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E2: Phase diagram of the system Fe-Al-Nb-N-C

(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


In the previous parts of example E1, various equilibria were calculated for the system with the constant temperature

the phase equilibria were investigated in the system having the fixed composition (E1-2, E1-3) or temperature (E1-4). In this example, a phase boundary will be in the scope of the interest and to follow it, the temperature and the system composition will be varied.

Problem formulation:

How does the value of Ae3 temperature vary with the carbon content in the system specified in E1-1 (provided that the contents of the other alloying elements are kept constant, i.e. 0,1% Nb, 0,1% Al, 0,005%N)

Solution philosophy:

The 'Ae3 temperature' is defned as the the lowest temperature at which ferrite is not an equilibrium phase and thus it is equivalent to the phase boundary between the . It would be possible to reproduce it by performing either several temperature-stepped equilibrium calculations for various carbon contents or composition-stepped equilibrium calculations for various temperatures. In MatCalc, this combination is introduced in another option of the stepped calculations, making the whole procedure easy to execute if used properly.

The procedure can be described as follows:

- Select the phase boundary under consideration. This is done by finding the according temperature for an initial composition or vice versa
- Define the values for the carbon content and temperature steps
- Vary carbon content (which is an independent value by default) and find the temperature for the phase boundary under consideration.
- If the temperature difference for two consecutive carbon contents is greater than the defined temperature step, the temperature will be set to the independent value and the carbon contents for the phase boundary under consideration will be determined.

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

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 E1-1) and click 'Open'

1.2 Selecting the phase boundary

To find the Ae3 temperature, a simple temperature-stepped calculation can be performed, as it was done in example E1-2. It shows the value of 887°C for the initial carbon content. To select this phase boundary, the 'Search phase boundary' option will be used. In order to perform a successful search, it is recommended (though not required) to calculate the equilibrium at the temperature in which:

- the phase related to the selected phase boundary does not occur
- the phase boundary itself is not far away (within 100°C)

In this case, the related phase is ferrite ('BCC_A2'), as it appears below the Ae3 temperature and does not exist below it. Hence, the selection of the phase boundary will be preceeded by the single equilibrium calculation above this temperature.

1.2.1 Calculate equilibrium at 900°C

Click on 'Equilibrium' in 'Calc' menu (keyboard shortcut 'Ctrl'+'E', icon on the toolbar). Set the temperature to 900°C and leave the default pressure (101023 Pa). Click on 'Go' button.

Be sure that the message '-OK-' appears in the 'Output' window!

1.2.2 Search phase boundary

1.2.2.1 Open the 'Search phase boundary' window

Click on 'Search phase boundary' in 'Calc' menu (keyboard shortcut 'Ctrl'+'Shift'+'T', icon on toolbar).

1.2.2.2 Specify the type of the performed search

To select the phase boundary, the temperature must be varied. Select 'Temperature' in 'Type' section.

1.2.2.3 Specify the phase boundary searched

Choose 'BCC_A2' in the 'Target phase' section.

After clicking on 'Go' button, the following message appears in 'Output' window:

Tsol 'BCC_A2': 886,93 C (1160,09 K) iter: 4, 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 the 'Phase summary' and 'Phase details' windows are changed. Although, ferrite is identified as an inactive phase, it's driving force equals zero.

1.3 Following the phase boundary

1.3.1 Open the stepped calculation window

Click on 'Stepped calculation' in 'Calc' menu (keyboard shortcut 'Ctrl'+'T', icon).

1.2.2 Select the type of the performed calculation

To follow the phase boundary select 'Phase boun...' in the 'Type' dialog.

1.2.3 Specify the conditions of the calculation

During the stepped calculation, the carbon content varies and the relevant temperatures will be calculated. Select 'C' in 'element' field in the 'Boundary conditions' section. Specify the range of 0-1 wt.% C by typing '0' in 'Start' and '1' in 'Stop' fields of 'Range' section. Also there, type '0.05' in 'Step interval' field (with 'linear' scale selected) to sample the system every 0.05 wt.% C. The phase boundary that will be followed is defined in 'Target phase' field - select 'BCC_A2' there.

