T9: Calculating
pseudobinary phase diagrams
This tutorial was created on
MatCalc version 5.23 rel 1.026
license: free
database: mc_sample_fe.tdb
A pseudobinary phase diagram is an equilibrium diagram calculated
for a ternary or higher-order system, in which the phase boundaries
resulting from the variation of two of the element contents are
calculated, while the amounts of all the other elements are kept
constant.
Contents:
- Further phase boundary calculations
- Coping with complex boundary shapes
- Diagrams with different reference elements
1. Setting up the system
Make a new workspace with the elements Fe, C and
Nb and the phases FCC_A1, BCC_A2, LIQUID and CEMENTITE. Verify
that Fe is selected as the reference element and enter the composition:
0.1 wt.% C, 0.3 wt.% Nb. Create a new p1-type plot window for the
phase diagram.
2. Fe-C pseudobinary with constant Nb content
This is similar in many respects to the Fe-Fe3C diagram calculated
in Tutorial 8, but the presence of niobium stabilises an additional
phase, FCC_A1#01 (which is essentially NbC). The stability of this
phase has a strong dependence on both carbon and niobium contents.
Only the low-carbon portion of the diagram, from 0 to 0.2 wt.%,
is of interest in this tutorial. Begin, as in Tutorial
8, by calculating
an equilibrium at 1550°C,
then search for the BCC_A2 phase boundary. Step from 0 to 0.2 wt.%
C, with an interval of 0.0005 and a maximum T-step of 20. Drag
and drop the T$C series into the plot and duplicate, lock and label
it.
Add the liquid and austenite (FCC_A1) upper boundaries and the
lower boundary of the delta-ferrite (BCC_A2) to the diagram. Suggested
equilibrium temperatures for finding these lines are as follows:
- LIQUID: 1450°C
- FCC_A1: 1500°C (N.B. the correct value of Tsol 'FCC_A1' should
be 1483.41°C.)
- BCC_A2: 1450°C
The high-temperature part of the diagram should
look like this:

Next, calculate the boundary for niobium carbide (FCC_A1#01).
The temperature of the boundary depends strongly on carbon content,
but an equilibrium at 1450°C gives a suitable starting point
for finding it.
Increase the maximum T-step to 100 to cope with the steepness
of the curve. The boundary may extend to very small temperature
values; in this case, change the scale on the y-axis to '500..' so that only the relevant information is shown.
The final three lines can be calculated as follows:
- Upper boundary of alpha-ferrite (BCC_A2): 900°C. The maximum
T-step can be reduced again to 20.
- Lower boundary of austenite (FCC_A1): 700°C.
- Upper boundary of cementite 800°C. In case of error message (because of the steep boundary), set the maximum T-step
to 100.
The finished diagram, with titles and labels added, should look
like this:

3. Fe-Nb pseudobinary with constant C content
In this case, the niobium content is to be varied from 0 to 1
wt.% for the stepped calculations. Proceed as before, by calculating
an equilibrium at 1550°C and searching for the BCC_A2 phase
boundary. For the stepped calculation, enter 0, 1 and 0.01 as the
start, stop and interval values and under 'Boundary
conditions',
change the varying element to 'NB'.
The boundaries can be calculated with the same starting equilibrium
temperatures as for the Fe-C diagram, because the basis composition
used for calculating the equilibrium and finding a point on the
boundary remains the same (0.1 wt.% C, 0.3 wt.% Nb). Search for
and plot all the following boundaries:
- Upper boundary of delta-ferrite (BCC_A2)
- Lower boundary of liquid
- Upper boundary of austenite (FCC_A1)
- Lower boundary of delta-ferrite
- Upper boundary of alpha-ferrite (BCC_A2)
- Lower boundary of austenite
- Upper boundary of cementite (may need modification of maximum
T-step)
The NbC (FCC_A1#01) boundary is slightly more complex
in this example, so it will be considered in more detail. Firstly,
calculate an equilibrium at 1000°C and search for
the FCC_A1#01 phase boundary. The solution temperature should be
1345.99°C. Make a stepped calculation from 0 to 1 wt.% Nb as usual. Part-way through this calculation, the following message is displayed:

