Entropic broadening of the spin-crossover pressure in ferropericlase

Abstract

The pressure-induced spin crossover of iron in ferropericlase, the Fe-bearing MgO, is a key to understanding the seismological observations in the lower mantle. However, the experimentally measured spin-crossover pressure zone (SCPZ) shows large variations, which disagree with the theoretically predicted values that are generally less than half of experimental ones. Here, we resolve this outstanding controversy by revealing the critical role of Fe distribution in MgO in broadening the Fe SCPZ, using comprehensive first-principles calculations combined with cluster expansion approach and Monte Carlo simulations. By employing a large supercell containing up to $\ensuremath{\sim}{10}^{6}$ atoms, we derive the spin-crossover pressures as functions of Fe concentration for different Fe distributions. We determine a critical temperature of ${T}_{c}\ensuremath{\sim}900\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, below which Fe segregation (clustering) occurs, in accordance with the thermodynamic phase diagram. Above ${T}_{c}$, an entropy-driven randomized Fe distribution creates large variations in Fe local environments, which in turn broadens the SCPZ, such as 17.5 GPa for 25 mol % Fe-bearing MgO in good agreement with experiments. Therefore, the broad SCPZ, rendering a smooth change of ferropericlase mechanical properties during the spin crossover, should be mainly caused by entropy, consistent with the high-temperature state of the lower mantle.