Electron-ion Coupling Research Articles

Electron-ion relaxation times in 1–100 eV warm dense aluminum and gold

We calculated the electron-ion energy relaxation times in warm dense aluminum and gold. Our calculations span a wide temperature range from a thousand to a million kelvins for both dense aluminum and gold. To determine the temporal evolution of electron and ion temperatures, we employed the two-temperature model with the SESAME equation-of-state tables, and well-known electron-ion coupling factors. Our calculations indicate that the relaxation times for warm dense aluminum were within 5 ps, whereas they were within 20 ps for warm dense gold. The maximum relaxation times were observed at initial electron temperatures of approximately 30,000 K for both aluminum and gold. Our calculated relaxation times using the SESAME database agree very well with the existing theories both in the cold-solid and hot-plasma limits. Furthermore, we found that the melting times calculated using the Lindemann criterion were in good agreement with the melting times for gold from measurements in recent literature.

A Modified Implicit Monte Carlo Method for Frequency-Dependent Three Temperature Radiative Transfer Equations

In this work, we develop a modified implicit Monte Carlo method for the frequency-dependent (multigroup) three-temperature (3T) radiative transfer equations. A new reformulation of the 3T model is utilized to deal with the coupling between the electron and ion energies. This will result in an effective scattering term, together with a combination source term of electron and ion energies, which can be resolved by the Monte Carlo simulations. The method is proven to retain the asymptotic preserving property in the limit where the electron-ion coupling coefficient tends to zero or infinity. Furthermore, numerical simulations confirm the unconditional stability of the new method as well as its ability to preserve the total energy conservation. Several numerical results are presented to showcase the efficacy of this new method.

Heat transfer within nonequilibrium dense aluminum heated by a heavy ion beam

Abstract Energetic laser-accelerated ions can heat a small solid-density sample homogeneously to temperatures over 10,000 K in less than a nanosecond. During this brief heating time, the electron temperature of the sample rises first, and then the ion temperature increases owing to the heat transfer between the hot electrons and cold ions. Since energy deposition from the incident heavy ion beam continues concurrently with the electron-ion relaxation process within the heated sample, the electron and ion temperatures do not reach equilibrium until the end of the heating. Here we calculate the temperature evolutions of electrons and ions within a dense aluminum sample heated by a laser-accelerated gold ions using the two-temperature model. For these calculations, we use the published stopping power data, known electron-ion coupling factors, and the SESAME equation-of-state (EOS) table for aluminum. For the first time, we investigate the electron and ion temperature distributions within the warm dense aluminum sample and the heating uniformity throughout the entire heating period. We anticipate that knowledge of the temperature evolution during heating will allow for the study of the stopping power, thermal conductivity, EOS, and opacity of warm dense matter heated by an energetic heavy ion beam.

Electronic nonequilibrium effect in ultrafast-laser-irradiated solids

This paper describes the effects of electronic nonequilibrium in a simulation of ultrafast laser irradiation of materials. The simulation scheme based on tight-binding molecular dynamics, in which the electronic populations are traced with a combined Monte Carlo and Boltzmann equation, enables the modeling of nonequilibrium, nonthermal, and nonadiabatic (electron-phonon coupling) effects simultaneously. The electron-electron thermalization is described within the relaxation-time approximation, which automatically restores various known limits such as instantaneous thermalization (the thermalization time τe−e→0 ) and Born-Oppenheimer (BO) approximation ( τe−e→∞ ). The results of the simulation suggest that the non-equilibrium state of the electronic system slows down electron-phonon coupling with respect to the electronic equilibrium case in all studied materials: metals, semiconductors, and insulators. In semiconductors and insulators, it also alters the damage threshold of ultrafast nonthermal phase transitions induced by modification of the interatomic potential due to electronic excitation. It is demonstrated that the models that exclude electron-electron thermalization (using the assumption of τe−e→∞, such as BO or Ehrenfest approximations) may produce qualitatively different results, and a reliable model should include all three effects: electronic nonequilibrium, nonadiabatic electron-ion coupling, and nonthermal evolution of interatomic potential.

