Equations of state of iron nitrides ε-Fe₃N_x and γ-Fe₄N_y to 30 GPa and 1200 K and implication for nitrogen in the Earth's core

Nitrogen abundance is one of the most uncertain among all elements in the Earth's interior. Recent data indicate an affinity between Fe-nitrides and Fe-carbides in the Earth's mantle and inner core. In this work P-V-T equations of state of ε-Fe₃N_0.8 and ε-Fe₃N_1.26 (which is close to Fe₇N₃) have been determined using a combination of multianvil and synchrotron radiation techniques at pressures up to 30 GPa and temperatures up to 1473 K. A fit of the P-V-T data to the Vinet-Rydberg and Mie-Grüneisen-Debye equations of state yields the following thermoelastic parameters for the ε-Fe₃N_0.8: V₀ = 81.44(2) Å³, K_T0 = 157(3) GPa, K_T′ = 5.3 (fixed), θ₀ = 555 K (fixed), γ₀ = 1.83(1), and q = 1.34(18). For ε-Fe₃N_1.26 we obtained V₀ = 86.18(2) Å3, K_T0 = 163(2) GPa, K_T′ = 5.3(2), θ₀ = 562(90) K, γ₀ = 1.85(2), and q = 0.55(24). It is likely that all presumably paramagnetic ε-Fe₃N_x with x = 0.75–1.5 have similar thermoelastic properties with a minor increase of the bulk modulus with increasing N content. The melting temperature of ε-Fe₃N_x increases from approximately 1473 to 1573 K in the pressure range from 5 to 30 GPa. We also determined a preliminary equation of state for γ-Fe₄N_y and calculated y = 0.35(2) from the data at 20–30 GPa. Combining the results with a recent experimental study on the stability of β-Fe₇N₃, isostructural with Fe₇C₃, and a theoretical study of the magnetic transitions in ε-Fe₃N_x, we estimate the density of Fe-nitrides at the Earth's inner core conditions. Our results indicate that at 5000–6000 K, 2.0–3.2 wt % N can explain the density deficit in Earth's inner core.