MatCalc version: 5.52.0038
Database: mc_fe.tdb, mc_sample_fe.ddb
Author: Georg Stechauner
Created: 2013-07-02
Revisions:
Following Part 1, where the corresponding models and parameters were discussed, we will show in Part 2 on the basis of the data of Goodman et al. (1973) the precipitation of Cu in Fe-cu. We start off with the nucleation of coherent bcc-Cu and let it evolve with the transformation to the semi-coherent 9R structure and the incoherent fcc-Cu. Many attempts on this simulation have already been published, although without fully satisfying the simulators wishes. A direct-particle transformation will be used for the evolution of Cu-precipitates.
Note: This is an advanced example and will not cover basics like “How to create a plot”, etc… . Please consider earlier P-examples for instructional purpose.
Note 2: The results below can only be reproduced by using both, the newest version of MatCalc as well as the newest thermodynamic database. Using sample databases can result in slightly different results due to dissimilar values in the databases.
If you are interested in some further information on G* calculation, please consider:
Click here to view the script for this example.
Set up the thermodynamics by either loading the mc_fe database.
Select the following phases, elements and enter the chemical composition in wt-%:
Elements | Chemical composition | Phases |
---|---|---|
Cu | 1.4 | - |
Set Fe to reference element.
Note: We do not need to load any phases as we will work solely with composition sets created in the following section.
Conclude the thermodynamic setup by loading the diffusion database for Fe.
The following tables of phase fraction, radius and number density are taken from Goodman et al. Feel free to enter your own data as well, but don't forget to change the chemical composition respectively. Internal testing with in-house atom probe results, showed a qualitative good result for values from 0.5 to 1.5 at.-%.
Create three new tables for phase fraction, radius and number density and enter the following values:
x-Value: time / s | y-value: phase fraction | y-value: radius / m | y-value: number density |
---|---|---|---|
1e3 | 0.08e-2 | - | - |
4e3 | 0.23e-2 | 0.8e-9 | 1.2e24 |
1e4 | 0.72e-2 | 1.4e-9 | 1e24 |
4e4 | 1.04e-2 | 3.0e-9 | 1e23 |
1.5e5 | 1.28e-2 | 4.8e-9 | 3e22 |
5e5 | 1.30e-2 | 7.0e-9 | 8e21 |
Next we enter the data for the precipitation domain. To do so, open the precipitation domain dialog and create a new domain. Select bcc_a2 as its matrix phase. Enter the following data in the corresponding tabs:
Tab | Option | Value |
---|---|---|
Microstructure | Grain diameter | 100e-6 |
Dislocation density | 1e12 | |
Special | Substitutional matrix diffusion enhancement | 10.0 |
Note: In the newest MatCalc version, it is not necessary to set the diffusion enhancements due to grain-boundary and dislocation pipes anymore. An assessment was performed on those parameters and the values are directly read for Fe, Ni and Al from the software.
It was shown by Jourdan et al. (2010) that the cluster mobility is responsible for an acceleration of the kinetics of around two orders of magnitude. This is considered with a MDEF of 10.
Follow by setting up the precipitates. Bring up the phase status dialog window and select the FCC_A1 phase. Click 'Create…' and select 'composition set'. Set the following settings as shown in the pictures and repeat it twice for BCC_A2 (create CU_BCC_1 and _2). These phases will serve as parent phases for the coherent bcc-Cu (CU_BCC_1), semi-coherent 9R-Cu (CU_BCC_2) and incoherent fcc-Cu (CU_FCC).
Your phase status dialog should look like this after correct setup and creation of precipitates (CU_BCC_1_P0, CU_BCC_2_P0 and CU_FCC_P0):
Configure the phases according to the following table to complete the setup:
Precipitate | Tab | Option | Value |
---|---|---|---|
CU_BCC_1_p0 | Precipitate | Kinetic alias name | Cu(bcc) |
CU_BCC_1_p0 | Interfacial energy | 0.95*CIE$CU_BCC_1 | |
CU_BCC_1_p0 | Diffuse interface correction | ✔, T_crit = 1860 | |
CU_BCC_1_p0 | Nucleation | Nucleation model | Becker/Doering time-dep. |
CU_BCC_1_p0 | Nucleus composition | minimum G* (press Calc) | |
CU_BCC_1_p0 | Restrict nucleation to prec domain | ✔, select domain_bcc | |
CU_BCC_1_p0 | Nucl. sites | Nucleation sites | bulk |
CU_BCC_1_p0 | Special | Binder-Staufer exponent | -3/4 |
CU_BCC_1_p0 | Coalescence factor | 2 | |
CU_BCC_1_p0 | Diff. in prec. (subst) | 1 | |
CU_BCC_1_p0 | Diff. in prec. (inter) | 1 |
Precipitate | Tab | Option | Value |
---|---|---|---|
CU_BCC_2_p0 | Precipitate | Kinetic alias name | Cu(9R) |
CU_BCC_2_p0 | Nucleation | Nucleation model | direct particle transformation |
CU_BCC_2_p0 | Nucleus composition | ortho-equilibrium | |
CU_BCC_2_p0 | Restrict nucleation to prec domain | ✔, select domain_bcc | |
CU_BCC_2_p0 | Nucl. sites | other precipitates | Add: CU_BCC_1_P0 |
CU_BCC_2_p0 | transform. radius | min. 2.0e-9 max. 3.0e-9 |
|
CU_BCC_2_p0 | Special | Binder-Staufer exponent | -3/4 |
CU_BCC_2_p0 | Coalescence factor | 3 | |
CU_BCC_2_p0 | Diff. in prec. (subst) | 1 | |
CU_BCC_2_p0 | Diff. in prec. (inter) | 1 |
Precipitate | Tab | Option | Value |
---|---|---|---|
CU_FCC_p0 | Precipitate | Kinetic alias name | Cu(fcc) |
CU_FCC_p0 | Nucleation | Nucleation model | direct particle transformation |
CU_FCC_p0 | Nucleus composition | ortho-equilibrium | |
CU_FCC_p0 | Restrict nucleation to prec domain | ✔, select domain_bcc | |
CU_FCC_p0 | Nucl. sites | other precipitates | Add: CU_BCC_2_P0 |
CU_FCC_p0 | transform. radius | min. 4.0e-9 max. 8.0e-9 |
|
CU_FCC_p0 | Special | Binder-Staufer exponent | -3/4 |
CU_FCC_p0 | Coalescence factor | 4 | |
CU_FCC_p0 | Diff. in prec. (subst) | 1 | |
CU_FCC_p0 | Diff. in prec. (inter) | 1 |
The interfacial energy correction has to be performed due to the diffuse conditions present at the interface.
To ensure correct thermodynamic values and no driving force errors (DFM-errors), set automatic start values and calculate an equilibrium at 500C.
Perform an isothermal kinetic simulation at 500°C
Open the Create new window dialog box, an switch to the user-defined tab. Select the variable 03_kinetics_4_frames_T_f_n_r_logX. Automatically the relevant plots will be created. Go to the options menu and select in the defaul x-axis
the scaling section and scale to 1..1e10.
Now add a sum-phase fraction to the phase fraction plot. Select the correct plot in the options window, right-click it and select (as shown) buffer results.
In the pop-up window, enter:
As a last step, select the plots in the options menu and right-click them as before, to add the experimental tables.
The final result should look like this:
Save your workspace, if you plan on performing the TTP simulation in the following article .