Energy transport analysis of NSTX plasmas with the TGLF turbulent and NEO neoclassical transport models

This work presents a study of plasma transport at low aspect ratio on the National Spherical Torus Experiment tokamak, where the turbulent and neoclassical energy fluxes calculated by the quasilinear Trapped Gyro Landau Fluid (TGLF) model and the multi species drift-kinetic Neoclassical solver (NEO) are validated against experimental data. The turbulent energy transport of two plasma discharges, one in the L-mode confinement regime and another in the H-mode regime, is dominated by electrostatic drift-wave instabilities, while the ion heat transport has a significant neoclassical contribution. The data analysis workflow is described in detail to understand how the variations of mapping and fitting of experimental data affect the power balance solution and subsequent flux-matching plasma profile predictions with the TGYRO solver. On average, the predicted plasma profiles are consistent with experimental data. However, the solutions are sensitive to various input parameters, including boundary conditions, and the electron-ion coupling. Linear gyrokinetic stability analysis demonstrates close agreement of the real frequencies of unstable modes between TGLF and CGYRO gyrokinetic simulations, but higher growth rates are predicted by TGLF, especially for the H-mode case. Estimates of the low-k modes’ contributions to the total flux are consistent with linear stability analysis and the E × B suppression of turbulence in TGLF simulations with the SAT1 saturation model, while the SAT2 saturation model over-predicts the low-k modes’ contribution in the H-mode case. Moreover, the results with SAT1 model are consistent with power balance analysis, which indicates only neoclassical ion energy fluxes inside ρ < 0.4 in the L-mode case and ρ⩽0.7 in the H-mode case. The presence of multi-scale turbulence and ion-scale driven zonal flow mixing effects are also observed in TGLF scans of the electron turbulent heat flux over a range of temperature gradients and the electron-ion temperature ratio, which could explain the strong model sensitivity to variations of input parameters.

Picosecond to microsecond dynamics of X-ray irradiated materials at MHz pulse repetition rate

Modern X-ray free-electron lasers (XFELs) produce intense femtosecond X-ray pulses able to cause significant damage to irradiated targets. Energetic photoelectrons created upon X-ray absorption, and Auger electrons emitted after relaxation of core-hole states trigger secondary electron cascades, which contribute to the increasing transient free electron density on femtosecond timescales. Further evolution may involve energy and particle diffusion, creation of point defects, and lattice heating. This long-timescale (up to a microsecond) X-ray-induced dynamics is discussed on the example of silicon in two-dimensional geometry. For modeling, we apply an extended Two-Temperature model with electron density dynamics, nTTM, which describes relaxation of an irradiated sample between two successive X-ray pulses, emitted from XFEL at MHz pulse repetition rate. It takes into account ambipolar carrier diffusion, electronic and atomic heat conduction, as well as electron-ion coupling. To solve the nTTM system of equations in two dimensions, we developed a dedicated finite-difference integration algorithm based on Alternating Direction Implicit method with an additional predictor-corrector scheme. We show first results obtained with the model and discuss its possible applications for XFEL optics, detectors, and for diagnostics tools. In particular, the model can estimate the timescale of material relaxation relevant for beam diagnostic applications during MHz operation of contemporary and future XFELs.

Direct Observation of Enhanced Electron-Phonon Coupling in Copper Nanoparticles in the Warm-Dense Matter Regime.

Warm dense matter (WDM) represents a highly excited state that lies at the intersection of solids, plasmas, and liquids and that cannot be described by equilibrium theories. The transient nature of this state when created in a laboratory, as well as the difficulties in probing the strongly coupled interactions between the electrons and the ions, make it challenging to develop a complete understanding of matter in this regime. In this work, by exciting isolated ∼8 nm copper nanoparticles with a femtosecond laser below the ablation threshold, we create uniformly excited WDM. Using photoelectron spectroscopy, we measure the instantaneous electron temperature and extract the electron-ion coupling of the nanoparticle as it undergoes a solid-to-WDM phase transition. By comparing with state-of-the-art theories, we confirm that the superheated nanoparticles lie at the boundary between hot solids and plasmas, with associated strong electron-ion coupling. This is evidenced both by a fast energy loss of electrons to ions, and a strong modulation of the electron temperature induced by strong acoustic breathing modes that change the nanoparticle volume. This work demonstrates a new route for experimental exploration of the exotic properties of WDM.

