# Using Cross Plots to Visualize the Tradeoff of Properties in Alloy Design

When designing alloys, there is often the need to trade off properties to find the optimal solution. This is most easily achieved when it is possible to visualize the properties on a common plot that shows the complex relationships between multiple variables such as alloy composition and temperature. These are commonly referred to as cross plots. The Grid calculation type in the Property Model Calculator in Thermo-Calc enables such plots to be generated easily for two properties as a function of two system design variables. One example using high strength steels is outlined below, but these concepts are also applicable to many other material systems and properties.

## Optimization of Precipitates in High Strength Steels

Some steels like AF1410 utilize a fine dispersion of M2C precipitates to achieve high strength and toughness. This is sometimes referred to as secondary hardening, as the hardness increases during a tempering treatment as the M2C precipitates form. To achieve the best properties, it is desirable to have both a high volume fraction and a fine dispersion of precipitates. This can be achieved by creating an alloy with a high driving force for that precipitate to form at the heat treatment temperature. However, if the precipitates coarsen too much, the strength will start to decrease (sometimes called overaging). In thick part sections it may be difficult to perform short heat treatments, so it is desirable that the coarsening rate of the precipitates is low, so that we can maintain a wide heat treatment process window.

To visually optimize these inherently competing properties, a cross plot can be created using the Property Model Calculator and a suitable database, in this case the Thermo-Calc Steel and Fe-Alloys Database, TCFE. Below is a cross plot for the driving force and coarsening rate of M2C vs V and Mo content for a fixed Fe-10Ni-14Co-0.15C (wt%) chemistry. In this case – increasing both V and Mo is beneficial as Mo has a strong effect on slowing down the coarsening rate, and both elements work to increase the driving force. To choose an optimum chemistry from this, we might set the Mo content to be 4 wt.%, since it has the strongest effect on lowering the coarsening rate. With Mo fixed at 4 wt%, adding some V will increase the driving force, but the effect is not very strong above about 0.5 wt%. So one possible optimum chemistry to maximize strength and processability would be Fe-10Ni-14Co-0.15C-4Mo-0.5V (wt%).

## Cross Plots in an ICME Framework

Cross plots are also a valuable tool in ICME frameworks. For the alloy listed above, further modifications could be made to reduce the amount of Co to decrease cost, and increase Cr to boost corrosion resistance. Changing these chemistries will have an effect on the driving force and coarsening rate as discussed above, and will also change the martensite start temperature. Since this is a quench and temper steel, we might want to take care not to depress the martensite start temperature Ms to avoid needing a cryo treatment. We could do this by changing the Ni content since it has a strong effect on Ms. To optimize on all these parameters simultaneously, it is useful to make a systems chart of the chemistry-process-structure-property relationships, which is an integral part of the materials design / ICME process. More on these relationships and how to construct a systems chart is discussed in another blog post:

## Setting up Cross Plots in Thermo-Calc

Setting up cross plot calculations in Thermo-Calc is easy to do with the Property Model Calculator. You can watch a video tutorial to see an example:

Whether you’re an experienced user or simply curious about Thermo-Calc, we’d be happy to show you over a web call how to set up a cross plot that could help you in your work. Schedule a free consultation today!

## About the Property Model Calculator in Thermo-Calc

The Property Model Calculator within Thermo-Calc offers predictive models for material properties based on their chemical composition and temperature and is included with all Thermo-Calc installations. This article is part of a series of blog posts that take a deeper dive into the different calculation types included in the Property Model Calculator and how they can be applied to materials design, process optimization, and ICME frameworks.