Two-temperature Approach Research Articles

Electron-phonon coupling dictates electron mean free paths and negative thermal diffusion in metals

The spatiotemporal dynamics of the fundamental energy carriers in metals underpin the efficiency of a wide array of technologies. Although much progress in our understanding of the temporal response of electronic relaxation processes following an external field perturbation has been achieved, the spatial relaxation dynamics of electrons after excitation remains unclear. Here, we employ a scanning ultrafast microscopy with high spatial resolution to directly measure the mean free paths of electrons in different metals. We show that the strength of electron-phonon coupling not only dictates the mean free paths, but also controls a peculiar spatial shrinking of the electronic temperature profile immediately after the electrons have thermalized with the ‘colder’ lattice. More specifically, from our experimental tracking of the spatial relaxation profiles, a clear observation of an effective negative thermal diffusion is apparent for metals with weaker electron-phonon coupling, while for metals with stronger electron-phonon coupling, the negative thermal diffusion effect is not observable. Our spatiotemporal modeling based on the two-temperature approach provides evidence that although negative diffusion occurs universally for materials with two different species that have varying diffusivities and are thermodynamically coupled, effective negative diffusion is masked for cases with stronger coupling between the species.

Energy ratio response at the interface of elastic and dual-porous thermoelastic half-spaces

The present study delves into the intricate examination of energy distribution inherent in plane waves interfacing with an elastic half-space and a thermoelastic half-space characterized by a dual porosity framework. Employing the memory-dependent dual-phase-lag (DPL) hyperbolic two-temperature (H2T) thermoelastic paradigm, the investigation encompasses various incident wave types. The governing equations, rendered in a non-dimensional format, are meticulously addressed by applying the rigorous technique of eigenmode analysis. The intricate energy ratios are meticulously ascertained through the judicious imposition of boundary conditions and the discerning employment of reflection and transmission coefficients. Graphical representations have been exhibited, elucidating the effects of diverse parameters on distinct energy ratios within crystalline structures akin to magnesium materials. These parameters encompass but are not confined to the H2T paradigm, the absence of the two-temperature influence, the classical two-temperature approach, memory effects, and a spectrum of distinct kernel functions. The proposed model emanates cross-disciplinary utility, traversing the domains of seismology, acoustics, optics, materials science, structural engineering, and geophysics.

Pump-probe reflectivity studies of ultrashort laser-induced acousto-mechanical strains in ZnO films

In the current work we report on the generation of acoustic strains in thin ZnO layers using optoacoustic transduction of ultrashort laser pulses into acoustic waves on an Au thin film transducer. After absorption of energy by the electron system of the metal, energy conversion, thermal expansion and mechanical deformation takes place. The generation and propagation of the induced acoustic strains are monitored in time via a degenerate pump-probe transient reflectivity optical setup at 800 nm, as opposed to most commonly used schemes that employ different wavelengths for the pump and probe beams, mostly in the vicinity of ZnO maximum absorption. The experimental results include energy relaxation times and phonon scattering frequencies and are supported by a thermal vibro-acoustic finite element model. The model is based on the combination of a revised two-temperature approach and elasticity theory, and considers anisotropic properties for the ZnO film and the computation of the elastic wave velocity for the first time. The outcomes are discussed in the context of electron–phonon coupling factors and other material properties. A good agreement between the experimental findings and the results from the numerical simulations has been established, regarding outcomes like the mean velocity of the strain waves, establishing a novel characterization method applicable to a variety of materials and structures.

Combustion dynamics of high Mach number scramjet under different inflow thermal nonequilibrium conditions

To characterize the impact of thermal nonequilibrium conditions in shock-induced combustion in high Mach number scramjet engines, a comparative numerical investigation has been performed. The combustor configuration was based on the HyShot II scramjet while the total enthalpy is 3.3 MJ/kg which resembles Mach 8 flight condition. The improved delay detached eddy simulation with Park two-temperature approach in combination with the vibration-chemical coupling model was employed in the nonequilibrium simulations. It is shown that under thermal nonequilibrium inflow conditions, noticeable stratification in the thermal state exists in the circumferential direction both in the combustor section and exhaust nozzle. In the inner core where the fuel mixes with the mainstream, flow deceleration caused by the heat release leads to a sufficient transformation of energy between the vibrational and translational-rotational modes approaching the thermal equilibrium state. However, the τv,mix is quite large in the supersonic mainstream, whereby the thermal nonequilibrium dominates. For the case with higher Tv in the inflow, the fuel jet's penetration height is lower while the local viscosity is higher which results in poor mixing between the fuel and air stream. Nevertheless, a 400 K increase in inflow Tv gives a higher effective temperature, which promotes the dissociation reactions, shortens the ignition distance and yields an 8% increase in the overall combustion efficiency. With better combustion performance, an additional 6% deceleration in the supersonic mainstream and the energy exchange rate between vibrational and translational-rotational modes becomes almost four times faster at the combustor outlet, which promotes the restoration of the thermal equilibrium state. Furthermore, under higher inflow vibrational temperature, the shock-induced combustion in supersonic crossflow becomes less stable with noticeable fluctuations in combustion heat release and local static pressure.

