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First principles studies of materials under extreme condition Tadashi Ogitsu

FADFT2007 ISSP 7/24/06. First principles studies of materials under extreme condition Tadashi Ogitsu. Quantum Simulations Group Lawrence Livermore National Laboratory. Collaborators. Andrea Trave, Alfredo Correa, Jonathan DuBois, Kyle Caspersen,

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First principles studies of materials under extreme condition Tadashi Ogitsu

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  1. FADFT2007 ISSP 7/24/06 First principles studies of materials under extreme conditionTadashi Ogitsu Quantum Simulations Group Lawrence Livermore National Laboratory

  2. Collaborators Andrea Trave, Alfredo Correa, Jonathan DuBois, Kyle Caspersen, Eric Schwegler, and Andrew Williamson (Physic Ventures) Lawrence Livermore National Laboratory (theory) Gillbert Collins, Andrew Ng, Yuan Ping Lawrence Livermore NationalLaboratory (experiment) David Prendergast Molecular Foundry, Lawrence Berkeley Laboratory François Gygi and Giulia Galli University of California, Davis Stanimir Bonev Dalhousie University, Canada Eamonn Murray and Steven Fahy Tyndall National Institute, University College, Ilreland David Fritz and David Reis University of Michigan Ann Arbor (experiments)

  3. Outline of my talk: • DFT: my viewpoint • Why we need large scale simulations? • Phase diagram of materials under pressure • Temperature and pressure are extremely high • Equilibrium property • Dynamical response of materials upon ultra fast laser pulse • Ultra fast (sub ps) time resolved measurement • Non-equilibrium dynamics (electrons and ions) • Non-adiabatic?

  4. DFT: my viewpoint • Rigorous theory for the ground state, but… • We need approximations (LDA/GGA, pseudopot) to apply it to a real system • The KS eigenvalues are not supposed to represent electron excitation in theory, while 104,000 papers on DFT band structure (as of 7/11/07) are found by google • So confusing… (as of April 1989) • Why justified for excited state? • Huge amount of literature seem to suggest qualitatively ok (sort of defacto standard) • For a certain limit, some theoretical requirement is satisfied (eg. Koopman’s theorem) Goal! Computational cost Tight binding DFT QMC Rigorousness Good cost efficiency made DFT popular, but need further improvement

  5. Why large scale simulations? • Complex material: elemental boron (8/1/07 at 17:00) • Finite size effects • Canonical ensemble • Long time scale simulations • A simple calculation could be expensive • Eg. 2() • Non-equilibrium (and/or non-adiabatic) dynamics?

  6. Phase diagram of materials under pressure: Significance of ab-initio approach • Phase boundaries are rich in physics • Crossing line of Gibbs free energies of different phases • Change in structure (static total energy) • Potential energy surface (ion dynamics -> entropy) • Electronic structure (direct and indirect) • Important applications in various sub-field of physics • Modeling of interior of planets • Fundamental questions in condensed matter physics • Designing a novel material

  7. Method: melting line calculation • Two-phase simulation method (nucleation is already introduced) • Ab initio method (GP and Qbox codes by Gygi at UC Davis) • Density Functional Theory with PBEGGA • Planewave expansion, nonlocal pseudo potential for ions • 432 atom cell, Ecut=45Ry, -point sampling T>Tmelt T<Tmelt J. Mei and J. W. Davenport, Phys. Rev. B 46, 21 (1992) A. Belonoshko, Geochim. Cosmochim. Acta 58, 4039 (1994) J. R. Morris, C.Z. Wang, K.M. Ho, and C.T. Chan, Phys. Rev. B 49, 3109 (1994)

  8. Ab-initio two-phase MD at P=100GPa T=2300K: melt T=2200K: solidify

  9. LiH melting lineOgitsu et al. PRL 91, 175502 (2003) • LiH: simple yet its phase diagram is not well understood • Ionic crystal with rocksalt structure (B1) • What is left? • Tmexp = 965 K • TmGGA = 795 K (18% lower than exp) • B1 phase stable up to 100GPa (exp) • No B2 (CsCl) phase found • All the other alkali hydride exhibit B1-B2 transition < 30GPa Liquid Solid (Rocksalt) X

  10. DFT DFT QMC QMC Quantum Monte Carlo Corrections to theDFT Melting Temperature of LiH (Tmdft=790K, Tmexp=965K) Solid LiH (T=TM) Liquid LiH (T=TM) -92.2 -91.4 -92.6 -91.8 DFT equilibrium volume Total Energy (au) -93.0 Internal Energy Correction -92.2 QMC equilibrium volume -93.4 -92.6 -93.0 -93.8 23 24 25 26 27 28 23.0 23.5 24.0 24.5 Simulation Cell Volume (au) Simulation Cell Volume (au) • QMC predicts corrections to the internal energy and equilibrium volume • These equation of state corrections are larger in the solid than the liquid • Preliminary results predict an increase in TM from 790K to 880K (exp=965K)

