element (select 'FE' and click on 'Set reference element')
- select 'weight percent' as a unit in which the composition will be expressed
- 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.
- close the window ('OK' button)

1.4 Calculation of the initial equilibrium

An initial equilibrium calculation is required for a successful start of any simulation. The first thing to be done is 'setting start values' - in this step, MatCalc adjusts the system to the boundary condition of the total system amount of 1 mole of atoms (as it can be seen in 'Phase summary' window, only 'FCC_A1' phase is present now while the amount of the others is 0 moles). 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 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.

Step 2: Stepped equilibrium calculation

The calculation of the initial equilibrium gave in result the system composition, as well as every phase composition at 1000°C. Analysing how these values change with temperature, some of the questions defined at the begining of this example can be answered. This can be done with 'Stepped calculation' option. Using this, a series of single equilibrium calculation is performed. Additionally, the temperatures at which any phase appears or disappears in equilibrium phase are found.

Let's perform equilibrium calculation for the temperature range of 400-1700°C with the stepvalue of 20°C. Click on 'Stepped calculation' in 'Calc' menu (keyboard shortcut 'Ctrl'+'T', icon on toolbar). Do the following setings:

- 'Type' window: select 'Temperature'
- 'Range' window: type '1700' in 'Start' window, '400' in 'Stop' window and '20' in 'Step interval' (set it to 'linear')
- 'Options' window: 'Temperatures in Celsius' should be selected

After clicking on 'Go' button, the 'Output' window will contain the following information:

