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Electronic stopping power of ions in insulator as calculated by TD-DFT

Electronic stopping power of ions in insulator as calculated by TD-DFT. Emilio Artacho. Department of Earth Sciences University of Cambridge. Miguel Pruneda Physics, UC Berkeley. Collaborators . Donostia International Physics Centre Daniel Sanchez-Portal (implementation) Andres Arnau

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Electronic stopping power of ions in insulator as calculated by TD-DFT

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  1. Electronic stopping power of ions in insulator as calculated by TD-DFT Emilio Artacho Department of Earth Sciences University of Cambridge

  2. Miguel Pruneda Physics, UC Berkeley Collaborators Donostia International Physics Centre Daniel Sanchez-Portal (implementation) Andres Arnau Inaki Juaristi Pedro Echenique & Discussions with Txema Pitarke & Thanks to Peter Bauer(Linz, Austria) Thanks to the Miller Institute at UCB

  3. Immobilisation of nuclear waste by dilution in ceramics SYNtheticROCkswith appropriate “minerals” to host high level nuclear waste Research in durability: We need them to last for ~ 1My Resistance to radiation damage Zircons have contained uranium for billions of years

  4. Durability: Radiation damage α-particle ~ 5 MeV α-decay process • It causes: • Amorphisation • (metamict) • Swelling • Cracks • Leaching Recoil ~ 100 keV Zircon: model study: old natural samples

  5. Recoil damage: amorphisation zircon K. Trachenko & M. T. Dove, with empirical potentials

  6. Electrons heat up: effect on the material? Effect on the simulations? The ion moving in the solid transmits energy to electrons. How much? How? Where? What consequences does it have? Coupled dynamics of both electrons & nuclei (realistic simulation demands ~ 2M atoms)

  7. Multiscale: Different timescales • this study (electronic excitation) • electron-phonon coupling + • heat conductivities for the electron • and phonon subsystems • Continuum description of excess energy • Eel ( r,t) First: how much energy is it pumped to the electrons per unit time

  8. High v: Bethe Low (and intermediate) v: Fine underst. Metals, P.T. Energy transfered to electrons: Measured by electronic stopping power dE/dx (eV/Ang) v (atomic units) 100 keV Recoiling Th nucleus: v = 0.1 a.u.

  9. Electronic versus nuclear stopping Metals: S ~ v for v -> 0 Nuclear stopping dominates at low velocities

  10. Stopping in noble gases Scattering cross section of H+ on He and Ne Experiments: JT Park & EJ Zimmerman, Phys. Rev.131, 1611 (1963) A Schiefermuller et al. Phys. Rev. A48, 4467 (1993) Calculations:R Cabrera-Trujillo et al., PRL 84, 5300 (2000) Nuclear stopping

  11. Electronic stopping in insulators: different? C Auth et a. PRL 81, 4831 (1998) Protons onto LiF: (5 keV ~ v = 1 a.u.) Grazing angle (on the surface) Threshold

  12. Electronic stopping power in LiF Across thin films H V = 0.4 a.u. dE/dx = 0.12 a.u. = 6.2 eV/Ang (But 1.6 error) = 3.9 eV/Ang Juaristi et al, PRL 84, 2124 (2000) No threshold

  13. Protons and antiprotons into LiF thin films “Antiproton Stopping at Low Energies: Confirmation of Velocity-Proportional Stopping Power” SP Møller et al. PRL 88, 193201 (2002) & PRL 93, 042512 (2004) No threshold

  14. Protons into LiF thin films again M. Draxler et al, PRL95,113201 (2005) Scale: v = 0.1 a.u. => Stopping ~ 1 eV/Ang Threshold

  15. Strict threshold: 1/2 (me +mh)vc2 = Egap Threshold: what to expect? TD Pertub. Th. (weak projectile potential) e-h excitations such that  / k = v Exc: V(q=k)

  16. TD-DFT: Our approach • Supercell of insulator’s bulk • Periodic boundary conditions • Density functional theory • Add external charge (potential) • Move it and follow electron wave-functions with Time-Dependent DFT

  17. The SIESTA method Linear-scaling DFT based on NAOs (Numerical Atomic Orbitals) P. Ordejon, E. Artacho & J. M. Soler , Phys. Rev. B 53, R10441 (1996) • Born-Oppenheimer (relaxations, mol. dynamics) • DFT (LDA, GGA) • Pseudopotentials (norm conserving, factorised) • Numerical atomic orbitals as basis (finite range) • Numerical evaluation of matrix elements (3D grid) Implemented in the SIESTA program J. M. Soler, E. Artacho, J. D. Gale, A. Garcia, J. Junquera, P. Ordejon & D. Sanchez-Portal, J. Phys.: Condens. Matter14, 2745 (2002)

  18. Time dependent DFT Usual (stationary) DFT: Time-dependent DFT: Neither forces on atoms (no MD), nor moving basis

  19. Real time evolution of the density • SIESTA (LCAO) • Evolution of the TD-KS equations: Crank-Nicholson

  20. Energy as a function of distance: LiF Quite stationary!Short transient, no obvious oscillation

  21. Rate of energy transfer: electronic stopping power Protons and antiprotons through LiF Threshold ~ 0.2 a.u. (exp ~ 0.1) Ratio SPp/SPa ~ 2.4 (exp ~ 2.1)

  22. Rate of energy transfer: electronic stopping power Protons and antiprotons through LiF Threshold ~ 0.2 a.u. (exp ~ 0.1) Ratio SPp/SPa ~ 2.4 (exp ~ 2.1) Absolute value: improve basis; sp basis along trajectory (for p)

  23. Rate of energy transfer: electronic stopping power Protons and antiprotons through LiF Threshold ~ 0.2 a.u. (exp ~ 0.1) Ratio SPp/SPa ~ 2.4 (exp ~ 2.1) Absolute value ~ 20-50% too small as compared to experiment But: Th is channelling, exp is average

  24. Stopping power dependence on charge For small positive charges,the linear regime is recovered. dE/dx ~ q2 v (small perturbation)

  25. Evolution of the charge on nearby Li atoms v = 1 au Nearest neighb. v = 0 2nd nearest neighb. Position of projectile along trajectory (x=0 closest to nearest Li) Screening of charge enhanced at finite v Extremely short-ranged mechanism

  26. Locality in the electronic stopping power Protons in LiF Compare bulk with small cluster Li6F5+

  27. Further Channeling vs average trajectories: Electronic stopping power in channels ~ average/2 JJ Dorado & F Flores, PRA 47, 3062 (1993) Combine nuclear & electron stopping Requires simultaneous dynamics. Hard technically and computationally (time scales) Charge states (momentum) Interesting. Right question to pose.

  28. Summary • Using TD-DFT for obtaining the energy transfer from moving ions to electrons in insulators. • New approach, complementary • Offers new kinds of information • Lots to do! Important: Recoiling velocity around threshold

  29. Funding

  30. Flat-band limit: Simple model

  31. Evolution of the charge

  32. Atomic Energies“Hamiltonian Population” Mulliken Atomic/Overlap Population Hamiltonian Atomic/Overlap Population: a way of defining “local energy” in our problem LCAO simplest version of energy density – R.M. Martin PRB-(‘92)

  33. Evolution of the local energy

  34. Flat-band limit: Simple model Gaussian perturbation as V0

  35. Dependence on basis set & other approx Dependence on technicalities (supercell size, numerical integrations, pseudos) But also on more fundamental aspects (Charge state, DFT kernel: instantaneous LDA)

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