Electronic stopping power of protons in platinum: Direct valence and inner-shell-electron excitations from first-principles calculations

The electronic energy loss of proton in platinum (Pt) is studied through nonadiabatic electron-ion coupling dynamic simulations within time-dependent density functional formalism. We have clarified the counterintuitive deviation from velocity proportionality due to the existence of kink velocity of the $d$ electron excitation for a slow proton moving in metal Pt, whose valence $d$ band indeed extends up above the Fermi energy. We have also quantitatively investigated the involvement of the host core electron excitation in the ion-target interaction, through monitoring the evolution of the bound electron number on a specific orbital of the host atom during the close encounter with the flying incident ion. It is found that the low-lying $5p$, $5s$, and $4f$ configuration excitations play significant roles in determining the profile of the stopping curve around and above the stopping maximum.

Metallic water: Transient state under ultrafast electronic excitation.

The modern means of controlled irradiation by femtosecond lasers or swift heavy ion beams can transiently produce such energy densities in samples that reach collective electronic excitation levels of the warm dense matter state, where the potential energy of interaction of the particles is comparable to their kinetic energies (temperatures of a few eV). Such massive electronic excitation severely alters the interatomic potentials, producing unusual nonequilibrium states of matter and different chemistry. We employ density functional theory and tight binding molecular dynamics formalisms to study the response of bulk water to ultrafast excitation of its electrons. After a certain threshold electronic temperature, the water becomes electronically conducting via the collapse of its bandgap. At high doses, it is accompanied by nonthermal acceleration of ions to a temperature of a few thousand Kelvins within sub-100fs timescales. We identify the interplay of this nonthermal mechanism with the electron-ion coupling, enhancing the electron-to-ions energy transfer. Various chemically active fragments are formed from the disintegrating water molecules, depending on the deposited dose.

Equilibrium properties of warm dense deuterium calculated by the wave packet molecular dynamics and density functional theory method.

A joint simulation method based on the wave packet molecular dynamics and density functional theory (WPMD-DFT) is applied to study warm dense deuterium (nonideal deuterium plasmas). This method was developed recently as an extension of the wave packet molecular dynamics (WPMD) in which the equations of motion are solved simultaneously for classical ions and semiclassical electrons represented as Gaussian wave packets. Compared to the classical molecular dynamics and WPMD simulations, the method of WPMD-DFT provides a more accurate representation of quantum effects such as electron-ion coupling and electron degeneracy. It allows studying nonadiabatic dynamics of electrons and ions in equilibrium and nonequilibrium states while being more accurate and efficient at high densities than WPMD and classical molecular dynamics. In the paper, we discuss particular features of the method such as special boundary conditions and the procedure of isentrope calculation as well as the results obtained by WPMD-DFT for the shock-compressed deuterium. The compression isentrope and principal Hugoniot curves obtained by WPMD-DFT are compared with available experimental data and other simulation approaches to validate the method. It opens up a possibility of further application of the method to study nonequilibrium states and relaxation processes.

Enzymatic Bioluminescence Modulation with an ATP Synthase Integrated Biotransducer

AbstractIon carriers play an important role in biology in terms of control of a biological system, whereas electron carriers are key to engineered systems. Therefore, a biodevice requires an electron–ion coupling mechanism that can transmit an ion signal from a device to a biological system via an external voltage. In this study, a protonic biodevice is demonstrated that translates the proton signals from the device into an enzyme cascade by means of an ATP synthase and bioluminescent luciferase. The proton signals can be modulated through the applied potential to a sulfonated polyaniline biotransducer, with such protonic modulation controlling ATP synthesis at the ATP synthase membrane, followed by bioluminescence in the luciferin–luciferase reaction. The present electron–proton‐transportation platform provides a new means of controlling biological cascade reactions, with proton signals mediated by an external voltage.

