T10: T0- temperature
in Fe-Cr-C
This tutorial was created on
MatCalc version 5.23 rel 1.026
license: free
database: mc_sample_fe.tdb
Contents:
- T0- temperature calculation
- Martensite / Bainite transformation
- Variation of T0- temperature with carbon and chromium content
- Import and display of experimental data into plots
The T0-temperature is defined as the temperature where two
phases of identical chemical composition have the same molar Gibbs free energy.
This temperature is an important quantity in the field of diffusionless
phase transformations, i.e. the bainitic and martensitic transformation. In the present
example, we will discuss some thermodynamic aspects of the austenite/martensite
transformation and apply T0-temperature calculations to the evaluation of transformation temperatures.
Step 1: Define the thermodynamic system (see also Tutorial
T2)
Create a new workspace file. From a suitable database (mc_sample_fe.tdb) define
the elements Fe, Cr and C as
well as the phases BCC_A2 (ferrite) and FCC_A1 (austenite).
Enter the system composition with wp(C) = 0.1 and wp(Cr)=1.0.
Set initial values with 'Calc - Set start
values' or Ctrl+Shift+F.
Calculate an equilibrium at 800°C.
Step 2: Calculate the T0- temperature
Before evaluation of the
T0-temperature, an equilibrium located in the one-phase
region of the parent phase must be calculated in order to set the composition
of one of the phases equal to the system composition. The parent phase is austenite so the solubility temperature
of BCC_A2 will be evaluated with 'Calc - Search phase boundary...' or
Ctrl+Shift+T. As a result, MatCalc displays in the 'Output'window
Tsol 'BCC_A2': 856,87 C (1130,03 K) iter: 5, time used: 0,03 s
In the 'Phase summary' and 'Phase
details' window, only the FCC_A1 phase is denoted as active (mole fracton = 1). We
can now proceed with this initial condition. For convenience,
store this (current) state in a calculation state with the name 'Start
austenite' by selecting 'Global - CalcStates - Create...'.


We can now
evaluate the T0- temperature for austenite and ferrite with 'Calc
- Search phase boundary...' or Ctrl+Shift+T.
The following, well-known, dialog box appears:

Select 'T0- temperature' in the type listbox, 'BCC_A2' as target phase and 'FCC_A1' as parent
phase. The check box 'Force target to parent composition' must
be chosen, because the composition of BCC_A2 wil be adjusted according
to the parent composition. The energy difference (DFM
offset) can be left as default (zero). Press 'Go' to
start the calculation. The result is shown below
T0(FCC_A1/BCC_A2): 793,396 C (1066,56 K)
iter: 2, time used: 0,05 s
- OK -
The phase details window shows:
#### /FCC_A1/ moles: 1, gm: -47047,3 (-47047,3), sff: 0,995371
Phasestatus: entered - active
FE +9,84677e-001 CR +1,06937e-002 C +4,62933e-003
### inactive ###
#### /BCC_A2/ moles: 0, gm: -47047,3 (-47047,3), sff: 0,995371
Phasestatus: entered - not active (dfm=3,354e-009)
FE +9,84677e-001 CR +1,06937e-002 C +4,62933e-003
It is obvious that, at the temperature of 793.396°C, FCC_A1
and BCC_A2 of the same composition have the same molar Gibbs free energy of gm=47047.3
J/mole.
Step 3: Evaluate T0- temperature as a function of chromium content
Let us now
investigate how the T0- temperature for ferrite and austenite varies
with the chromium content. From the menu select 'Calc -
Stepped calculation…'or press Ctrl+T.
In the left listbox of the 'Step equilibrium ...' window, select type 'T0 temperature'.
Select 'FCC_A1' for the parent phase and 'BCC_A2' for the target phase. Don't forget
to select chromium as the independent element. Enter the chromium range between
'0' and '10' weight percent in steps of '0.5' and don't forget to mark the 'Force
identical composition' box. The 'Step equilibrium ...' window
looks now as follows.
Press 'Go' to start the calculation. The result
can be displayed in the well known 'XY-data' plot. Create
the plot and drag and drop the T$c variable from
the variables window into the plot. Edit the 'x-axis', 'y-axis' and 'legend' (see also
Tutorial 4 or Tutorial 5) such that the result of the stepped T0- temperature
calculation looks as follows.

