Example TP20: Simulation of DSC experiment involving a precipitation reaction, part 1: Simple cooling from above solution temperature

Compatibility

MatCalc version: 5.43.1016
Author: Peter Lang
Created: 2011-09-03
Revisions:

Objectives

This example was designed to explain on how to generate a DSC signal curve. There will be no interface energy corrections involved, as this example aims on showing the methods, and not fitting an experiment.

Part 1 will concentrate on a simple cooling from a solution-annealed condition. A typical DSC curve showing the heat flow as a function of temperature will be shown. Part 2 of this example will then continue with a full heat treatment, starting from the liquid. We will attempt to reproduce a DSC curve, which was measured in lab experiments.

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Complementary files

Click here to view the script for this tutorial.

Main document

Consider a Nickel-based alloy during cooling, from a solutionized state, with the chemical composition given in the following table (composition given in wt%).

Al Co Cr Ta Ti W
5.00 5.00 10.00 12.00 1.50 4.00

At first, the only stable phase is FCC_A1. During cooling, the Gamma_Prime phase will precipitate. In the first part, we will consider this given state and simply cool down. We will see the DSC curve, as well as three populations of precipitates, with different sizes.

Setup thermodynamics

For simulation, the 'mc_ni' database, version 1.011, is used, with the elements and phases selection as shown in the dialog below:

 Database dialog for TP20

Open the database, select elements and phases, and read the database. Then enter the composition of the system in the 'Composition …' dialog of the 'Global' menu according to the table shown above.

Next, read the diffusion database “mc_ni” (version 1.000 was used in this example).

Evaluate temperatures

As we want to cool down from a one phase field, we first need to establish the temperatures, where only FCC_A1 is present. To do so, we make use of the stepped equilibrium calculation. Use a large enough temperature range with small steps tough, to be sure to find the important one phase field (e.g. calculate from 1000 to 1600C with a step of 10C). There are now two ways to identify the one phase field:

  • Have a look into the buffer states and click through the temperatures. You will see how the phase details change according to the temperature. The temperature range between the solidification of liquid, and the precipitation of Gamma_Prime is the one phase field we were looking for.
  • The second way is to generate an easily interpreted graphic image of the phase fraction. Add a p1 plot to the workspace, and draf & drop the F$* variable into it.

 Phase fraction to identify the one phase field

Both methods are an easy way of finding the solutionizing temperature of 1280C.

The output file of the calculated equilibrium at 1280C is shown below:

#### /FCC_A1/ moles: 1, gm: -115980 (-115980), sff: 1
Phasestatus: entered - active
NI +6,46660e-001 CR +1,16786e-001 AL +1,12529e-001 CO +5,15195e-002
TA +4,02706e-002 TI +1,90238e-002 W +1,32116e-002

### inactive ###

#### /GAMMA_PRIME/ moles: 0, gm: -121774 (-121774), sff: 1
Phasestatus: entered - not active (dfm=-41,23)
NI +6,68807e-001 AL +1,54318e-001 CR +5,36536e-002 CO +4,27120e-002
TA +4,20863e-002 TI +2,71675e-002 W +1,12551e-002

#### /LIQUID/ moles: 0, gm: -119414 (-119414), sff: 1
Phasestatus: entered - not active (dfm=-68,57)
NI +6,10910e-001 AL +1,29780e-001 CR +1,09191e-001 CO +6,15037e-002
TA +5,30532e-002 TI +2,52059e-002 W +1,03565e-002

As we stay below the solidus line during this example, we suspend the liquid phase from now on. The plot will not be needed anymore and can be closed.

Setup functions

In this example, we make use of some functions, which describe the temperature dependence of Young's modulus and the volumetric misfit parameter.

Open up the 'Variables & Functions' dialog and enter the following functions:

  • Volumetric Misfit Parameter - misfit: ((-5.3e-13)*T$C^4+(6.43e-10)*T$C^3-(2.04e-7)*T$C^2-(9.29e-5)*T$C+0.632)/100
  • Young's modulus, Matrix - y_modul_matrix: (-0.112*T$C+231.3)*1e9
  • Young's modulus, Gamma_Prime - y_modul_gamP: (-0.052*T$C+189)*1e9

Setup precipitates

Open up the 'Precipitation domains …' dialog and create a new domain called 'ni-matrix '. Select FCC_A1 to be its matrix phase. Enter the following constants in the same dialog window to setup the microstructure:

