Extending the domain of quantum mechanical simulations

with HPCx: Melting

Dario AlfèUniversity College London

Why Melting ?

• The Earth’s core is mainly iron

• Melting temperature of Fe at ICB

• Constraint on the temperature of the core

Melting

Free energy approach

Coexistence approach

Free energy approach

liquid solidG (P,T) G (P,T)

T 100 K G 10 meV/atom

Calculating free energies

Thermodynamic integration:

1

ref ref

0

F F d U U

λ refU (1 λ)U λU

BU(R)/ TB 3N

V

1F(V,T) T ln dR e

N!kk

Size and k-points tests

Lidunka Vočadlo & Dario Alfè, PRB, 65, 214105 (2002)

The coexistence approach

• Density Functional Theory • Generalized Gradient Approximation (PW91)

• VASP code (Kresse and Furthmuller, PRB 54, 11169 (1996))

• USPP (130 eV PW-cutoff) • Finite temperature Fermi smearing • K-points sampling• Efficient charge density extrapolation (Alfe`, Comp.

Phys. Comm. 118, 31 (1999))

Ab-initio technical details

Scaling tests (Al, 1000 atoms)

512 atoms ()(~2 weeks HPCx, 64 PEs)

1000 atoms()(~3 weeks HPCx, 128 PEs)

Dario Alfè, Phys. Rev. B, 68, 064423 (2003)

512 atoms (2x2x1)(~4 weeks SUN-SPARC, 16 PEs)

1728 atoms()(~7 months SUN-SPARC, 16 PEs)

Conclusions

• Coexistence of phases for melting is now possible even with first principles techniques (though still very expensive).

• Next step: Iron ? (One order of magnitude more expensive than Aluminium).