A material's equation of state (EOS) ― which indicates its state under various conditions of pressure, temperature, volume, and energy, and relates them to various phases ― is a vital part of understanding the material’s behavior and response in different environments and applications. However, determining the EOS and complete phase diagrams of some materials can pose daunting challenges. One of these materials is cerium, for which some regions of the phase diagram have proven elusive. Investigators from the U.S. Department of Energy’s (DOE’s) Los Alamos National Laboratory (LANL) employed the U.S. DOE’s Advanced Photon Source (APS) to probe the high-pressure solid phase of cerium through shock-wave experiments that provided a detailed look at the cerium's transition from the α- ε phases. Their work, which provides the first evidence that an α-ε phase transition can be shock-induced in cerium, was published in the Journal of Applied Physics.
The principal Hugoniot (which defines conditions on both sides of a shock wave) of cerium has already been measured through traditional shock-wave techniques, but to go beyond it to find the secondary Hugoniot that marks the boundary of the ε-Ce phase requires a more complex approach that uses multiple shock loading. Data from regions beyond the principal Hugoniot are needed to determine multiphase equations of state. Toward this end, diamond anvil cell (DAC) experiments were conducted at the HPCAT-XSD 16-BM-D x-ray beamline at the APS, an Office of Science user facility at Argonne National Laboratory, while double-shock experiments were conducted at Los Alamos National Laboratory.
In the shock impact work, two different experimental configurations were performed: front surface impact experiments (FSI), which used a cerium impactor; and double-shock transmission experiments, which used a cerium target and a complex projectile launched using high-performance gun systems. The researchers also performed static high-pressure DAC experiments at HPCAT-XSD to complement the dynamic measurements. Together, these different configurations allowed the researchers to study cerium using very different loading paths and time scales.
The dynamic studies showed that a secondary Hugoniot centered around 5.2-5.7 gigapascals (GPa) and extends with the second shock to a peak stress of 25-30 GPa and beyond. DAC data were obtained along an isotherm of 773 K and shows that a gradual transition from α-Ce to ε-Ce begins at about 6 GPa. This mixed phase completely changes to ε-Ce at 12.1 GPa for both static and dynamic experiments.
The experimental team obtained simulated shock wave profiles for comparison with the experimental data, using a one-dimensional hydrodynamic code and a two-phase model to separately account for both the α-Ce to ε-Ce phases. The simulations generally showed good agreement with the experimental profiles, although some discrepancies were seen with the α-Ce phase model and the second high-pressure shock state above 12 GPa.
The necessity of a two-phase model to accommodate the disagreement in measured shock velocities of the second shock wave between the experimental data and the predictions from simulated profiles strongly supports a α-Ce to ε-Ce phase transition at a peak stress of about 12.25 GPa.
The complete transition to the ε phase is similar to the DAC experiments performed in this work, though the DAC data show a gradual transition from one phase to another. The research team next plans to repeat similar experiments under x-ray diffraction observation to study the evolution of the cerium microstructure across the phase transition. ― Mark Wolverton
See: B. J. Jensen, F. J. Cherne, and N. Velisavljevic‡, “Dynamic experiments to study the α−ϵ phase transition in cerium,” J. Appl. Phys. 127, 095901 (2020). DOI: 10.1063/1.5142508
Author affiliation: Los Alamos National Laboratory ‡Present address: Lawrence Livermore National Laboratory
This work was supported by the U.S. Department of Energy (DOE) through the Los Alamos National Laboratory’s Science Campaign C2. The Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration (NNSA) of the U.S. DOE (Contract No. 89233218CNA000001). HPCAT-XSD operations are supported by the DOE-NNSA Office of Experimental Sciences. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Ofﬁce of Science User Facility operated for the DOE Ofﬁce of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357.
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