Temperature properties in magnetized and radiatively cooled two-temperature accretion flows on to a black hole

ABSTRACT Simplified assumptions about the thermodynamics of the electrons are normally employed in general-relativistic magnetohydrodynamic (GRMHD) simulations of accretion on to black holes. To counter this, we have developed a self-consistent approach to study magnetized and radiatively cooled two-temperature accretion flows around a Kerr black hole in two spatial dimensions. The approach includes several heating processes, radiative cooling, and a coupling between the electrons and the ions via Coulomb interaction. We test our approach by performing axisymmetric GRMHD simulations of magnetized tori accreting on to a Kerr black hole under various astrophysical scenarios. In this way, we find that the inclusion of the Coulomb interaction and the radiative cooling impacts the thermodynamical properties of both the ions and electrons, changing significantly the temperature distribution of the latter, and underlining the importance of a two-temperature approach when imaging these flows. In addition, we find that the accretion rate influences the bulk properties of the flow as well as the thermodynamics of the electrons and ions. Interestingly, we observe qualitatively distinct temperature properties for SANE and MAD accretion modes while maintaining the same accretion rates, which could help distinguishing MAD and SANE accretion flows via observations. Finally, we propose two new relations for the temperature ratios of the electrons, ions, and of the gas in terms of the plasma-β parameter. The new relations represent a simple and effective approach to treat two-temperature accretion flows on supermassive black holes such as Sgr A* and M 87*.

Internal Structure and Heat Conduction in Rigid Solids: A Two-Temperature Approach

Abstract A non-Fourier thermal transport regime characterizes the heat conduction in solids with internal structure. Several thermodynamic theories attempt to explain the separation from the Fourier regime in such kind of systems. Here we develop a two-temperature model to describe the non-Fourier regime from the principles of non-equilibrium thermodynamics. The basic assumption is the existence of two well-separated length scales in the system, namely, one related with the matrix dimension (bulk) and the other with the characteristic length of the internal structure. Two Fourier type coupled transport equations are obtained for the temperatures which describe the heat conduction in each of the length scales. Recent experimental results from several groups on the thermal response of different structured materials are satisfactorily reproduced by using the coupling parameter as a fitting parameter. The similarities and differences of the present formalism with other theories are discussed.

Non-equilibrium dissociation and relaxation behind the shock wave within two-temperature approach

Within the recently proposed asymptotic method for solving the Boltzmann equation for chemically reacting gas mixture, the equations for a dissociating diatomic gas have been derived assuming two-temperature (translational-rotational + vibrational) approximation. Corresponding expressions for the reaction and relaxation rates, determined by the quasi-stationary vibrational distributions, have been obtained under assumption of dissociation from the highest vibrational level. Cut-off harmonic oscillator approximation for the diatomic molecules is assumed. It is shown that all reaction rates are the complex functions of the species densities. Analysis of a flow behind a shock wave is performed in a wide range of the flow parameters. It is shown that under strong non-equilibrium condition the dissociation rate is determined not by the dissociation probability, but by the vibration probability, since the excitation of highest vibrational levels is the bottleneck of dissociation process. This means that the procedure of obtaining the data on dissociation rates needs the accurate revision.