1, 0,01 s, 1000,00 C (1273,16 K), its 2, FCC_A1 FCC_A1#01 ALN - OK -
2, 0,00 s, 1020,00 C (1293,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
3, 0,00 s, 1040,00 C (1313,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
4, 0,01 s, 1060,00 C (1333,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
5, 0,02 s, 1080,00 C (1353,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
6, 0,00 s, 1100,00 C (1373,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
7, 0,00 s, 1120,00 C (1393,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
8, 0,00 s, 1140,00 C (1413,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
9, 0,02 s, 1160,00 C (1433,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
10, 0,02 s, 1180,00 C (1453,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
11, 0,00 s, 1200,00 C (1473,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
Tsol 'FCC_A1#01': 1219,66 C (1492,82 K) iter: 3, time used: 0,00 s
12, 0,02 s, 1220,00 C (1493,16 K), its 3, FCC_A1 ALN - OK -
13, 0,00 s, 1240,00 C (1513,16 K), its 4, FCC_A1 ALN - OK -
Tsol 'ALN': 1251,17 C (1524,33 K) iter: 3, time used: 0,00 s
14, 0,02 s, 1260,00 C (1533,16 K), its 3, FCC_A1 - OK -
15, 0,00 s, 1280,00 C (1553,16 K), its 2, FCC_A1 - OK -
16, 0,00 s, 1300,00 C (1573,16 K), its 2, FCC_A1 - OK -
17, 0,01 s, 1320,00 C (1593,16 K), its 2, FCC_A1 - OK -
18, 0,02 s, 1340,00 C (1613,16 K), its 2, FCC_A1 - OK -
19, 0,00 s, 1360,00 C (1633,16 K), its 2, FCC_A1 - OK -
20, 0,00 s, 1380,00 C (1653,16 K), its 2, FCC_A1 - OK -
21, 0,01 s, 1400,00 C (1673,16 K), its 2, FCC_A1 - OK -
22, 0,00 s, 1420,00 C (1693,16 K), its 2, FCC_A1 - OK -
23, 0,00 s, 1440,00 C (1713,16 K), its 2, FCC_A1 - OK -
Tsol 'BCC_A2': 1445,10 C (1718,26 K) iter: 3, time used: 0,00 s
24, 0,03 s, 1460,00 C (1733,16 K), its 3, FCC_A1 BCC_A2 - OK -
25, 0,00 s, 1480,00 C (1753,16 K), its 5, FCC_A1 BCC_A2 - OK -
Tsol 'LIQUID': 1487,05 C (1760,21 K) iter: 4, time used: 0,01 s
Tsol 'FCC_A1': 1487,65 C (1760,81 K) iter: 5, time used: 0,00 s
26, 0,03 s, 1500,00 C (1773,16 K), its 5, LIQUID BCC_A2 - OK -
27, 0,02 s, 1520,00 C (1793,16 K), its 6, LIQUID BCC_A2 - OK -
Tsol 'BCC_A2': 1529,06 C (1802,22 K) iter: 4, time used: 0,00 s
28, 0,01 s, 1540,00 C (1813,16 K), its 4, LIQUID - OK -
29, 0,00 s, 1560,00 C (1833,16 K), its 2, LIQUID - OK -
30, 0,01 s, 1580,00 C (1853,16 K), its 2, LIQUID - OK -
31, 0,02 s, 1600,00 C (1873,16 K), its 2, LIQUID - OK -
32, 0,02 s, 1620,00 C (1893,16 K), its 2, LIQUID - OK -
33, 0,00 s, 1640,00 C (1913,16 K), its 2, LIQUID - OK -
34, 0,00 s, 1660,00 C (1933,16 K), its 2, LIQUID - OK -
35, 0,02 s, 1680,00 C (1953,16 K), its 2, LIQUID - OK -
36, 0,02 s, 1700,00 C (1973,16 K), its 2, LIQUID - OK -
changing step direction ...
37, 0,01 s, 980,00 C (1253,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
38, 0,02 s, 960,00 C (1233,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
39, 0,00 s, 940,00 C (1213,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
40, 0,00 s, 920,00 C (1193,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
41, 0,00 s, 900,00 C (1173,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
Tsol 'BCC_A2': 886,93 C (1160,09 K) iter: 4, time used: 0,00 s
42, 0,03 s, 880,00 C (1153,16 K), its 4, FCC_A1 FCC_A1#01 BCC_A2 ALN - OK -
43, 0,02 s, 860,00 C (1133,16 K), its 6, FCC_A1 FCC_A1#01 BCC_A2 ALN - OK -
44, 0,00 s, 840,00 C (1113,16 K), its 6, FCC_A1 FCC_A1#01 BCC_A2 ALN - OK -
45, 0,00 s, 820,00 C (1093,16 K), its 6, FCC_A1 FCC_A1#01 BCC_A2 ALN - OK -
46, 0,00 s, 800,00 C (1073,16 K), its 6, FCC_A1 FCC_A1#01 BCC_A2 ALN - OK -
47, 0,00 s, 780,00 C (1053,16 K), its 6, FCC_A1 FCC_A1#01 BCC_A2 ALN - OK -
48, 0,01 s, 760,00 C (1033,16 K), its 6, FCC_A1 FCC_A1#01 BCC_A2 ALN - OK -
49, 0,02 s, 740,00 C (1013,16 K), its 7, FCC_A1 FCC_A1#01 BCC_A2 ALN - OK -
Tsol 'FCC_A1': 727,87 C (1001,03 K) iter: 4, time used: 0,00 s
Tsol 'CEMENTITE': 727,91 C (1001,07 K) iter: 5, time used: 0,00 s
50, 0,05 s, 720,00 C (993,16 K), its 5, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
51, 0,00 s, 700,00 C (973,16 K), its 5, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
52, 0,00 s, 680,00 C (953,16 K), its 5, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
53, 0,01 s, 660,00 C (933,16 K), its 5, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
54, 0,02 s, 640,00 C (913,16 K), its 5, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
55, 0,01 s, 620,00 C (893,16 K), its 5, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
56, 0,02 s, 600,00 C (873,16 K), its 5, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
57, 0,02 s, 580,00 C (853,16 K), its 5, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
58, 0,00 s, 560,00 C (833,16 K), its 6, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
59, 0,00 s, 540,00 C (813,16 K), its 6, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
60, 0,00 s, 520,00 C (793,16 K), its 6, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
61, 0,00 s, 500,00 C (773,16 K), its 6, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
62, 0,01 s, 480,00 C (753,16 K), its 6, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
63, 0,02 s, 460,00 C (733,16 K), its 6, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
64, 0,01 s, 440,00 C (713,16 K), its 6, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
65, 0,02 s, 420,00 C (693,16 K), its 7, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
66, 0,02 s, 400,00 C (673,16 K), its 7, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
67, 0,01 s, 400,00 C (673,16 K), its 2, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
Steps: 68, CalcTime: 1,00 s
AktStepVal: 673,160000
- OK -

