A team of researchers led by the California Institute of Technology has figured out the secret to one of the most mysterious properties of a certain class of metals. The team used the resources of the Advanced Photon Source (APS), a U.S. Department of Energy (DOE) Office of Science user facility at DOE’s Argonne National Laboratory, in solving this decades-long puzzle.

Nearly every material you can imagine, whether it is solid, liquid or gas, shares the property of expanding when its temperature goes up and contracting when its temperature goes down. This property, called thermal expansion, makes a hot air balloon float and has been harnessed to create thermostats that automatically turn a home furnace on and off. Railroads, bridges and buildings are designed with this property in mind so they have room to expand without buckling or breaking on a hot day.

There are a few exceptions, but by and large, materials conform strictly to this principle. There is, however, a class of metal alloys called invars (think invariable), that stubbornly refuse to change in size and density over a large range of temperatures. That anomalous behavior makes them useful in applications where extreme precision is required, such as in the manufacture of parts for clocks, telescopes and other fine instruments. Until now though, no one knew why invars behave this way.

“This study benefitted from a plethora of X-ray techniques established at the APS that allow researchers to measure multiple properties of a sample in a complex environment, such as the small invar sample in a diamond anvil cell.”  — Guoyin Shen, Argonne physicist

“It’s almost unheard of to find metals that don’t expand, but in 1895, physicist Charles Guillaume 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,” says Stefan Lohaus, a graduate student in materials science at Caltech and lead author of the new paper published in Nature Physics. Guillaume won the 1920 Nobel prize in physics for this discovery.

Argonne regularly makes use of invars, according to Argonne mechanical engineer Steven Kearney, and is incorporating them into the ongoing comprehensive upgrade to the APS. Because of their inherent stability, invars make for excellent reference guides when focusing the optic systems of beamlines, Kearney said. Four of the beamlines built as part of the upgrade will use invars to make sure their optics are incredibly precise and stable.

Lohaus says that it had been long suspected that these materials’ lack of expansion was somehow related to magnetism, because only certain alloys that are ferromagnetic (capable of being magnetized) behave 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.”

The research team found a way to use the relationship between entropy, thermal expansion and pressure to measure independently the expansion caused by magnetism and atom vibrations. They measured the vibrations and magnetism of small samples of invar under extreme pressures at two different experiment stations, called beamlines, at the APS: 3-ID, where the team performed nuclear resonant inelastic X-ray scattering, and the High-Pressure Collaborative Access Team (HP-CAT) beamline at 16-ID, where synchrotron X-ray diffraction was done.

The experimental setup consisted of what’s known as a diamond anvil cell, which is basically just two precisely ground diamond tips between which samples of materials can be tightly squeezed, in this case, at a pressure of 200,000 atmospheres. The APS allows researchers to pass a powerful beam of X-rays through one such sample, which in this case was a small piece of invar alloy. As those X-ray beams passed through the invar, they interacted with the structure and the vibrations of its atoms.

The interaction with the vibration changed the amount of energy carried by the X-ray beams, allowing the researchers to measure how much the atoms were vibrating. Around the diamond anvil cell, they also placed sensors that can detect interference patterns created by the so-called spin state of the electrons belonging to the sample’s atoms.

Likewise, the interaction with the structure changed the scattering pattern of the X-ray beams, allowing researchers to measure the size of the atomic structure at different temperatures for any detectable thermal expansion.

“This study benefitted from a plethora of X-ray techniques established at the APS that allow researchers to measure multiple properties of a sample in a complex environment, such as the small invar sample in a diamond anvil cell,” said Argonne physicist Guoyin Shen, an author on the paper.

The team used their experimental setup, a unique one in the United States, to observe the atomic vibrations of an invar sample, the spin state of its electrons, and the size of the atomic structure as they increased the sample’s temperature. At cooler temperatures, more of the invar’s electrons shared the same spin state, causing them to push farther apart, and push their atoms farther apart in the process.

As the temperature of the invar rose, the spin state of some of those electrons increasingly flipped. As a result, the electrons became more comfortable cozying up to their neighboring electrons. Typically, this would cause the invar to contract as it warmed up, except for the fact that the invar’s atoms were also vibrating more and taking up more room. The contraction due to changing spin states and the atomic vibration expansion counteracted each other, and the invar stayed the same size.

Such coupling between vibrations and magnetism could be useful for understanding thermal expansion in other magnetic materials, or useful for developing materials for magnetic refrigeration.

“This is exciting because this has been a problem in science for the past 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.”

The paper describing the research, ​“Thermodynamic explanation of the Invar effect by experiment and computation,” appears in Nature Physics. A version of this release was originally published by Caltech.