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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:

 

 

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