Session Y23: Materials in Extremes: Warm Dense Matter and HED Physics

Live

We put together an equation of state database for matter at extreme conditions by combining results from path integral Monte Carlo and density functional molecular dynamics simulations of eleven elements and ten compounds. For all these materials, we provide the pressure and internal energy over a wide density-temperature range from 0.5 to 50 g/cc and from 10⁵ to 10⁹ K, which are based on 5000 first-principles simulations. We compute isobars, adiabats and shock Hugoniot curves in the regime of L and K shell ionization. Invoking the linear mixing approximation, we study the properties of mixtures at high density and temperature. We derive the Hugoniot curves for water and alumina as well as for various carbon-oxygen, helium-neon, and CH-silicon mixtures and predict their maximal shock compression ratio. Finally we employ the database to determine the points of maximum shock compression for all possible binary mixtures. We identify mixtures that have a higher shock compression than their endmembers. We discuss trends common to all mixtures in pressure-temperature and particle-shock velocity spaces.   

Live

Average atom (AA) models allow one to efficiently compute electronic and optical properties of materials over a wide range of conditions and are often employed to interpret experimental data. However, at high pressure, predictions from AA models have been shown to disagree with results from ab initio computer simulations. We represent a new AA model, AvIon, that computes the electronic eigenstates with novel boundary conditions within the ion sphere. Bound and free states are derived consistently. We drop the common AA assumption that the free-particle spectrum starts at the potential threshold, which we found to be incompatible with ab initio calculations. We perform ab initio simulations of crystalline and liquid states for several elements over a wide range of densities and show that the computed band structures are in excellent agreement with predictions from AvIon.   

Live

Time-dependent density functional theory (TDDFT) enables calculating electronic transport properties in warm dense matter (WDM) and is an alternative to present state-of-the-art approaches. In TDDFT, the electrical conductivity is computed from the time evolution of the electronic current density and provides direct means to assess the validity of Ohm's law in WDM. We present TDDFT calculations of the electrical conductivity, for example in iron within the pressure and temperature range found in Earth's core. We discuss the ramifications of using TDDFT for calculating the electrical conductivity in contrast to the Kubo-Greenwood formalism and dielectric models.   

Live

In simulations of the warm dense matter regime, it is typical to use a combined finite-temperature Kohn-Sham density-functional theory (KS-DFT) and molecular dynamics approach. However, in KS-DFT, (i) scaling worsens with increasing temperature, and (ii) temperature dependence is usually neglected in the exchange-correlation (XC) functional. We present a derivation from first-principles which reduces the full many-body Hamiltonian to an average-atom model in the dilute gas limit, which significantly reduces the computational cost of the KS-DFT calculation. We also show preliminary results including a comparison of temperature-dependent and zero-temperature XC functionals.   

Live

Shock compression experiments enable us to probe the physical properties of warm dense matter (WDM) and to check the validity of predictions derived from first-principle computer simulations. At sufficiently high temperatures, WDM becomes fully ionized and its properties closely resemble an ideal mixture. As temperature decreases, systems become strongly coupled, making WDM characterization more challenging. A detailed knowledge of WDM allows us to constrain the interior of stars and planets and also enables us to make predictions for inertial confinement fusion experiments.

Here, we study how well the ideal mixing approximation works in the WDM regime for BN, MgO, and MgSiO₃. For each material, we build an equation of state (EOS) table from first-principles simulations for the fully interacting mixture. Starting from EOS table for the individual elements, we invoke the linear mixing approximation to compare the prediction for shock Hugoniot curves with those derived from the fully interacting EOS. Our results show that the linear mixing approximation works remarkably well over a wide range of temperatures and pressures. We identify conditions where nonideal effects are relevant.   

Live

The x-rays produced by a laser wakefield accelerator could be an invaluable source for x-ray absorption near-edge spectroscopy (XANES) measurements of warm dense matter due to their large spectral bandwidth and femtosecond pulse durations. Femtosecond x-ray absorption spectroscopy can provide time-resolved information on the ultrafast dynamics of the non-equilibrium transition of a metal foil from solid to the warm dense matter state: an opportunity to provide information to better describe and understand astrophysical and fusion plasmas. This work portrays the focusing of laser-wakefield acceleration produced betatron radiation for sub-100 fs XANES snapshots of the L-edge (707 eV) of laser-heated iron. The betatron was focused with a toroidal mirror to a spot size of ≈ 50 × 35 μm. The laser heated spot size is ≈ 300 μm enabling all photons emitted by the source to probe a homogeneous region of the warm dense sample, minimizing temperature and density gradients for accurate XANES measurements. We present a ray-tracing model used to compare the performance of the focusing system with the experimental betatron spot measurement, as well as an analysis of the XANES spectra of an unheated thin (50 nm) iron sample.   

Live

The free-free opacity in plasmas is fundamental to our understanding of energy transport in stellar interiors and for inertial confinement fusion. However, theoretical predictions in dense plasmas are conflicting and there is a dearth of accurate experimental data for direct model validation. Here we present a novel functional exploration approach to extract the temperature-dependent absorption coefficient of a warm dense aluminium plasma for the first time. The plasma was created via isochoric heating at the XUV free-electron laser FLASH, and was probed with femtosecond time resolution showing the separate contributions to the opacity from hot electrons and ions. We find a pronounced enhancement of the opacity as the plasma electrons are heated to temperatures around the Fermi energy, with further opacity rises observed on ps timescales due to ion heating, melt, and the formation of the warm dense state.

