Investigation of the solid–liquid phase transition of carbon at 150 GPa with spectrally resolved X-ray scattering
Introduction
A deeper understanding of carbon under extreme conditions is highly relevant to various fields of science [1]. Prominent examples are the internal structure and evolution of the carbon-bearing ice giants in our solar system [2], [3], [4], extrasolar carbon planets [5] or the outer layers of white dwarfs [6]. In these systems, warm dense carbon, i.e. carbon with temperatures from 5000 K to 100,000 K at solid density or above, is supposed to be highly abundant and models remain challenging since the complex underlying physics of warm dense matter (WDM) is still poorly understood [7]. In the low-temperature regime of WDM, the available energy from pressure and temperature are on the order of chemical bonding and thus, remaining bonds can strongly influence the microscopic structure [8]. In the laboratory, WDM states are traversed in every process where a solid density sample is rapidly heated to a plasma state. Within the Inertial Confinement Fusion experiments presently ongoing at the National Ignition Facility [9], carbon is one possible ablator material which is currently being investigated [10]. Here, the high-pressure solid–liquid transition of carbon is of special interest, since re-freezing of the ablator layer can occur after the first shock, leading to density fluctuations which can seed hydrodynamic instabilities. Therefore, an improved knowledge of the microscopic structure and the ion–ion potential close to the melting line is needed for accurate models of these experiments. Classical measurements of the shock Hugoniot, giving the macroscopic quantities pressure and density, can only give hints of the underlying microscopic properties [11], [12]. Whereas for high-pressure solid–solid transitions, fast X-ray diffraction has usually been the method of choice [13], liquid structure can hardly be resolved in a single event. This is especially true for low-Z materials, which have a small elastic scattering amplitude. Spectrally resolved X-ray scattering, however, has been proven to be capable of directly determining the microscopic structure of short-lived warm dense matter samples [14], [15], recently revealing the importance of short-time chemical bonds in liquid carbon around 100 GPa pressure [8]. Here we show a further development of these experiments using graphite samples of different initial density. In this way, a broader variety of final states can be achieved, in particular creating states of very similar pressure at different temperatures for a given drive [16]. Our results show that this method is capable of resolving the solid–liquid transition of carbon at relatively constant pressure.
Section snippets
Experiment setup
The experiments were performed at Target Area West of the Central Laser Facility based at STFC Rutherford Appleton Laboratory, UK. A sketch of the experiment setup is shown in Fig. 1. Four beams of the VULCAN laser system were focused onto graphite samples with a spot diameter of 700 μm, an accumulated energy of 250 J at a wavelength of 527 nm and 6–7 ns pulse duration. These laser parameters were used for all runs. Random phase plates were implemented to ensure planar and homogeneous shock
Spectrally resolved X-ray scattering
The scattering of X-ray radiation from matter is generally dominated by the electrons. For small momentum transfers, where the energy of the scattered photon is nearly unchanged, the magnitude of the scattering vector k = ki−ks, which is the difference of the incident wave vector ki and the scattered wave vector ks, can be approximated as [21].where ωi is the frequency of the incident light and θ denotes the scattering angle. For our experiment, the magnitude of the
Simulations
The temporal evolution of the laser-driven graphite samples was simulated using the one-dimensional hydrodynamic code HELIOS [31] in combination with the SESAME equation of state No. 7832 [32] and adapted to the measurements of the shock breakout time. At 8 ns after the shock drive, which is comparable to the time when the sample is probed during the experiment, the simulations predict a density of 3.30 g/cm3 for FG, 3.82 g/cm3 for RG and 3.96 g/cm3 for HOPG, temperatures of 14,500 K for FG,
Results
Fig. 4 shows an example of an optical streak camera image recorded during the experiment. The temporal pulse shape of the drive lasers is monitored using a mirror leakage and is used as a timing reference at the same time. Specular reflections inside the interaction chamber show the relative timing of the short pulse probe laser. Additionally, the optical self-emission of the hot compressed material is visible from the moment when the shock wave has reached the target rear side and, thus,
Conclusions
Using laser-driven shock-compression of graphite samples with different initial densities in combination with spectrally resolved X-ray scattering we have been able to resolve the carbon solid–liquid phase transition at a relatively constant pressure of ∼ 150 GPa. Rigid and Flexible Graphite with initial densities of 1.84 g/cm3 and 1.30 g/cm3 were transferred to the fluid phase while we interpret the HOPG (ρ0 = 2.25 g/cm3) data that the samples remained solid for identical drive laser
Acknowledgements
We thank the staff scientists, laser technicians and the target lab engineers of the Central Laser Facility at Rutherford Appleton Laboratory for their assistance and motivation. This work was supported by the BMBF Project 05P12RDFA1 and by EPSRC grant EP/K009591/1.
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