New Experimental Evidence Shows Why Crystalline Materials Shrink on Heating

At the U.S. Department of Energy’s Brookhaven National Laboratory, researchers have come up with the latest experimental proof as well as a predictive theory that explains an age-old materials science mystery—that is, why specific crystalline materials shrink upon heating.

Recently reported in Science Advances, the researchers’ study can have major implications for matching the properties of materials to certain applications in electronics, medicine, and other domains. The study may also offer a better understanding of unusual superconductors—materials that are known to carry electric current without any energy loss.

Accurate measurements of the distances between atoms in scandium fluoride (ScF₃) crystals provided the evidence. ScF₃ is a material that is known to contract unusually under high temperatures (also referred to as “negative thermal expansion”). The researchers identified a new kind of vibrational motion that renders the sides of the cube-shaped, apparently solid crystals of the ScF₃ to buckle on heating, thereby pulling the corners of the crystals closer together.

Normally as something heats up, it expands. When you heat something up, atomic vibrations increase in magnitude, and the overall material size increases to accommodate the larger vibrations.

Igor Zaliznyak, Project Lead and Physicist, Brookhaven National Laboratory

However, that association does not work for specific flexible materials, including chainlike polymers such as rubber and plastics. When those materials are subjected to increased heat, vibrations increase perpendicular to the chains’ length (one can imagine the sideways vibrations of a plucked string of a guitar). These are transverse vibrations that pull the chains’ ends closer together, leading to overall shrinkage.

However, what about ScF₃? With a solid and cubic crystalline structure, it does not appear like a polymer at all—at least at the initial glance. There is also a widespread assumption that the atoms present in a solid crystal need to preserve their relative orientations, regardless of the size of the crystal. This assumption made it difficult for physicists to elucidate how this material shrinks upon heating.

Neutrons and a Dedicated Student to the Rescue

At the California Institute of Technology (Caltech), a research team used a technique to analyze this mystery at the Spallation Neutron Source (SNS)—a DOE Office of Science user facility located at Oak Ridge National Laboratory.

Valuable data about the atomic-scale arrangement of crystals can be obtained by measuring how neutron beams scatter off the atoms in a crystal. Neutrons can be described as a type of subatomic particle. Such measurements are specifically useful for lightweight materials (for example, fluorine), which are not visible to X-rays, added Zaliznyak.

When Zaliznyak learned about this work, he believed that Emil Bozin, his coworker and an expert in a different neutron-scattering analysis method, could perhaps provide a better understanding of the issue.

Bozin’s technique, called “pair distribution function,” elucidates the prospect of identifying a pair of atoms divided by a specific distance in a material. Computational algorithms subsequently sort through the probabilities to locate the structural model that optimally fits the data.

Bozin and Zaliznyak teamed up with the Caltech research team to gather data at the SNS. They achieved this by utilizing Caltech’s ScF₃ samples to monitor how the distances between adjacent atoms altered with increasing temperatures.

Most of the data analysis was handled by David Wendt, a student who started a Brookhaven Lab High School Research Program internship in Zaliznyak’s laboratory after his sophomore year in high school. Wendt is currently a freshman at Stanford University.

Throughout his high-school days, Wendt continued working on the project and earned the position of the paper’s first author.

David basically reduced the data to the form that we could analyze using our algorithms, fitted the data, composed a model to model the positions of the fluorine atoms, and did the statistical analysis to compare our experimental results to the model. The amount of work he did is like what a good postdoc would do!

Igor Zaliznyak, Project Lead and Physicist, Brookhaven National Laboratory

“I am very grateful for the opportunity Brookhaven Lab provided me to contribute to original research through their High School Research Program,” stated Wendt.

Results: “Soft” Motion in a Solid

The measurements demonstrated that heating did not really alter the bonds between fluorine and scandium. “In fact, they expand slightly,” Zaliznyak stated, “which is consistent with why most solids expand.”

However, the distances between neighboring fluorine atoms turned out to be extremely variable with rising temperatures.

“We were looking for evidence that the fluorine atoms were staying in a fixed configuration, as had always been assumed, and we found quite the opposite!” added Zaliznyak.

The explanation for this unanticipated data was crucially provided by Alexei Tkachenko, an expert in the theory of soft condensed matter at Brookhaven Lab’s Center for Functional Nanomaterials (another Office of Science user facility).

Since the atoms in fluorine do not seem to be restricted to rigid positions, the explanation can possibly draw on a relatively older theory. This theory was initially devised by Albert Einstein to elucidate the movement of atoms by factoring each individual atom separately. Remarkably, the ultimate explanation demonstrated that heat-induced shrinkage in the ScF₃ material bears a striking resemblance to the behavior of soft-matter polymers.

“Since every scandium atom has a rigid bond with fluorine, the ‘chains’ of scandium-fluoride that form the sides of the crystalline cubes (with scandium at the corners) act similar to the rigid parts of a polymer,” explained Zaliznyak.

However, the fluorine atoms located at the middle of each side of the cube are not restricted by any other bonds. Hence, when there is a rise in temperature, the “underconstrained” fluorine atoms freely oscillate independently in perpendicular directions to the rigid Sc-F bonds. Transverse thermal oscillations like those pull the Sc atoms located at the corners of the cubic lattice closer together, leading to shrinkage that is similar to that seen in polymers.

Thermal Matching for Applications

This novel insight will improve researchers’ potential to strategically design or predict the thermal response of a material for applications where temperature variations are anticipated. For instance, in precision machining, the materials used should not exhibit major changes in response to cooling and heating to maintain the same accuracy throughout all conditions.

Materials employed in medical applications, like bone replacements or dental fillings, should have thermal expansion characteristics that are almost similar to those of the biological structures in which they are incorporated (one can envision how painful it would be when the filling expands while the tooth contracted when drinking hot coffee).

In undersea fiberoptic transmission lines and semiconductors, the thermal expansion of insulating materials should correspond with that of the functional materials so that signal transmission can be impeded.

Zaliznyak also observed that an underconstrained open framework design like that in ScF₃ material is present in iron and copper-oxide-based superconductors—where the vibrations of the crystal lattice are believed to a play a role in the ability of these materials to carry electric current without any resistance.

“The independent oscillation of atoms in these open-framework structures may contribute to these materials’ properties in ways we can now calculate and understand,” Zaliznyak said. “They might actually explain some of our own experimental observations that still remain a mystery in these superconductors,” he added.

This work profoundly benefitted from the important advantages of the DOE national laboratories—including unique DOE facilities and our ability to have long-time-span projects where important contributions accumulate over time to culminate in a discovery.

Igor Zaliznyak, Project Lead and Physicist, Brookhaven National Laboratory

Zaliznyak continued, “It represents the unique confluence of different expertise among the coauthors, including a dedicated high-school student intern, which we were able to integrate synergistically for this project. It would not have been possible to successfully carry out this research without the expertise provided by all the team members.”

The DOE Office of Science funded Brookhaven Lab’s role in this study.