We see that 
becomes
larger if 
and 
become larger.
Details of the structure of the phase diagram affect all three
factors in the equation for 
. In particular, the value of
at the ICB depends on the number of the triple points. This
is illustrated by two cases of the phase diagram in Figure 2.
Compare the Anderson case (Figure 2b) with the Boehler case (Figure 2c).
Both show the same value of 
at 200 GPa. In case 2d (Boehler),
the melting curve at 200 GPa is extrapolated continuously
in a clear field above 200 GPa, leading to
.
But in the 2b case (Anderson), the solid-solid transition of Brown and McQueen at 200 GPa is retained. This s-
point
is an impediment to a simple extrapolation
of Boehler's data past 200 GPa, and there arises a triple-point in the 200 GPa
vicinity. This t.p. forces the melting curve up, and by the Lindemann law,
is 6000 K, so that with the addition of this
triple point 
increases by 1200 K above Boehler's estimate.
The addition of a t.p. in the phase diagram also increases
[ Anderson, 1990] as well as T.
That is because around a t.p., the sum of the three 
's
must vanish. If two branches join at a t.p., and the
third branch goes into a higher pressure region, the 
of the emerging branch is the sum of the two 
's
of the lower branches (see Figure 4 of Anderson [1990]).
The effect of a triple point is to increase the product
. Adding a t.p. generally increases 
,
which tends to lower 
, but
the effect of 
dominates.
Verhoogen [1980] calculated
that 
for iron by estimating
and 
at core conditions.
Anderson [1990] showed that the effect of a t.p.
placed at 190 GPa is to increase 
to 229 cal g-1 (20 J mol-1),
a significant amount (perhaps one third)
of the heat generated gravitationally.
Anderson kept the location of a
t.p. at 190 GPa, but with the advent
of pressure measurements of 
by Boehler,
added another t.p. at 100 GPa (see Figure 5 of
Anderson [1993]). So 
would be
even larger.
The effect of a complicated phase diagram
on the heat of crystallization may be substantial
(depending on the rate of crystallization) and goes in the direction of
creating a large 
and a
correspondingly large heat flow. In order to quantify the heat flow
from the inner core to the outer core, the phase diagram should be
well known for all branches connecting to the melting curve.
Values for T, 
, and 
at the triple point
are needed. Poirier and Shankland [1994]
give 
for the latent heat of crystallization
calculated from dislocation theory. The actual number
depends on the freezing point depression.
Stacey [1992] pointed out that electrical
conductivity has a dramatic effect on
the conducted heat flux. His values are
for the inner core
and 
for the outer core (see
Stacey's [1994] Appendix G), resulting in 
for thermal conductivity. Braginsky and Roberts [1995]
estimated 
for the outer core.
The value given by Jeanloz
and Wenk [1988] is 
for the inner core.
(For a useful analysis of core properties,
see Poirier [1994b]).
Recommended values of physical properties of the core are found in Table 1.