The program did a single equilibrium calculation in the defined range 400-1700°C, changing the input temperature value by 20°C. It started form the temperature value of the initial equilibrium calculation (1000°C) and proceeded into higher temperatures (1020°C, 1040°C, ...) till the higher limit was reached (1700°C). Next ('changing step direction ...' message), it moved back to 1000°C and proceeded into lower temperatures (980°C, 960°C, ...) till the lower limit was reached (400°C). For every temperature value, the phases in equilibrium were found. If the qualitative phase composition for the consecutive temepratures was different (an existing phase disappeared or/and a new phase appeared), the exact temperature of this effect was found ('Tsol 'phasename':' message). The results of every single equilibrium calculation are stored in the buffer (named '-default_', if no other was created by user). With this one calculation, some of the questions can be already answered:

2.1 Which are the equilibrum phases in some defined temperature range (e.g. 400-1700°C) ?

Summarising the data from the 'Output' window, the following answer is given:

- 400°C - 728°C, the phases are: ferrite (BCC_A2), cementite, AlN, NbC (FCC_A1#01)
- 728°C - 887°C, the phases are: ferrite, austenite (FCC_A1), AlN, NbC
- 887°C - 1220°C, the phases are: austenite, AlN, NbC
- 1220°C - 1251°C, the phases are: austenite, AlN
- 1251°C - 1445°C, the phases are: austenite
- 1445°C - 1487°C, the phases are: austenite, delta-ferrite (BCC_A2)
- 1487°C - 1529°C, the phases are: delta-ferrite, liquid
- 1529°C - 1700°C, the phases are: liquid

2.2 Which microstructure (delta-ferrite, austenite, mixed) is expected after solidification of the melt ?

In order to predict qualitatively the alloy microstructure, the knowledge of the consecutive phase transitions is desirable. Such an analysis is done below.

Cooling the liquid alloy, the first solid phase in equilibrium is delta-ferrite which appears at 1529°C. Still, some part of the liquid phase is present below this temperature down to 1487°C. Below this temperature, the liquid phase disappears but simultaneously the austenite phase appears. As this happens at the same temperature, it is a symptom of a phase transition. If the user has no idea about the Fe-C phase diagram, the question arises if this is a eutectic or a peritectic reaction. The kind of the reaction can be determined, if the amounts of the delta-ferrite phase before and after reaction are compared. This can be revoked when the buffer records are examined. To do this, click on 'Edit buffer states' in 'Global'>'Buffers' (keyboard shortcut 'Ctrl'+'L'). A window appears in which the temperatures for every single equilibrium calculation are given. By clicking on a given value, the phase amounts and compositions can be reviewed in the 'Phase summary' and 'Phase details' windows for this temperature (provided that 'auto load' box is ticked'). Click on '1487,6469 Tsol'FCC_A1':' and check the amount of the delta-ferrite phase. This is:

BCC_A2 * act
9,80963e-001 dfm: +0,00000e+000

When the slightly lower temperature '1487,0527 Tsol'LIQUID':' is chosen, the 'Phase summary' window gives the following information:

BCC_A2 * act
8,91152e-001 dfm: +0,00000e+000

As ferrite content diminishes during the reaction, the reaction equation can be written in form of liquid + delta-ferrite -> austenite, and thus the reaction is peritectic. After the whole liquid is consumed, the newly created austenite and the leftover ferrite are found in the system

The conclusions for the alloy microstructure are as follows. First, the delta-ferrite grains are growing during the cooling of the alloy down to 1487°C. At this temperature, the liquid reacts with the grains and the austenite is formed on their surface. Depending on the size of the delta-ferrite grains before the reaction, the alloy contains these with the austenite either in the voids (for large grains) or surrounding the grains (for small grains).

2.3 What is the value of the Ae3 temperature (the lowest temperature at which ferrite is not an equilibrium phase) ?

This question can be now easily answered. The ferrite phase disappears at 887°C and this is the value of Ae3 temperature for this alloy.

