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Fiquet et al ., 2001; Antonangeli et al ., 2004), and
shock compression experiments (e.g., Brown &
McQueen, 1986; Nguyen & Holmes, 2004). There
is a discrepancy regarding the compressional ve-
locity and density relation (Birch's law) between
the datasets obtained by NRIXS and IXS. The
density-compressional velocity relations of hcp-
Fe determined by these methods are shown in
Figure 8.11. The effect of temperature on Birch's
law is also a matter of debate. Fiquet et al . (2001)
suggested that Birch's law had no temperature
dependency, whereas Lin et al . (2005) suggested
that it had a large temperature dependency.
Recent ab initio calculations indicated small
or almost no temperature dependency from low
temperature to 1000 K, but with large temper-
ature dependencies for Birch's law at higher
temperatures (Vo cadlo et al ., 2009; Sha & Cohen,
2010a,2010b). Antonangelli et al . (2012) measured
the sound velocity of hcp-iron up to 93 GPa and
1100 K and reported no temperature dependency
at least in the pressure and temperature range
studied. Experimental confirmation of the effect
of temperature on Birch's law is one of the most
important topics in the inner core research.
Assuming no temperature dependency for Birch's
law and using the sound velocity values of FeS,
FeS 2 , FeO, and FeSi determined by IXS at room
temperature, Badro et al . (2007) estimated the
amount of light elements in the core, i.e., an
inner core with 2.3 wt% Si and trace of O, and
an outer core containing 2.8 wt% Si and around
5.3 wt% O. Antonangeli et al . (2010) estimated
the composition of the inner core based on the
sound velocity measurement of an Fe-Ni-Si alloy.
They estimated that the inner core contains
4 wt% to 5 wt% of Ni and 1 wt% to 2 wt% of Si.
The compositional range estimated by Anto-
nangeli et al . (2010) is shown in Figure 8.22 as the
gray-shaded region (for color version, see Plate 6),
which has a lower Si content than the compo-
sitional range estimated in this work based on
the compression experiments of the iron alloys
(the blue-shaded region (for color version of Fig.
8.22, see Plate 6)). The discrepancy may be caused
by the difference in the pressure scale, i.e., the
pressure scale used by Antonangeli et al . (2010)
was based on Holme's Pt pressure scale, which
is about 37 GPa higher than the other pressure
scales at the center of the Earth as shown in the
above. The red dashed lines in Figure 8.22 (for
color version, see Plate 6) are our density iso-
chors (in g / cm 3 )based on the Pt pressure scale
of Holmes et al . (1989). The compositional range
explaining the inner core density by this scale is
given as a red shaded area (for color version, see
Plate 6) in this figure, which is consistent with
the compositional area estimated by Antonangeli
et al . (2010). Thus, it is essential to establish the
pressure scale at high pressure and temperature
covering the entire core conditions in order to
make a definitive conclusion on the composition
of the core.
The estimation of the inner core composition
based on the sound velocity measurement is not
unique at present. Shibazaki et al . (2012) esti-
mated that the inner core contains only 0.23 wt%
of H based on the sound velocity measurement
of FeH at high pressure. Furthermore, all of these
estimates of the light element content in the
inner core are based on the sound velocity at
room temperature assuming no temperature de-
pendency for Birch's law. We need to perform
sound velocity measurements at high tempera-
ture and to test the temperature dependency of
Birch's law. More work needs to be done on the
pressure scale, equation of state, and sound veloc-
ity measurements of the core materials under the
Earth's core conditions.
Acknowledgments
The author is grateful to T. Sakai, S. Kamada, K.
Nishida, and Y. Shibazaki for collaboration and
discussions on this manuscript. This work was
supported by grants-in-aid for scientific research-
from the Ministry of Education, Culture, Science,
Sport, and Technology of the Japanese Govern-
ment to E.O. (nos. 18104009 and 22000002). The
work was conducted as a part of the Global COE
program, Global Research and Education Center
for the Earth and Planetary Dynamics at Tohoku
University.
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