An approach for the measurement of the bulk temperature of single crystal diamond using an X-ray free electron laser

Abstract

We present a method to determine the bulk temperature of a single crystal diamond sample at an X-Ray free electron laser using inelastic X-ray scattering. The experiment was performed at the high energy density instrument at the European XFEL GmbH, Germany. The technique, based on inelastic X-ray scattering and the principle of detailed balance, was demonstrated to give accurate temperature measurements, within 8% for both room temperature diamond and heated diamond to 500 K. Here, the temperature was increased in a controlled way using a resistive heater to test theoretical predictions of the scaling of the signal with temperature. The method was tested by validating the energy of the phonon modes with previous measurements made at room temperature using inelastic X-ray scattering and neutron scattering techniques. This technique could be used to determine the bulk temperature in transient systems with a temporal resolution of 50 fs and for which accurate measurements of thermodynamic properties are vital to build accurate equation of state and transport models. From the thermal shield of a spacecraft during atmospheric re-entry 1 to the interior of Jovian planets 2 , matter is often found at pressures and temperatures that are at the limits of where conventional condensed matter and plasma physics formalisms are valid 3. At such extreme conditions, the kinetic energy of the electrons is comparable to the potential energy of interaction between electrons and the nuclei. For these systems, direct and accurate measurements of thermodynamic and transport properties are vital. Extreme states of matter can be produced by dynamic laser-driven compression 4-6 and laser heating techniques 7,8. These methods can excite a material into a transient state of simultaneously high density and temperature, and thereby enable access to previously unexplored regions of phase space. State-of-the-art experiments investigate the properties of materials driven into these conditions by coupling high-energy lasers with suitable probing techniques 9,10. In particular, X-ray scattering has proven to be a powerful tool for determining the structure and density, and the development of

Demonstration of an x-ray Raman spectroscopy setup to study warm dense carbon at the high energy density instrument of European XFEL

“…The elastic scattering of hard x-rays can be estimated with a delta function in this work, since x-ray scattering from phonons is on the order of 100 meV. 51 Therefore, the peak shape at 6 keV of the elastic scattering signal, presented in Fig. 3 (left), can serve as a good approximation of the instrument function, which describes the broadening of the signal due to beamline and spectrometer contributions.…”

Thermal excitation signals in the inhomogeneous warm dense electron gas

“…These physical effects are interesting in their own right, and the required perturbation amplitudes can be realized in experimental facilities. We also show that the energy resolution of present experiments 85 is sufficient to resolve the emerging modes and features.…”

“…Importantly, this example is as an illustration and, in general, other (smaller) values of the wave numbers can be probed. We note that recently an energy resolution better than for diagnostics using inelastic X-ray scattering at the high energy density instrument of the European XFEL has been reported 85 . This enables probing various new features in the electronic excitation spectrum discussed in this work.…”

An \textit{ab initio} study of shock-compressed copper

“…We observed the hardening of phonon spectra in the solid regime of the Hugoniot compression and, analogously, studied the shift of ion acoustic modes to higher excitation energies. Phonon hardening is currently lively debated and recent work has shown that phonons can be resolved at free electron laser facilities [17][18][19], enabling future direct observations of phonon hardening in shock compression experiments. We found the adiabatic speed of sound along the Hugoniot to be slightly underestimated by DFT-MD relative to recent experimental results.…”

“…[16]. With novel improvements to the spectral resolution at X-ray free electron laser facilities, it is now becoming possible to measure the ion-ion DSF of transient WDM states [17][18][19]. This allows us to probe the ion dynamics of dynamically compressed targets, requiring sophisticated many-body simulations, that take into account the quantum mechanical nature of WDM states, to compare with the experimental observations.…”