Entropic broadening of the spin-crossover pressure in ferropericlase

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 $\sim {10}^6$ atoms, we derive the spin-crossover pressures as functions of Fe concentration for different Fe distributions. We determine a critical temperature of $T_c\sim 900\mathrm{K}$, 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.

Figure 1

Snapshots of Fe distributions. The Fe distributions of $\left({\mathrm{Mg}}_{0.9375}{\mathrm{Fe}}_{0.0625}\right)\mathrm{O}$, $\left({\mathrm{Mg}}_{0.75}{\mathrm{Fe}}_{0.25}\right)\mathrm{O}$, and $\left({\mathrm{Mg}}_{0.6}{\mathrm{Fe}}_{0.4}\right)\mathrm{O}$ at 300 K are shown in (a)–(c), respectively, and their counterparts at 1800 K are shown in (d)–(f), respectively. Fe atoms are presented by brown balls, whereas Mg and O atoms are not displayed. At 300 K, in the configurations of $\left({\mathrm{Mg}}_{0.75}{\mathrm{Fe}}_{0.25}\right)\mathrm{O}$ and $\left({\mathrm{Mg}}_{0.6}{\mathrm{Fe}}_{0.4}\right)\mathrm{O}$, iron-rich and iron-poor zones can be clearly identified, whereas randomized iron distributions appear at the temperatures of 1800 K. Because the Fe concentration of $\left({\mathrm{Mg}}_{0.9375}{\mathrm{Fe}}_{0.0625}\right)\mathrm{O}$ is too low, Fe aggregation supposed to occur at 300 K cannot be resolved.

Figure 2

Histograms showing the number of segments with the same local iron concentration and the same spin-crossover pressure. (a)–(c) Results of $\left({\mathrm{Mg}}_{0.9375}{\mathrm{Fe}}_{0.0625}\right)$, $\left({\mathrm{Mg}}_{0.75}{\mathrm{Fe}}_{0.25}\right)\mathrm{O}$, and $\left({\mathrm{Mg}}_{0.6}{\mathrm{Fe}}_{0.4}\right)\mathrm{O}$, respectively. The upper $X$ axis (lower $X$ axis) presents the segments distribution feature with local iron concentration (spin-crossover pressure). The segments containing 64 cation sites and 64 anion sites are used. Red lines are the results of Gaussian fittings. Bimodal and mono Gaussian fittings are used for the configurations with and without Fe enrichments, respectively, and the fitted peak positions (pp) are indicated next to the peaks. The purple-dashed line represents the assumed detectable critical number of 10% of the highest histogram bar.

Figure 3

Low-spin Fe fractions and phase diagram. The fraction of LS iron in Fe-bearing MgO is shown as functions of pressure and iron concentration. Red zone and violet zone show Fe in the HS and LS state, respectively. The area located between two white solid lines presents the coexisting zone of HS and LS Fe. Experimental results at room temperature are shown in horizontal bars. The simulated spin-crossover pressure zones agree well with experimental ones.