Introductory Guide to Tailored Thermal Expansion

Introductory Guide to Tailored Thermal Expansion

Introduction to Tailored Thermal Expansion

Have you ever designed a product that required a specific thermal expansion? If you have, you know how challenging it can be. You might use multiple material types that have coefficient of thermal expansions (CTEs) that are close enough to not cause issues in your design. You hope this low thermal mismatch will prevent undesirable outcomes like exceeding a safety margin at the extremes of the operating temperature or poor performance in applications with tight tolerancing, but you cannot always be sure. Another solution involves creating a monolithic design—a design that uses a single material to prevent mismatches between components. If these solutions work for your design, great!

However, on some projects with strong performance requirements and tight specifications, thermal expansion mismatch can be a serious problem. The above solutions might not get you the result you need. They could lead to tight tolerancing, performance loss, or countless redesigns.

What if you could create your own thermal expansion values?

Harness Negative Thermal Expansion to Specify a Tailored Thermal Expansion

While ALLVAR Alloys are known as the only negative thermal expansion alloys in the world, they offer an even more powerful design tool—tailored thermal expansion. ALLVAR Alloys give designers the ability to specify or match a desired CTE in one direction, from -30 ppm/°C to the CTE of the chosen material. This wide range allows some clever engineering, like creating an ultra-low thermal expansion strut or creating an optical spacer that perfectly matches the thermal properties of the optical lenses in your design. This tailored or matched thermal expansion has many useful applications for designers and engineers.  

A Simple Tailored Thermal Expansion Example

The idea is simple. If you want to tailor the thermal expansion of length in a particular direction, you combined two materials with different thermal expansions in the right lengths to get an effective CTE that lies somewhere between the CTE of the two materials. This can become more complicated as more elements are added, but it is a relatively simple idea to create stability. There is a wide range of potential CTEs that can be tailored in a setup like this. The room temperature CTE values possible in this setup range from the positive CTE of the positive component to the -30 ppm/°C of ALLVAR Alloy 30. You tailor the thermal expansion by changing the respective lengths of each component. Two formulas are shown below that are useful for this two-metal structure. The first is the combined CTE of the total structure. The second is the ratio needed between the ALLVAR Alloy 30 and the Other Metal to achieve the selected CTE of the total structure. 

In this example, we want a 10cm long length of material that has a near zero CTE at room temperature. To keep it simple, we will assume that the bond is seamless with no effect on CTE. 

Term and Symbol Value
Target CTE of Length ( αTot)
0 ppm/°C
Desired Total Length (𝐿0𝑇𝑜𝑡)
10 cm
-30 ppm/°C
CTE of Aluminum 25°C ( αother)
23.2 ppm/°C
Formulas to use Negative Thermal Expansion ALLVAR Alloy with another metal to create a tailored thermal expansion.

Calculating the lengths for Zero CTE

Since we know the total length desired for this component, we will first calculate the ratio needed of ALLVAR to Aluminum. This is done using the following formula.

This formula is used to calculate the ratio needed between ALLVAR and another material to hit a tailored thermal expansion

After calculating, we find that the 43.6% of the length of the component should be negative CTE ALLVAR Alloy 30. If you multiply that value by 10cm, it shows that 4.36cm of ALLVAR Alloys will cancel out the positive expansion of 5.64cm of Aluminum to achieve a 0ppm/°C length.

These formulas help calculate the lengths needed for a tuned CTE length once a ratio has been established.

While this is a simple example, it shows that it is possible to tailor the CTE of a given length. What could you do with this type of CTE control?

In our next blog post, we will take this concept a step further—discussing a real-world example. We will discuss the effect of joints, machining tolerances, and how to calculate a CTE with more than one material. Can’t wait until then? Find out more about the zero CTE struts project in  our webinar.

Don’t forget to follow ALLVAR on our LinkedIn page, check out our YouTube page, and subscribe to our newsletter to stay up to date with our latest news and events! As a team of passionate material scientists and engineers, we would love to connect and answer any questions you may have about our revolutionary material.  

Contact Us Today to Revolutionize Your Thermal Performance

Have an application in mind? Please let us know if you have any questions.


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