Knowledge of the composition of the Earth's core(1-3) is important for unde
rstanding its melting point and therefore the temperature at the inner-core
boundary and the temperature profile of the core and mantle. In addition,
the partitioning of light elements between solid and liquid, as the outer c
ore freezes at the inner-core boundary, is believed to drive compositional
convection(4), which in turn generates the Earth's magnetic field. It is ge
nerally accepted that the liquid outer core and the solid inner core consis
t mainly of iron(1). The outer core, however, is also thought to contain a
significant fraction of light elements, because its density-as deduced from
seismological data and other measurements-is 6-10 per cent less than that
estimated for pure liquid iron(1-3). Similar evidence indicates a smaller b
ut still appreciable fraction of light elements in the inner core(5,6). The
leading candidates for the light elements present in the core are sulphur,
oxygen and silicon(3). Here we obtain a constraint on core composition der
ived from ab initio calculation of the chemical potentials of light element
s dissolved in solid and liquid iron. We present results for the case of su
lphur, which provide strong evidence against the proposal that the outer co
re is close to being a binary iron-sulphur mixture(7).