2.4 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 ?

To answer this question, the equilibrium calculations for the various alloy composition must be performed. This will be done in the next step.

Step 3: Finding the phase boundary for different compositions - drawing of the phase diagrams

Now, the phase amounts and compositions, together with the temperatures of the phase transition variation dependent on the amount of the alloying element will be investigated. Till now, the stepped equilibrium calculation was performed for one composition only. Doing this for various compositions could solve this problem but it might consume a lot of work. Usually, it is a better solution when the phase boundary at the initial boundary is selected and followed with increasing a content of one element.

Note: The term 'Phase boundary of A' in this text referes to the boundary between the two phase fields, where on one side phase 'A' does exist and on the other side phase 'A' does not exist. It is NOT a boundary of the one-phase field of 'A' !!!

Selecting a phase boundary is done by clicking on 'Search phase boundary' in 'Calc' menu (keyboard shortcut 'Ctrl'+'Shift'+'T', icon on toolbar). This opens a dialog in which the search parameters can be defined. In the 'type' section, one can define if the phase boundary should be found with the temperature variation (and fixed composition) or the composition variation (and fixed temperature). In the 'Target phase' section, the phase can be defined for which the phase boundary will be searched (and selected). In order to perform a successful search, it is recommended (though not required) to calculate the equilibrium at the temperature in which:

- the phase under consideration does not occur
- the phase boundary is not far away (within 100°C)

Let's select the phases boundary of ferrite which will be needed for the analysis of the Ae3 temperature. During the stepped equilibrium calculations, it was established that the phase boundary is at 887°C. First calculate the equilibrium for 900°C (ferrite does not occur for this temperature). Next, find the phase boundary, selecting 'BCC_A2' in 'Target phase' and 'Temperature' in 'Type' dialogs. After clicking on 'Go' button, the following message appears in 'Output' window:

Tsol 'BCC_A2': 886,93 C (1160,09 K) iter: 5, time used: 0,03 s

At the same time, MatCalc performed an equilibrium calculation for the temperature of the phase boundary so that the contents of 'Phase summary' and 'Phase details' windows are changed.

When the phase boundary was selected, let's see it's flow with the varying content of the alloying elements. Click again on 'Stepped calculation' but this time select 'Phase boun...' in the 'type' section. In 'Range' section, enter the following values:

- '0' in 'Start'
- '1' in 'Stop'
- '0.01' in 'Step interval' (select 'linear')

In 'Boundary conditions' section, do the following settings:

- 'C' in 'Element'
- 'BCC_A2' in 'Target phase'

With these selection, MatCalc will find the phase boundaries of ferrite, varying the carbon content in the system from 0 to 1 wt.% with the stepwidth of 0.01 wt.%. Click on 'Go' button. The content of 'Output' window should look similar to this:

