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E1-4: Equilibrium calculus in Fe-Al-Nb-N-C system - equilibrium phases at various carbon contents

(calculating equilibrium, performing stepped calculations, variation of composition)

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


Sometimes, it is desired to know the solubility of the alloying elements in a given phase in order to design the material or the process to activate or to prevent the presence of the other phases. The equilibrium calculations will be used for the determination of these solubilities.

Problem formulation:

Which phases are in equilibrium in the alloy specified in example 1-1 if the carbon content is varied (on the extent of iron) in the range 0-5 wt.% C at 1300°C ?

Solution philosophy:

The problem could be solved with the equilibrium calculations performed for various compositions of the system. Manual changing of the system composition and calculating the relevant single equilibrium would be a laborious process so that again, the benefits of the stepped calculations will be used. This will allow to scan the phase equilibria for the various system compositions with one calculation only.

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 this equilibrium calculation, the system composition will be varied, so select 'Element con...' in the 'Type' dialog.

1.2.3 Specify the conditions of the calculation

During the stepped calculation, only the content of one of the elements can be varied on the extent of the reference element (defined in 'Global'>'Composition'). In this case, let the carbon content increase and the iron content decrease. Hence, in the 'boundary condition' section, select 'C' as 'element' and '1300' as 'temperature'. 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).

The investigated composition range is defined in the 'Start' and 'Stop' fields of the 'Range' section where the boundary carbon contents are defined. It doesn't matter if the 'Stop' value is greater or lower than the 'Start' value. Type the values of '0' and '5' which defines the temperature range of 0-4 wt.% C (The element content is defined by the 'Composition in weight percent' field in 'Options' section - it is expressed in weight percent if the field is ticked, otherwise it is expressed in mole fractions).

The value given in the 'Step interval' field specifies the intervals between the niobium contents for which the single equilibrium calculations will be performed. Type the value of '0.1' (with 'linear' scale selected) and click on 'Go' button to proceed.

The 'Output' window will contain the following information:

1, 0,01 s, 0,1, its 10, FCC_A1 - OK -
2, 0,02 s, 0,2, its 4, FCC_A1 - OK -
Xsol 'FCC_A1#01': X(C): 0,010549006, WP(C): 0,22895914 - OK -
3, 0,03 s, 0,3, its 5, FCC_A1 FCC_A1#01 - OK -
4, 0,02 s, 0,4, its 5, FCC_A1 FCC_A1#01 - OK -
5, 0,00 s, 0,5, its 5, FCC_A1 FCC_A1#01 - OK -
6, 0,00 s, 0,6, its 5, FCC_A1 FCC_A1#01 - OK -
7, 0,01 s, 0,7, its 4, FCC_A1 FCC_A1#01 - OK -
8, 0,02 s, 0,8, its 4, FCC_A1 FCC_A1#01 - OK -
9, 0,01 s, 0,9, its 4, FCC_A1 FCC_A1#01 - OK -
Xsol 'ALN': # extrapolation # X(C): 0.043818274, WP(C): 0.97676609 - OK -
10, 0,06 s, 1, its 79, FCC_A1 FCC_A1#01 ALN - OK -
11, 0,00 s, 1,1, its 4, FCC_A1 FCC_A1#01 ALN - OK -
12, 0,01 s, 1,2, its 4, FCC_A1 FCC_A1#01 ALN - OK -
Xsol 'LIQUID': X(C): 0,055719026, WP(C): 1,254183 - OK -
13, 0,03 s, 1,3, its 5, LIQUID FCC_A1 FCC_A1#01 ALN - OK -
14, 0,00 s, 1,4, its 3, LIQUID FCC_A1 FCC_A1#01 ALN - OK -
15, 0,00 s, 1,5, its 3, LIQUID FCC_A1 FCC_A1#01 ALN - OK -
Xsol 'FCC_A1#01': X(C): 0,069023785, WP(C): 1,5708155 - OK -
16, 0,01 s, 1,6, its 4, LIQUID FCC_A1 ALN - OK -
17, 0,02 s, 1,7, its 4, LIQUID FCC_A1 ALN - OK -
18, 0,00 s, 1,8, its 4, LIQUID FCC_A1 ALN - OK -
19, 0,00 s, 1,9, its 4, LIQUID FCC_A1 ALN - OK -
20, 0,00 s, 2, its 4, LIQUID FCC_A1 ALN - OK -
21, 0,02 s, 2,1, its 4, LIQUID FCC_A1 ALN - OK -
22, 0,01 s, 2,2, its 4, LIQUID FCC_A1 ALN - OK -
23, 0,02 s, 2,3, its 4, LIQUID FCC_A1 ALN - OK -
24, 0,00 s, 2,4, its 4, LIQUID FCC_A1 ALN - OK -
25, 0,00 s, 2,5, its 4, LIQUID FCC_A1 ALN - OK -
26, 0,01 s, 2,6, its 4, LIQUID FCC_A1 ALN - OK -
27, 0,02 s, 2,7, its 4, LIQUID FCC_A1 ALN - OK -
28, 0,02 s, 2,8, its 5, LIQUID FCC_A1 ALN - OK -
29, 0,00 s, 2,9, its 4, LIQUID FCC_A1 ALN - OK -
Xsol 'FCC_A1': X(C): 0,12311439, WP(C): 2,9334694 - OK -
30, 0,02 s, 3, its 4, LIQUID ALN - OK -
31, 0,01 s, 3,1, its 4, LIQUID ALN - OK -
32, 0,02 s, 3,2, its 4, LIQUID ALN - OK -
33, 0,00 s, 3,3, its 4, LIQUID ALN - OK -
34, 0,00 s, 3,4, its 4, LIQUID ALN - OK -
35, 0,00 s, 3,5, its 4, LIQUID ALN - OK -
36, 0,02 s, 3,6, its 4, LIQUID ALN - OK -
37, 0,02 s, 3,7, its 4, LIQUID ALN - OK -
38, 0,01 s, 3,8, its 4, LIQUID ALN - OK -
39, 0,00 s, 3,9, its 4, LIQUID ALN - OK -
40, 0,00 s, 4, its 4, LIQUID ALN - OK -
changing step direction ...
41, 0,02 s, 1e-009, its 5, FCC_A1 - OK -
Steps: 42, CalcTime: 0,69 s
AktStepVal: 0,000000
- OK -

The program did a single equilibrium calculation in the defined range 0-4 wt.% C, changing the carbon content value by 0,1 wt.%. For every carbon content value, the phases in equilibrium were found. 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 carbon content at which a given phase appears/disappears (given next to 'Xsol '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 carbon contents 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 carbon content in range of 0-4 wt.% C:

- 0 - 0.23, only one phase is stable: austenite (FCC_A1)
- 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…