Electron Density Changes across the Pressure-Induced Iron Spin Transition

High-pressure single-crystal x-ray diffraction is used to experimentally map the electron-density distribution changes in (Fe,Mg)O as ferrous iron undergoes a pressure-induced transition from high- to low-spin states. As the bulk density and elasticity of magnesiowüstite—one of the dominant mineral phases of Earth’s mantle—are affected by this electronic transition, our results have applications to geophysics as well as to validating first-principles calculations. The observed changes in diffraction intensities indicate a spin-transition-induced change in orbital occupancies of the Fe ion in general accord with crystal-field theory, illustrating the use of electron density measurements for characterizing high-pressure $d$-block chemistry and motivating further studies characterizing chemical bonding under pressure.

Figure 1

Structure factors for $({\mathrm{Fe}}_{0.53}{\mathrm{Mg}}_{0.47})\mathrm{O}$ as a function of compression at room temperature. Values are given relative to the structure factor with the largest value, $F(002)$ [34], with results for compression and decompression indicated by closed and open symbols, respectively. The straight lines show the result of a least-squares fit to all of the data, assuming two linear trends with a single break in slope: the loss-function minimization documents preference for the break in slope at 56 GPa (Fig. S2). This two-trend fit to the structure factors has statistical significance, after Bonferroni correction of fourteen structure factors [not including $(002)$], when compared with a linear fit with no break in slope (Table SI [34]).

Figure 2

Electron-density distribution difference maps in the (100) plane for $({\mathrm{Fe}}_{0.53}{\mathrm{Mg}}_{0.47})\mathrm{O}$ at room temperature, with red and blue respectively indicating increased and decreased electron density with pressure. (a) End-transition-compression (56 GPa) minus minimum-compression (18 GPa) difference map, with arrows illustrating transfer of electron density. (b) Maximum-compression (74 GPa) minus end-transition-compression (56 GPa) difference map: the pressure-induced electron-density increase between the iron-magnesium and oxygen sites indicates an increase in covalency of the compressed bond, labeled with $+$. The scale is relative to the maximum electron density at 18 GPa, and a Butterworth filter has been applied here to account for frequency-cutoff aliasing. See Supplemental Material [34] for additional details.

Figure 3

Electron-density-distribution difference map in the (100) plane across the high- to low-spin transition in $({\mathrm{Fe}}_{0.53}{\mathrm{Mg}}_{0.47})\mathrm{O}$, corrected for pressure-induced covalency changes. The effect of compression increasing electron density between nearest neighbors [Fig. 2] is subtracted from the change in electron density between end-transition (56 GPa) and minimum-compression (18 GPa) [Fig. 2] in order to isolate the change in electron density due to the spin transition alone (See Fig. S13.). Orientations of $t_{2g}$ and $e_g$ orbitals are labeled, and the lowest peak intensities (to $-0.187$) are saturated on the present color scale. See Fig. S14 for more details.

Figure 4

(a) Three-dimensional contours of increased (red) and decreased (blue) electron density across the spin transition, with the Fe-Mg (cation) site on the left and the O (anion) site on the right, as derived from room-temperature unfiltered (no Butterworth filter applied) end-transition-compression (56 GPa) minus minimum-compression (18 GPa) results for $({\mathrm{Fe}}_{0.53}{\mathrm{Mg}}_{0.47})\mathrm{O}$ (See Fig. 2: constant-value isosurface maps are for $\pm 0.013$ relative to the maximum electron density at 18 GPa, hence dimensionless, and are plotted using vesta [51].). (b) Hydrogenic $3d$ orbitals, distinguishing the $d_{x^2-y^2}$ and $d_{z^2}$ (teal) from the $d_{xy}$, $d_{xz}$, and $d_{yz}$ (orange) orbitals, which make up the $e_g$ (c) and $t_{2g}$ (d) orbitals, respectively (isosurface values at $1.78e^{-}/{\mathrm{nm}}^3$). See Supplemental Material [34]. Panels (b)–(d), based on hydrogen orbitals, use a different color scheme to that of (a), which depicts measured data.