Heat causes the atoms in scandium trifluoride to vibrate, as captured in this snapshot from a simulation. Fluorine atoms are in green while scandium atoms are in yellow. Image: Caltech/C. Li et al. |
They shrink when you heat them. Most materials expand
when heated, but a few contract. Now engineers at the California Institute of
Technology (Caltech) have figured out how one of these curious materials, scandium
trifluoride, does the trick—a finding, they say, that will lead to a deeper
understanding of all kinds of materials.
The researchers, led by graduate student Chen Li,
published their results in Physical
Review Letters (PRL).
Materials that don’t expand under heat aren’t just an
oddity. They’re useful in a variety of applications—in mechanical machines such
as clocks, for example, that have to be extremely precise. Materials that
contract could counteract the expansion of more conventional ones, helping
devices remain stable even when the heat is on.
“When you heat a solid, most of the heat goes into
the vibrations of the atoms,” explains Brent Fultz, professor of materials
science and applied physics and a coauthor of the paper. In normal materials,
this vibration causes atoms to move apart and the material to expand. A few of
the known shrinking materials, however, have unique crystal structures that
cause them to contract when heated, a property called negative thermal
expansion. But because these crystal structures are complicated, scientists
have not been able to clearly see how heat—in the form of atomic vibrations—could
lead to contraction.
But in 2010 researchers discovered negative thermal
expansion in scandium trifluoride, a powdery substance with a relatively simple
crystal structure. To figure out how its atoms vibrated under heat, Li, Fultz,
and their colleagues used a computer to simulate each atom’s quantum behavior.
The team also probed the material’s properties by blasting it with neutrons at
the Spallation Neutron Source at Oak Ridge National Laboratory (ORNL) in Tennessee; by measuring
the angles and speeds with which the neutrons scattered off the atoms in the
crystal lattice, the team could study the atoms’ vibrations. The more the
material is heated the more it contracts, so by doing this scattering
experiment at increasing temperatures, the team learned how the vibrations
changed as the material shrank.
The results paint a clear picture of how the material
shrinks, the researchers say. You can imagine the bound scandium and fluorine
atoms as balls attached to one another with springs. The lighter fluorine atom
is linked to two heavier scandium atoms on opposite sides. As the temperature
is cranked up, all the atoms jiggle in many directions. But because of the
linear arrangement of the fluorine and two scandiums, the fluorine vibrates
more in directions perpendicular to the springs. With every shake, the fluorine
pulls the scandium atoms toward each other. Since this happens throughout the
material, the entire structure shrinks.
The surprise, the researchers say, was that in the large
fluorine vibrations, the energy in the springs is proportional to the atom’s
displacement—how far the atom moves while shaking—raised to the fourth power, a
behavior known as a quartic oscillation. Most materials are dominated by quadratic (or harmonic) oscillations—characteristic
of the typical back-and-forth motion of springs and pendulums—in which the
stored energy is proportional to the square of the displacement.
“A nearly pure quantum
quartic oscillator has never been seen in atom vibrations in crystals,”
Fultz says. Many materials have a little bit of quartic behavior, he explains,
but their quartic tendencies are pretty small. In the case of scandium
trifluoride, however, the team observed the quartic behavior very clearly.
“A pure quartic oscillator is a lot of fun,” he says. “Now that
we’ve found a case that’s very pure, I think we know where to look for it in
many other materials.” Understanding quartic oscillator behavior will help
engineers design materials with unusual thermal properties. “In my
opinion,” Fultz says, “that will be the biggest long-term impact of
this work.”