1, 0,00 s, 0,100000, T=886,93 C (1160,09 K), its 2, FCC_A1 FCC_A1#01 ALN - OK -
2, 0,00 s, 0,110000, T=882,87 C (1156,03 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
3, 0,00 s, 0,120000, T=878,92 C (1152,08 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
4, 0,01 s, 0,130000, T=875,07 C (1148,23 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
5, 0,00 s, 0,140000, T=871,33 C (1144,49 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
6, 0,02 s, 0,150000, T=867,68 C (1140,84 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
7, 0,00 s, 0,160000, T=864,12 C (1137,28 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
8, 0,00 s, 0,170000, T=860,64 C (1133,80 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
9, 0,01 s, 0,180000, T=857,24 C (1130,40 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
10, 0,00 s, 0,190000, T=853,92 C (1127,08 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
11, 0,02 s, 0,200000, T=850,68 C (1123,84 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
12, 0,00 s, 0,210000, T=847,50 C (1120,66 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
13, 0,00 s, 0,220000, T=844,39 C (1117,55 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
14, 0,02 s, 0,230000, T=841,34 C (1114,50 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
15, 0,00 s, 0,240000, T=838,35 C (1111,51 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
16, 0,00 s, 0,250000, T=835,42 C (1108,58 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
17, 0,00 s, 0,260000, T=832,55 C (1105,71 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
18, 0,00 s, 0,270000, T=829,73 C (1102,89 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
19, 0,02 s, 0,280000, T=826,96 C (1100,12 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
20, 0,00 s, 0,290000, T=824,24 C (1097,40 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
21, 0,00 s, 0,300000, T=821,57 C (1094,73 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
22, 0,00 s, 0,310000, T=818,95 C (1092,11 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
23, 0,00 s, 0,320000, T=816,37 C (1089,53 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
24, 0,02 s, 0,330000, T=813,83 C (1086,99 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
25, 0,00 s, 0,340000, T=811,33 C (1084,49 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
26, 0,00 s, 0,350000, T=808,88 C (1082,04 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
27, 0,02 s, 0,360000, T=806,46 C (1079,62 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
28, 0,00 s, 0,370000, T=804,08 C (1077,24 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
29, 0,02 s, 0,380000, T=801,74 C (1074,90 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
30, 0,00 s, 0,390000, T=799,43 C (1072,59 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
31, 0,00 s, 0,400000, T=797,16 C (1070,32 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
32, 0,00 s, 0,410000, T=794,91 C (1068,07 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
33, 0,00 s, 0,420000, T=792,71 C (1065,87 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
34, 0,02 s, 0,430000, T=790,53 C (1063,69 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
35, 0,00 s, 0,440000, T=788,38 C (1061,54 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
36, 0,01 s, 0,450000, T=786,26 C (1059,42 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
37, 0,00 s, 0,460000, T=784,18 C (1057,34 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
38, 0,00 s, 0,470000, T=782,12 C (1055,28 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
39, 0,01 s, 0,480000, T=780,08 C (1053,24 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
40, 0,00 s, 0,490000, T=778,08 C (1051,24 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
41, 0,02 s, 0,500000, T=776,10 C (1049,26 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
42, 0,00 s, 0,510000, T=774,14 C (1047,30 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
43, 0,00 s, 0,520000, T=772,21 C (1045,37 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
44, 0,00 s, 0,530000, T=770,30 C (1043,46 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
45, 0,00 s, 0,540000, T=768,43 C (1041,59 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
46, 0,02 s, 0,550000, T=766,58 C (1039,74 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
47, 0,00 s, 0,560000, T=764,77 C (1037,93 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
48, 0,00 s, 0,570000, T=762,98 C (1036,14 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
49, 0,00 s, 0,580000, T=761,22 C (1034,38 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
50, 0,00 s, 0,590000, T=759,48 C (1032,64 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
51, 0,02 s, 0,600000, T=757,77 C (1030,93 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
52, 0,00 s, 0,610000, T=756,08 C (1029,24 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
53, 0,01 s, 0,620000, T=754,42 C (1027,58 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
54, 0,00 s, 0,630000, T=752,77 C (1025,93 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
55, 0,00 s, 0,640000, T=751,14 C (1024,30 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
56, 0,02 s, 0,650000, T=749,53 C (1022,69 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