The Charge-State and Structural Stability of Peptides Conferred by Microsolvating Environments in Differential Mobility Spectrometry

The presence of solvent vapor in a differential mobility spectrometry (DMS) cell creates a microsolvating environment that can mitigate complications associated with field-induced heating. In the case of peptides, the microsolvation of protonation sites results in a stabilization of charge density through localized solvent clustering, sheltering the ion from collisional activation. Seeding the DMS carrier gas (N2) with a solvent vapor prevented nearly all field-induced fragmentation of the protonated peptides GGG, AAA, and the Lys-rich Polybia-MP1 (IDWKKLLDAAKQIL-NH2). Modeling the microsolvation propensity of protonated n-propylamine [PrNH3]+, a mimic of the Lys side chain and N-terminus, with common gas-phase modifiers (H2O, MeOH, EtOH, iPrOH, acetone, and MeCN) confirms that all solvent molecules form stable clusters at the site of protonation. Moreover, modeling populations of microsolvated clusters indicates that species containing protonated amine moieties exist as microsolvated species with one to six solvent ligands at all effective ion temperatures (Teff) accessible during a DMS experiment (ca. 375-600 K). Calculated Teff of protonated GGG, AAA, and Polybia-MPI using a modified two-temperature theory approach were up to 86 K cooler in DMS environments seeded with solvent vapor compared to pure N2 environments. Stabilizing effects were largely driven by an increase in the ion's apparent collision cross section and by evaporative cooling processes induced by the dynamic evaporation/condensation cycles incurred in the presence of an oscillating electric separation field. When the microsolvating partner was a protic solvent, abstraction of a proton from [MP1 + 3H]3+ to yield [MP1 + 2H]2+ was observed. This result was attributed to the proclivity of protic solvents to form hydrogen-bond networks with enhanced gas-phase basicity. Collectively, microsolvation provides analytes with a solvent "air bag," whereby charge reduction and microsolvation-induced stabilization were shown to shelter peptides from the fragmentation induced by field heating and may play a role in preserving native-like ion configurations.

Two-temperature preparation method for PDMS-based canine training aids for explosives

Canine training aids based on vapor capture-and-release into a flexible polymer, polydimethylsiloxane (PDMS), have been used for in canine detection of explosives that have volatile or semi-volatile odorants. To enhance the rate of odor capture for less volatile targets, two temperatures are used for aid preparation. By using an elevated temperature for the target explosive, the amount of vapor is enhanced, increasing the production of the characteristic odor profile. The polymeric adsorbent is maintained at a cool temperature, favoring vapor capture. The success of this two-temperature approach is demonstrated for training aids targeting the low volatility explosive TNT using SPME (solid-phase microextraction) headspace analysis. In addition, the effect of using two temperatures on preparing training aids based on TNT and its more volatile impurities 2,4-DNT and 2,6-DNT are evaluated in canine trials. A thermal pretreatment to minimize the non-target odors in the PDMS polymer is presented.

Magnetocaloric properties of spheroidal La(Fe,Mn,Si)13H[formula omitted] granules and their performance in epoxy-bonded active magnetic regenerators

Magnetic cooling has been researched as an alternative near room-temperature refrigeration technology for the past two decades. However, one of its greatest limitations is the lack of materials which can be properly shaped for optimal thermal-hydraulic performance while maintaining a substantial magnetocaloric effect at moderate fields (i.e., between 1 and 2 T) and remaining mechanically (and chemically) stable. In this paper, we thoroughly characterized a commercially accessible La(Fe,Mn,Si)13Hy material (available as spheroidal granules), in terms of its magnetocaloric properties and thermal-hydraulic performance in an Active Magnetic Regenerator (AMR) device. The regenerator bed built from epoxy-bonded spheroidal particles endured dozens of hours of operation in AMR cycles without any noticeable degradation of their mechanical integrity, thanks to a comparatively larger α−Fe content and granule porosity. As for the magnetic cooling performance, the AMR reached zero-span specific cooling capacities as high as 300 W kg−1. A 1-D two-temperature approach AMR model predicted the performance data with average deviations smaller than 7% for the zero-span specific cooling capacity and 5% for the AMR pressure drop.

Makemake + Sedna: A Continuum Radiation Transport and Photoionization Framework for Astrophysical Newtonian Fluid Dynamics

Astrophysical fluid flow studies often encompass a wide range of physical processes to account for the complexity of the system under consideration. In addition to gravity, a proper treatment of thermodynamic processes via continuum radiation transport and/or photoionization is becoming the state of the art. We present a major update of our continuum radiation transport module, Makemake, and a newly developed module for photoionization, Sedna, coupled to the magnetohydrodynamics code PLUTO. These extensions are currently not publicly available; access can be granted on a case-by-case basis. We explain the theoretical background of the equations solved, elaborate on the numerical layout, and present a comprehensive test suite for radiation–ionization hydrodynamics. The grid-based radiation and ionization modules support static one-dimensional, two-dimensional, and three-dimensional grids in Cartesian, cylindrical, and spherical coordinates. Each module splits the radiation field into two components, one originating directly from a point source—solved using a ray-tracing scheme—and a diffuse component—solved with a three-dimensional flux-limited diffusion (FLD) solver. The FLD solver for the continuum radiation transport makes use of either the equilibrium one-temperature approach or the linearization two-temperature approach. The FLD solver for the photoionization module enables accounting for the temporal evolution of the radiation field from direct recombination of free electrons into hydrogen's ground state as an alternative to on-the-spot approximation. A brief overview of completed and ongoing scientific studies is given to explicitly illustrate the multipurpose nature of the numerical framework presented.

