Stability field and thermal equation of state of -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 1500 K. The stability field of the hexagonal phase ( -Fe) is characterized by the triple point of the body-centered cubic (bcc) ( ), , and face-centered cubic (fcc) ( ) phases, located at 8.0( 0.3) GPa and 680( 50) K with the slope of the phase boundary between the and phases being 36 3 K GPa . Pressure-volume-temperature (P-V-T) data for the -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, K T,0 6.0 0.4, and V0 22.7 0.3 Å , where KT,0, K T,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 , with the zero-pressure thermal expansivity in the form T,0 a bT cT , where a 3.98 0.24 10 5 K , b 5.07 0.88 10 8 K , and c is nonresolvable from 0. The thermal pressure approach based on the Mie-Grüneisen-Debye theory gives ( T,0KT,0) and ( P/ T)V to be 6.88 0.30 10 3 GPa K 1 and 4.63 0.53 10 6 GPa K , respectively. The thermoelastic parameters obtained from various EOSs are mutually consistent. The edge lengths (a and c) for the -Fe are also fit with the Mie-Grüneisen-Debye EOS based on fictitious volumes (a and c, 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 and -Fe stability fields was observed, and no anomaly in the c/a ratio was detected. Under the assumption that -Fe is stable at the corresponding P and T conditions of the Earth’s inner core, the density of -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.