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Why Do Some Alloys Not Expand When Heated?

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A new study by researchers at the California Institute of Technology (Caltech) has uncovered the reason why some metal alloys don’t expand when they get hot. At higher temperatures, the intrinsic magnetic properties of the so-called Invar alloys can cause just enough contraction to cancel out any expected thermal expansion. The research findings are published in the journal Nature Physics.

Investigating Invar

Thermal expansion occurs when a material absorbs heat, causing its atoms to vibrate more strongly and push away from their neighbors. As a result, the material becomes less dense and will increase slightly in size.

These atomic-scale movements may not sound like much, but they add up – the Eiffel Tower can expand by up to 15 centimeters during Paris’ hotter days.

While this makes for a fun factoid about a tourist attraction, thermal expansion can mean disaster when metal is required for high-precision applications. Nobody wants a finely calibrated telescope or wristwatch to swell up and stop working.

"It's almost unheard of to find metals that don't expand," says Stefan Lohaus, a graduate student in materials science and lead author of the new paper. "But in 1895, a physicist discovered by accident that if you combine iron and nickel, each of which has positive thermal expansion, in a certain proportion, you get this material with very unusual behavior."

This nickel–iron alloy is known as Invar, a name that derives from the word invariable, referring to its resistance to change.

Historically, researchers have suspected that this unusual resistance to thermal expansion could have something to do with the metal’s magnetic properties, as only alloys that are ferromagnetic (capable of being magnetized) have been observed to act as Invars.

"We decided to look at that because we have this very neat experimental setup that can measure both magnetism and atomic vibrations," Lohaus says. "It was a perfect system for this."

Magnetism appears to counteract thermal expansion

Using a synchrotron at the Advanced Photon Source at Argonne National Laboratory, the researchers took measurements of the vibrational spectra and magnetism of small samples of Invar.

The Invar pieces were held at pressure in a diamond anvil cell – a setup where two precisely ground diamond tips sandwich and tightly squeeze the sample. Here the Invar alloy was compressed at a pressure of 200,000 atmospheres before beams of powerful X-rays were blasted at the alloy, where they interact with the vibrations of the sample’s atoms. By measuring changes in the amount of energy carried by the X-rays, scientists can infer how much the atoms in the sample are vibrating.

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The researchers also placed sensors around the diamond anvil cells that are capable of detecting interference patterns created by the spin state of electrons in the sample. This is crucial, as a ferromagnetic material’s magnetic properties are caused by the spin state of its electrons – which can be thought of as a sort of quantum measure for angular momentum, with spins normally being spoken of being “up” or “down”. In a ferromagnetic metal, these spins will align in parallel with each other to form magnetic “domains” with the same spin direction.

With this setup, the researchers examined the spin state of electrons in an Invar sample, as well as its atomic vibrations, while they increased the sample’s temperature.

At cool temperatures, more of the Invar’s electrons shared the same spin state, causing the electrons to move farther apart. This pushes their parent atoms farther apart, hence allowing for thermal expansion.

But as the temperatures rose, the spin state of electrons increasingly flipped. At the same time, the thermal energy was causing the atoms to vibrate more and take up more room. These two opposing forces – contraction due to changing spin states and atomic vibration expansion – effectively canceled each other out within the Invar alloy, resulting in no net size increase when heat was applied.

"This is exciting because this has been a problem in science for over a hundred years or so," Lohaus says. "There are literally thousands of publications trying to show how magnetism causes contraction, but there was no holistic explanation of the Invar effect."


Reference: Lohaus SH, Heine M, Guzman P, et al. A thermodynamic explanation of the Invar effect. Nat Phys. 2023. doi: 10.1038/s41567-023-02142-z


This article is a rework of a press release issued by the California Institute of Technology. Material has been edited for length and content.