Similarity in ruthenium damage induced by photons with different energies: From visible light to hard X-rays

We performed combined experimental and computational research on damage processes in ruthenium thin films induced by femtosecond lasers with various photon energies. We present an experiment with an optical laser at normal incidence conditions and compare it with previously reported experiments at grazing incidence conditions with XUV and hard X-ray photons, covering a large range of photon energies. Analysis of ablation craters in Ru shows very similar crater morphology and depth of about 10–20 nm for all considered irradiation conditions. Simulations of light-matter interactions are performed with our combined Monte Carlo and two-temperature hydrodynamics approach. The simulation results show that the primal cause of eventual ablation is Auger decay of core-shell holes created after absorption of XUV and hard X-ray photons in the vicinity of ruthenium surface. They lead to the creation of many low-energy electrons which consequently release the absorbed energy near the surface, resembling the optical irradiation case. Similar absorbed energy distributions in the top part of ruthenium induce a similar thermo-mechanical response and, therefore, similar ablation process. Our results suggest that such mechanism is universal in a wide range of photon energies at grazing incidence conditions, when the photon absorption depth is smaller than the photoelectrons range.

Microscopic analysis of heat transfer in I1/N/I2 heterogeneous nanostructures at low temperatures

A kinetic approach to analytically considering the lateral heat transfer through a metal layer located between two massive dielectrics. The effective transverse thermal conductivity of such a layered system with an arbitrary thickness of the metal layer is calculated, and the thicknesses at which the size effect is manifested in thermal conductivity, are found. The transverse heat transfer is also analyzed using the phenomenological two-temperature (2TM) model, i.e. in terms of electron and phonon temperatures. Comparing the results of 2TM and the microscopic approach allows us to find out the conditions under which the frequently used two-temperature approach is not applicable.

EXOCROSS: a general program for generating spectra from molecular line lists

EXOCROSS is a Fortran code for generating spectra (emission, absorption) and thermodynamic properties (partition function, specific heat, etc.) from molecular line lists. Input is taken in several formats, including ExoMol and HITRAN formats. EXOCROSS is efficiently parallelized showing also a high degree of vectorization. It can work with several line profiles such as Doppler, Lorentzian and Voigt and support several broadening schemes. Voigt profiles are handled by several methods allowing fast and accurate simulations. Two of these methods are new. EXOCROSS is also capable of working with the recently proposed method of super-lines. It supports calculations of lifetimes, cooling functions, specific heats and other properties. EXOCROSS can be used to convert between different formats, such as HITRAN, ExoMol and Phoenix. It is capable of simulating non-LTE spectra using a simple two-temperature approach. Different electronic, vibronic or vibrational bands can be simulated separately using an efficient filtering scheme based on the quantum numbers.

A two-temperature six-moment approach to the shock wave problem in a polyatomic gas

Starting from a two-velocity version of a recently derived six-moment closure of the kinetic Boltzmann description of a polyatomic gas, based on a discrete structure of internal energy levels, the classical shock wave problem is analyzed in some detail. Explicit analytical results are achieved under a simplifying assumption equivalent to the standard approximation of polytropic gases, to which this paper is generally restricted. In particular, existence of smooth solutions, occurrence of jumps in the kinetic and excitation temperatures, and possible temperature overshooting are emphasized.

