A team employed Summit, the nation’s fastest supercomputer, to model the behavior of carbon under extreme temperatures and pressures

Are diamonds even stronger than we’ve ever imagined? Can other post-diamond phases appear when diamond is subjected to extreme pressures? A team used machine-learned descriptions of interatomic interactions on the 200-petaflop Summit supercomputer at the US Department of Energy’s (DOE’s) Oak Ridge National Laboratory (ORNL) to model more than a billion carbon atoms at quantum accuracy and observe how diamonds behave under some of the most extreme pressures and temperatures imaginable. The results are nothing short of incredible.

Photo of Ivan Oleynik

Ivan Oleynik and team are studying how diamond behaves under extreme pressures and temperatures. Image Credit: USF

The team was led by scientists at the University of South Florida (USF), DOE’s Sandia National Laboratories (Sandia), DOE’s National Energy Research Scientific Computing Center (NERSC), and the NVIDIA Corporation. The researchers found that under extreme conditions, a shock wave strongly compresses the diamond as it passes through and forces it to crack under the pressure.

The study will help scientists better understand how carbon behaves under extreme conditions. This understanding is crucial for inertial confinement fusion, in which hydrogen fuel is kept inside a diamond capsule and nuclear fusion reactions are initiated by compressing the collapsing diamond shell. It is also important for uncovering the internal structure of carbon-rich planets—like Uranus—and carbon-rich exoplanets. Exoplanets exist around stars outside of our solar system, and observations suggest they can be rich in diamond and silica.

“Observations have shown that some exoplanets consist of carbon-rich constituents, such as methane, which, upon compression, convert to diamond,” said Ivan Oleynik, a professor of physics at USF and principal investigator on the project. “To understand the structure of these exoplanets, scientists need to understand the behavior of carbon at extreme conditions.”

Scientists had believed that under extreme temperatures and pressures, diamond can experience plasticity similar to metals. But as it turns out, diamond experiences a brittle behavior while sustaining its exceptional strength. The team found that these cracks are healed through the formation of amorphous carbon. This carbon is eventually converted into regions of hexagonal diamond, thus explaining the underlying mechanism of diamond’s strength.

For this work, the team has been named a finalist for the Association for Computing Machinery Gordon Bell Prize. This prize has been awarded each year since 1987 at the International Conference for High-Performance Computing, Networking, Storage and Analysis (SC). It recognizes outstanding achievements in applying high-performance computing (HPC) to challenges in science, engineering, and large-scale data analytics. The team’s results will be presented at SC21, to be held November 14–19, 2021, in St. Louis, MO.

Diamonds take the heat

Experiments at Sandia’s Z Pulsed Power Facility and at Lawrence Livermore National Laboratory’s (LLNL’s) National Ignition Facility (NIF)—facilities capable of creating tens of millions of atmospheres, or 100s of millions of pounds per square inch—have shown that diamond retains extremely high strength even when subjected to enormous compression and heating. It retains this strength up to the state when it should start melting. These experiments involved pressures above several million atmospheres. However, there has been controversy around what actually happens to diamonds under such extreme pressures.

“When you load diamond with enormous pressure, it was assumed to turn into a plastic-like state. But we know diamonds are brittle and don’t behave in this way,” Oleynik said. “Our simulations have uncovered an unexpected mechanism of inelastic deformations. Diamond cracks when it is compressed by the enormous shock waves generated at these gigantic compression facilities. These cracks are then reformed during an amorphous-like carbon state inside these cracks. They are then followed by recrystallization into hexagonal stacking faults where the atomic planes are shifted, compared with those in ideal diamond crystals.”

Under such extreme conditions, atoms are squeezed together so tightly that only quantum mechanics, which describes how materials behave at the atomic scale, can provide a sufficiently detailed picture of how they interact with one another. But using quantum mechanics to study the dynamics of atoms is computationally expensive.

“If you want to simulate something approaching experimental length and timescales, such as micrometers and nanoseconds, you need millions and even billions of atoms and millions of molecular dynamics time steps. But with quantum mechanics, the largest amount of particles you can do is no more than 1,000 atoms. And the largest number of steps is 10,000.”

