E1-2: Equilibrium
calculus in Fe-Al-Nb-N-C system - equilibrium phases at various temperatures
(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
Saved files used: E1-1
Here, the procedure for finding of the phase composition at various temperatures will be described. This will base on the stepped equilibrium calculation, the results of which will be interpreted accordingly.
Problem formulation:
Which phases are in equilibrium in the alloy specified in example E1-1 for the temperature range 400-1600°C ?
Solution philosophy:
As it was demonstrated in example E1-1 with the initial equilibrium calculation, it is possible to find the equilibrium phase composition of the system at the given temperature with the 'calculate equilibrium' operation. To find these compositions for a temperature range, such a calculation would need to be performed for every single temperature value. It would be quite labourious, however, to manually input the temperature value into the 'calculate equilibrium' window and to repeat the calculation for every single temperature. The 'stepped calculation' operation was designed for such repetitive tasks and this will be used to answer the question.
Procedure:
1.1 Loading the saved workspace
There are the following possibilities to load the saved workspace in MatCalc:
- Click on the icon
- Click on 'Open' in 'File' menu
- Press 'Ctrl'+'O'
In the window that appears select the according file (the one saved in example 1-1) and click 'Open'
1.2 Performing the stepped equilibrium calculation
1.2.1 Open the stepped calculation window
This is done by selecting 'Stepped calculation' in 'Calc' menu (keyboard shortcut 'Ctrl'+'T', icon).
1.2.2 Select the type of the performed calculation
For the equilibrium calculation, the temperature will be varied, so select 'Temperature' in the 'Type' dialog.
1.2.3 Specify the conditions of the calculation
The temperature range is defined in the 'Start' and 'Stop' fields of the 'Range' section. It doesn't matter if the 'Stop' value is greater or lower than the 'Start' value. The temperature unit is defined by the 'Temperatures in Celsius' field in 'Options' section - the unit is Celsius (°C) if the field is ticked, otherwise it is Kelvin (K). Leaving the default values of '1600' and '400' defines the temperature range of 400-1600°C.
The value given in the 'Step interval' field specifies the intervals between the temperatures for which the single equilibrium calculations will be performed. Leave the default value of '25' (with 'linear' scale selected). Click on 'Go' button to proceed.

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, 1025,00 C (1298,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
3, 0,00 s, 1050,00 C (1323,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
4, 0,02 s, 1075,00 C (1348,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
5, 0,01 s, 1100,00 C (1373,16 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
6, 0,02 s, 1125,00 C (1398,16 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
7, 0,00 s, 1150,00 C (1423,16 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
8, 0,00 s, 1175,00 C (1448,16 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
9, 0,00 s, 1200,00 C (1473,16 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
Tsol 'FCC_A1#01': 1219,66 C (1492,82 K) iter: 4, time used: 0,00 s
10, 0,03 s, 1225,00 C (1498,16 K), its 4, FCC_A1 ALN - OK -
11, 0,02 s, 1250,00 C (1523,16 K), its 4, FCC_A1 ALN - OK -
Tsol 'ALN': 1251,17 C (1524,33 K) iter: 3, time used: 0,02 s
12, 0,02 s, 1275,00 C (1548,16 K), its 3, FCC_A1 - OK -
13, 0,01 s, 1300,00 C (1573,16 K), its 2, FCC_A1 - OK -
14, 0,00 s, 1325,00 C (1598,16 K), its 2, FCC_A1 - OK -
15, 0,00 s, 1350,00 C (1623,16 K), its 2, FCC_A1 - OK -
16, 0,02 s, 1375,00 C (1648,16 K), its 2, FCC_A1 - OK -
17, 0,01 s, 1400,00 C (1673,16 K), its 2, FCC_A1 - OK -
18, 0,00 s, 1425,00 C (1698,16 K), its 2, FCC_A1 - OK -
Tsol 'BCC_A2': 1445,10 C (1718,26 K) iter: 4, time used: 0,00 s
19, 0,01 s, 1450,00 C (1723,16 K), its 4, FCC_A1 BCC_A2 - OK -
20, 0,02 s, 1475,00 C (1748,16 K), its 5, FCC_A1 BCC_A2 - OK -
Tsol 'LIQUID': 1487,05 C (1760,21 K) iter: 4, time used: 0,00 s
Tsol 'FCC_A1': 1487,65 C (1760,81 K) iter: 5, time used: 0,01 s
21, 0,03 s, 1500,00 C (1773,16 K), its 5, LIQUID BCC_A2 - OK -
22, 0,02 s, 1525,00 C (1798,16 K), its 6, LIQUID BCC_A2 - OK -
Tsol 'BCC_A2': 1529,06 C (1802,22 K) iter: 4, time used: 0,00 s
23, 0,03 s, 1550,00 C (1823,16 K), its 4, LIQUID - OK -
24, 0,00 s, 1575,00 C (1848,16 K), its 2, LIQUID - OK -
25, 0,00 s, 1600,00 C (1873,16 K), its 2, LIQUID - OK -
changing step direction ...
