Igor A. Abrikosov Theoretical Physics, Department of Physics, Chemistry and Biology, Linköping University, Sweden

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1 Ab initio simulations of materials properties: from fundamental theory towards materials design Igor A. Abrikosov Theoretical Physics Department of Physics Chemistry and Biology Linköping University Sweden

2 Theory and Modeling Theoretical Physics Computational Physics Bioinformatics Computational Biology Theoretical Biology Igor Abrikosov Sven Stafström Bengt Persson Jesper Tegner Bo Ebenman

3 Igor Abrikosov Bo Sernelius Theoretical Physics Igor Abrikosov Professor Ab initio electronic structure theory Materials simulations Mesoscopic physics semiconductor structures in the quantum regime transport and chaos Understanding of fundamental molecular interactions Dynamical simulations of metallic heterostructures Energy localization in descrete systems Non-linear dynamics of anharmonic lattices Karl-Fredrik Berggren Magnus Johansson Sergei Simak Leonid Pourovskii Irina Yakimenko Ferenc Tasnadi Peter Münger

4 Students and Postdoctoral Fellows (totally 46 PhDs from Theoretical Physics): Hans Lind Marcus Ekholm Olga Vekilova Tobias Marten Postdoc Olle Hellman Peter Steneteg Prof. Eyvaz Isaev ALVA lector Björn Alling Assistant Professor Dr. Arkady Mikhaylushkin ALVA lectro

5 Prof. Igor A. Abrikosov Head of Theory and Modelling Division IFM Linköping University Sweden Electronic Theory of Materials Properties Basic research Applied Studies Methodological developments Properties vs external parameters Theory of magnetism (INVA effect) Materials for nuclear Hard coatings waste disposal Environmentally friendly materials Magnetism for nanotechnology

6 Linköping KTH

7 DECISION Your application has been granted in the manner described below HPCN: Akka 30 x 000 core hours/month NSC: Neolith 30 x 000 core hours/month Kappa 0 x 000 core hours/month UPPMAX: Kalkyl 0 x 000 core hours/month LUNAC: Platon 0 x 000 core hours/month C3SE: Beda 0 x 000 core hours/month PDC: Ferlin 60 x 000 core hours/month Lindgren 500 x 000 core hours/month

8 INALLOY toolkit Coherent potential approximation: KK-ASA basis set Exact Muffin-Tin Orbitals (EMTO) basis set Screened Impurity Model for charge fluctuations Model treatment of the local lattice relaxations Locally self-consistent Green s function method an O(N) method that works for metals Conventional band structure methods (VASP Quantum Espresso) DMFT implementation in FLAPW Multiscale modeling based on Hamiltonians with parameters determined ab initio

9 Density Functional Theory (DFT) ) ( ) ( ) ( M M M N N N N N N r r r V N i i m H r r r el many E r r r H σ σ σ σ σ σ σ σ σ + = = Ψ = Ψ h = + + = + = = occ r v v v r eff v r eff v m eff H r el one r eff H XC EXT H ψ ψ σ ρ ρ ρ ρ σ ρ σ ρ σ ψ ε σ ψ * )... ( ] [ ] [ ] [ )]... ( [ )]... ( [ )... ( )... ( M M M M M h

10 Density Functional Theory (DFT) W. Kohn

11 A. V. uban and I. A. Abrikosov ep. Prog. Phys (008). 990s: LDAGGA LDA+U 000+: DMFT hybrid etc VASP WienkCASTEP ABINIT KK EMTO etc. + V KS (x... N m I ) φ i (x... N e I ) = ε i φ i (x... N I ) h Supercell CPA O(N) AIMD etc. It is NOT a trivial task to run ab initio software!

12 CoSn S. I. Simak U. Häußermann I. A. Abrikosov et al. Phys. ev. Lett (997)

13 From T. S. Duffy Nature (004) ecent seismological model of the Earth

14 From Vocadlo et al. Phys. Earth Planet. Sci. 7 3 (000) Structural complexity: pure Fe

15 Structural complexity: pure Fe A. B. Belonoshko. Ahuja and B. Johansson Nature (003); L. Vocadlo et al. Nature (003): ΔG bcc-hcp ~ mev A. Mikhailushkin et al. Phys. ev. Lett (007) ΔG fcc-hcp ~ -(3-5) mev. fcc? A. Mikhailushkin et al. Phys. ev. B (009) From Vocadlo et al. Phys. Earth Planet. Sci. 7 3 (000)

16 Ab initio molecular dynamics simulations of Fe-rich FeNi alloy with the bcc crystal structure simulated with an SQS. P=300 GPa T=6000 K + V KS (x... N m I ) φ i (x... N e I ) = ε i φ i (x... N I ) h

17 4000 Melt Shen et al. 004 Lin et al. 00 Boehler 993 HP-bcc 3000 Temperature K 000 fcc 000 bcc hcp L. Dubrovinsky... I. A. Abrikosov Science (007) Pressure GPa

18 A. V. uban and I. A. Abrikosov ep. Prog. Phys (008). 990s: LDAGGA LDA+U 000+: DMFT hybrid etc VASP WienkCASTEP ABINIT KK EMTO etc. + V KS (x... N m I ) φ i (x... N e I ) = ε i φ i (x... N I ) h Supercell CPA O(N) AIMD etc. It is NOT a trivial task to run ab initio software!

19 [ ev. Mod. Phys (996)]

20 DMFT calculations: FLAPW implementation [M. Aichhorn et al. PB (009)] continuous-time quantum Monte Carlo impurity solver Wannier-like functions for the Fe-3d shell U varied in the range from.0 to 3. ev J=0.9 ev

21 V = 67.5 a.u. 3 /at DMFT LDA

22 V = 70 a.u. 3 /at

23 V = 67.5 a.u. 3 /at

24 V = 65 a.u. 3 /at

25 V = 6.5 a.u. 3 /at

26 V = 60 a.u. 3 /at

27 Optimization of ionic conductivity in doped ceria CeO is known to be good solid elictrolyte when it is doped with cations of lower valence than the host cation. Attractive electrolyte for solid-oxide fuel cells It is important to optimize the ionic conductivity in order to decrease the operation temperature

28 Activation energy for diffusion E a determines the ionic conductivity (σ): E = a σ σ 0 T exp kbt E = E + a ass E m D. A. Andersson S. I. Simak N. V. Skorodumova I. A. Abrikosov and B. Johansson PNAS (006)

29 Confirmed experimentally: S. Omar E. D. Wachsman Activation energy for diffusion and J. C. Nino Appl. Phys. Lett (007). E a determines the ionic conductivity (σ): E = a σ σ 0 T exp kbt E = E + a ass E m

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31 Dramatic advances in theory and algorithms In Computational Materials Science the amplification from intellect (new theory algorithms and insights) is at least equal to the speed -up from hardware E0 E9 E8 E7 relative performance Moore s law computer speed David Landau: UGA elative performance increase of Ising model simulations ( ) compared the normalized speed of the computers ( ) the simulations were executed on. The dashed line is a schematic of the increase in peak performance of the fastest supercomputers since 97.