Diamond is more than a dazzling gem - the extremely hard form of carbon makes up the pellet that encases fuel for inertial confinement fusion, and scientists believe it rains down deep inside ice giant planets like Neptune and Uranus.
In both cases, the material experiences enormous pressures. Until now, experiments and simulations have disagreed about how it actually behaves under those conditions.
In a new study, published in Nature Physics, researchers at Lawrence Livermore National Laboratory (LLNL) document how diamond melts under pressures three times greater than the conditions at the Earth's core.
"We were able to take tiny diamond samples and shock compress them to temperatures hotter than the surface of the sun and to pressures higher than the center of Neptune and Uranus - and still measure atomic structure, temperature, density and optical reflectivity," said author and LLNL scientist Marius Millot.
The study resolves two long-standing discrepancies in the field, finally matching experimental results to simulations based on quantum mechanics. Applying the findings to inertial confinement fusion could triple energy gain, and the new understanding of diamond's high-pressure phases could reshape models of planetary interiors.
Melting mysteries
LLNL has been studying diamond's extreme behavior for decades. Lab scientist Jon Eggert and colleagues pioneered high-pressure melting experiments about 20 years ago, when they observed that diamond's density increased when melting.
"While this is rather unusual among most materials, we all know an example of such behavior," said LLNL scientist Marius Millot. "Liquid water is denser than ice, which makes ice cubes float. Jon's finding means that diamond would float in liquid carbon at high pressures."
While that work was a landmark in the field, it led to more questions. One in particular stumped the research community: there was a roughly 20% difference between the observed and predicted melting temperatures of diamond.
"No matter what the theorists did - even with the most advanced computer simulation techniques - they could not reproduce the experiments," said Millot.
At Sandia National Laboratories, using the extreme magnetic fields of the Z machine to shock compress small diamond samples revealed yet another mystery. The Sandia researchers obtained experimental fingerprints that may suggest that diamond takes an extra step on its way to melting, transforming from diamond to another crystalline structure before finally becoming a liquid. Simulations agreed with that result, but no one could directly measure the atomic structure to confirm it.
Experiments bring resolution
To address both questions, the LLNL team conducted laser-driven dynamic compression experiments at the University of Rochester's Laboratory for Laser Energetics (LLE). Using the Omega Laser Facility, the scientists vaporized the outside layer of a tiny sample, sending a squeezing shockwave rocketing through its diamond interior.
Making detailed, unambiguous and precise measurements during compression was a complicated process. The high-pressure states were short-lived, lasting for only a billionth of a second. The team had to capture all the crucial information, including X-ray diffraction data that illuminates atomic structure, in that tiny timeframe.
"This was the first time that shock-compressed diamond was probed with X-ray diffraction all the way up to melting," said Millot. "These measurements are extremely difficult because carbon is a small and lightweight atom. It scatters very few X-rays, so the signal we needed to measure was quite faint."
The LLE team played a crucial role in developing and maintaining the enhanced diagnostic tools. Those capabilities led to a new measurement of melting temperature - one that agreed almost perfectly with simulations and closed the 20-year gap.
"While it was frustrating to discover that our original temperature measurements were off by more than 1,000 degrees, it is exciting to see such a dramatic improvement in data quality with our new diagnostics," said Eggert. "Even better, our original inference of melting has now been confirmed directly with X-ray diffraction."
In contrast to the new, agreed upon melting temperature, the work told a different story than the phase change that was indicated at Sandia. The carbon remained in a diamond structure all the way until it melted, skipping any intermediate phases.
"We think that is because the sample does not have time to change when it only experiences a single shock. It remains 'trapped' in the diamond structure," said Millot.
That difference could be key for future high-energy-density experiments and simulations. It suggests that material response depends on exactly how the shock is applied, not just on pressure and temperature.
From fusion gain to diamond rain
The newly found agreement between theory and experiment has direct implications for fusion energy research.
In inertial confinement fusion experiments, powerful lasers generate shock waves that drive a tiny diamond capsule inward. The resulting implosion compresses the fusion fuel inside the capsule to the extreme pressures and temperatures needed for fusion.
Melting the diamond into a uniform, smooth fluid during the initial shock is critical to minimize implosion imperfections, which can cause a fusion reaction to fizzle. To make sure the first shock melts the diamond capsule, National Ignition Facility (NIF) scientists at LLNL usually use a relatively strong first shock.
"Our work indicates that we could use slightly slower initial shocks and still achieve full melting of the diamond in our NIF implosions," said Millot. "This is exciting because such a slower shock would make the fusion fuel more compressible. That in turn increases the maximum energy yield we could obtain with the same laser energy."
Predictions suggest that these slower shocks could triple energy gain, provided that other degradation mechanisms can be controlled.
The findings also give planetary scientists a new foothold. Interiors of ice giants like Neptune and Uranus are essentially inaccessible, so researchers rely on laboratory experiments and models to guess at what's happening beneath the surface. Some studies suggest that ice giant planets may crystallize carbon deep in their interior, where it would fall and form "diamond rain." Because the experiments probed diamond behavior at pressures exceeding those inside ice giants, the latest melting data provides a strong basis for more realistic planetary formation and evolution predictions.
Going forward, the LLNL team plans to leverage the experimental capabilities of NIF to study diamond's behavior at harder-to-reach, unprecedented extreme conditions. They aim to refine the understanding of the diamond capsule response in subsequent stages of implosion and to identify the limits of diamond structure stability under a series of multiple shock waves.
Other LLNL authors include Federica Coppari, Amy Lazicki, Yong-Jae Kim, Otto Landen, Vladimir Smalyuk and Peter Celliers. LLNL's target fabrication specialist Renee Posadas and Eric Folsom at the HED Science Center Technology Facility also contributed to the work. This study was supported by LLNL's Laboratory Directed Research and Development program.
