P_12: Comparing Growth Rate Models for an Al-Zr System

This example compares the Simplified, General, and Advanced growth rate models for an Al-Zr system. The resulting plot compares the mean radius of the spheres for each AL3ZR_D023 precipitate phase calculated for each type of growth rate model.

All models treat a spherical particle (precipitate) of stoichiometric composition or with negligible atomic diffusivity. Local equilibrium at the precipitate-matrix interface is assumed.

When you use the Advanced model, the velocity of a moving phase interface and the operating tie-line are solved together from flux-balance equations. This model can treat both high supersaturation and cross diffusion rigorously. It can also capture the transition between NPLE (non-partitioning local equilibrium) and PLE (partitioning local equilibrium) without any ad hoc treatment.

The Simplified model is based on the quasi-steady state diffusion approximation, and estimates solute partitioning with matrix composition and nuclei composition instead of time-consuming stepwise tie-line calculations. It also neglects cross diffusion for simplicity.

The General model can be considered the same theoretical approximation as, but an improvement over, the Simplified model, with cross-diffusion terms taken into account, as well as adjustment of Gibbs-Thomson effect and effective diffusivity implemented. A dataset based on Knipling et al. [2008Kni] data is compared with the calculated results.

For more background information, see the theory described in Growth.

Example Settings

System (System Definer)
Database package	Demo: Aluminum-based Alloys (ALDEMO, MALDEMO)
Elements	Al, Zr
Conditions (Precipitation Calculator)
Composition	Al-0.2Zr Mole percent
Matrix phase	FCC_A1 All other defaults are kept.
Precipitate phase	AL3ZR_D023 Click Show Details to select the Growth rate model (Simplified, Advanced and General). All other defaults are kept.
Calculation Type (Precipitation Calculator)
Calculation type	Isothermal
Temperature	425 Celsius
Simulation time	400 hours
Datasets (Experimental File Reader)
2008 Knipling	Data set included with this example and imported to one Experimental File Reader.

Visualizations

Many of our Graphical Mode examples have video tutorials, which you can access in a variety of ways. When in Thermo‑Calc, from the menu select Help → Video Tutorials, or from the main My Project window, click Video Tutorials. Alternately, you can go to the website or our YouTube channel.

Open the example project file to review the node setup on the Project window and the associated settings on the Configuration window for each node. For some types of projects, you can also adjust settings on the Plot Renderer Configuration window to preview results before performing the simulation. Click Perform Tree to generate plots and tables to see the results on the Visualizations window.

When you run (Perform) this example, it takes a few minutes for the calculations to complete.

There is a variety of information shown in the Visualizations window that can be viewed during configuration and after performing the calculation.

• Thermal Profile: When setting up a calculator on a Configuration window for Isothermal or Non-isothermal Calculation Types, you can preview the profile and adjust settings as needed. When you click a calculator node in the Project window, the matching name of the node is on the tab(s) displayed in the Visualizations window.

  For TTT Diagram and CCT Diagram calculations there is nothing shown for the Precipitation Calculator tab in the Visualizations window as there is no Thermal Profile to be defined.

• Plot or Table results: After completing the set up and performing the calculation, to view the matching name of the node on tab(s) in the Visualizations window, either click a Plot Renderer or Table Renderer node in the Project window or click the tabs individually in the Visualizations window.

For this Isothermal example, its Thermal Profile is also displayed in the Visualizations window showing the constant temperature entered for this calculation type. The tab names match the node names in the Project window.

Reference

[2008Kni] K. E. Knipling, D. C. Dunand, D. N. Seidman, Precipitation evolution in Al–Zr and Al–Zr–Ti alloys during isothermal aging at 375–425 °C. Acta Mater. 56, 114–127 (2008).