Chemical and Physical Properties and Thermal State of the Core - Physics and Chemistry of the Deep Earth - page 259

approximately polar. If their results are correct,
the observed anisotropy can be explained by a
modest lattice-preferred orientation. Recent stud-
ies, however, have showed that the temperature
dependence of the c/a ratio is much smaller than
that reported by Steinle-Neumann et al . (2001).
Using the weak temperature dependency of the
c/a ratio calculated by Gannarelli et al . (2005),
Vo cadlo et al . (2009) suggested theoretically that
c 33 is still larger than c 11 up to 5000 K. The
weak temperature dependence of the axial ratio
of hcp-Fe 90 Ni 10 and hcp-Fe 87.9 Ni 4.4 Si 7.7 was deter-
mined experimentally at about 250 GPa and about
300 GPa, for hcp-Fe (Tateno et al ., 2010; Sakai
et al ., 2011b) and for hcp-Fe10 at. % Ni (Lin et al .,
2002), which were consistent with the above the-
oretical calculations, but inconsistent with the
theoretical prediction by Steinle-Neumann et al .
(2001). These results are consistent with the in-
ner core anisotropy with the c axis parallel to the
Earth's rotation axis (Stixrude & Cohen, 1995).
The most reliable computational results (Vo cadlo
et al ., 2009; Sha & Cohen, 2010a,2010b) show a
rather weak anisotropy that is dependent on the
inner core temperature, and thus we have a poten-
tial difficulty in explaining the observed seismic
anisotropy of the inner core by hcp-iron alone.
Some additional phases might exist in the inner
core together with hcp-iron.

140

2000 K

120

100

hcp

B2

80

60

40

20

fcc

ε -FeSi

0

0 10 20 30

Fe wt % Si FeSi

Fig. 8.21 The phase relation of the Fe-Si alloy at high
pressure and 2000 K (Kuwayama et al ., 2009).
Reproduced with permission of Springer.

amount in the inner core has been estimated to
be 2.3-8.5 wt% based on the compressibility mea-
surements at high pressure (Dobson et al ., 2003;
Hirao et al ., 2004), high pressure sound velocity
measurements (Lin et al ., 2003; Badro et al ., 2007)
and ab initio calculations (Alfe et al ., 2002).
Seismic anisotropy is also provides a clue for ex-
plaining the seismic properties of the inner core.
The elastic anisotropy of the high-pressure poly-
morphs of iron alloys has been studied by several
authors both experimentally and theoretically
(e.g., Stixrude & Cohen, 1995; Antonangeli et al .,
2004). The pressure and temperature dependence
of the axial ratio c/a of the hcp phase may be a clue
for the elastic anisotropy. Stixrude and Cohen
(1995) calculated the elasticity of hcp-iron using
ab initio calculations, and argued that the elas-
tic anisotropy with concentration of the c-axis of
hcp-Fe toward the polar axis of the core. However,
they found that the anisotropy is not strong and
thus the inner core may be single crystal. Steinle-
Neumann et al . (2001) published different compu-
tational results showing very strong temperature
dependence of the c/a ratio and resultant strong
anisotropy with the a-axis, the fast crystallo-
graphic direction to be aligned with the observed
symmetry axis of the inner core anisotropy, i.e.,

8.4.3 Density and sound velocity
of the inner core

The elastic parameters and the pressure-volume
data of iron, iron-nickel, iron-nickel-light el-
ement alloys are important for discussing the
composition and structure of the inner core. As
discussed earlier, there is an important issue re-
garding the reliability of the pressure scale under
the pressure and temperature conditions of the
core. Currently there is a consensus on the pres-
sure scales calibrated using the Pt pressure scale
of Holmes et al . (1989) and some related pressure
scales calibrated using this scale overestimate
the pressure by about 37GPa at the center of the
Earth. The pressure values of the revised Pt scales
such as those of Fei et al . (2007), Dorogokupets