T15: Effect
of microstructure and conditions (Part 1)
This tutorial was created on
MatCalc version 5.23 rel 1.026
license: free
database: mc_sample_fe.tdb; mc_sample_fe.ddb
The Fe-Cr-C system forms the basis of many industrially useful
alloys. The aim of this and Tutorial 16 is to produce a simulation
of the precipitation behaviour in a Fe-9Cr-0.1C (wt.%) alloy during
heat-treatment at 600°C. This involves considering several
aspects, such as the chemical compositions of nuclei, the microstructural
sites on which nuclei form, and the density of these sites in the
microstructure under consideration. This first of two tutorials
will focus on modelling the formation of the metastable cementite
(Fe3C) phase, and Tutorial 16 will consider the interaction
between this and the more stable phase M23C6.
Contents:
- Choice of nucleation model
- Diffusivity in precipitates
- Nucleation sites for the precipitate phase
- Microstructural parameters of the precipitation domain
Equilibrium calculations
Create a new workspace with the elements Fe, C and Cr and the
phases BCC_A2, CEMENTITE and M23C6. Enter the composition 9 wt.%
Cr, 0.1 wt.% C.
Calculate an equilibrium at 600°C and observe the contents
of the 'Phase summary' window. It
can be seen that M23C6 is the
stable phase at equilibrium. However, it is known from experience
that the first phase to form on heat-treatment is cementite.
Go
to 'Global > Phase status' and
suspend the 'M23C6' phase
so as to study the metastable equilibrium between BCC_A2 and cementite.
The composition of cementite in metastable equilibrium with BCC_A2
is, in wt.%, 84 % Cr, 7 % C, 9 % Fe; this is very rich in Cr compared
to the overall system composition of 9 % Cr, 0.1 % C and 90.1 %
Fe.
In practice, it is found that cementite forms rapidly on heat-treatment
at 600°C; this is more consistent with a mechanism which primarily
involves the diffusion of C rather than the slower-diffusing Cr.
It is therefore likely that the initial nuclei do not form with
the equilibrium composition, but are initially much richer in Fe
than Cr. Part 1 of this tutorial considers how such effects can
be modelled. Re-open 'Global > Phase status' and remove the
'suspended' flag for M23C6.
1. Nucleation model for cementite
Setting up the simulation
Create a precipitate phase CEMENTITE_P0, using 'Global > Phase
status'. In the 'Precipitate' tab,
set the number of size classes to '25', and in the 'Nucleation' tab,
set the nucleation sites to 'Dislocations' and change the 'Nucleus
composition' model from 'ortho-equilibrium' to 'para-equilibrium' using the drop-down menu. 'Para-equilibrium' means that the nucleus
is assumed to have the same composition in terms of substitutional
elements as the matrix from which it forms, and only the carbon
is partitioned between the two phases. In the 'ortho-equilibrium' model, by contrast, the composition of the nucleus is calculated
assuming full equilibrium with the BCC_A2 matrix.

In 'Global > precipitation domains',
create a new domain named
'ferrite' with 'BCC_A2' as its matrix
phase. Click on 'Attach', select 'CEMENTITE_P0' and click 'OK'. The system
is now set up so that cementite can precipitate in this domain.
Accept the changes by clicking
'OK' to close the window.

Load the
mobility data as described in Tutorial
14.
Graphical display of results
Create a new XY-plot window and define a default x-axis with the
following properties:
- Use for all plots: yes
- Title: Time [h]
- Type: log
- Scaling: auto
- Factor: 1/3600 (to convert seconds to hours)
Add four new plots to the window and drag and drop the following
series to the plots:
- F$CEMENTITE_P0
- X$CEMENTITE_P0$CR (Cr content of the cementite precipitate
phase) and X_NUCL$CEMENTITE_P0$CR (Cr content of the nucleus).
The latter can be found under 'kinetics: nucleation'.
- X$BCC_A2$C (carbon content of BCC matrix)
- NUM_PART$CEMENTITE_P0
- R_MEAN$CEMENTITE_P0
Label the y-axes as follows
- 'f<sub>CEM</sub>' (fCEM)
- 'x<sub>Cr</sub>' (xCr)
- 'x<sub>BCC_A2, C</sub>' (xBCC_A2, C)
- 'N<sub>ppt</sub> [m<sup>-3</sup>]' (Nppt
[m-3])
- 'R<sub>mean</sub> [m]' (Rmean [m]); y-axis set to 'log'
Save the workspace.
Calculation
Select 'Calc > precipitate kinetics'. Enter the finish time
of the calculation: '3.6e13' s (= 1e10 hours). The isothermal treatment
temperature should be set to '600' and 'Temperature
in C' selected.
Leave the other settings as they are, and click on "Go".
(The calculation may take some time, especially on slower machines,
because of the long treatment time.)
After the calculation has finished, duplicate and lock all the
series in the plot window. Return to 'Global > Phase
status' and set the nucleation model for CEMENTITE_P0
to 'ortho-equilibrium' and
re-open 'Calc > precipitation kinetics'.
There is no need to change anything; simply click on 'Go'.
A warning appears that the contents of the current buffer will
be overwritten. As the series have been locked, this does not matter;
accept the warning with "Yes".
Interpretation of results
The onset of precipitation occurs much earlier in
the para-equilibrium case, beginning around 1e-7 hours (~ 1e-3
seconds), as compared to ~1 hour for ortho-equilibrium. The para-equilibrium
cementite fraction reaches a plateau at a smaller value than for
the ortho-equilibrium case, but after a longer time at temperature,
this fraction rises, eventually reaching the same value as
for ortho-equilibrium.