26, 0,00 s, 975,00 C (1248,16 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
27, 0,00 s, 950,00 C (1223,16 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
28, 0,02 s, 925,00 C (1198,16 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
29, 0,01 s, 900,00 C (1173,16 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
Tsol 'BCC_A2': 886,93 C (1160,09 K) iter: 5, time used: 0,00 s
30, 0,03 s, 875,00 C (1148,16 K), its 5, FCC_A1 FCC_A1#01 BCC_A2 ALN - OK -
31, 0,01 s, 850,00 C (1123,16 K), its 10, FCC_A1 FCC_A1#01 BCC_A2 ALN - OK -
32, 0,02 s, 825,00 C (1098,16 K), its 7, FCC_A1 FCC_A1#01 BCC_A2 ALN - OK -
33, 0,01 s, 800,00 C (1073,16 K), its 7, FCC_A1 FCC_A1#01 BCC_A2 ALN - OK -
34, 0,02 s, 775,00 C (1048,16 K), its 6, FCC_A1 FCC_A1#01 BCC_A2 ALN - OK -
35, 0,02 s, 750,00 C (1023,16 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: 6, time used: 0,00 s
36, 0,05 s, 725,00 C (998,16 K), its 6, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
37, 0,00 s, 700,00 C (973,16 K), its 5, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
38, 0,00 s, 675,00 C (948,16 K), its 5, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
39, 0,00 s, 650,00 C (923,16 K), its 6, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
40, 0,01 s, 625,00 C (898,16 K), its 6, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
41, 0,02 s, 600,00 C (873,16 K), its 6, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
42, 0,02 s, 575,00 C (848,16 K), its 6, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
43, 0,01 s, 550,00 C (823,16 K), its 6, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
44, 0,02 s, 525,00 C (798,16 K), its 6, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
45, 0,02 s, 500,00 C (773,16 K), its 7, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
46, 0,01 s, 475,00 C (748,16 K), its 7, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
47, 0,02 s, 450,00 C (723,16 K), its 10, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
48, 0,01 s, 425,00 C (698,16 K), its 10, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
49, 0,02 s, 400,00 C (673,16 K), its 10, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
50, 0,00 s, 400,00 C (673,16 K), its 2, FCC_A1#01 BCC_A2 ALN CEMENTITE - OK -
Steps: 51, CalcTime: 0,83 s
AktStepVal: 673,160000
- OK -
The program did a single equilibrium calculation in the defined range 400-1600°C, changing the input temperature value by 25°C. It started with the temperature value of the initial equilibrium calculation (1000°C) and proceeded into higher temperatures (1025°C, 1050°C, ...) till the higher limit was reached (1600°C). Next ('changing step direction ...' message), it moved back to 1000°C and proceeded into lower temperatures (975°C, 950°C, ...) till the lower limit was reached (400°C). For every temperature value, the phases in equilibrium were found.
In other words, the system was sampled every 25°C in the temperature range 400-1600°C. Additionally, if the qualitative phase composition for the consecutive temperatures was different (an existing phase disappeared or/and a new phase appeared), MatCalc finds the exact temperature at which a given phase appears/disappears (given next to 'Tsol 'phasename':' message). This allows to give some insight beyond the step interval "mesh points".
Note: Be careful with the step interval value. If it is too large, MatCalc will miss the phases having the fields within the narrow range between the temperatures of the consecutive single equilibrium calculations.
The results of every single equilibrium calculation are stored in the buffer (named '_default_', if no other was created by user).
Result interpretation:
Summarising the data from the 'Output' window, the following phases are in equilibrium for the temperature range of 400-1600°C:
- 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 - 1600°C (and above...), the phases are: liquid
Try it out and feel free to experiment...
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