Step 4: Evaluate T0-temperature as a function of carbon content
In the same way, similar to the evaluation of the dependence of the T0-
temperature on the chromium content, it is possible to calculate the T0-
temperature as a function of the carbon content. Therefore, rename the '_defaullt_'buffer
selecting 'Global - Buffers - Rename ...' and give it
the name T0 - chromium. Then create a new
buffer ('Global
> Buffers > Create ...') with the
name T0 - carbon and load the calculation state
'Start austenite' (make sure that
the current buffer is the 'T0 - carbon' - buffer).
Analogously to the calculation before, carry out a stepped calculation. Press 'Calc
- Stepped calculation ...' or press Ctrl+T, enter the following settings and press 'Go'.

The graph for the T0- temperature dependence for varying carbon
content should look like the figure below. There is no need
to create
a new plot.
The T0- temperature line in the figure can be simply changed by switching
from 'T0 - chromium' buffer to the 'T0 - carbon' buffer in the options window.

Afterwards,
the x- and y-axes must be rescaled and in the case of the x-axis renamed.
So the result looks as follows.
The strong dependence of the T0- temperature on the carbon content
is evident. This is reflected in the strong influence of carbon on the martensite
start temperature.
Step 5: Add some experimental data on martensite start temperatures
The experimental data, which will be added to the recent plot, are taken from
ref. [1]. Before doing so, we must create a new buffer. So, none
of the former results will be lost. Name the new buffer as 'T0
with offset' (further calculations with various dfm-offsets well be done ...)
and create a table selecting 'Global - Tables ...'.
Press 'New
...' and call
the table 'Exp. data'. Enter the following measured
martensite start temperatures into the table by selecting 'Edit
...' or import them by reading from a file.
Carbon content
[wt%] |
Marteniste start
temperature |
0 |
540 |
0.086 |
510 |
0.1936 |
475 |
0.2409 |
480 |
0.2495 |
470 |
0.2581 |
440 |
0.3011 |
430 |
0.3226 |
410 |
0.3871 |
410 |
0.3871 |
400 |
0.3871 |
395 |
0.4560 |
405 |
0.4947 |
355 |
0.5054 |
375 |
0.6022 |
330 |
0.6022 |
320 |
0.7097 |
280 |
0.7312 |
280 |
0.7743 |
265 |
0.8173 |
240 |
0.8603 |
225 |
Press 'OK' twice and insert the experimental
data into the plot as a new series (right-click in 'options' window and select 'New series > table experimental data') and switch to 'Exp. data' in 'connected to' box (see also Tutorial 5).

Rescale the y-axis (set scaling as 'auto') and edit the legend and the series names. The result looks
as follows.
Apparently, the calculated T0- temperature does not fit
the experimental data, however the curve runs parallel to it with the calculated temperatures being higher.
The reason is that a certain amount of driving force is required to start the martensite transformation. This extra energy, or extra driving force, is of the order of 1.2 to 2.5 kJ/mol (depending on the composition of the alloy) and can be defined in the field dfm-offset. Default value for this parameter is zero.
To evaluate how high this extra energy is as a function of carbon content, stepped calculations with different dfm-offsets can be performed.
Carry out two simulations, one as a steped T0- temperature calculation with a dfm-offset of 1200
J/mole and one with 1700
J/mole. Before starting lock the first series (T0- dfm=0 J/mole).
So the first graph will be conserved for further comparison. Select 'Calc - Stepped
calculation ...'and complete the dialog box as follows:

Drag and drop the 'T$c' variable again into the
plot and rename the series to T0
- dfm=1200 J/mole. Do the same for a dfm-offset of 1700 J/mole. The plot now
looks like follows.
A dfm-offset in the range of 1200-1700 J/mole can be used to obtain reasonable agreement between the calculations
and the experimental data.
References
[1] Z. Jicheng and J. Zhanpeng, Acta met. mater. 38 (1990)
425-431.
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