Ultrafast visualization of phase transitions in nonequilibrium warm dense matter

Intense ultrafast laser excitation brings materials into highly nonequilibrium states with complex solid–liquid phase transitions. These ultrafast processes yield warm dense matter (WDM) conditions characterized by comparable thermal and Fermi energies, and strong ion–ion coupling. Here, we review recent studies employing mega-electron-volt ultrafast electron diffraction to resolve the structural dynamics of nonequilibrium WDM created by femtosecond laser heating of solids. For the study of warm dense gold, the results showed homogeneous melting that occurs within tens of picoseconds at absorbed energy densities of 0.4–1.4 MJ/kg. These results constrained the electron–ion coupling rate and revealed the melting sensitivity to nucleation seeds. For the study of radiation-damaged tungsten, the results showed a melting transition below the melting temperature. Molecular dynamics simulations suggested that this melting behavior is driven by vacancy defect clusters from radiation damage. These studies provided atomic-level insights into the melting behavior of materials under extreme conditions.

Downfolding approaches to electron-ion coupling: Constrained density-functional perturbation theory for molecules

Constrained electronic-structure theories enable the construction of effective low-energy models consisting of partially dressed particles. However, the interpretation and physical content of these theories is not straightforward. Here, we carefully explore the properties of downfolding theories for electron-ion problems, in particular constrained density-functional perturbation theory (cDFPT). We show that the dipole selection rules determine whether the partially dressed phonons satisfy Goldstone's theorem, and we prove that electronic screening always lowers the phonon frequencies. We illustrate the theory with cDFPT calculations for minimal example systems: the nitrogen and benzene molecule as well as graphene.

Self-similar solutions for high-energy density radiative transfer with separate ion and electron temperatures

We consider a non-equilibrium plasma radiatively heated by an external source in the high-energy density regime. It is shown that self-similar solutions resembling the classic Marshak wave exist for the ion and electron temperatures, if the electron–ion coupling coefficient scales inversely proportional to either the time from when the heating begins or to the square of the distance from the surface of the plasma. We discuss how such a coupling coefficient may arise, and demonstrate that these solutions are also useful for verifying simulation codes that treat radiation–electron–ion coupling in high-energy density plasmas.

High performance wave packet molecular dynamics with density functional exchange-correlation term for non-ideal plasma simulations

We report on development of the wave packet molecular dynamics (WPMD) with density functional theory (DFT) simulation technique that we proposed earlier for nonideal plasma and warm dense matter simulations. The method is based on the WPMD where the electron exchange-correlation effects are taken into account using the DFT approach. It is aimed at studying simultaneous dynamics of electrons and ions in equilibrium and non-equilibrium conditions for a wide range of temperatures and densities. Compared to classical molecular dynamics and WPMD simulations the method of WPMD-DFT provides more accurate representation of quantum effects such as electron–ion coupling and electron degeneracy. At this stage of the method development we pay a special attention to the performance issues such as acceleration with graphical processing units, the choice of an optimal simulation box size with respect to the boundary conditions, the use of an adaptive mesh for calculation of the exchange-correlation energy, and implementation of our algorithm in the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The results for internal energy of equilibrium dense hydrogen plasma are presented for evaluation of the method.

Tunable ionic conductivity and photoluminescence in quasi-2D CH3NH3PbBr3 thin films incorporating sulphur doped graphene quantum dots.

Ion migration in hybrid halide perovskites is ubiquitous in all conditions. However, the ionic conductivity can be manipulated by changing the material composition, operating temperature, light illumination, and applied bias as well as the nature of the interfaces of the devices. There have been various reports on electron ion coupling in hybrid perovskite semiconductors which gives rise to anomalous charge transport behavior in these devices under an applied bias. In this investigation, we have synthesized a mixture of 2D/3D perovskites by incorporating sulphur-doped graphene quantum dots (SGQDs) and demonstrated that the optical and electrical properties of the hybrid system can be tuned by controlling the ion conductivity through the active layer. It has been observed that the recombination resistance in undoped CH3NH3PbBr3 perovskites follows an anomalous behavior while the doped CH3NH3PbBr3 perovskite shows a monotonic increase with increasing applied bias due to reduced ionic conductivity. SGQDs at the grain boundaries of 2D/3D perovskites prohibit ion migration through the active layer, and therefore the electronic-ionic coupling is reduced. This results in increased recombination resistance with increasing applied bias.

