Nonlinear stopping power of an electron gas for slow ions

Echenique, Pedro M.; Nieminen, Risto M.; Ashley, J. C.; Ritchie, R.H.

doi:10.1103/physreva.33.897

Cited by 367 publications

(194 citation statements)

References 32 publications

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“…This friction force acting on the gas-phase atom, −ηðr i Þ_ r i , is evaluated in the local density friction approximation (LDFA) [21]. The latter uses, at each time step, the friction coefficient ηðr i Þ of the atom embedded in a homogeneous free electron gas [31][32][33] with density equal to the ab initio electron density of the bare surface at the position r i of the gas-phase atom. This methodology, which we have implemented in the VASP package based on density functional theory (DFT) [34], is used here for the first time in combination with AIMD.…”

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confidence: 99%

Electronic Friction Dominates Hydrogen Hot-Atom Relaxation on Pd(100)

et al. 2014

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We study the dynamics of transient hot H atoms on Pd(100) that originated from dissociative adsorption of H 2 . The methodology developed here, denoted AIMDEF, consists of ab initio molecular dynamics simulations that include a friction force to account for the energy transfer to the electronic system. We find that the excitation of electron-hole pairs is the main channel for energy dissipation, which happens at a rate that is five times faster than energy transfer into Pd lattice motion. Our results show that electronic excitations may constitute the dominant dissipation channel in the relaxation of hot atoms on surfaces. DOI: 10.1103/PhysRevLett.112.103203 PACS numbers: 68.43.-h, 34.35.+a, 34.50.Bw, 82.20.Gk Electron-hole (e-h) pair excitations are an unquestioned efficient energy drain in the interaction of fast atoms with solids and surfaces [1][2][3][4]. In contrast, the relevance of this dissipation channel in gas-surface interactions that involve energies up to a few eV is not so clear. It depends not only on the specific system, but also on the elementary process considered, as shown by different studies on scattering [5][6][7][8][9][10][11][12] and adsorption [6,[13][14][15][16][17][18][19][20][21][22][23][24][25][26] of atoms and molecules on surfaces. Low-energy e-h pair excitations have been detected as chemicurrents on Schottky diode devices during the chemisorption of atomic and molecular species on metals [13][14][15]. The correlation found between chemicurrent intensities and adsorption energies is a strong indication that a large fraction of the energy dissipated in both the dissociative and nondissociative adsorption processes is used to excite e-h pairs. However, this strongly contrasts with examples showing that the dissociative adsorption is reasonably well described within the electronically adiabatic approach, which neglects the coupling between electronic excitations and the nuclear motion [6,[18][19][20]23,25], and that the effect of electronic energy dissipation seems negligible [21,24,26]. Therefore, a question that is raised here is at what stage of the dissociative adsorption process e-h pair excitations do become relevant.In a typical adsorption event, the incoming gas species gain additional kinetic energy when entering the attractive adsorption well. In the particular case of dissociative adsorption, this energy gain can lead to the formation of so-called "hot" atoms or fragments, with energies much larger than the corresponding thermal energies of the substrate atoms. The formed hot species will then propagate along the surface until they dissipate the excess kinetic energy and finally accommodate at a stable adsorption position. This stage of the dissociative adsorption process, where the relevance of e-h pair excitations has been traditionally neglected, is the focus of the present work.In this Letter we show that while e-h pair excitation may not be relevant on the molecule-bond-breaking time scale, it is an efficient dissipative channel in the subsequent relaxation of the...

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Electronic Friction Dominates Hydrogen Hot-Atom Relaxation on Pd(100)

et al. 2014

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“…1 highlights that, under the usual conditions relevant for gas-surface reactions, e-h pair excitations will dominate energy dissipation only for light atoms (γ 1). In principle, the kinetic energy of a free atom in a free electron gas (FEG) decays at a rate 2η/m A , where m A is the atom mass and its friction coefficient η depends nontrivially on the atomic number Z and the FEG density (Z oscillations) [32]. Nevertheless, for typical electron densities probed by hot atoms and molecules on metal surfaces, η varies slowly with Z [32][33][34] and thus the electronic decay rate is dominated by m A .…”

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Ab initiomolecular dynamics with simultaneous electron and phonon excitations: Application to the relaxation of hot atoms and molecules on metal surfaces

