of 
iron and
the PREM 
at inner core densities. We can expect the thermal pressure,
, to be about 
at inner core temperatures at those densities [Anderson, 1995,
Page 269]. So there is about a 40 GPa
discrepancy to account for by light impurities. This problem
has been examined by Jephcoat and Olson [1987],
who proposed that a substantial amount of FeO would
be needed to satisfy PREM's density at the
inner core. Their analysis was based on the 
phase as the stable phase at core pressures. As
described above, in the section on phase diagrams,
the 
phase may be the dominant phase in the
inner core. In that case, the quantity of impurities
in the inner core will almost certainly be
less than calculated by Jephcoat and Olson,
[ Isaak et al., 1994].
Poirier [1994a] has critically reviewed the literature regarding the types and quantities of light impurities in the outer core. He concludes that there is no reason to consider that only one light element is in the outer core. Several light elements (Si, S, O, H, C) seem certain to be in the outer core. Poirier concludes, ``it is not even obvious that one element should be particularly dominant.''
Although not a light element, nickel is one
of the elements we should expect to find in the inner
and outer core. Mao et al. [1990] showed
experimentally that an iron-nickel alloy,
Fe
Ni
, has
virtually the same 
relationship as pure iron up
to 300 GPa at 300 K. Therefore the presence of
nickel will not disturb the calculation of density
effects due to other impurities, and so the geophysical
model may safely ignore, at least as a first approximation,
the presence of nickel as other alloys are considered.
From the shock wave experiments of
Jeanloz and Ahrens [1980] on Fe and FeO, we know that about 45% FeO
by weight is required in combination with 55% pure iron by weight to satisfy the
outer core density data. Similarly, using the shock wave data
of Ahrens [1979] on
FeS
and Fe
S, an even
larger amount of sulfur can be mixed with iron to satisfy the outer core
density. Therefore oxygen and/or sulfur have been assumed
by several [ Ringwood and Hibberson, 1991;
Knittle and Jeanloz, 1991;
Usselman, 1975] as likely candidates
for impurities of the inner core in order
to satisfy the density deficit.
Poirier's [1994a] calculations show that
if silicon, oxygen, and sulfur were simultaneously
present, a number of combinations of mass fractions would give
the required 10% density deficit.
It is of interest to consider how these light elements, when
mixed with iron, might affect the melting temperature
of the resulting alloy. Boehler [1992] measured melting of
the Fe-FeS and Fe-FeO systems up to 50 GPa. His 
's
were substantially lower than those for these same systems
as determined by Knittle and
Jeanloz [1991]. For Fe
0,
Boehler's curve passed through the
point at 17 GPa measured by Ringwood
and Hibberson [1990]. Boehler found that for FeO,
increases with 
faster than it does for
pure iron itself, at least up to 80 GPa, the limit
of the experiment. For FeS, the rate of increase of 
with 
is less than for pure iron. Therefore, it is possible that
FeO in the inner core will not diminish the value of 
significantly, although it will diminish the density
(see also a similar conclusion by Knittle and Jeanloz, 1991).
However, other abundant elements may cause
the lowering of 
. Fukai [1992] reported that
the presence of iron hydride substantially
lowered the melting temperature at high pressure.
Yagi et al. [1994] reported that when
Fe, MgSiO
, and water are mixed at high pressure,
both FeH
and FeO are formed, and the resulting
FeH
has a much lower 
and a
lower density than pure iron. Similarly,
Wood [1993], who presented a detailed analysis
of Fe-C and the Fe-C-S systems at high pressure,
showed that carbon is likely present
in the inner core. Its effect would be
to depress the melting point
significantly.
In trying to estimate the melting temperature depression of
iron by the concentration of minor elements,
we have no compelling theory to help us.
We cannot even usefully predict whether a given
system will have a eutectic or act
as a solid solution at very high pressures.
There are a number of experiments that show
a miscibility gap between the metallic F and the ionic
oxide (such as FeO). In general, the experiments show
that the miscibility gap decreases as the pressure
increases, indicating that the eutectic behavior
may disappear at sufficiently high P.
For example, Wood [1993] found experimentally that the
eutectic 
for the Fe-S-C system rises
with pressure from 
to 15 GPa,
and the miscibility gap decreases.
He suggested that Fe-S-C liquids
could form one stable liquid at core temperatures.
The experimental data are incomplete, and
such as exist are limited to pressures up to about 50 GPa.
If the eutectic type phase diagrams are valid
at core pressure, then calculations and measurements
of 
described in the previous section
may not help very much in determining core temperatures.
If, on the other hand, eutectic phase diagrams
do not persist up to core pressures and impurities
go into the iron lattice as solutes, making
solid solutions, then the resulting 
can be calculated by finding the freezing point depression
based on the melting curve of pure iron.
There is an experimental result suggesting that
solid solutions are favored at very high pressures
for iron systems. W.W. Anderson and Ahrens [1994]
reported that the bulk modulus of pure liquid iron
at outer core conditions is virtually identical
to the seismic bulk modulus of the outer core.
