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E1-3: Equilibrium calculus in Fe-Al-Nb-N-C system - microstructure prediction.

(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


This time, the equilibrium calculations will be used for the prediction of the alloy microstructure based on some simple assumptions.

Problem formulation:

Which kind of microstructure is expected (qualitatively) to occur in the system after its solidification ?

Solution philosophy:

The modelling of the microstructure is a complex task. Here, some qualitative conclusions will be made on the basis of the equilibrium calculations. The stepped calculation will be performed from the temperature at which only liquid phase exists to the temperature below which the liquid phase dissappears. Based on the results performed in example E1-2, the temperature range will be set to 1450°C-1550°C. The following assumptions will be also made:

- If the phase is a product of the reaction of two or more phases, it will occur at the phase boundary of the reactants.

- If the phase is not a product of the reaction of two or more phases then it will appear in the bulk of the existing phase (parent phase).

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). Type the values of '1550' and '1450' which defines the temperature range of 1450-1550°C.

The value given in the 'Step interval' field specifies the intervals between the temperatures for which the single equilibrium calculations will be performed. Type the value of '5' (with 'linear' scale selected) and click on 'Go' button to proceed.

The 'Output' window will contain the following information:

1, 0,02 s, 1450,00 C (1723,16 K), its 14, FCC_A1 BCC_A2 - OK -
2, 0,02 s, 1455,00 C (1728,16 K), its 4, FCC_A1 BCC_A2 - OK -
3, 0,02 s, 1460,00 C (1733,16 K), its 4, FCC_A1 BCC_A2 - OK -
4, 0,00 s, 1465,00 C (1738,16 K), its 4, FCC_A1 BCC_A2 - OK -
5, 0,00 s, 1470,00 C (1743,16 K), its 4, FCC_A1 BCC_A2 - OK -
6, 0,02 s, 1475,00 C (1748,16 K), its 4, FCC_A1 BCC_A2 - OK -
7, 0,01 s, 1480,00 C (1753,16 K), its 4, FCC_A1 BCC_A2 - OK -
8, 0,00 s, 1485,00 C (1758,16 K), its 4, FCC_A1 BCC_A2 - OK -
Tsol 'LIQUID': 1487,05 C (1760,21 K) iter: 3, time used: 0,02 s
Tsol 'FCC_A1': 1487,65 C (1760,81 K) iter: 4, time used: 0,00 s
9, 0,03 s, 1490,00 C (1763,16 K), its 4, LIQUID BCC_A2 - OK -
10, 0,00 s, 1495,00 C (1768,16 K), its 4, LIQUID BCC_A2 - OK -
11, 0,00 s, 1500,00 C (1773,16 K), its 4, LIQUID BCC_A2 - OK -
12, 0,02 s, 1505,00 C (1778,16 K), its 4, LIQUID BCC_A2 - OK -
13, 0,01 s, 1510,00 C (1783,16 K), its 4, LIQUID BCC_A2 - OK -
14, 0,00 s, 1515,00 C (1788,16 K), its 4, LIQUID BCC_A2 - OK -
15, 0,00 s, 1520,00 C (1793,16 K), its 4, LIQUID BCC_A2 - OK -
16, 0,00 s, 1525,00 C (1798,16 K), its 5, LIQUID BCC_A2 - OK -
Tsol 'BCC_A2': 1529,06 C (1802,22 K) iter: 3, time used: 0,00 s
17, 0,03 s, 1530,00 C (1803,16 K), its 3, LIQUID - OK -
18, 0,00 s, 1535,00 C (1808,16 K), its 2, LIQUID - OK -
19, 0,00 s, 1540,00 C (1813,16 K), its 2, LIQUID - OK -
20, 0,02 s, 1545,00 C (1818,16 K), its 2, LIQUID - OK -
21, 0,02 s, 1550,00 C (1823,16 K), its 2, LIQUID - OK -
changing step direction ...
Steps: 22, CalcTime: 0,36 s
AktStepVal: 1723,160000
- OK -

The program did a single equilibrium calculation in the defined range 1450-1550°C, changing the input temperature value by 5°C. For every temperature value, the phases in equilibrium were found. MatCalc shows that the solidification starts at 1529°C, at which point delta-ferrite ('BCC_A2') phase appears. Lowering the temperature, at 1487°C two things happen: The liquid phase dissapears and the austenite phase ('FCC_A1') appears. As both of the processes occur at the same temperature (the discrepancy lower than 1°C can be neglected), this would indicate that it is a phase transition. Let's have a look on the phase amounts before and after this reaction.

1.3 Retrieving data from the buffer

During the stepped calculation, the equilibrium phases, their amount and composition were found for every temperature, though these are not displayed in the 'Phase summary' and 'Phase details' windows. It is possible, however, to investigate the results by editing the buffer in which the calculated single equilibria are stored.

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 for this temperature can be reviewed in the 'Phase summary' and 'Phase details' windows (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 it can be seen, the content of delta-ferrite diminishes which means that it is consumed during the reaction.

Result interpretation:

The following observations are noted:

- Solidification begins at 1529°C. At this temperature, delta-ferrite ('BCC_A2' phase) precipitates.

- At 1487°C a reaction occurs during which the liquid phase is consumed and the austenite ('FCC_A1') phase is produced.

- The reaction at 1487°C could be of either eutectic (liquid -> bcc + fcc) or peritectic (liquid + bcc -> fcc) type. As the content of the delta-ferrite phase is lower after the reaction (decreased from 0.98 to 0.89 within less than 1°C range), the reaction is found to be of the peritectic type.

Note: If the eutectic reaction had occured, the content of the delta-ferrite phase would have increased, as this would have been produce during the process

These observations yield the following conclusions about the alloy microstructure.

- Delta-ferrite precipitate appears at 1529°C in the bulk of the liquid phase. The grains are growing within the liquid phase during the cooling of the alloy down to 1487°C.

- At 1487°C, a peritectic reaction occurs at which two phases react together. The product of the reaction (austenite) is formed on the phase boundaries of the reactants.

- The alloy after the complete solidifaction is expected to consist of delta-ferrite grains dispersed in the austenite phase.

Try it out and feel free to experiment…