A Computational Study of Ionic Vacancies and Diffusion in MgSiO3 Perovskite and PostPerovskite Bijay

1
A Computational Study of Ionic Vacancies and
Diffusion in MgSiO3 Perovskite and
Post-PerovskiteBijaya B Karki1,2 and Gaurav
Khanduja11Department of Computer Science,
Louisiana State University, Baton Rouge LA-70803
2Department of Geology and Geophysics, Louisiana
State University, Baton Rouge LA-70803


2007 COMPRES Annual Meeting Lake Morey,
Vermont June 17-21, 2007
Schottky Defect Pressure dependence of the
Schottky formation enthalpy of perovskite (filled
circles) and post-perovskite (open circles). Also
shown are the results from previous calculations
for pv. The errors are within the size of the
symbols used.
Abstract We have performed first-principles
simulations within density functional theory to
investigate the effects of pressure on the
formation of defects (ionic vacancies) and ionic
diffusion in the perovskite (pv) and
post-perovskite (ppv) phases of MgSiO3. Our
results show that the predicted formation
enthalpies of three Schottky (MgO, SiO2 and
MgSiO3) defects are similar between the two
phases at high pressures (100 to 150 GPa) with
MgO Schottky defect being the most favorable.
However, the calculated activation enthalpies and
activation volumes of diffusion are shown to
differ substantially between them. In
particular, the activation enthalpies for Mg and
Si diffusion in ppv are smaller than the
corresponding values for pv, for example, by
factors of 2.2 and 3.4, respectively, at 120 GPa,
whereas the O migration enthalpy of ppv is only
slightly larger than that of pv. The easy
migration paths of the cations in ppv are shown
to take place along the lt100gt direction in which
Si-O octahedra share the edges. Visualization of
the simulation data reveals that the vacancy
defects and migrating ions induce substantial
distortions in the atomic and electronic
structures around them. It is suggested that
diffusion is equally easy for all three species
in ppv and is likely to occur through extrinsic
processes near the bottom of the lower mantle.
Our results are expected to be useful in modeling
mantle conductivity and dynamics. Future work
will focus on investigation of more complex
mechanisms such as coupled diffusion or diffusion
in the presence of other vacancies, and
interstitial mechanisms. Our preliminary results
show that in the presence of an O vacancy, the
activation volume of Si diffusion becomes
negative.
Diffusion Activation Enthalpy and Volume Figure
Pressure dependence of the activation enthalpies
for extrinsic (left) and intrinsic (right)
diffusion in pv (filled symbols) and ppv (open
symbols). The circles, diamonds and squares
represent the Mg, Si and O migration enthalpies,
respectively. Also shown are the results from
previous calculations for perovskite asterisks
(Wright and Price, 1993). Table Calculated
activation volumes (in the units of cm3/mol) for
extrinsic (VM) and intrinsic (VD) diffusion in
perovskite (pv) and post-pervoskite (ppv). Both
the predicted values of activation enthalpies and
volumes of ionic diffusion differ largely between
the two phase

• Introduction
• MgSiO3 pv and ppv are the most abundant phases
  of the lower mantle
• Our knowledge of defects and diffusion in these
  phases is critical to our understanding of mantle
  rheology.
• Ionic diffusion determines electrical
  conductivity in minerals, which is important in
  modeling mantle conductivity
• A relatively few studies on defects and
  diffusion currently exist
• Computations are mainly based on simplified
  models and only performed for pv
• Experimental studies are available at low
  pressures for only pv
• Here, we report important results on the
  energetics, geometry, and electronic structures
  of defects and diffusion in pv and ppv at mantle
  pressures from first-principles quantum
  mechanical computations
• Compare and contrast the defects and diffusion
  between pv and ppv.

• Atomic Structure
• Visualization of atomic displacements of
  individual atoms in a defective crystal relative
  to their positions in a perfect crystal.
• Upper row Mg (left), Si (center), and O
  (right) vacancies in the 60-site ppv system at
  120 GPa. Green, blue and red spheres represent
  Mg, Si and O atoms, respectively. A black sphere
  at the center of the cell indicates the defect
  (vacant site) site.
• Lower row Mg (left), Si (center) and O (right)
  migrating ions located at the center of the cell.
  Adjacent vacancy sites are indicated by two black
  spheres located on each side of the center along
  the line of migration.
• Migrating cations open their paths along the a-
  direction by pushing the nearest O atoms away
  from their positions.

Post-perovskite structure, view down the c-axis
and a-axis. Si-O octahedral (blue) and Mg atoms
(green spheres) are shown. The easier diffusion
of Mg and Si in ppv compared to that in pv can be
attributed to structural differences between the
two phases. The ppv phase shows a layered
structure consisting of alternate layers of
Si-octahedra and Mg atoms, which are
perpendicular to the b-direction.

• Methodology
• Computational Details
• PWSCF code (LDA and and pseudopotentials)
• Supercell with PBC (80 atoms for pv and 60
  atoms for ppv)
• Single isolated charged defects Mg2-, Si4- and
  O2 vacancies
• Defect-defect correction (?E ) included
• Defect Energetics
• Defect extraction energy for a given vacancy
  type
• EION(V) E(N - 1, V) E(N, V) - ?E
• Schottky defect formation enthalpy
• HS EMg(V) ESi(V) 3EO(V) HMgSiO3
• where HMgSiO3 is the enthalpy of the removed
  formula unit
• Activation Enthalpy and Volume for Diffusion
• HM HSP HGS (extrinsic
  diffusion)
• HD HM HS / n (intrinsic
  diffusion)
• Where n is the number of ions in the Schottky
  defect.
• VM dHM/dP and VDdHD/dP

• Electronic Structure
• Visualization of electron density difference (in
  units of Å-3) in MgSiO3 ppv.
• Upper three images are for vacancies and lower
  three images are for migrating ions Mg (left),
  Si (center) and O (right).
• In each case, the vertical surface represents
  the clipping plane passing through the defect
  site or migrating ion site, which is located at
  the centre of the image. Note that the plane also
  contains the migration direction.
• In case of migrating ions, the electronic
  structures of the neighborhood ions remain
  essentially unchanged, and the structures in the
  vicinity of each migrating ion clearly represents
  the existence of two half-vacancies separated by
  the ion itself.

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Acknowledgements This work is supported by NSF
Career (EAR 0347204) grant. Computing facilities
are provided by LSU-CCT.