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).