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  1. Abstract We present LDA + U sc calculations of high-spin (HS) and low-spin (LS) states in ferropericlase (fp) with an iron concentration of 18.75%. The Hubbard parameter U is determined self-consistently with structures optimized at arbitrary pressures. We confirm a strong dependence of U on the pressure and spin state. Static calculations confirm that the antiferromagnetic configuration is more stable than the ferromagnetic one in the HS state, consistent with low-temperature measurements. Phonon calculations guarantee the dynamical stability of HS and LS states throughout the pressure range of the Earth mantle. Compression curves for HS and LS states agree well with experiments. Using a non-ideal mixing model for the HS to LS states solid solution, we obtain a crossover starting at ∼45 GPa at room temperature and considerably broader than previous results. The spin-crossover phase diagram is calculated, including vibrational, magnetic, electronic, and non-ideal HS–LS entropic contributions. Our results suggest the mixed-spin state predominates in fp in most of the lower mantle. 
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  2. 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. 
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