Abstract We perform ab initio simulations of beryllium (Be) and magnesium oxide (MgO) at megabar pressures and compare their structural and thermodynamic properties. We make a detailed comparison of our two recently derived phase diagrams of Be (Wu et al 2021 Phys. Rev. B 104 014103) and MgO (Soubiran and Militzer 2020 Phys. Rev. Lett. 125 175701) using the thermodynamic integration technique, as they exhibit striking similarities regarding their shape. We explore whether the Lindemann criterion can explain the melting temperatures of these materials through the calculation of the Debye temperature at high pressure. From our free energy calculations, we find that the melting line of both materials is well represented by the Simon–Glazel fit T m ( P ) = T 0 (1 + P / a ) 1/ c , where T 0 = 1564 K, a = 15.8037 GPa and c = 2.4154 for Be, while T 0 = 3010 K, a = 10.5797 GPa and c = 2.8683 for the MgO in the B1. For the B2 phase, we use the values a = 26.1163 GPa and c = 2.2426. Both materials exhibit negative Clapeyron slopes on the boundaries between the two solid phases that are strongly affected by anharmonic effects, which also influence the location of the solid–solid–liquid triple point. We find that the quasi-harmonic approximation underestimates the stability range of the low-pressure phases, namely hcp for Be and B1 for MgO. We also compute the phonon dispersion relations at low and high pressure for each of the phases of these materials, and also explore how the phonon density of states is modified by temperature. Finally, we derive secondary shock Hugoniot curves in addition to the principal Hugoniot curve for both materials, and study their offsets in pressure between solid and liquid branches.
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Ab Initio Melting Temperatures of Bcc and Hcp Iron Under the Earth’s Inner Core Condition
There has been a long debate on the stable phase of iron under the Earth’s inner core conditions. Because of the solid‐liquid coexistence at the inner core boundary, the thermodynamic stability of solid phases directly relates to their melting temperatures, which remains considerable uncertainty. In the present study, we utilized a semi‐empirical potential fitted to high‐temperature
- Award ID(s):
- 1918134
- NSF-PAR ID:
- 10400532
- Publisher / Repository:
- DOI PREFIX: 10.1029
- Date Published:
- Journal Name:
- Geophysical Research Letters
- Volume:
- 50
- Issue:
- 5
- ISSN:
- 0094-8276
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Earth’s inner core is predominantly composed of solid iron (Fe) and displays intriguing properties such as strong shear softening and an ultrahigh Poisson’s ratio. Insofar, physical mechanisms to explain these features coherently remain highly debated. Here, we have studied longitudinal and shear wave velocities of hcp-Fe (hexagonal close-packed iron) at relevant pressure–temperature conditions of the inner core using in situ shock experiments and machine learning molecular dynamics (MLMD) simulations. Our results demonstrate that the shear wave velocity of hcp-Fe along the Hugoniot in the premelting condition, defined as
T/Tm (Tm : melting temperature of iron) above 0.96, is significantly reduced by ~30%, while Poisson’s ratio jumps to approximately 0.44. MLMD simulations at 230 to 330 GPa indicate that collective motion with fast diffusive atomic migration occurs in premelting hcp-Fe primarily along [100] or [010] crystallographic direction, contributing to its elastic softening and enhanced Poisson’s ratio. Our study reveals that hcp-Fe atoms can diffusively migrate to neighboring positions, forming open-loop and close-loop clusters in the inner core conditions. Hcp-Fe with collective motion at the inner core conditions is thus not an ideal solid previously believed. The premelting hcp-Fe with collective motion behaves like an extremely soft solid with an ultralow shear modulus and an ultrahigh Poisson’s ratio that are consistent with seismic observations of the region. Our findings indicate that premelting hcp-Fe with fast diffusive motion represents the underlying physical mechanism to help explain the unique seismic and geodynamic features of the inner core. -
The Earth's inner core started forming when molten iron cooled below the melting point. However, the nucleation mechanism, which is a necessary step of crystallization, has not been well understood. Recent studies have found that it requires an unrealistic degree of undercooling to nucleate the stable, hexagonal, close-packed (hcp) phase of iron that is unlikely to be reached under core conditions and age. This contradiction is referred to as the inner core nucleation paradox. Using a persistent embryo method and molecular dynamics simulations, we demonstrate that the metastable, body-centered, cubic (bcc) phase of iron has a much higher nucleation rate than does the hcp phase under inner core conditions. Thus, the bcc nucleation is likely to be the first step of inner core formation, instead of direct nucleation of the hcp phase. This mechanism reduces the required undercooling of iron nucleation, which provides a key factor in solving the inner core nucleation paradox. The two-step nucleation scenario of the inner core also opens an avenue for understanding the structure and anisotropy of the present inner core.more » « less
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Among transition metal carbides and nitrides, zirconium, and hafnium compounds are the most stable and have the highest melting temperatures. Here we review published data on phases and phase equilibria in Hf-Zr-C-N-O system, from experiment and ab initio computations with focus on rocksalt Zr and Hf carbides and nitrides, their solid solutions and oxygen solubility limits. The systematic experimental studies on phase equilibria and thermodynamics were performed mainly 40–60 years ago, mostly for binary systems of Zr and Hf with C and N. Since then, synthesis of several oxynitrides was reported in the fluorite-derivative type of structures, of orthorhombic and cubic higher nitrides Zr3N4 and Hf3N4. An ever-increasing stream of data is provided by ab initio computations, and one of the testable predictions is that the rocksalt HfC0.75N0.22 phase would have the highest known melting temperature. Experimental data on melting temperatures of hafnium carbonitrides are absent, but minimum in heat capacity and maximum in hardness were reported for Hf(C,N) solid solutions. New methods, such as electrical pulse heating and laser melting, can fill the gaps in experimental data and validate ab initio predictions.more » « less
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SUMMARY The seismic anisotropy of the Earth's solid inner core has been the topic of much research. It could be explained by the crystallographic preferred orientation (CPO) developing during convection. The likely phase is hexagonal close-packed iron (hcp), alloyed with nickel and some lighter elements. Here we use high energy synchrotron X-rays to study CPO in Fe-9wt%Si, uniaxially compressed in a diamond anvil cell in radial geometry. The experiments reveal that strong preferred orientation forms in the low-pressure body-centred cubic (bcc) phase that appears to be softer than pure iron. CPO is attributed to dominant {110}<111> slip. The onset of the bcc→hcp transition occurs at a pressure of ≈15 GPa, and the alloy remains in a two phase bcc + hcp state up to 40 GPa. The hcp phase forms first with a distinct {11$\bar{2}$0} maximum perpendicular to compression. Modelling shows that this is a transformation texture, which can be described by Burgers orientation relationship with variant selection. Experimental results suggest that bcc grains oriented with <100> parallel to compression transform into hcp first. The CPO of the hcp changes only slowly during further pressure and deviatoric stress increase at ambient temperature. After heating to 1600 K, a change in the hcp CPO is observed with alignment of (0001) planes perpendicular to compression that can be interpreted as dominant (0001)<11$\bar{2}$0> slip, combined with {10$\bar{1}$2}<$\bar{1}$011> mechanical twinning, which is similar to the deformation modes suggested previously for pure hcp iron at inner core conditions.