The vertical structure of the boundary layer around compact objects

Context. Mass transfer due to Roche lobe overflow leads to the formation of an accretion disk around a weakly magnetized white dwarf (WD) in cataclysmic variables. At the inner edge of the disk, the gas comes upon the surface of the WD and has to get rid of its excess kinetic energy in order to settle down on the more slowly rotating outer stellar layers. This region is known as the boundary layer (BL). Aims. In this work we investigate the vertical structure of the BL, which is still poorly understood. We shall provide details of the basic structure of the two-dimensional (2D) BL and how it depends on parameters such as stellar mass and rotation rate, as well as the mass-accretion rate. We further investigate the destination of the disk material and compare our results with previous one-dimensional (1D) simulations. Methods. We solve the 2D equations of radiation hydrodynamics in a spherical geometry using a parallel grid-based code that employs a Riemann solver. The radiation energy is considered in the two-temperature approach with a radiative flux given by the flux-limited diffusion approximation. Results. The BL around a non-rotating WD is characterized by a steep drop in angular velocity over a width of only 1% of the stellar radius, a heavy depletion of mass, and a high temperature (500 000 K) as a consequence of the strong shear. Variations in Om_star, M_star, and M_dot influence the extent of the changes of the variables in the BL but not the general structure. Depending on Om_star, the disk material travels up to the poles or is halted at a certain latitude. The extent of mixing with the stellar material also depends on Om_star. We find that the 1D approximation matches the 2D data well, apart from an underestimated temperature.

Nonthermal model for ultrafast laser-induced plasma generation around a plasmonic nanorod

The excitation of plasmonic gold nanoparticles by ultrashort laser pulses can trigger interesting electron-based effects in biological media such as production of reactive oxygen species or cell membrane optoporation. In order to better understand the optical and thermal processes at play, we modeled the interaction of a subpicosecond, near-infrared laser pulse with a gold nanorod in water. A nonthermal model is used and compared to a simple two-temperature thermal approach. For both models, the computation of the transient optical response reveals strong plasmon damping. Electron emission from the metal into the water is also calculated in a specific way for each model. The dynamics of the resulting local plasma in water is assessed by a rate equation model. While both approaches provide similar results for the transient optical properties, the simple thermal one is unable to properly describe electron emission and plasma generation. The latter is shown to mostly originate from electron-electron thermionic emission and photoemission from the metal. Taking into account the transient optical response is mandatory to properly calculate both electron emission and local plasma dynamics in water.

Melting of aluminum with ideal or defect lattice: Molecular dynamics simulations with accounting of electronic heat conductivity

In this work, the atomistic simulations of rapid melting of aluminum are performed. We use the two-temperature approach separately describing the ionic and electronic subsystems of crystal. Both ideal and defect states of initial lattice are considered. The dependence of melting temperature on pressure is investigated in the simulations of thermal equilibrium establishment in the systems with plate interphase boundaries. Non-equilibrium melting of aluminum is studied in simulations with the constant rate of heat energy supply. The maximal temperatures of overheated material before complete melting are obtained in dependence of energy supply rate. Presence of initial defects of lattice substantially decreases the overheating of material. Electronic heat conductivity significantly accelerates the thermal equilibrium establishment in systems with interphase boundaries and decreases the drop of temperature after beginning of melting in the systems with constant rate of heating.

A Thermo-Mechanical Model for a Counterflow Biomass Gasifier

This article presents a thermo-mechanical approach to investigate heat transfer between solid and fluid phases in a model gasifier. A two-temperature equation approach is applied in addition to a macroscopic model for laminar flow through a porous moving bed. Transport equations are discretized using the control-volume method and the system of algebraic equations is relaxed via the SIMPLE algorithm. The effects on inter-phase heat transfer due to variation of medium permeability, thermal conductivity and thermal capacity are analyzed. Results indicate that for smaller medium permeabilities, as well as for higher solid-to-fluid thermal capacity and thermal conductivity ratios, enhancement of heat transfer between phases is observed.

Rippled area formed by surface plasmon polaritons upon femtosecond laser double-pulse irradiation of silicon

The formation of near-wavelength laser-induced periodic surface structures (LIPSS) on silicon upon irradiation with sequences of Ti:sapphire femtosecond laser pulse pairs (pulse duration 150 fs, central wavelength 800 nm) is studied theoretically. For this purpose, the nonlinear generation of conduction band electrons in silicon and their relaxation is numerically calculated using a two-temperature model approach including intrapulse changes of optical properties, transport, diffusion and recombination effects. Following the idea that surface plasmon polaritons (SPP) can be excited when the material turns from semiconducting to metallic state, the "SPP active area" is calculated as function of fluence and double-pulse delay up to several picoseconds and compared to the experimentally observed rippled surface areas. Evidence is presented that multi-photon absorption explains the large increase of the rippled area for temporally overlapping pulses. For longer double-pulse delays, relevant relaxation processes are identified. The results demonstrate that femtosecond LIPSS on silicon are caused by the excitation of SPP and can be controlled by temporal pulse shaping.