Lights, camera, action: Researchers develop method to measure crystalline equation of state

Beginning in the 19th century, scientists developed equations of state (EoS) to describe how material properties such as volume or internal energy are affected by intensive pressure or temperature. Experiments are conducted to determine the volume a sample occupies at various pressure-temperature conditions. But what happens when a suitable experimental technique does not exist or is prohibitively expensive?

Create a new experimental technique. In new research, Lawrence Livermore scientists did just that, using lights and a camera to make direct volume measurements in small-scale highly pressurized crystals to determine the equation of state of a special material.

"In order to accurately predict performance characteristics for an important Department of Defense material, we needed to know its equation of state," said Sorin Bastea, an LLNL computational physicist and project leader. "Normally our team of experimentalists conducts high-pressure X-ray diffraction measurements, sound-speed measurements or ultrafast tabletop shock compression studies to determine pressure-dependent sample volumes."

Unfortunately the material, α-NTO (an insensitive energetic material), has an extraordinarily complicated crystal structure and limits conclusive volume determinations from high pressure X-ray diffraction  (XRD) data. After one year, national lab and academic teams were unable to physically prepare α-NTO for small-scale shockwave EoS or sound-speed diagnostic measurements.

"The material simply wouldn’t cooperate; each time we attempted to prepare this sample for existing diagnostics something would go wrong," LLNL physical chemist Joe Zaug said. "Then I remembered a mid-1970s paper where a pioneering Cornell University group made direct volume measurements from large and compressed sodium chloride crystals — I wondered if direct measurements could work on a much smaller scale for highly pressurized crystalline samples."

At this point, Zaug conducted interferometry measurements using a halogen lightbulb, and microscopy measurements using a CCD camera. He tested the technique on a 10-micron dimensional triaminotrinitrobenzene (TATB) crystal pressurized in a diamond-anvil cell  (TATB is an explosive more powerful than TNT).

"We were quite surprised by our first results," LLNL physicist Jonathan Crowhurst said. "They matched remarkably well with published X-ray results, and at the same time we were able to extend the pressure range of TATB’s EoS."

Elissaios (Elis) Stavrou, an LLNL physicist who is internationally recognized as a high pressure X-ray crystallographer, was intrigued by the prospect. "I had never heard of such an approach being applied to crystalline materials, but I kept an open mind and tried it out on α-NTO."

Stavrou measured the EoS up to nearly 30 GPa (300,000 times normal atmospheric pressure) and the results enabled Bastea to calculate performance characteristics for an important DoD material.

"This is another great leadership example where the Lab innovated a solution to resolve a long-standing technical problem," Bastea said. The team’s NTO results matched well with a recent theory paper, too.

Stavrou explained: "This versatile experimental method gives research groups access to simply and directly measure high-pressure EoS data from crystalline materials."

In addition to EoS, the new high-pressure experimental approach can be used to measure a crystal’s indices of refraction. The research appears in the April 7 edition of the Journal of Applied Physics. Using their lights, camera and more innovative action, they plan to make optical microscopy-interferometry-based (OMI) measurements on pressurized polymer blended composites and alloyed materials.

The research was funded by the DoD/DOE Joint Munitions Program and the LLNL HE Science Campaign-2 program.