Example P2: Precipitation sequence in Al-Cu, Part 3: Simulation of a DSC curve

Compatibility

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

Objectives

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.

Complementary files

Click here to view the script for this example.

Main document

Setup thermodynamics

Set the thermodynamics up according to part one.

Precipitation domain and precipitates

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:

Tab Option Value
Structure Grain diameter 200e-6
Dislocation density 1e11
Strength Young's modulus 69.22e9-(4.01e7)*T
Poisson's ratio 0.33
Special Diffusion ratio grain boundary
and bulk (substitutional)
(10^(11-0.005*T$C))
Diffusion ratio grain boundary
and bulk (interstitional)
(10^(11-0.005*T$C))
Diffusion ratio dislocation
and bulk (substitutional)
(10^(7-0.0025*T$C))
Diffusion ratio dislocation
and bulk (interstitional)
(10^(7-0.0025*T$C))
Vacancies Consider excess vacancies ✔, Enter 1
Vacancy evolution model FSK vacancy dynamics

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:

Precipitate Tab Option Value
THETA_AL2CU_p0 Precipitate #size classes 25 (Initialize!)
Attached to pd almatrix
Nucl. sites Nucleation sites dislocations
Nucleation account for coherent misfit stress
Nucleation constant 0.01
Structure Volumetric misfit no flag, 0.12
Precipitate Tab Option Value
THETA_PRIME_P0 Precipitate #size classes 25 (Initialize!)
Attached to pd almatrix
Nucl. sites Nucleation sites dislocations
Nucleation account for coherent misfit stress
Structure Volumetric misfit no flag, 0.01
Precipitate Tab Option Value
TH_DP_GPB_P0 Precipitate #size classes 25 (Initialize!)
Attached to pd almatrix
Nucl. sites Nucleation sites bulk
Nucleation account for coherent misfit stress
Structure volumetric misfit no flag, 0.03
Special Excess vacancy trapping fraction 0.002

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:

Precipitate Tab Option Value
FCC_A1#01_p0 Precipitate #size classes 25 (Initialize!)
Attached to pd almatrix
Nucl. sites Nucleation sites bulk
Nucleation Nucleus composition Select: Fixed molar site fraction
Set: xy_Al(0) - 0.99999, xy_CU(0) - 0.00001

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.

Functions

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.

Setup the plots

In the step above the specific enthalpy, with the unit , 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.

 Options window for derivation of HM

The derivated curve now shows the heat flow, . 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.

Starting the calculation

FIXME

Results: General

FIXME

Consecutive articles

FIXME

examples/precipitation/p2/p2_3.txt · Last modified: 2012/11/20 14:06 (external edit)