MatCalc version: 5.50.0022
Database: mc_sample_al2.tdb, mc_sample_al.ddb
Author: Georg Stechauner
Created: 2012-03-15
Revisions:

The final part of example P2 simulates a heat flow diagram and compares it to values measured during a DSC experiment. In order to accurately describe the measured behavior, some parameters have to be changed from their default values. Values for pure Al will be used as a reference.

• Part 1: Isothermal treatment of Al-Cu
• Part 2: Evolution of excess vacancies
• Part 3: Simulation of a DSC curve

Click here to view the script for this example.

Set the thermodynamics up according to part one.

The parameter set used in this example reproduces the DSC experiment considerably well. Feel free to use these values for your own simulations!

Open the precipitation domain window and create a new precipitation domain called 'almatrix'. Attach it to fcc_a1 phase. Enter the following value for shown settings:

Be aware that the change performed at vacancies is of utmost importance. The FSK model is necessary for a more realistic consideration of vacancy dynamics.

Follow by setting up the precipitates. Bring up the phase status dialog window and select the three Theta phases. Click 'Create new phase' and select 'precipitate'. This produces one precipitate phase for each of the selected phases. Enter the following parameters:

To be able to plot the relative heat flow, a reference sample has to be created. Select therefore the FCC_A1 and create an equilibrium phase. Select the newly created FCC_A1#01 and create a precipitate.

Note: It is necessary to create the precipitate from an equilibrium phase, and not the matrix phase. The parent phase receives a flag at 'fixed phase fraction' which results in no further changes. Choosing the matrix as the parent phase would totally mess up the calculation!

Enter following parameters for the FCC_A1#01_p0 phase:

Note: As it can sometimes cause problems to set chemical compositions to 100% respectively 0%, a site fraction very close to 1 is selected to simulate pure Al.

There is no built-in variable to plot the heat flow in the system with respect to pure Al. To do this, we need to create a function first. Therefore open the Functions & Variables window, and switch to the functions tab. Create a new function, name it, and enter the following expression:

((HM$k-HMp$fcc_a1#01_p0$k)*1/3)/1000*10/60

where HM$k is specific enthalpy of the system and HMp$fcc_a1#01_p0$k is the specific enthalpy of the reference phase of pure Al. The factor 1/3 is a calibration factor to correctly account for the measured values, the factor 1000 changes the unit from kg to g, and 10/60 represents the heating rate.

Note: The variable HM and HMp respectively are normally the 'molar enthalpy'. By adding the $k modifier, the variable is converted from 'per mole' to 'per kilogram'. Hence HM$k and HMp$*$k, respectively, are specific enthalpies.

In the step above the specific enthalpy, with the unit $\frac{J}{g}$, was added as function. As we want to plot the heat flow, the derivation of the specific enthalpy is needed. Begin with plotting the created variable 'enthalpy' to a P1 plot. Further plot the phase fractions of precipitates f_prec$* for later discussion. Have a look at the presented results and rename the axes accordingly.

To derive the function, use the MatCalc options panel, switch to series, and select '1' at derivation.

The derivated curve now shows the heat flow, $\frac{W}{g}$. Note: This curve is highly sensitive for spikes and drops. These will occur whenever the slope changes, both numerically and phenomenologically.

To plot the experimental results, either copy the data from the script provided above and import it to MatCalc, or modify the script to the effect of only plotting the data.