Geoscience Reference
In-Depth Information
for this kind of calculations was often limited to
less than 100 atoms (Oganov
et al
., 2001; Stack-
house
et al
., 2005). Those calculations likely fail
in capturing correct finite-temperature atomic
dynamics, when considering that phonon den-
sity of states get converged by sampling a large
number of q points, corresponding to the super-
cell size typically containing more than hundreds
(or sometimes a thousand) of atoms (Karki
et al
.,
2000a,b; Oganov
et al
. (2001); Stackhouse
et al
.
(2005).
also materials science (e.g., Lay
et al
., 2005;
Hirose, 2006). MgPPv is presently thought to be
a key to understanding, at least in part, several
enigmatic
properties
observed
in
this
region
(from the core-mantle boundary (CMB) to
300
km above), such as lateral seismic wave velocity
variations, large heterogeneity, anisotropy, and
thin ultra-low seismic wave velocity layer atop
the CMB. Post-perovskite (PPv) MgSiO
3
has the
CaIrO
3
-type structure with a space group
Cmcm
(Tsuchiya
et al
., 2004a). From the overall behavior
of the elastic constants (Tsuchiya
et al
., 2004b), it
is clear that this structure is quite anisotropic and
that anisotropy is strongly pressure dependent.
Two particular features can be immediately
noticed: (1)
c
22
is considerably smaller than
c
11
and
c
33
at relevant pressures; and (2)
c
66
is quite
large compared with
c
55
and
c
44
. The first feature
is typical of layered minerals. It shows that this
structure is more compressive in the direction
perpendicular to the layers (layers parallel to
(010)). The second feature is very intriguing. It
indicates that a lateral shift of layers ((010) planes)
parallel to the edge sharing octahedral columns
(along [100]) faces the greatest resistance. This is
counterintuitive. In a typical layered structure,
lateral shear of layers, along any direction, should
offer less resistance than the deformation of the
layers themselves, here represented by
c
55
.
It was found that bulk modulus (
B
) of both Pv
and PPv phases are very similar throughout most
of the pressure range of the lower mantle, while
PPv has considerably larger shear modulus (
G
)
than Pv in the pressure range corresponding to
the lower part of the lower mantle (7% larger at
120 GPa). This large
G
is caused by the large
c
66
.
The isotropic averaged compressional (
P
), shear
(
S
) and bulk (
) wave velocities of Pv and PPv
are plotted in Figure 7.2. At zero pressure, all
velocities are smaller than those of Pv, while at
high pressure,
V
P
and
V
S
of PPv are distinctly
larger than those of Pv.
V
is quite comparable.
The discontinuities in
V
P
,
V
S
and
V
at the static
transition pressure (
P
T
) of 100 GPa are 0.5, 1.5
and
∼
7.3
Major Lower Mantle Phases
7.3.1 MgSiO
3
(Mg, Fe)SiO
3
perovskite (Pv) is considered the
most abundant mineral, more than 60% in vol-
ume, in the Earth's lower mantle. It has the
orthorhombicly distorted Pv structure with the
space group
Pbnm
(
Z
4). Orthorhombic cells
have 9 independent elastic constant components,
and all the atomic positions must be fully relaxed
against for individual strain as mentioned before.
For the computation of this kind of complicated
crystal, the planewave basis and pseudopotential
method is the most practical technique providing
results with high numerical accuracy. The elastic
constants of MgSiO
3
Pv were calculated within
the density functional
ab initio
framework by
Karki
et al
. (1997c) at static (0 K) condition and
by Wentzcovitch
et al
. (2004) at high temper-
atures as a function of pressure. These studies
indicate that the pressure dependence of the elas-
tic wave velocities, both
V
P
and
V
S
,ofMgSiO
3
Pv match the reference Earth model in the lower
mantle condition fairly well, which supports a
current generally accepted idea that this phase is
the most dominant there.
A phase transition of MgPv was discovered
=
at
2500 K (Murakami
et al
.,
2004a; Tsuchiya
et al
., 2004a; Oganov and Ono,
2004). Since this
P
,
T
condition corresponds
closely to the depth where so-called D
seismic
discontinuity is observed, this phase change
has attracted considerable multidisciplinary
interest over geophysics, mineral physics, and
∼
125 GPa and
∼
0.5%, respectively. This indicates that the
PPv transition produces a
V
S
/
V
anti-correlation,
−