The team made a major breakthrough in describing with quantum accuracy how carbon atoms interact under such enormous pressure and temperature. The team fingerprinted each atom in a diamond using a set of so-called descriptors, which were then used to construct an accurate representation of the system’s potential energy using powerful machine-learning techniques. This innovative machine-learning approach enabled the team to make predictions of atomic-scale dynamics for a billion atoms to within 3 percent accuracy when compared with extremely precise quantum mechanical calculations.

GPUs illuminate new diamond properties

PhD student Jonathan Willman and postdoctoral associate Kien Nguyen-Cong, both in Oleynik’s group at USF, performed the simulations on Summit using a billion-atom sample on the full machine for 24 hours.

“Simulating billions of atoms at this nanometer timescale could only be done on Summit. GPU acceleration was the key to achieving these results,” Oleynik said. “Our team made a major algorithmic breakthrough that allowed our GPU-enabled code to run one hundred times faster than it does on CPU-only machines.”

In these billion-atom simulations, the team observed for the first time the shock wave propagation in micrometer-thick diamond at fine resolution, down to the atomic scale. This allowed the team to observe details of diamond cracking and reforming, as well as complex interference patterns created by multiple local sound waves initiated at the crack tips.

The Oleynik team simulated a split elastic-inelastic shock wave moving through a single crystal diamond. Image Credit: Jonathan Willman, Materials Simulation Laboratory, Oleynik’s Group at USF

“We couldn’t see this before because we had never done such grand-scale simulations,” Oleynik said. The cross section of the diamond sample the team used in simulations is 100 by 100 nanometers and 1 micron—or 1,000 nanometers—in length.

“Running the simulations at such a grand scale is important because now we can achieve high fidelity, and we can say for certain that our results are close to reality,” Oleynik said.

Reaching an unknown phase of carbon

Thanks to Summit, the team also has a better understanding of why diamonds haven’t been transformed to the so-called BC8 high-pressure, post-diamond phase in billion-dollar experiments at the NIF at LLNL.

“These experiments pursued conventional thinking of concerted transformation of atoms from a diamond lattice to that of the BC8 phase. This phase transition requires overcoming an enormous energy,” Oleynik said. “Our hypothesis, which was brilliantly confirmed in our billion-atom simulations, is that the liquid-like, amorphous carbon can facilitate the nucleation of the BC8 phase. This provides a viable pathway for synthesis of this post-diamond phase. Within the NIF Discovery Science program, we are working with our experimental collaborators to confirm our predictions.”

The team plans to extend their simulations to even bigger, trillion-atom systems using emerging exascale HPC systems. These include the nation’s first exascale supercomputer, Frontier at the Oak Ridge Leadership Computing Facility (OLCF), a DOE Office of Science user facility located at ORNL.

“Such tour de force simulations will provide even deeper insight into mystery of diamond rain upon compression of methane inside of ice giants Uranus and Neptune,” Oleynik said. “The beauty of these simulations is that we can see how nature responds to these extreme pressures and temperatures at the atomic level. We can also see how individual atomic motions combine together in a collective macroscopic behavior, which can then be observed in state-of-the art experiments.”

The team members include Jonathan Willman, Kien Nguyen-Cong, and Ivan Oleynik from USF; Stan Moore, Mitchell Wood, and Aidan Thompson from Sandia; Rahulkumar Gayatri from NERSC; and Evan Weinberg from the NVIDIA Corporation

Sandia is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for DOE’s National Nuclear Security Administration (NNSA).

The research is supported by NNSA; the Exascale Computing Project, a collaborative effort of the DOE’s Office of Science and NNSA; and DOE’s Advanced Scientific Computing Research Leadership Computing Challenge and Innovative and Novel Computational Impact on Theory and Experiment awards. This research used resources of NERSC and the OLCF.

Related Publication: Nguyen-Cong, Kien, Jonathan T. Willman, Stan G. Moore, Anatoly B. Belonoshko, Rahulkumar Gayatri, Evan Weinberg, Mitchell A. Wood, Aidan P. Thompson, and Ivan I. Oleynik. “Billion Atom Molecular Dynamics Simulations of Carbon at Extreme Conditions and Experimental Time and Length Scales.” Paper to be presented at SC21: The International Conference for High Performance Computing, Networking, Storage and Analysis, St. Louis, MO, November 2021.

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