Strong electron-ion coupling in gradient halide perovskite heterojunction

The electron-ion coupling in iontronics has great significance and potential for energy conversion and storage devices. However, it is a substantial challenge to integrate iontronics into all-solid-state semiconductor circuits and explore the electron-ion coupling in semiconductor devices. Here, by utilizing the organic-inorganic halide perovskite, we fabricate a planar heterojunction with a gradient distribution of halide anions. The diode-like halide migration was investigated by bias voltage induced asymmetric blue shift in photoluminescence spectrum. This pseudo-ionic diode behaviour was found to result from asymmetric charge injection characterized by I–V curves and gradient-halides-induced vacancy hopping indicated by energy dispersive spectroscopy (EDS). The planar gradient perovskite heterojunction provides a viable route for extending iontronic devices into the regime of all-solid-state semiconductors.

Review of the first charged-particle transport coefficient comparison workshop

We present the results of the first Charged-Particle Transport Coefficient Code Comparison Workshop, which was held in Albuquerque, NM October 4–6, 2016. In this first workshop, scientists from eight institutions and four countries gathered to compare calculations of transport coefficients including thermal and electrical conduction, electron–ion coupling, inter-ion diffusion, ion viscosity, and charged particle stopping powers. Here, we give general background on Coulomb coupling and computational expense, review where some transport coefficients appear in hydrodynamic equations, and present the submitted data. Large variations are found when either the relevant Coulomb coupling parameter is large or computational expense causes difficulties. Understanding the general accuracy and uncertainty associated with such transport coefficients is important for quantifying errors in hydrodynamic simulations of inertial confinement fusion and high-energy density experiments.

Electron-phonon coupling in metals at high electronic temperatures

Electron-phonon coupling, being one of the most important parameters governing the material evolution after ultrafast energy deposition, yet remains the most unexplored one. In this work, we applied the dynamical coupling approach to calculate the nonadiabatic electron-ion energy exchange in nonequilibrium solids with the electronic temperature high above the atomic one. It was implemented into the tight-binding molecular dynamics code, and used to study electron-phonon coupling in various elemental metals. The developed approach is a universal scheme applicable to electronic temperatures up to a few electron-Volts, and to arbitrary atomic configuration and dynamics. We demonstrate that the calculated electron-ion (electron-phonon) coupling parameter agrees well with the available experimental data in high-electronic-temperature regime, validating the model. The following materials are studied here - fcc metals: Al, Ca, Ni, Cu, Sr, Y, Zr, Rh, Pd, Ag, Ir, Pt, Au, Pb; hcp metals: Mg, Sc, Ti, Co, Zn, Tc, Ru, Cd, Hf, Re, Os; bcc metals: V, Cr, Fe, Nb, Mo, Ba, Ta, W; diamond cubic lattice metals: Sn; specific cases of Ga, In, Mn, Te and Se; and additionally semimetal graphite and semiconductors Si and Ge. For many materials, we provide the first and so far the only estimation of the electron-phonon coupling at elevated electron temperatures, which can be used in various models simulating ultrafast energy deposition in matter. We also discuss the dependence of the coupling parameter on the atomic mass, temperature and density.

Nonthermal phase transitions in metals

It is well known that sufficiently thick metals irradiated with ultrafast laser pulses exhibit phonon hardening, in contrast to ultrafast nonthermal melting in covalently bonded materials. It is still an open question how finite size metals react to irradiation. We show theoretically that generally metals, under high electronic excitation, undergo nonthermal phase transitions if material expansion is allowed (e.g. in finite samples). The nonthermal phase transitions are induced via an increase of the electronic pressure which leads to metal expansion. This, in turn, destabilizes the lattice triggering a phase transition without a thermal electron-ion coupling mechanism involved. We find that hexagonal close-packed metals exhibit a diffusionless transition into a cubic phase, whereas metals with a cubic lattice melt. In contrast to covalent solids, nonthermal phase transitions in metals are not ultrafast, predicative on the lattice expansion.