The calculation starts at the niobium content used to calculate
the equilibrium (0.3 wt.%), and this is first increased up to the
'stop' value (1 wt.%, in this case) and then decreased to the 'start' value (0). The message above implies that the calculation cannot
proceed any further in the increasing-Nb direction. Click on 'Yes'
to calculate the decreasing-Nb part of the boundary. It can be seen that the NbC curve terminates at a niobium content
of around 0.62 wt.%. On zooming into the region around this point,
it can be seen that this point (marked A in the image below) is
associated with a change of slope of the 'bcc_high_2' boundary.
A similar slope change can be seen in the 'liquid' boundary, at
the point marked B. This strongly suggests that the 'NbC' boundary
continues between the points A and B.

Open 'Global > Composition' and change the Nb content to '0.6' wt.%, since this composition is at the centre of the complex region.
It is clear that the boundary has more than one temperature value
at this composition, so the choice of starting equilibrium temperature
is important to obtain the required line sections.
Start by calculating an equilibrium at 1480°C (i.e. above
the A-B region) and searching for the FCC_A1#01 phase boundary.
The temperature of the boundary should be 1466.77°C; this point
lies on the line from B to the edge of the diagram at 1 wt.% Nb. Perform a stepped calculation with the 'max. T-step' set to '1'. The finished diagram is shown below.

3. Nb-C pseudobinary with constant Fe content
The final part of this tutorial considers the effect of both C
and Nb contents on the stability of NbC. Previously, iron has been
set as the 'reference element'; this
means that when the amount of the varying species increases, the
amount of iron in the system decreases so that the total composition
sums to unity. For the Nb-C pseudobinary, niobium will instead
be set as the reference element, and a fixed iron content will
be imposed, so that the sum of niobium content and carbon content
is constant. In addition, the element contents will be expressed
in mole fractions, so that the effect of Nb:C ratio on carbide
stability can be investigated. Open 'Global > Composition' and
switch to 'mole
fraction'.
Change the reference element from Fe to Nb. Enter the compositions
0.995 Fe, 0.004 C.
As usual, search for the upper boundary of the
delta-ferrite phase. This should be found at 1529.63°C. In
the stepped calculation dialogue box, enter 0, 0.005 and 1e-5 as
the start, stop and interval values. Set the varying element to
'C' and the maximum T-step to 20. In the 'Options' section on the
right-hand side of the box, remove the selection mark by the side
of 'Composition in weight percent' so that it will instead be in
mole fraction.
Calculate the following lines. The solution temperatures are given
as a guide, as well as notes on calculation settings.
- BCC_A2: 1529.63°C
- LIQUID: 1486.84°C. A warning message may appear; accept this
with 'Yes'.
- FCC_A1: 1487.04°C. The same warning may appear.
- BCC_A2: 1447.56°C
- BCC_A2: 882.04°C. Step from 0 to 0.00498 rather than 0.005
to avoid convergence problems.
- FCC_A1: 726.62°C. Step from 0 to 0.00498.
- CEMENTITE: 726.62°C
Finally, the line for FCC_A1#01 can be calculated. Search for
this line, which should be found at 1255.79°C. The temperature of
this phase boundary decreases very steeply at both extremities
of the x-axis, because the phase becomes less and less stable as
either the niobium content or the carbon content tends to zero.
To obtain an idea of the shape of the curve, set the start and
stop-values as 0.0001 to 0.0049 (A maximum T-step of 20 is OK for this calculation.) Modifications can then be made to the calculation
parameters, decreasing the start value, increasing the stop-value
and increasing the maximum T-step to try to extend the curve further
towards the edges.
The finished diagram should look like this:

‹‹ to the Top ›› ‹‹ to
the Tutorial files ›› |