University of Nebraska-Lincoln physicist Christian Binek found that the magnetic properties of a material could predict the relationship between the material's elasticity and temperature under certain conditions.

Christian Binek has found that the elasticity of a material can be predicted from its magnetic properties and that magnetism, in turn, might be tailored or applied to control elasticity (Source: Craig Chandler|University Communication|University of Nebraska-Lincoln)

This finding could point toward controlling a material's elasticity by designing its magnetic properties or applying a magnetic field. Magnetic fields are easily manipulated, which means that tailoring elasticity with the press of a button or the turn of a knob may be a reality in the near future.

In the meantime, the discovery that magnetism alone can predict elasticity’s response — or lack of response — to changes in temperature may help engineers better select or design materials for specific purposes.

Binek cited the disintegration of the Challenger space shuttle in 1986 as an example of elasticity’s importance in engineering. The hardening and ultimate failure of the elastic O-ring on the Challenger’s rocket booster, which is a consequence of cold temperatures, is what ultimately caused the failure of the shuttle.

"So you can find materials that do not change elastic properties with temperature," said Binek, professor of physics and astronomy at Nebraska-Lincoln. "You may find materials that change with temperature at will. And you may find materials where you can, at a given temperature, change the elastic properties by an external control."

The laws of thermodynamics describe relationships and the many factors — temperature, entropy, volume and pressure — that affect how heat is converted into other forms of energy. It has long been known that these laws encompass the properties of magnetism and elasticity.

Binek derived a new formula from the existing ones. He managed to show that the elasticity-temperature relationship is encoded in the magnetism of a material.

But Binek’s new formula has limitations. It only applies to a material’s magnetic behavior changes linearly with the magnetic field that is being applied to it. Also, the material’s elasticity has to be linear. This means that the amount of strain it exhibits has to always be proportional to the amount of physical stress that is being extorted on it.

Despite this, the formula applies to materials with many forms of magnetism. This includes diamagnetism, which is technically found in every material. Diamagnetism describes a tendency to repel magnetic fields so weakly that it goes unnoticed unless the researcher has specialized instruments.

Superconductive materials have no resistance to electricity and therefore display a pronounced form of diamagnetism below a critical temperature. At this point, they are completely repelling magnetic fields. Binek found something interesting below the temperature threshold: the superconductor's elasticity no longer responded to temperature changes. This was discovered when Binek performed calculations for ceramic and single-crystal superconductors, both of which have different microscopic surfaces and atomic structures.

"My (mathematical) expression makes no claims about the material," Binek said. "It's very general. It only says: If the susceptibility (to magnetism) is constant, then the elastic property should be constant. If that is so, nothing else (about the superconductor) should matter, which is honestly a little difficult to believe. You wonder: How can something like an elastic property, which surely depends on structural details, be independent of anything related to the structure? But then you go to the (scientific) literature, apply your formula, and you find that, yes, it is correct."

The elastic-magnetic formula applies to materials that have a weakened attraction when introduced to magnetic fields, also known as paramagnetism. Ferromagnetic materials — materials that are strongly attracted to magnetic fields and are usually called “magnetic”— obey Binek’s formula above a certain temperature that makes them behave like paramagnetic materials.

Binek believes that the formula might work for ferroelectric materials for which polarization can be reversed by an electric field. Ferroelectricity facilitates the storage of electrical energy and makes it useful in devices ranging from capacitors to random-access memory.

"Rather than tuning the elastic properties by a magnetic field, you may be able to tune them by electric fields," he said. "Technologically, that could be even more interesting. There are certainly many applications that one could think of, and I think many of them can be useful. I hope this is not the end of the story, but rather the beginning."

This research was conducted as part of the Nebraska Materials Research Science and Engineering Center, one of 21 MRSEC centers funded by the National Science Foundation.