57, 0,00 s, 0,660000, T=747,94 C (1021,10 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
58, 0,01 s, 0,670000, T=746,36 C (1019,52 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
59, 0,00 s, 0,680000, T=744,80 C (1017,96 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
60, 0,00 s, 0,690000, T=743,26 C (1016,42 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
61, 0,02 s, 0,700000, T=741,73 C (1014,89 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
62, 0,00 s, 0,710000, T=740,21 C (1013,37 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
63, 0,01 s, 0,720000, T=738,71 C (1011,87 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
64, 0,00 s, 0,730000, T=737,22 C (1010,38 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
65, 0,00 s, 0,740000, T=735,74 C (1008,90 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
66, 0,00 s, 0,750000, T=734,27 C (1007,43 K), its 3, FCC_A1 FCC_A1#01 ALN - OK -
67, 0,00 s, 0,760000, T=732,82 C (1005,98 K), its 3, FCC_A1 FCC_A1#01 ALN - OK -
68, 0,02 s, 0,770000, T=731,37 C (1004,53 K), its 3, FCC_A1 FCC_A1#01 ALN - OK -
69, 0,00 s, 0,780000, T=729,94 C (1003,10 K), its 3, FCC_A1 FCC_A1#01 ALN - OK -
Tj(BCC_A2/CEMENTITE): 728,83 C (1001,99 K), X(C)=0,0355786, WP(C)=0,787817, its 4
70, 0,03 s, 0,787817, T=728,83 C (1001,99 K), its 4, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
71, 0,02 s, 0,797817, T=728,83 C (1001,99 K), its 7, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
72, 0,00 s, 0,807817, T=728,83 C (1001,99 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
73, 0,02 s, 0,817817, T=728,84 C (1002,00 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
74, 0,00 s, 0,827817, T=728,84 C (1002,00 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
75, 0,01 s, 0,837817, T=728,84 C (1002,00 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
76, 0,00 s, 0,847817, T=728,85 C (1002,01 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
77, 0,00 s, 0,857817, T=728,85 C (1002,01 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
78, 0,00 s, 0,867817, T=728,85 C (1002,01 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
79, 0,00 s, 0,877817, T=728,86 C (1002,02 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
80, 0,02 s, 0,887817, T=728,86 C (1002,02 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
81, 0,00 s, 0,897817, T=728,87 C (1002,03 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
82, 0,02 s, 0,907817, T=728,87 C (1002,03 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
83, 0,00 s, 0,917817, T=728,87 C (1002,03 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
84, 0,00 s, 0,927817, T=728,88 C (1002,04 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
85, 0,00 s, 0,937817, T=728,88 C (1002,04 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
86, 0,00 s, 0,947817, T=728,88 C (1002,04 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
87, 0,00 s, 0,957817, T=728,89 C (1002,05 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
88, 0,00 s, 0,967817, T=728,89 C (1002,05 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
89, 0,01 s, 0,977817, T=728,90 C (1002,06 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
90, 0,00 s, 0,987817, T=728,90 C (1002,06 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
91, 0,02 s, 0,997817, T=728,90 C (1002,06 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
92, 0,00 s, 1,000000, T=728,90 C (1002,06 K), its 2, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
changing step direction ...
93, 0,00 s, 0,090000, T=891,11 C (1164,27 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
94, 0,02 s, 0,080000, T=895,42 C (1168,58 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
95, 0,00 s, 0,070000, T=899,85 C (1173,01 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
96, 0,00 s, 0,060000, T=904,43 C (1177,59 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
97, 0,01 s, 0,050000, T=909,14 C (1182,30 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
98, 0,00 s, 0,040000, T=913,99 C (1187,15 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
99, 0,00 s, 0,030000, T=918,94 C (1192,10 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
100, 0,02 s, 0,020000, T=923,86 C (1197,02 K), its 6, FCC_A1 FCC_A1#01 ALN - OK -
101, 0,01 s, 0,010000, T=928,41 C (1201,57 K), its 8, FCC_A1 FCC_A1#01 ALN - OK -
Tj(BCC_A2/FCC_A1#01): 931,60 C (1204,76 K), X(C)=9,65535e-005, WP(C)=0,00207843, its 13
102, 0,03 s, 0,002078, T=931,60 C (1204,76 K), its 13, FCC_A1 ALN - OK -
103, 0,02 s, 0,000000, T=932,82 C (1205,98 K), its 11, FCC_A1 ALN - OK -
Steps: 104, CalcTime: 1,06 s
AktStepVal: 0,000000
- OK -

It can be seen, that MatCalc starts with the carbon content 0.1 wt.% and raise it stepwise by 0.01 wt.% (0.11%, 0.12%, ...) finding for each composition the temperature of the phase boundary. After reaching the upper limit of 1 wt.% C, it lowers the carbon content ('changing step direction ...' message) by 0.01 wt.%, starting again from the initial content of 0.1 wt.% C.

3.1 How does the value of the Ae3 temperature change with the alloy composition ?

Looking at the obtained results, it can be seen that Ae3 temperature falls with the increasing carbon content from 933°C (where there is no carbon present in the system) to 729°C (for 0.79 wt.% C, where the cementite phase precipitates).

Try it out …

 

... and don't forget to save the file! (FeMnC.mcw)