Stability field and thermal equation of state of epsilon-iron determined by synchrotron X-ray diffraction in a multianvil apparatus

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 150 0 K. The stability field of the hexagonal phase (epsilon -Fe) is characteri zed by the triple point of the body-centered cubic (bcc) (alpha), epsilon, and face-centered cubic (fcc) (gamma) phases, located at 8.0(+/-0.3) GPa an d 680(+/- 50) K with the slope of the phase boundary between the epsilon an d gamma phases being 36 +/-3 K GPa(-1). Pressure-volume-temperature (P-V-T) data for the epsilon -Fe enable us to extract thermal equation of state (E OS) parameters accurately. Least squares fit of a combination of our room t emperature data with previous results using the diamond anvil cell (DAC) to the third-order Birch-Murnaghan EOS yields K-T,K-O = 135 +/- 19 GPa, K'(T) ,(O) = 6.0 +/-0.4, and V-O = 22.7 +/-0.3 Angstrom3, where KT,O, and VO are zero-pressure isothermal bulk modulus, its pressure derivative, and zero-pr essure volume, respectively. Volume data at high temperatures are fit with various high-temperature EOSs. A fit using the high-temperature Birch-Murna ghan EOS yields the temperature derivative of the bulk modulus (partial der ivativeK(T,0)/partial derivativeT)(p) = -4.48 +/-0.56 X 10(-2) GPa K-1, wit h the zero-pressure thermal expansivity in the form alpha (T,0) = a + bT - cT(-2), where a = 3.98 +/- 0.24 X 10(-5) K-1, b = 5.07 +/-0.88 X 10(-8) K-2 , and c is nonresolvable from Q. The thermal pressure approach based on the Mie-Gruneisen-Debye theory gives (alpha K-T,O(T,Q)) and (partial derivativ e P-2/partial derivativeT(2))(v) to be 6.88 +/-0.30X10(-3) GPa K-1 and 4.63 +/-0.53X10(-6) GPa K-2, respectively. The thermoelastic parameters obtaine d from various EOSs are mutually consistent. The edge lengths (a and c) for the epsilon -Fe are also fit with the Mie-Gruneisen-Debye EOS based on fic titious volumes (a(3) and c(3), respectively) to obtain pressure and temper ature dependence of cla. Linear thermal expansivity for the c axis is sligh tly larger than that of the a axis while incompressibilities are similar. T hus pressure dependence of cla at each temperature is quite similar, althou gh absolute values of cla become higher with increasing temperature. Below 20 GPa, no new phase between the epsilon- and gamma -Fe stability fields wa s observed, and no anomaly in the cla ratio was detected. Under the assumpt ion that epsilon -Fe is stable at the corresponding P and T conditions of t he Earth's inner core, the density of e-Fe is significantly higher than tha t of the Preliminary Reference Earth Model, indicating light element(s) mus t be present not only in the outer core but also in the inner core.