Floppy vibration modes explain negative thermal expansion in solids

Animation showing how solid crystals of ScF3 shrink upon heating. While the bonds between scandium (green) and fluorine (blue) remain relatively rigid, the fluorine atoms along the sides of the cubic crystals oscillate independently, resulting in a wide range of distances between neighboring fluorine atoms. The higher the temperature, the greater the buckling in the sides of the crystals leading to the overall contraction (negative thermal expansion) effect. Credit: Brookhaven National Laboratory

Matching the thermal expansion values of materials in contact is essential when manufacturing precision tools, engines, and medical devices. For example, a dental filling would cause a toothache if it expanded a different amount than the surrounding tooth when drinking a hot beverage. Fillings are therefore comprised of a composite of materials with positive and negative thermal expansion, creating an overall expansion tailored to the tooth enamel.

The underlying mechanisms of why crystalline materials with negative thermal expansion (NTE) shrink when heated have been a matter of scientific debate. Now, a multi-institutional research team led by Igor Zaliznyak, a physicist at Brookhaven National Laboratory, believes it has the answer.

As recently reported in Science Advances, the scientists measured the distance between atoms in scandium trifluoride powder, a cubic NTE material—at temperatures ranging from 2 K to 1099 K—using total neutron diffraction. The research team determined the probability that two particular atomic species would be found at a given distance. They studied scandium trifluoride because it has a simple atomic structure in which each scandium atom is surrounded by an octahedron of fluorine atoms. According to the prevailing rigid-unit-mode (RUM) theory, each fluorine octahedron should vibrate and move as a rigid unit when heated — but that is not what they observed.

“We found that the distances between scandium and fluorine were pretty rigidly-defined until a temperature of about 700 K, but the distances between the nearest-neighbor fluorines became ill-defined at temperatures above 300 K,” says Zaliznyak. “Their probability distributions became very broad, which is basically a direct manifestation of the fact that the shape of the octahedron is not preserved. If the fluorine octahedral had been rigid, the fluorine-fluorine distance would have been as well defined as scandium-fluorine.”

With the help of high school researcher David Wendt and condensed matter theorist Alexei Tkachenko, Zaliznyak developed a simple model to explain these experimental results. The team went back to the basics—the fundamental laws of physics.

“When we removed the ill-controlled constraint that there must be these rigid units, then we could explain the fundamental interactions that govern the atomic positions in the [ScF3] solid using just Coulomb interactions.”

The team developed a negative thermal expansion model that treats each Sc-F bond as a rigid monomer link and the entire ScF3 crystal structure as a floppy, under-constrained network of freely jointed monomers. Each scandium ion is constrained by rigid bonds in all three directions, whereas each fluorine ion is free to vibrate and displace orthogonally to its Sc-F bonds. This is a direct three-dimensional analogy of the well-established behavior of chainlike polymers. And their simple theory agreed remarkably well with their experiments, accurately predicting the distribution of distances between the nearest-neighbor fluorine pairs for all temperatures where NTE was observed.   

“Basically we figured out how these ceramic materials contract on warming and how to make a simple calculation that describes this phenomenon,” Zaliznyak says.

Angus Wilkinson, an expert on negative thermal expansion materials at the Georgia Institute of Technology who is not involved in the project, agrees that Zaliznyak’s work will change the way people think about negative thermal expansion in solids.

“While the RUM picture of NTE has been questioned for some time, the experimental data in this paper, along with the floppy network (FN) analysis, provide a compelling alternative view,” says Wilkinson. “I very much like the way the FN approach is applicable to both soft matter systems and crystalline materials. The floppy network analysis is novel and gives gratifyingly good agreement with a wide variety of experimental data.”

According to Zaliznyak, the next major step of their work will be to study more complex materials that exhibit NTE behavior now that they know what to look for.

Read the article in Science Advances.

This is a reposting of my news brief, courtesy of MRS Bulletin.

Ultrafast Laser Synchronization Breakthrough

AMO experiment schematic
Set-up of a nitrogen pulse-pump experiment that uses pulse arrival time information from a cross-correlator mounted downstream from the experiment. Figure courtesy of SLAC National Accelerator Laboratory.

A journal article, just published in Applied Physics Letters, details a major breakthrough for experiments at SLAC’s Linac Coherent Light Source (LCLS).

LCLS delivers intense ultrashort x-ray pulses that can be used to study the motion of atoms as they respond to external triggers, such as an optical laser. In these “pump-probe” experiments, the optical laser “pump” pulse starts a reaction in the material, while the x-ray “probe” pulse investigates the state of the material after a defined time delay. A sequence of x-ray pulses, with different time delays between the laser and x-ray pulses, is used to “film” the reaction in the material.

LCLS ultrafast x-ray pulses basically act like high-speed flashes of a camera strobe, allowing scientists to capture images with a “shutter speed” of less than 100 femtoseconds – the time it takes light to travel the width of a human hair.

In order to be able to “film” optically-induced ultrafast processes, however, scientists need more than just ultrashort x-ray and laser pulses. They also need to synchronize the x-ray pulses to the optical laser pulses with almost femtosecond accuracy, in order to have snapshots with good time resolution (“sharp focus”). This is a major challenge, since the main laser system for the x-ray free electron laser is a kilometer away from the optical laser and experiment.

State-of-the-art synchronization is performed at LCLS by accurately measuring the arrival times of the electron bunches (and corresponding x-ray pulses) relative to the radiofrequency that drives the accelerator, since the optical laser is locked to this reference radiofrequency. The best time resolution so far achieved with this approach is 280 fs (full width at half maximum, FWHM).

Recently, scientists at the LCLS Atomic, Molecular and Optical Science Instrument (AMO) dramatically improved the time resolution for their pump-probe experiments. Their new synchronization strategy is to directly measure the relative arrival time of both the x-ray and optical laser pulses at the experiment on a shot-by-shot basis. They do this by introducing into the x-ray beam what they call a cross-correlator, which is mounted downstream of the main experiment.

AMO scientists split their laser beam, sending it to both a pump-probe experiment and the cross-correlator (with a time delay). In the cross-correlator, the laser beam is reflected off a Si3N4 thin film. The spot of the laser pulse is then imaged with a long-distance microscope on a CCD camera. X-ray pulses also hit the same surface of the Si3N4 film, quasi-instantaneously changing the surface reflectivity.

The x-ray pulse very briefly changes the surface reflectivity. By imaging and measuring the position of this reflectivity change with the reflected laser, AMO scientists can directly measure the relative arrival time of the x-ray and optical laser pulses at their experiment. The scientists then use this pulse arrival time information from the cross-correlator to correct their corresponding experimental data on a shot-by-shot basis.

The AMO team demonstrated their improved time resolution with a nitrogen pump-probe experiment. With the time information from the cross-correlator, they were able to decrease the time resolution of their nitrogen experiment down to only 50 fs (FWHM). That’s almost down to the theoretical limit, allowing scientists to investigate all sorts of new ultrafast science.