In situ synchrotron X-ray diffraction measurements have been carried out on Fe using a T cup multianvil high-pressure apparatus up to 20 GPa and 1500 K. The stability field of the hexagonal phase (ϵ-Fe) is characterized by the triple point of the body-centered cubic (bcc) (α), ϵ, and face-centered cubic (fcc) (&ggr;) phases, located at 8.0(¿0.3) GPa and 680(¿50) K with the slope of the phase boundary between the ϵ and &ggr; phases being 36¿3 K GPa-1. Pressure-volume-temperature (P-V-T) data for the ϵ-Fe enable us to extract thermal equation of state (EOS) parameters accurately. Least squares fit of a combination of our room temperature data with previous results using the diamond anvil cell (DAC) to the third-order Birch-Murnaghan EOS yields KT,0=135¿19 GPa, KT,0'=6.0¿0.4, and V0=22.7¿0.3 ¿3, where KT,0, KT,0', and V0 are zero-pressure isothermal bulk modulus, its pressure derivative, and zero-pressure volume, respectively. Volume data at high temperatures are fit with various high-temperature EOSs. A fit using the high-temperature Birch-Murnaghan EOS yields the temperature derivative of the bulk modulus (∂KT,0/∂T)P=-4.48¿0.56¿10-2 GPa K-1, with the zero-pressure thermal expansivity in the form αT,0=a+bT-cT-2, where a=3.98¿0.24¿10-5 K-1, b=5.07¿0.88¿10-8 K-2, and c is nonresolvable from 0. The thermal pressure approach based on the Mie-Gr¿neisen-Debye theory gives (αT,0KT,0) and (∂2P/∂T2)V to be 6.88¿0.30¿10-3 GPa K-1 and 4.63¿0.53¿10-6 GPa K-2, respectively. The thermoelastic parameters obtained from various EOSs are mutually consistent. The edge lengths (a and c) for the ϵ-Fe are also fit with the Mie-Gr¿neisen-Debye EOS based on fictitious volumes (a3 and c3, respectively) to obtain pressure and temperature dependence of c/a. Linear thermal expansivity for the c axis is slightly larger than that of the a axis while incompressibilities are similar. Thus pressure dependence of c/a at each temperature is quite similar, although absolute values of c/a become higher with increasing temperature. Below 20 GPa, no new phase between the ϵ- and &ggr;-Fe stability fields was observed, and no anomaly in the c/a ratio was detected. Under the assumption that ϵ-Fe is stable at the corresponding P and T conditions of the Earth's inner core, the density of ϵ-Fe is significantly higher than that of the Preliminary Reference Earth Model, indicating light element(s) must be present not only in the outer core but also in the inner core. ¿ 2001 American Geophysical Union