Vinko et al., Phys. Rev. Lett. 124, 225002 (2020), DOI: 10.1103/PhysRevLett.124.225002   

Live

Measuring atomic-resolution images of materials using time-resolved diffraction techniques has transformed our understanding on material behaviors and phase transition dynamics under extreme conditions. In particular, the advances in X-ray Free Electron Lasers and field-accelerated ultrafast electrons have allowed unprecedented explorations in this area of research, enabling femtosecond visualization of transient dynamics at atomic length scales. In this talk, I will present our recent work of using time-resolved diffraction technique based on relativistic electrons, also known as ultrafast-electron diffraction (UED), to study matter in extreme conditions created by ultrafast-laser excitation of solids.

I will first present results of ultrafast melting of solids induced by femtosecond laser excitation. By measuring melt time with UED, we resolved melting mechanism transition between heterogeneous and homogeneous melting regimes in warm dense Au [1]. These results provided direct comparison with molecular-dynamics (MD) simulations and revealed missing physical phenomena that will need to be included in simulations. Using the same technique, we also investigated the impact of radiation-driven defects on ultrafast melting [2]. More recently, we have performed UED experiments to visualize lattice response of single-crystal Al to ultrafast laser-induced compression. We observed lattice transitioning from a purely elastic to a plastically relaxed state. From the transverse plastic strain evolution, we found two distinct regimes of lattice relaxation: dislocation nucleation and transport. Our MD simulations showed excellent agreement with the experimental results. These results provided important insights into the dislocation dynamics during incipient plastic deformation.
[1] M. Mo, et al. Science 360, 1451 (2018).
[2] M. Mo, et al. Science Adv. 5, eaaw0392 (2019).   

Live

Electronic structure methods for hot, dense plasmas often use density functional theory (DFT) with major additional approximations. For example, orbital-free DFT currently uses functionals that do not recover discrete core states, while average atom methods model one atom in an averaged plasma. Here we use the so-called multiple scattering method to solve the Kohn-Sham DFT equations for dense plasmas. The method is all-electron and does not use pseudopotentials. We find that equation of state calculations result in good agreement with other state-of-the-art methods, and find that computational cost does not increase with temperature, allowing access to very high temperature, non-degenerate systems.   

Live

Warm dense matter (WDM) is an exotic state that occurs in astrophysical objects and is on the pathway towards inertial confinement fusion.
Yet, the theoretical description of WDM remains difficult. Here, we present an effective static approximation (ESA) for the local field correction, that combines a neural net representation [1] of G(q,0) with a consistent limit for large wave numbers q determined from the on-top pair distribution function g(0) [2]. Our scheme allows for the computation of electronic properties with high accuracy over the entire WDM regime without any additional computational cost compared to the random phase approximation. Therefore, it can be directly used for many applications such as the computation of conductivities and stopping powers, and as input for (TD-)DFT simulations, and for the interpretation of XRTS experiments.

[1] T. Dornheim et al., J. Chem. Phys. 151, 194104 (2019)
[2] T. Dornheim et al., arXiv:2008.02165 (submitted)   

Live

We present our progress in developing free-energy density functionals that include exchange-correlation (XC) thermal effects for improving the accuracy of Kohn-Sham calculations at elevated temperatures (T). The recently developed local-density approximation corrKSDT, generalized-gradient approximation (GGA) KDT16 [1], and hybrid-level KDT0 [2] show that XC thermal effects are significant in certain thermodynamic conditions and that further development of thermal functionals is necessary. Here, we present a finite-T version of the meta-GGA functional SCAN-L (the de-orbitalized version of SCAN [3]) and the popular hybrid functional HSE06. Our results show an improved agreement with experiment in calculations such as Hugoniot and optical properties of materials of interest to planetary science and inertial confinement fusion.

[1] V. V. Karasiev, J. W. Dufty, and S. B. Trickey, Phys. Rev. Lett. 120, 076401 (2018).
[2] D. I. Mihaylov, V. V. Karasiev, and S. X. Hu, Phys. Rev. B 101, 245141 (2020).
[3] D. Mejia-Rodriguez and S. B. Trickey, Phys. Rev. A 96, 052512 (2017).   

Live

To accurately model ongoing and proposed inertial confinement fusion platforms, accurate equations-of-state for bulk systems are not enough to account for inhomogeneities, interfaces, and multispecies transport. The evolution of a macroscopic interface is heavily determined by the electron and ion interactions which can not be approximated classically at lower temperatures due to degenerate electrons and strongly-coupled ions. We propose an approach to benchmark and validate the assumptions underpinning a large class of transport models, complementary to ongoing experimental efforts at several national labs. Specifically, by force-matching radial pair potentials and many-body potentials to Kohn-Sham density functional theory data across a range of elements, densities, and temperatures, we are able to directly assess the quality of the pair potential approximation invoked in several transport theories using multiple metrics of accuracy. Beyond providing rough accuracy boundaries, this approach allows for a comparison between Kohn-Sham density functional theory and existing transport theories, potentially allowing one to tweak or improve more computationally affordable pair potential ansatzë.   

Live

The uniform electron gas (UEG) constitutes one of the most important model systems in quantum physics and theoretical chemistry. While many of its properties at zero temperature have been known for decades, only recently it has become possible to obtain accurate data at Warm Dense Matter conditions, i.e. extreme pressure and finite temperature using ab-initio Path integral Monte Carlo (PIMC) methods.^[1] While many static quantities can be computed directly, the investigation of dynamics is generally limited to an imaginary-time argument. We present a novel method for overcoming the ill-posed problem of recovering real-time properties based on sampling the dynamic local field correction, which has been used to obtain the first ab-initio results for the dynamic structure factor,^[2] dielectric function, dynamic susceptibility and conductivity.^[3]

[1] Dornheim et. al, Phys. Rep. 744 (2018)
[2] Dornheim et. al, Phys. Rev. Let. 121, 255001 (2018)
[3] Hamann et. al, Phys. Rev. B 102, 125150 (2020)