  Light elements in the iron-rich core of the Earth are important indicators
for the evolution of our planet. Their amount and distribution, and the
temperature in the core, are essential for understanding how the core and the
mantle interact and for modelling the geodynamo which generates the planetary
magnetic field. However, there is a longstanding controversy surrounding the
identity and quantity of the light elements. Here, the theory of tricritical
phenomena is employed as a precise theoretical framework to study
solidification at the high pressures and temperatures where both experimental
and numerical methods are complicated to implement and have large uncertainties
in their results. Combining the theory with the most reliable iron melting data
and the Preliminary Reference Earth Model (PREM) seismic data, one obtains the
solidification temperature at the inner core boundary (ICB) for both pure iron
and for the alloy of iron and light elements in the actual core melt. One also
finds a value of about 2.5 mole% for the amount of light matter. In addition,
the density of both solid and liquid pure iron at its melting temperature is
found. This allows one to obtain the density of the light matter and thus to
identify it to be MgSiO3.
