First Principles Thermoelasticity of Mantle Minerals

1
The role of first principles calculations

• The message we must invigorate quickly the area
  of first
• principles simulations
  in earth and planetary
• materials.
• First principles simulations today under gird all
  areas of
• materials research and address all sorts of
  materials
• properties.
• The field changed in the second half of the 80s
• (Car Parrinello).

2
Research in the early nineties
Development of a variable cell shape (VCS)
molecular dynamics (MD) method (Wentzcovitch,
PRB,1991) Development of first principles MD
I. Self-consistent method with iterative
diagonalization used in MD simulations
(Wentzcovitch and Martins, SSC,1991) II.
Implementation of finite temperature DFT
(Wentzcovitch, Martins, and Allen, PRB
,1992) Some original applications of combined
methodologies Collaborators J. L. Martins
(INESC, Lisbon) and P.
B. Allen (SUNY-Stony Brook, CHiPR)
3
First Principles VCS-MD (Wentzcovitch, Martins,
Price, PRL 1993)
Damped dynamics
MgSiO3
P 150 GPa
4
Thermodynamic Method
VDoS and F(T,V) within the QHA
N-th order isothermal finite strain EoS
(N3,4,5)

• Density Functional Perturbation Theory for
  phonons
• xxxxxxxxxxxxxxxxxx(Gianozzi, Baroni, and de
  Gironcoli, 1991)

5
(Thermo) Elastic constant tensor ?
?kl
equilibrium structure
re-optimize
6
Phonon dispersion of MgSiO3 perovskite
Calc Exp
-
Calc Exp
0 GPa
-
Calc Karki, Wentzcovitch, de Gironcoli, Baroni
PRB 62, 14750, 2000 Exp Raman Durben
and Wolf 1992 Infrared Lu et al. 1994
100 GPa
7
MgSiO3-perovskite and MgO
Exp. Ross Hazen, 1989 Mao et al., 1991 Wang
et al., 1994 Funamori et al., 1996
Chopelas, 1996 Gillet et al., 2000 Fiquet et
al., 2000
8
Elasticity of MgO
(Karki et al., Science 1999)
9
Thermodynamic method 2
MD sampling of phase space
??i ? i(t)
-??i
cij
?j
(P,T)eq
(P,T, ??j)
Constant T MD (Nose,1984)
10
cij
300 K 1000K 2000K 3000 K 4000 K
Cij(P,T)
(Oganov et al,2001)
(Wentzcovitch, Karki, Coccociono, 2002)
11
Aggregate Moduli
38 GPa
88 GPa
12
Effect of Fe alloying

• (Kiefer, Stixrude,Wentzcovitch, GRL 2002)
• (Mg0.75Fe0.25)SiO3

4
13
Pyrolite (20 V mw) Perovskite
0.10ltxFelt0.15
100 GPa
38 GPa
aaaa
Brown Shankland T
aaaa
(Jeanloz and Thomson, 1983)
14

• What do we need to do
• A repository for well supported and user friendly
  methods
• where users of this community can turn to.
• We need access to Tflops supercomputers. THIS IS
  KEY!
• We need to educate a new generation to be
  informed in
• both fields.
• -We will benefit greatly by closing ranks with
  condensed
• matter physicists.

15
table
10.97