The properties of the inner core (1C) of the Earth are widely assumed to be consistent with those of pure, solid iron in the hexagonal close-packed (e) phase. This hypothesis is re-examined here using a density model of the Earth's core generated from extrapolated, static high-pressure data for e iron and pyrite. Densities of constant-composition mixtures at room temperature and core pressures are compared with corresponding Earth-model densities. An effective volume thermal expansivity, αeff, is calculated for a range of expected core temperatures that brings the room-temperature density into agreement with the Earth-model density at the pressure of the inner-core boundary (ICB). It seems that αeff would have to be significantly larger than previous estimates of the thermal expansion at core conditions. A qualitatively similar conclusion is obtained if an isotherm reduced from shock-wave data is used for e iron instead of the static data. We argue that, of several explanations for this difference (errors in Earth-model densities, a high-volume thermal expansivity at megabar pressures, a high-temperature core (>7,000 K), and the presence of a light component), the last alternative is the most probable and that the IC is not, therefore, pure iron.