  11. Solid/solid phase boundary: Quasi Harmonic Approximation (QHA)Karki, Wentcovitch, Gironcoli, and Baroni, PRB 62, 14750 (2000) • Free energy surface of phases match at the phase boundary • Free energy surface, G(P,T), of solid can be well described by harmonic phonon model F (V,T) = U(V) + ZPE(V) + FH(V,T) G(P,T) =F(V,T)+PV; P = -dF/dV LiH: NaCl phase -point phonon (a) PRB 28 3415 (1983)

  12. LiH phase diagram Theory: • B1-B2 boundary determined by ab initio QHA method • B2-liquid boundary determined by ab initio two-phase method Experiments: • Low-T B1-B2 boundary is being explored by DAC experiments (Spring-8) • High-T B2-liquid boundary by isentrope experiments (LLNL)

  13. Property of LiH fluid under pressure • Strong correlation between Li and H dynamics • Velocity distributions reflect the mass difference • Diffusion constants of Li and H are almost the same • Dynamical H2 (Hn) formation observed at high temperature • Charge state of H2 in LiH fluid is nearly neutral • Ionicity of LiH fluid is weakened upon dynamical H2 formation

  14. Ab-initio two-phase method:Computational cost • Two approaches successfully mapped liquid/solid phase boundaries of materials in ab-initio level • Two-phase: Ogitsu et al. PRL 2003 • Potential switching: Sugino and Car PRL 1995 • Which is more cost efficient? • Two-phase method is computationally intensive, while potential switching method demands intensive human labor (many many MD runs on P, T and the switching parameter space) Example with LiH: Each two-phase simulation was roughly 2-10 ps MD run with 432 atoms cell In total, to map out the melting line for 0-200 GPa, the CPU cost equivalent to a half year with a linux cluster (128 cpu) was used (2002-2003) Note: low density costs more (nature of planewave + faster dynamics at higher pressure)

  15. Summary on LiH phase diagram • It has been demonstrated first time that ab-initio two-phase method is feasible • LDA/GGA seems to underestimate the melting temperature • QMC corrections look promissing • B1/B2/liquid phase boundaries of LiH have been calculated for a wide range of P, T space • Property of compressed LiH fluid has been studied from first-principles • Correlated Li and H dynamics • Dynamical Hn clustering yielding weakening of ionicity

  16. Group I Group VII Molecular hydrogen solid Atomic hydrogen solid bcc bcc Pressure r bcc Liquid bcc hcp structure - insulator bcc structure (?) - metal Metal Insulator bcc Large zero-point motion => possible low-T liquid state? [Brovman, Kagan, Kholas, JETP (1972)] bcc Two possible scenarios [N. Ashcroft, J Phys. Cond. Matt. (2000)] Liquid Insulator Metal Melting line of hydrogen Metallic hydrogen under pressure [Wigner and Huntington (1935)]

  17. H H H H H2 A hypothetical scenario towards the low-T liquid liquid liquid: H liquid: H2 solid solid

  18. Measured melting line of hydrogen: Gregoryanz et al. PRL 90 175701 (2003) ? Exp can reach the P, T range of interest Exp could not locate the melting point above 44GPa

  19. Ab initio melting curve supports low-T liquid scenario Experiments: Gregoryanz et al. PRL (2003). Datchi et al. PRB (2000). Diatschenko et al PRB (1985). Theory: Bonev, Schwegler, Ogitsu and Galli, Nature, 2004. Non-molecular fluid Metallic super fluid at around 400GPa? Babaev, Subda and Ashcroft, Nature 2004 Babaev and Ashcroft, PRL 2005 Molecular fluid Solid

  20. Reminder: experiment can reach to the P, T rangeCould we suggest how to detect melting? • Change in distribution comes from the tail of MLWF spread • Net overlap is changing at high P • Stronger asymmetry observed in liquid MLWFs at high P • Suggest enhanced IR activity in liquid solid liquid MLWF spread distribution at Tm

  21. Summary on the melting line of hydrogen • Maximum in melting line of hydrogen is found by ab-initio two-phase method • The negative slope is explained by weakening of effective inter molecular potential. Dissociation of molecule is not necessary • IR activity measurement might be able to detect the high pressure melting curve (given that the condition is experimentally accessible)

  22. Why higher pressure phase has not been well understood? Limit in computational approach • Does LDA/GGA work? • ~200GPa might be OK (Pickard and Needs, Nature Physics Jul, 2007) • No well established reference system to compare with • Quantum effect of proton • DFT/path-integral (maybe DMC/path-integral) is feasible, however, within adiabatic approx. • Full (elec & ion) path-integral: lowest temperature record is about 5000K • Non-adiabatic electron-phonon coupling • Crucial if metallic Breakthrough in computational approach needed

