Role of electrons in collision cascades in solids. I. Dissipative model

M. Caro, A. Tamm, A. A. Correa, and A. Caro

Phys. Rev. B 99, 174301 – Published 7 May 2019

Abstract

We present a detailed model for the nonadiabatic coupling between ions and electrons in energetic ion-solid interactions over a wide range of energies in concentrated solid-solution fcc alloys of the $3 d$ transition metals Ni, Co, Fe, and Cr. The model is based on general statistical mechanical principles and results in a stochastic modification of the classical nuclei motion which is parameterized by the first-principles calculation of a dissipation function produced by explicit time-dependent electronic evolution. This model provides a full picture of an entire collision process, from the ballistic to the thermal phases of a cascade, giving a detailed description of the energy exchange between ions and electrons till their final thermalization, removing in this way some ad hoc assumptions used in the state-of-the-art atomistic two-temperature models. This work is separated in two papers; in the present Part I, we report on the ab initio methodology used to translate stopping power and electron-phonon interaction into a parameterized dissipation function; Part II, to be published, addresses the nonadiabatic ion dynamics using our modified Langevin dynamics [Tamm et al. Phys. Rev. Lett. 120, 185501 (2018)] applying the dissipation functions developed here to specific collision cascade events.

Received 10 December 2018

DOI:https://doi.org/10.1103/PhysRevB.99.174301

Physics Subject Headings (PhySH)

Electronic structure First-principles calculations Ion impact & scattering Irradiation effects

Langevin algorithm Molecular dynamics Time-dependent DFT

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

M. Caro¹, A. Tamm^2,*, A. A. Correa^2,†, and A. Caro³

¹Department of Mechanical Engineering, Virginia Polytechnic Institute, Falls Church, Virginia 22043, USA
²Quantum Simulations Group, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
³College of Professional Studies, George Washington University, Ashburn, Virginia 20147, USA

^*Corresponding author: tamm3@llnl.gov
^†Corresponding author: correaa@llnl.gov

Role of electrons in collision cascades in solids. II. Molecular dynamics

A. Tamm, M. Caro, A. Caro, and A. A. Correa

Phys. Rev. B 99, 174302 (2019)

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Vol. 99, Iss. 17 — 1 May 2019

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Images

Figure 1
Energy transfer to the electronic system by a Ni projectile traveling in fcc Ni at $v = 0.3$ a.u., along three different trajectories. The dashed lines are obtained from TDDFT calculations and solid lines from the fitted MD model. The main plot represents the incommensurate trajectory where the site density is also added for informative purposes. The subset shows the energy transfer along the channel in the center (channel 4/16) and offset from the channel (channel 2/16).
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Figure 2
Electronic energy as a function of projectile position for Ni (black), Co (green), Fe (blue), Cr (yellow) projectiles at $v = 0.3 a . u .$ along rectilinear trajectories. Left column: Total nonadiabatic electronic energy. Center column: Adiabatic or BOA electronic energy. Right column: Difference between them. Top row: Along $〈 100 〉$ direction passing at the center of the channel. Center row: “Off-center” along $〈 100 〉$ direction with an impact parameter of $1.19 a . u .$ from closest atoms at the channel. Bottom row: Along an incommensurate direction starting at the center of a $〈 100 〉$ channel. The target is a quasirandom solid solution alloy of equiatomic NiCoFeCr.
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Figure 3
Energy transfer to electronic system as four different projectiles travel along three different trajectories through NiCoFeCr alloy. Also shown are electronic site densities (solid black line) along the trajectories. The element types selected for projectiles are Ni (purple), Co (green), Fe (blue) and Cr (yellow), with arbitrary vertical offsets. The trajectories studied are (a) channelling (4/16), (b) off-center channel (2/16), and (c) incommensurate. The data plotted with colored dotted lines are obtained from TDDFT calculations and the MD model predictions are shown with colored solid lines.
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Figure 4
Electronic density as a function of distance to the nucleus calculated for isolated atoms in vacuum, used for approximating electronic densities along the trajectory of projectiles in our model.
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Figure 5
Coupling parameter $β (ρ)$ for a Ni projectile moving with velocity $v = 0.3 a . u .$ into a fcc Ni target. The trajectories studied are channelling (4/16), off-center channel (2/16), and incommensurate, as a function of the unperturbed local electronic density $ρ_{0}$ , from Ref. [45].
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Figure 6
Dissipation function for each element of interest $α_{Ni,} Co, Fe, Cr (ρ)$ that parameterizes $W_{I J}$ in Eq. (4). These functions univocally relate unperturbed electronic density to dissipation, and represent a simplification to the real relationship such as that given in Fig. 5 and in Ref. [45].
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