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Ab-initio simulations of matter at extreme conditions: a window into the centers of planets Sandro Scandolo (ICTP, Trieste, Italy) Seminario Galileiano, Pisa 29/04/2010 Scandolo Scandolo & Jeanloz, & Jeanloz, American American Scientist Scientist 2003 (2003) Scandolo & Jeanloz, American Scientist (2003) Diamond Graphite High pressure in Physics 1935: prediction of metallic hydrogen Materials Science 1951: the first manmade diamonds Planetary Science 1991: Earth’s core conditions reproduced in the laboratory Shock waves Diamond anvil cell Scandolo & Jeanloz, American Scientist (2003) Quantum simulations: The “standard model” “Molecular dynamics” for atoms Ma = F = -dE/dR Schroedinger equation for electrons Hy = Ey R. Cohen Electron charge density in SiO2 stishovite “Ab-initio” molecular dynamics = e--e- interactions: Density Functional Theory e--nuclei interactions: Pseudopotentials Classical molecular dynamics in the potential energy surface generated by the electrons in their quantum ground state Asian-Pacific School, Beijing, July 2004 Quantum ESPRESSO is an open-source suite of computer codes for electronic-structure calculations and materials modeling. It is based on density-functional theory, plane waves, pseudopotentials. Features include: structural optimizations, phonons elastic constants ab-initio molecular dynamics and dielectric and Raman tensors infrared spectra NMR spectra etc… “First-principles codes for computational crystallography in the Quantum-ESPRESSO package” S. Scandolo et al., Z. Kristallogr. 220, 574 (2005) www.quantum-espresso.org Water and methane at planetary conditions 60% molar fraction phase diagram of water from first principles C. Cavazzoni et al., Science 283, 44 (1999) Experimental confirmation (?) of superionic phase: A. Goncharov et al., Phys. Rev. Lett. (2006) C. Cavazzoni et al., Science 283, 44 (1999) Superionic Water P = 150 GPa T = 2500 K Proton diffusion by hopping Oxygen sublattice remains crystalline Scandolo & Jeanloz, American Scientist (2003) H2O+CH4+NH3 Marvin Ross, “Diamonds in the sky” Nature (1981) Methane was found to dissociate under a shock wave Dissociation of methane at extreme (planetary) conditions F. Ancilotto et al., Science 275, 1288 (1997) Compressed methane Compressed methane after heating to 4000 K L.R. Benedetti et al., Science 283, 100 (1999) 92% molar fraction CH4 / H2O mixtures at extreme conditions 92% of the Uranus and Neptune ice layer Fluid inclusions, abiogenic formation of methane Prototype of hydrophobic interactions How corrosive is ionized water? Methane hydrate clathrates SIMULATIONS: 26 CH4 + 38 H2O at 4 different P-T CH4 / H2O mixtures at extreme conditions Choice of P-T points on the water phase diagram CH4 / H2O CH4 / H2O mixtures at extreme conditions Radial distribution functions CH4 / H2O mixtures at extreme conditions Softening of the C—O intermolecular potential CH4 / H2O mixtures at extreme conditions Distortion of CH4 at 15 GPa C...O distance about 3 A C-H bond becomes more ionic with increasing pressure Increased ionicity and thermal disorder cause CH4 to acquire a significant instantaneous dipole moment (about 0.5 D at 15 GPa) M.-S. Lee and S. Scandolo, in preparation Maximally localized molecular orbitals (Wannier functions) Methane / water mixture at 50 GPa Fast proton diffusion by proton hopping between adjacent molecules Methane “attacked” by ionized water Occasional formation of C-O bonds No formation of longer hydrocarbons (C-C bonds) M.-S. Lee and S. Scandolo, In preparation CH4 / H2O mixtures at extreme conditions Metallic behavior at milder conditions than pure water >90% molar fraction E. Wigner and H.B. Huntington “On the possibility of a metallic modification of hydrogen” J. Chem. Phys. 3, 764 (1935) Hemley and Mao, Rev Mod Phys ? ? • At which depth does hydrogen become an electrical conductor? • Is metallization accompanied by a sharp density change? Molecular to non-molecular transition S. Scandolo, Proc. Natl. Acad. Sci. USA, 2003 Is there a first-order phase transition inside Jupiter/Saturn? S. Scandolo, Proc. Natl. Acad. Sci. USA, 2003 Jupiter/Saturn isentrope Down to Earth… solid liquid How hot is the centre of the Earth? Inner core (solid Fe) Outer core (liquid Fe) Mantle The temperature at the inner core boundary coincides with the melting temperature of Fe at 330 GPa A number of mineral physics phenomena are difficult to address or even beyond reach for first-principles simulations, because of time scale and size limitations. Examples include thermal conductivity highly viscous silicate melts melting temperatures (some aspects of) rheological properties at high T etc… The “optimized” potential method “Optimized” potential at P,T A. Laio et al, Science 287, 1027 (2000) P. Tangney and S. Scandolo JCP 117, 8898 (2002) How hot is the Earth’s core? A. Laio et al, Science 287, 1027 (2000) Shock wave experiments DFT-based calculation by Alfe’ et al Liquid Fe Static experiments Solid Fe Our results Inner-Outer core boundary D. Stevenson, Nature 423, 239 (2003) Thanks to: M.-S. Lee M. Fontana L. Giacomazzi J. Christie Y. Liang ICTP A. Young A. Hernandez Nieves J. Montoya R. Rousseau C. Miranda P. Tangney A. Laio S. Serra E. Tosatti F. Tassone SISSA G. Profeta L’Aquila R. Car X. Wang Princeton ...and a countless number of experimentalists...