It is not unusual for the phase boundaries to have a steep flow, i.e. changing a little the system composition results in a huge temperature difference. In this range it would be rather more convenient to use temperature as an independent variable instead of a given component's content. In order to diagnose whether or not the phase boundary is steep, MatCalc uses the 'max. T-step' parameter. If the temperatures for the consecutive calculations exceed the value defined here, the temperature will be varied for the subsequent calculations and the component's contents will be determined for the phase boundary in question. In this case, the temperature will also step with this value. Set this value to '30' for the following calculation.

Note: There are two possibilities to avoid the switch of the independent value if it is not favoured for any reason. The first is to increase the 'max. T-step' value and the tolerance of MatCalc for the temperature jumps for the consecutive calculations. The second is to decrease the composition step interval which would decrease the temperature jumps for the consecutive calculations. Of course, both of them can be combined.

Click on 'Go' to proceed.

The following information should appear in the 'Output' window:

1, 0,02 s, 0,100000, T=886,93 C (1160,09 K), its 2, FCC_A1 FCC_A1#01 ALN - OK -
2, 0,00 s, 0,150000, T=867,68 C (1140,84 K), its 7, FCC_A1 FCC_A1#01 ALN - OK -
3, 0,00 s, 0,200000, T=850,68 C (1123,84 K), its 6, FCC_A1 FCC_A1#01 ALN - OK -
4, 0,00 s, 0,250000, T=835,42 C (1108,58 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
5, 0,01 s, 0,300000, T=821,57 C (1094,73 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
6, 0,00 s, 0,350000, T=808,88 C (1082,04 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
7, 0,00 s, 0,400000, T=797,16 C (1070,32 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
8, 0,02 s, 0,450000, T=786,26 C (1059,42 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
9, 0,00 s, 0,500000, T=776,10 C (1049,26 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
10, 0,00 s, 0,550000, T=766,58 C (1039,74 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
11, 0,02 s, 0,600000, T=757,77 C (1030,93 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
12, 0,00 s, 0,650000, T=749,53 C (1022,69 K), its 5, FCC_A1 FCC_A1#01 ALN - OK -
13, 0,00 s, 0,700000, T=741,73 C (1014,89 K), its 4, FCC_A1 FCC_A1#01 ALN - OK -
14, 0,01 s, 0,750000, T=734,27 C (1007,43 K), its 4, 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 5
15, 0,02 s, 0,787817, T=728,83 C (1001,99 K), its 5, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
16, 0,00 s, 0,837817, T=728,84 C (1002,00 K), its 9, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
17, 0,00 s, 0,887817, T=728,86 C (1002,02 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
18, 0,00 s, 0,937817, T=728,88 C (1002,04 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
19, 0,00 s, 0,987817, T=728,90 C (1002,06 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
20, 0,01 s, 1,000000, T=728,90 C (1002,06 K), its 3, FCC_A1 FCC_A1#01 ALN CEMENTITE - OK -
changing step direction ...
21, 0,02 s, 0,050000, T=909,14 C (1182,30 K), its 6, 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 23
22, 0,05 s, 0,002078, T=931,60 C (1204,76 K), its 23, FCC_A1 ALN - OK -
23, 0,01 s, 0,000000, T=932,82 C (1205,98 K), its 11, FCC_A1 ALN - OK -
Steps: 24, CalcTime: 0,34 s
AktStepVal: 0,000000
- OK -



Result interpretation:

The performed calculations allowed to find the maximal temperatures at which ferrite (BCC_A2) is an equilibrium phase in the system. If the Ae3 temperatures are to be limited to the point at which cementite appears the upper carbon content would be 0.78 wt.% C. The range of Ae3 temperatures is thus 933-729°C and decreases with the increasing carbon content.

Try it out and feel free to experiment…