MatCalc version: 5.60
Database: mc_sample_fe.tdb, mc_sample_fe.ddb
Author: Georg Stechauner
Created: 2012-02-08
Revisions: Heinrich Buken 2014-03-20 (Updated to GUI v.5.6)
This example demonstrates the basics of every precipitation simulation and thoroughly guides through setup and calculation. The precipitation of cementite in ferrite is of special interest in this example. Furthermore will be the grain size, nucleation rate and other general precipitation-related features. A comparison of the numerical simulation with the classical Lifshitz-Slyozov-Wagner (LSW) size distribution is also presented.
Click here (25) to view the script for this example with #25 size classes, and here (1000) for the script with #1000 size classes.
Click here to view the script for the plots.
Set up the thermodynamics by loading the mc_sample_fe database. Select the following phases, elements and enter the chemical composition in wt-%:
Elements | Chemical composition | Phases |
---|---|---|
Fe | ref. | BCC_A2 |
C | 0.1 | CEMENTITE |
Fe is the reference element.
Complete the thermodynamic setup by loading the diffusion database for Fe (mc_sample_fe.ddb).
To facilitate identification of a first thermodynamic equilibrium, set automatic start values. Then calculate an equilibrium at 700C.
Next, we enter the parameter settings for the precipitation domain. To do so, open the precipitation domain dialog and create a new domain. Select bcc_a2 as its matrix phase. No further settings need to be done here. The cementite_p0 precipitate will be created in the next step.
Open the phase status dialog now and select the cementite phase on the left hand side. Press the 'Create' button on the left bottom side and select 'Precipitate (_Pnn)'.
Switch to the precipitate tab and initialize the precipitate with #25 size classes. This is the number which is usually used for precipitation simulation. It is precise enough for a simulation of mean precipitate quantities such as mean radius or number density. As we will see in part 2, to reproduce the precipitate size distribution with good accuracy, many more classes are needed.
Important …
As an example:
In the actual simulation procedure, you do not have to think about the actual handling of the precipitate size distribution, as this is managed internally by MatCalc. However, if you are interested in this functionality in more detail, have a look at the primary precipitates HowTo, especially the manually defined size distributions section.
As a last step, change the nucleation site from bulk to dislocation in the 'Nucleation' tab:
The nucleation site is a major parameter determining the maximum number density of precipitates. Whereas selection of 'bulk' allows the nucleation events to occur everywhere in the material,1) the other choices limit nucleation to certain heterogeneous sites by lowering the possible number density.2)
In order to plot the LSW size distribution function, you need to enter the following expression for the user-defined function 'LSW' in the 'variables & functions' dialog and name it accordingly:
x^2*(3/(3+x))^(7/3)*((3/2)/(3/2-x))^(11/3)*exp(-x/(3/2-x))*4/9
Alternatively, enter the following line into the command line processor:
set-function-expression LSW x^2*(3/(3+x))^(7/3)*((3/2)/(3/2-x))^(11/3) *exp(-x/(3/2-x))*4/9
To display the results of this example, we need 3 windows with several plots. As a shortcut, feel free to download and execute the 'plot' script. It should setup all 3 windows and name everything accordingly if you named all your variables as shown in this example.
Plot | 1 | 2 | 3 | 4 |
---|---|---|---|---|
Title | Phase fraction of cementite precipitate | Number of precipitates | Nucleation rate | Precipitation radius |
Data | F$CEMENTITE_P0 | NUM_PART$CEMENTITE_P0 | NUCL_RATE$CEMENTITE_P0 | R_MEAN$CEMENTITE_P0 R_CRIT$CEMENTITE_P0 R_MIN$CEMENTITE_P0 R_MAX$CEMENTITE_P0 |
Legend | No | No | No | Bottom |
Y-Axis Title | Phase fraction | Number of precipitates [m-3] | Nucleation rate [m-3s-1] | Precipitate radius [nm] |
Y-Axis Factor | 1 | 1 | 1 | 1e9 |
Y-Axis Type | Lin | Log | Log | Log |
Title | Cementite precipitate distribution |
---|---|
Data | CEMENTITE_P0 |
X-Axis Title | Scaled radius [nm] |
X-Axis Scale | 0..1.499 |
Y-Axis Title | Scaled number |
Legend | Bottom |
Scale histogram frequency | density |
Scale histogram radius | yes |
Add new series | Function → LSW |
Histogram columns | 25 |
Open the 'Precipitation simulation' dialog window to perform the last necessary settings. Set the simulation end time to 3.6e6 seconds and select an isothermal temperature control at 500C.
Everything should be in place now and we are ready to start.
After a short calculation, the figures below were calculated and show the final results. The LSW theory on the Ostwald ripening was reproduced to some degree, but not very smooth and accurately. A more detailed and accurate version, as well as a discussion on the different areas of nucleation and growth, re-distribution, and growth follows in part 2.
The analysis of this example will be continued in Setup of simulation for analysis of precipitate distributions.