Thus 
of the
outer core is
independent of the concentration of the impurities
in the iron. D.L. Anderson [1976] showed
empirically that for silicate solid solutions
(garnets, oxides, and pyroxenes), the
bulk modulus is virtually independent of iron
concentrations. This
was verified in detail experimentally
for olivine, pyroxenes, and
garnets [ Isaak, 1992;
Weidner et al., 1982]. The theory for the
-
relationship in solid solutions
was established by Shankland [1972],
who showed that the law 
holds, where 
is the bulk sound velocity
for solid solutions. This law is equivalent
to saying that 
is independent of 
for solid solutions at constant crystal structure.
It is derived from Debye theory for a solid solution, where
the crystal structure is held constant, and the concentration
of impurities is varied. Iron fulfills the criteria
of a Debye solid. Therefore, the W.W. Anderson
and Ahrens [1994] report on bulk modulus supports
the assumption that iron, under high compression and
with a few percent impurities, is a solid solution,
and eutectics need not be considered.
In addition, there are theoretical results indicating the onset of solubility conditions at high pressure. Boness and Brown [1990] and Sherman [1991] suggested that Fe-S exhibits continuous solution at core pressures. Using the van der Laar equation, Boness and Brown [1990] estimated that the melting depression drop from pure iron to an outer core composition is about 1000 K.
A solid solution is favored for an oxide in the
core if the bonding is metallic. There has been a
persistent effort to see whether FeO becomes more
metallic at the pressure of its transition
at about 80 GPa. The polymorphic wüstite
transition found by Jeanloz and Ahrens [1980]
was described as probably from 
to 
(NaCl to CsCl), implying ionic bonding
in the high pressure phase. Jackson
and Ringwood [1981] presented arguments that the
transition should be to a nickel arsenide structure
with a more covalent bond involving spin pairing.
Isaak et al. [1993],
in a first principles calculation, (LSDA) investigated the
phase stability of wüstite at high pressure. They predicted
a transition to a metallic 
structure at 500 GPa.
Sherman [1994], following the path of Isaak et al. [1993]
but using the more general model called full potential linearized
augmented wave (FLAPW) method of calculation, found the
Ni-As structure at 125 GPa, which is metallic.
Fei et al. [1994] determined experimentally that wüstite transforms to the Ni-As-type structure at 93 GPa and 800 K, indicating a substantial increase in the metallicity of the structure.
Thus the evidence, both experimental and theoretical, has accumulated in favor of a solid solution of iron and other light impurities for the composition of the core.
Poirier and Shankland [1994] speculated that the temperature
of the inner core at the ICB is the 
of pure
iron less the freezing point depression due to about 10%
light impurities, that is, a drop of 500--1000 degrees.
Braginsky and Roberts [1995] adopted a melting point depression
of 700 K. Stacey [1995], following
Poirier's [1986] suggestion on melting depression,
found the value of 
at the ICB to be about 5000 K. To
quote Stacey, ``clearer evidence is needed.''
Boehler [1993] estimated a value close to that of
Poirier, 
,
using a different approach. Using his experimental results
on the variation of 
with pressure for the
Fe-(Fe-FeO) system, he noted that 
is linear in
density (a variation of the Kraut-Kennedy law), so a simple
extrapolation of his measured results to the ICB pressure gave
him 4640 K for the Fe-FeO system. He assumed no
triple points or eutectics above his measurements terminating
at 60 GPa. It might be that triple points occurring
in pure iron as seen in the phase
diagram are absent in the Fe-FeO system. In the Poirier calculation,
light impurities are not specified, except as
a concentration value, whereas in the Boehler extrapolation,
an assumed light impurity is used.
These estimates are based on incomplete data, however. To find
the quantity of impurities, we must know the crystallographic
structure of pure iron that exists at inner core 
conditions. Four years ago, it was universally assumed
that the phase would be hcp, and the high pressure
density was promptly determined [ Mao et al., 1990].
But now we see that the structure might be
fcc. The arguments in favor of
this are as follows: at ambient
conditions, pure iron (bcc) tends to change to fcc when alloyed
with small amounts of nickel, copper, palladium,
or platinum; the fcc phase might be the phase found
in pure iron at high 
conditions; or the high P, high 
phase
could be an unforeseen phase, such as a simple cubic
cell with a large number of atoms per cell, as found,
for example, in manganese at high 
and high
[ Young, 1991]. Also we must know more about the
kinds of impurities and their relative concentrations
in the inner core.
Current thinking of geophysicists ignores potassium as a significant impurity, although it was considered a viable alternative two decades ago. (A good discussion of the feasibility of potassium in the core is found in Jacobs [1987]).
To sum up, in spite of reservations, these various estimates
of melting point depression lead to a value of 
near 5000 K. Braginsky
and Roberts [1995] adopted 
.