Tue.27 Nov.Wed.28 Nov.Thu.29 Nov. 8h30 - 9h45 Topical lecture Planets / High Pressure Topical lecture Atmospheric physics Methods: Ab-initio Molecular Dynamics 9h h15Coffee break 10h15 -11h30 Methods Plane waves, cut-off, k-points, pseudopotentials, DFT, etc SeminarsComputer Lab 3 11h30 – 13h30Lunch time 13h30 – 16h00Computer Lab 1Computer Lab 2Computer Lab 4 The 6th School on Simulation and Modeling Physics "Ab-initio methods and their applications" Hanoi, November 2007

Exploring planetary interiors by ab-initio molecular dynamics 6 th SMP, Hanoi, Nov 27-29, 2007 Sandro Scandolo (the Abdus Salam ICTP, Trieste, Italy)

The Abdus Salam International Centre for Theoretical Physics (under UNESCO / IAEA), Trieste, Italy ICTP’s mission: To foster the growth of advanced studies and research in physics and mathematics, especially among researchers from developing countries Opportunities - Conferences / Schools throughout the year - Associates (our faculty “in the field”) - Visitors (junior, STEP, TRIL, etc) - Diploma Course

Materials SciencePlanetary Science High pressure in 1951: the first man-made diamonds 1991: Earth’s core conditions reproduced in the laboratory

Shock wavesDiamond anvil cell

Approximations - Born-Oppenheimer - Classical nuclei - Density functional theory from “first principles” Variable-cell molecular dynamics [Parrinello & Rahman, 1981]

Outline High Pressure in Materials Science: + “Carbonia”: a silica-like CO 2 amorph + Novel transition metal nitrides High pressure in Planetary Science: + Carbon in planetary interiors + Melting of iron

Silica-like CO 2 : the crystal phases + Molecular CO 2 predicted to tranform into a silica- like crystal at high pressure + Silica-like phases of CO 2 predicted to be ultrahard Molecular CO 2 Candidate theoretical structures for silica-like CO 2 Serra, Cavazzoni, Chiarotti, Scandolo, Tosatti, Science 284, 788 (1999) Crystal structure of silica-like CO 2 not yet determined Is there a glass analog? Experimental confirmation of silica-like CO 2 Yoo et al, Science 283, 1510 (1999)

“Carbonia”: the silica-like CO 2 glass Experimental evidence for amorphous CO 2 Santoro, Gorelli, Bini, Ruocco, Scandolo, Crichton, Nature, in press (2006) Compression by ab-initio molecular dynamics gives: At 1000 K and 100 GPa: a crystalline phase At 2000 K and 80 GPa: an amorphous phase Octahedral CO 6 Tetrahedral CO 4

Platinum nitride: PtN or PtN 2 ? Raman shift (cm-1) Gregoryanz et al, Nature Mat. (2004) Crowhurst et al, Science (2006) Ab-initio calculations on structures with 1:1 stoichiometry fail to reproduce the experimental Raman spectra Single-bonded polymeric nitrogen Eremets et al, Nature Mat. (2004) Molecular N 2 Polymeric N

Platinum nitride: PtN 2 pyrite Young, Montoya, Lazzeri, Sanloup, Gregoryanz, Scandolo, PRB 2006 Raman spectra X-ray diffraction

MN 2 with interstitial N 2 units: a new class of transition metal nitrides? Young, Sanloup, Gregoryanz, Scandolo, Hemley, Mao, PRL 96, (2006) IrN 2 Single bonded N-N PtN 2 pyrite New “heavy” metal nitrides are superhard Bulk modulus: 428 GPa (IrN 2 ), 358 GPa (OsN 2 )

H 2 O+CH 4 +NH 3 Marvin Ross, “Diamonds in the sky” Nature (1981) Methane was found to dissociate under a shock wave Scandolo & Jeanloz, American Scientist (2003)

Methane dissociation: what do simulations say F. Ancilotto et al., Science 275, 1288 (1997) Compressed methane heated up to 4000 K

Before compressionAfter compression Methane dissociation: the experimental confirmation L.R. Benedetti et al., Science 283, 100 (1999)

Melting of Carbon diamondliquid BC8, SC ?? Neptune and Uranus isentrope X. Wang, S. Scandolo, R. Car, Phys. Rev. Lett Coordination number

Accuracy of DFT?: Melting of silicon Solid Liquid T m (LDA) = 1380 K T m (GGA) = 1520 K T m (meta-GGA) = 1700 K T m (experiment) = 1687 K X. Wang, S. Scandolo, R. Car

How hot is the centre of the Earth? liquid solid 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

The “optimized” potential method “Optimized” potential at P,T A. Laio et al, Science 287, 1027 (2000)

Melting of Iron at Earth’s core pressures Inner-Outer core boundary A. Laio et al, Science 287, 1027 (2000) Our results Shock wave experiments Static experiments DFT-based calculation by Alfe’ et al

D. Stevenson, Nature 423, 239 (2003)

The crew: J. Montoya A. Young R. Rousseau C. Cavazzoni Y. Liang X. Wang A. Laio R. Car ….