  23. What is limiting high pressure experiments? • To reach high P, T itself is challenging (diamonds break) • Small sample • Probe signal needs to go through diamond/gasket • S/N ratio problem • Direct structural measurement (X-ray, neutron) cannot reach too high pressure • X-ray cannot determine the orientation of H2 (X-ray scatter off electrons) • Most reliable experimental techniques, Raman/IR, provide only indirect information to the structure • Hidden challenge for theory: How do we know the structure? [Pickard and Needs, Nature Phys 2007] By Russel Hemley at Carnegie Institution

  24. Dynamical response of materials upon ultra fast laser pulse • Advance in the pump and probe experiments made sub pico second time resolution possible with • Ultra-fast Electron Diffraction • Dielectric function measurement • Raman/IR • X-ray • Time evolution of phase transition, chemical reaction (breaking/making a bond) can be directly measured! • Big challenge for theory since • Non-equilibrium • Adiabatic approximation might be breaking down Time evolution of electron diffraction of Al At t = 0, the laser pulse (70 mJ/cm2) is induced Siwik et al. Science302, 1382 (2003)

  25. The Jupiter Laser Facility at LLNL Probe Pump Transmitted Probe Reflected Probe

  26. Schematics of experiment Pump laser pulse t T* R* 50nm thick free standing gold foil Probe laser pulse Broad band =400~800 nm • t=0: electrons are excited by 3.1eV photons • t>0: Transmission and Reflection (T*,R*) gives 2() • Electronic states evolve (Auger, el-el and el-ph scattering) • Atomic configuration evolves (energy dissipation from electrons)

  27. For 1.2-4 ps, 2(), does not change (quasi steady state) The inter-band transition peak at 2.5eV is present in the quasi steady state The peak is enhanced from ambient condition Time evolution of 2() of 50nm Au film triggered by a laser pulse [Ping et al, PRL 96, 25503 (2006)] • Fine time resolution, simple and reliable technology • Interpretation of results is challenging due to missing information • Electronic states • Atomic configurations

  28. Parallel pair of bands (ll1) contribute on a peak in 2() • Inter-band transition no-momentum change • Kubo-Greenwood formalism • Intra-band transition require change in momentum • Electron-phonon coupling • The transportation function (2F()) to DC conductivity and the Drude form Ef

  29. Current formalisms for 2() does not describe low and high energy regimes seamlessly • Inter-band transition no-momentum change • Kubo-Greenwood formalism • Intra-band transition require change in momentum • Electron-phonon coupling • The transportation function (2F()) to DC conductivity and the Drude form Ef Super-cell + Kubo-Greenwood No-inelastic el-ph scattering counted • In a disordered system, elastic scattering becomes dominant, therefore, Kubo-Greenwood formula is good enough • The quasi-steady state of warm dense gold: ordered or disordered? • The inter-band transition peak suggests presence of long range order

  30. Procedure of ab-initio 2() calculation Two temperature model: • Underlying assumptions: • Electrons are in thermal equilibrium • Heating of ions is slow (el-ph coupling of gold is small) • Ions are also in thermal equilibrium Kubo-Greenwood with elevated Tel Tion(t) Ab-initio MD at T 2() Tel(t=0) + el-ph Note: TD-DFT-MD plus non-adiabatic correction might provide the direct answer

  31. Comparison of exp and ab-initio2() • No enhancement of inter-band peak observed in ab-initio2() • Missing el-ph coupling (eg. intra-band transition)? • Thermalized electrons (Fermi distribution) incorrect? • Inter-band peak implies long range order of lattice? Note: single 2 calculation generate 1TB data

  32. Summary • Ab-initio2() does not agree with experimental measurement • No inter-band peak above 2eV • There are many assumptions to be re-examined • Electron distribution function • Application of Kubo-Greenwood formalism to small  (Drude) regime • Electron-phonon coupling constant upon excited electrons

  33. How fast do electrons thermalize? E=120J/cm2 • There seems to be a general consensus on electronic thermalization time scale of several hundred femto second • Only one quantitative experimental measurement on gold found [PRB 46, 13592 (1992)] • Residual in high energy is not explained • Energy density is very small compared to Ping’s experiments • Residual seems to grow as a function of input energy E=300J/cm2 Thermalization time scale as a function of input energy should be re-examined

  34. Concluding remark • Physics under extreme condition provide exciting and challenging problems to computational physics community • Significance of computational approach in high-pressure physics has been and will be growing • Ultra-fast pump and probe experimental technique provide exciting new physics that challenges theory. Novel computational approaches will be needed • Ab-initio MD beyond BO approximation • Seamless transport calculation formalism (elastic and in-elastic el-ph scattering)

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