et al. 2015

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The relaxation dynamics of hot H, N, and N 2 on Pd(100), Ag(111), and Fe(110), respectively, is studied by means of ab initio molecular dynamics with electronic friction. This method is adapted here to account for the electron density changes caused by lattice vibrations, thus treating on an equal footing both electron-hole (e-h) pair and phonon excitations. We find that even if the latter increasingly dominate the heavier is the hot species, the contribution of e-h pairs is by no means negligible in these cases because it gains relevance at the last stage of the relaxation process. The quantitative details of energy dissipation depend on the interplay of the potential energy surface, electronic structure, and kinetic factors. DOI: 10.1103/PhysRevB.92.201411 PACS number(s): 82.65.+r, 34.35.+a, 34.50.Bw, 68.43.−h In dynamic gas-surface environments, where gas-phase atomic and molecular species impinge on the surface at energies of the order of up to a few eV, energy dissipation occurs by the excitation of electron-hole (e-h) pairs and the excitation of lattice vibrations, i.e., phonons [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In the adsorption processes of atomic and molecular species, dissociative as well as nondissociative, the species trapped by the surface gradually lose their energy until they become thermalized on the surface. The competition between the e-h pairs and phonon channels governs the relaxation dynamics of the transient hot species, and thus it plays a decisive role in the system reactivity properties. The reason is that it rules the traveled length and relaxation time of a hot atom or molecule on the surface and, consequently, the probability to undergo a recombination reaction with another adsorbate [18][19][20][21][22][23].Recent ab initio molecular dynamics (AIMD) simulations with electronic friction (AIMDEF) have shown that e-h pair excitations are the dominant relaxation mechanism for hot H atoms on Pd(100) that originate from the dissociative adsorption of H 2 [16]. More particularly, this channel dissipates energy at a five times faster rate than the phonon channel [10]. The two main reasons behind this behavior are the long H-Pd interaction time, of hundreds of fs, and the low adsorbate-tosurface atom mass ratio, γ = m H /m Pd = 0.0094. The case of H on Pd(100) represents a limiting case. For heavier adsorbates, the relative weight of e-h pairs and phonons in the energy loss is expected to vary. The energy transfer to the substrate will be determined not only by kinetic factors, such as the value of γ and the incidence conditions, but also by the topography of the multidimensional potential energy surface (PES) and the electronic structure details of the configurations probed along the relaxation trajectory.In this Rapid Communication, we investigate the relaxation dynamics of hot species in three adsorption scenarios that are representative of different energy loss regimes. We have chosen atomic N on Ag(111) (γ = 0.13), N 2 on Fe(110) (γ = 0.5), and the aforemen...

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“…7 Pioneering nonlinear calculations of the electronic energy loss of low-energy ions in an electron gas were performed by Echenique et al . 8 These authors computed the scattering cross section for a statically screened potential, which was determined self-consistently using densityfunctional theory (DFT). 9 These static-screening calculations have recently been extended to velocities approaching the Fermi velocity.…”

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Nonlinear interaction of charged particles with a free electron gas beyond the random-phase approximation

Río‐Gaztelurrutia¹,

Pitarke

2000

Phys. Rev. B

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A nonlinear description of the interaction of charged particles penetrating a solid has become of basic importance in the interpretation of a variety of physical phenomena. Here we develop a manybody theoretical approach to the quadratic decay rate, energy loss, and wake potential of charged particles moving in an interacting free electron gas. Explicit expressions for these quantities are obtained either within the random-phase approximation (RPA) or with full inclusion of short-range exchange and correlation effects. The Z 3 1 correction to the energy loss of ions is evaluated beyond RPA, in the limit of low velocities.When charged particles pass through a solid, energy can be lost to the medium through various types of elastic and inelastic collision processes. 1 While at relativistic velocities radiative losses may become important, for moving charged particles in the non-relativistic regime the energy loss is primarily due to electron-electron (e-e) interactions giving rise to the generation of electron-hole pairs, collective excitations such as plasmons, and innershell excitations and ionizations. Energy losses due to nuclear recoil are negligible, unless the projectile velocity is very small compared to the mean speed of electrons in the solid. 2 The inelastic decay rate of charged particles in a degenerate interacting free electron gas (FEG) has been calculated for many years in the first-Born approximation or, equivalently, within linear-response theory. This is a good approximation when the velocity of the projectile is much greater than the average velocity of target electrons. However, in the case of projectiles moving with smaller velocities, nonlinearities have been shown to play a key role in the interpretation of a variety of experiments. Energy-loss measurements have revealed differences, not present within linear-response theory, between the energy loss of protons and antiprotons. 3,4 Moreover, experimentally observed coherent double-plasmon excitations 5,6 cannot be described within linear-response theory, and nonlinearities may also play an important role in the electronic wake generated by moving ions in a FEG. 7 Pioneering nonlinear calculations of the electronic energy loss of low-energy ions in an electron gas were performed by Echenique et al . 8 These authors computed the scattering cross section for a statically screened potential, which was determined self-consistently using densityfunctional theory (DFT). 9 These static-screening calculations have recently been extended to velocities approaching the Fermi velocity. 10 Second-order perturbative calculations, which do not have the limitation of being restricted to low projectile velocities, have been reported by different authors with use of the random-phase approximation (RPA) and by treating the moving charged particle as a prescribed source of energy and momentum. [11][12][13][14][15] In this paper, we report a many-body theoretical approach to the quadratic decay rate, energy loss, and wake potential of charged particles moving in ...

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Nonlinear stopping power of an electron gas for slow ions

Cited by 367 publications

References 32 publications

Electronic Friction Dominates Hydrogen Hot-Atom Relaxation on Pd(100)

Electronic Friction Dominates Hydrogen Hot-Atom Relaxation on Pd(100)

Ab initiomolecular dynamics with simultaneous electron and phonon excitations: Application to the relaxation of hot atoms and molecules on metal surfaces

Nonlinear interaction of charged particles with a free electron gas beyond the random-phase approximation

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