  • Grain diameter [m]: 500e-4
  • Equilibrium dislocation density [m-2]: 1e11
  • Young's modulus matrix [Pa]: y_modul_matrix
  • Subst. gb diffusion as ratio from matrix: 10^(11-0,005*T$C)
  • Interst. gb diffusion as ratio from matrix: 10^(11-0,005*T$C)
  • Subst. disl. diffusion as ratio from matrix: 10^(7-0.0025*T$C)
  • Interst. disl. diffusion as ratio from matrix: 10^(7-0.0025*T$C)

Close this dialog window, and open the 'Phase status …' dialog. Create a Gamma_Prime precipitate with 40 size classes, attach it to the 'ni-matrix' domain and set the nucleation site to bulk; then set the following parameters:

  • Young's modulus gamma_prime [Pa]: y_modul_gamP
  • Volumetric misfit (dV/V): misfit (Make sure that the 'Account for coherent misfit stress' option is selected!)
  • Coherency radius [m]: 30e-9

 Schematic figure of DSC

Next we have to generate a reference phase for the DSC curve (see figure above). To do so, open up the 'Phase status …' dialog window, and create an equilibrium phase for the FCC_A1 phase. Set the newly created FCC_A1#01 to 'fixed phase fraction', as we want the FCC_A1 to be the prevailing one, and calculate an equilibrium in the one phase field. Note how the chemical composition of both phases becomes identical!

Important note …

If we would not set FCC_A1#01 to 'fixed phase fraction', it could happen, that this phase becomes the predominant one!

Set the phase status of FCC_A1#01 to dormant, as we do not want it to change anymore. All the phases should be set now, and we can soon start the calculation!

Setting up output plots and histogram

The next step of this example is to set up the plots, which will show us the phase fraction of Gamma_Prime_Precipitates, the DSC curve as well as the histogram showing the size of the precipitations.

Create a p1 plot, add a second plot. Change the default x-axis data to 'T$C' and rename it 'Temperature [°C]'. Make sure, you selected 'Yes' for using the x-axis on all plots. To plot the phase fraction of Gamma_Prime, we simply have to drag & drop the f_prec$gamma_prime_p0 to the first plot. Change title of plot and y-axis respectively.

The tricky part comes when plotting the DSC curve. As we cannot plot the heat flow with the given tools, we have to create a function on our own, to do so. Open the variables dialog once more, and add the following function to it:

  • (HM$k-HMp$fcc_a1#01$k)/1000*(-50/60)

This function can now be found in the variables window. Add it to the second plot by dragging & dropping it. Derive the newly added series once and change the title and y-axis to DSC and heat flow [W/g] respectively.

To add the histogram, we need to add a p5 plot. When asked, select the Gamma_Prime_Precipitation. Then change the axes to logarithmic, change the factor on the x-axis to '1e9' as it will display the radius in [nm], and scale it to '0.1..'. Y-axis will show the number density in [m-3], scale it to '10..'.

Move all windows to where you want them to be. Preferably in a way you can see the results.

Let's go

Everything is set up, so let's get the calculation started!

Open the 'Precipitation simulation …' dialog window and select continuous cooling. Enter the start and end temperature, as well as the desired cooling rate in the according dialog boxes. For the figure below, we used a starting temperature of 1280C, an end temperature of 25C, and a cooling rate of 50K/min (enter as -0.8333).Change the initial time step to 1e-10, as a lower value will result in a wrong, vertical line at the beginning. If your settings look like ours (check figure below), start the simulation.

Important note …

When using the continuous option from the 'Precipitation simulation …', keep in mind, that a positive value in the T_dot dialog box results in heating, whereas a negative value results in cooling!

 Precipitation simulation settings

Results

If all the prior steps were executed correctly, and the calculation finished without any errors, the below shown figures should be calculated.

 Resulting plots of DSC simulation

We can see three peaks in the DSC curve. If you have a look at the buffer states, and go to the temperature of the first peak (~1110C), you can see the precipitation of mainly large, 1000nm big preciptates. Upon lowering the temperature, and reaching the second peak (~900C), a second population of smaller, 100nm in size precipitates can be seen. For temperatures below the last peak, a huge amount of the small, 1 to 10 nm in size precipitates form. This exact behavior can be measured experimentally and seen with TEM.

We will continue in part 2, with simulating a full heat treatment, compared to only cooling in part 1. A comparison with real, experimental data will also be given.

Consecutive articles

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examples/tprops/tp20/tp20_1.txt · Last modified: 2019/06/27 18:37 by pwarczok
 
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