The para-equilibrium model stipulates that the Cr content of the
nuclei (XNUCL, CEM, Para) be equal to that of the matrix.
This decreases towards longer times at temperature, as the matrix
becomes depleted in Cr. This depletion is caused by the Cr-enrichment
of the precipitates by diffusion; their Cr content (XCEM, Para) increases
up to the equilibrium value of around 0.69 (mol. fr.).
In the ortho-equilibrium case, the cementite nucleates with its
equilibrium Cr content, and there is little or no change in the
Cr content of the precipitates during the heat-treatment. It is
this requirement for full equilibrium which accounts for the long
incubation time for cementite when the ortho-equilibrium model
is used; the formation of a critical nucleus with ortho-equilibrium
composition requires the (slower) diffusion of Cr.

In the plot of X$BCC_A2$C (the carbon content of the BCC matrix),
it can be seen that the depletion of the matrix in carbon exactly
follows the increase in precipitate fraction for both models.

The plot of the number of cementite precipitates shows that in
the ortho-equilibrium case, nucleation occurs at a later stage
and the precipitates are less numerous.

Coarsening of the precipitates is more rapid in the para-equilibrium
case, as can be seen from the plot below:

The use of the para-equilibrium nucleation model gives better
qualitative agreement with experimental observations of the rapid
precipitation of cementite at temperatures such as 600°C in
alloy steels. An example in the Applications section, in which
this issue is considered in more detail, will be available shortly.
2. Diffusivity in precipitates
Setup
It was seen above that, using the para-equilibrium model, cementite
precipitates formed with a Fe-rich composition and subsequently
enriched in Cr. The rate of enrichment depends on the ease with
which chromium can diffuse into existing precipitates.
Duplicate and lock all the series in the plots. Re-open 'Global > Phase
status'. In the 'Nucleation' tab,
set the cementite nucleation model to back to 'para-equilibrium'.
Open the 'Special' tab. In
the 'Diffusion in precipitate' section, 'consider
as ratio from matrix diffusivity' is selected by default,
and the value of the ratio set to 0.01. This means that the diffusivities
of all elements within the cementite precipitate are considered
to be one hundredth of their values within the matrix. Changing
this value will affect the rate of Cr-enrichment of the cementite.
To demonstrate this, change the value of the ratio to '0.25', click
on 'OK' and re-run
the simulation.

Interpretation of results
In this case, precipitation occurs at the same rate as in the
first para-equilibrium calculation, but the Cr-enrichment of the
precipitates is more rapid. Consequently, the increase in precipitate
phase fraction and the decrease in matrix carbon content occur
earlier. It is also notable that coarsening is delayed and the
distribution of more numerous, relatively fine particles is stabilised
to longer times, as shown by the two plots below.


3. Microstructural parameters and nucleation sites
Setup
At this stage, it may be helpful to remove all the series except
the original para-equilibrium calculation results from the plots
to avoid them becoming cluttered. (If required, the numerical data
from the series can first be exported in text form using 'Copy
data' from the right-click menu and then pasting these data into
a spreadsheet or text editor. Alternatively, the plots can be exported
in graphical form using 'Copy pixmap'.) To remove a series from
a plot, first click on that plot and then select the name of the
series in the 'Options' window. (Failure to do this can result
in series from other plots being deleted instead.) Multiple series
can be selected using the Ctrl button. Remove them using the Delete
button or 'Remove series' from the right-click menu.
Reset the 'consider as ratio from matrix
diffusivity' value back
to its default value of '0.01' in the 'Special' tab, keep the nucleus
composition model set at 'para-equilibrium' and click 'OK' to save
the changes.
Open 'Global > precipitation domains' and
click on the 'Structure' tab.
The default values for each of the structural parameters are shown
in the image below.

The nucleation sites for CEMENTITE_P0 have been set to 'Dislocations' (see
Part 1 of this tutorial) so the dislocation density will determine
the number of nucleation sites. The default dislocation density,
which has been used so far, is 1e12, which is typical of an annealed
structure. Change this value to '1e14' and re-run the simulation.
The following images show the phase fraction, the number of precipitates
(note the log scale) and the mean radius for dislocation densities
of 1e12, 1e14 and 1e16. It can be seen that increasing the nucleation
site density accelerates the reaction kinetics and results in a
larger number of precipitates with a smaller mean radius.



To finish...
Save the workspace file.
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