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

Abstract

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) (γ) phases, located at 8.0(±0.3) GPa and 680(±50) K with the slope of the phase boundary between the ε and γ 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 K T ,0 = 135±19 GPa, K ′ T ,0 = 6.0±0.4, and V 0 = 22.7±0.3 Å 3 , where K T ,0 , K ′ T ,0 and V 0 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 (∂ K T ,0 /∂ T ) P = −4.48 ±0.56 × 10 −2 GPa K −1 , with the zero‐pressure thermal expansivity in the form α T ,0 = a + bT − cT −2 , where α = 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‐Grüneisen‐Debye theory gives (α T ,0 K T ,0 ) and (∂ 2 P /∂ T 2 ) 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‐Grüneisen‐Debye EOS based on fictitious volumes ( a 3 and c 3 , 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 γ‐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.