Most materials exhibit some degree of thermal expansion – that is, they expand when heated and shrink when cooled. Concrete structures are designed with joints that allow for this expansion and contraction, to prevent cracking and structural failure.

Some materials, however, exhibit what’s known as negative thermal expansion (NTE), where expansion occurs as the material cools. The most recognizable example is water; anyone who’s had a pipe burst in winter has seen it firsthand.

Knowing which are NTE materials and which are not is important in applications ranging from microelectronics to space travel, where materials with different thermal-expansion values might be layered and subjected to temperature extremes. But determining if a material exhibits NTE – and, more importantly, why – isn’t easy.

There are long-held rules of thumb regarding NTE, but recent work from the lab of Nicole Benedek, Cornell assistant professor of materials science and engineering, has shown that these rules don’t apply for all materials. That made searching for NTE materials a wild goose chase of sorts.

“You want to have some systematic set of rules or clues, like a map, and that’s what we work on – making maps,” Benedek said. “And the map for negative thermal expansion, we discovered, was not so accurate. We were able to use theory and computation to sort of formulate a new set of rules, to help us make a more accurate map.”

Benedek and doctoral student Ethan Ritz documented their findings in “Interplay Between Phonons and Anisotropic Elasticity Drives Negative Thermal Expansion in PbTiO3,” published Dec. 19 in Physical Review Letters.

Benedek and Ritz chose the perovskite lead titanate (PbTiO3), a well-understood NTE compound that undergoes a phase transition at approximately 908 degrees Fahrenheit. From there, it undergoes volumetric NTE all the way down to room temperature.

Benedek and Ritz used theory and computer simulations to analyze NTE in lead titanate, and found the assumptions many scientists commonly use to find new negative thermal expansion materials are not fully justified for many types of materials. In fact, they say, two factors previously held as necessary for NTE are neither necessary nor sufficient.

Their work highlights the important role played by two material properties that are usually ignored: the behavior of the electrons and the material’s elastic properties (the ability to stretch or compress a material along different axes).

“Our results not only shed light on the fundamental causes of negative thermal expansion,” Benedek said, “they could also be used to formulate new design principles for negative thermal expansion materials.”

These principles, Benedek and Ritz wrote, should help steer scientists toward promising materials, or inform the design of new materials that may not exist in nature.

This research was supported by a NASA Space Technology Research Fellowship grant and by the National Science Foundation. High-performance computational resources were provided by the Cornell Center for Advanced Computing, and the NSF’s Extreme Science and Engineering Discovery Environment (XSEDE) program.