To calculate the thermodynamic properties of recently discovered high-pressure mixed valence iron oxides in the system Fe–Mg–O, information on the equation of state of precursor inverse spinel phases along the magnetite–magnesioferrite join is needed. The existing equation of state data, particularly for magnesioferrite, are in poor agreement and no data exist for intermediate compositions. In this study, the compressibility of nearly pure magnesioferrite as well as of an intermediate \({{\mathrm{Mg}}_{0.5}}^{\vphantom{2+}}\mathrm{Fe}_{0.5}^{2+}{\mathrm{Fe}}_{2}^{3+}{\mathrm{O}}_{4}^{\vphantom{2+}}\) sample have been investigated for the first time up to approximately 19 and 13 GPa, respectively, using single-crystal X-ray diffraction in a diamond anvil cell. Samples were produced in high-pressure synthesis experiments to promote a high level of cation ordering, with the obtained inversion parameters larger than 0.83. The room pressure unit cell volumes, V₀, and bulk moduli, K_T0, could be adequately constrained using a second-order Birch–Murnaghan equation of state, which yields V₀ = 588.97 (8) ų and K_T0 = 178.4 (5) GPa for magnesioferrite and V₀ = 590.21 (5) ų and K_T0 = 188.0 (6) GPa for the intermediate composition. As magnetite has K_T0 = 180 (1) GPa (Gatta et al. in Phys Chem Min 34:627–635, 2007. https://doi.org/10.1007/s00269-007-0177-3), this means the variation in K_T0 across the magnetite–magnesioferrite solid solution is significantly non-linear, in contrast to several other Fe–Mg spinels. The larger incompressibility of the intermediate composition compared to the two end-members may be a peculiarity of the magnetite–magnesioferrite solid solution caused by an interruption of Fe²⁺–Fe³⁺ electron hopping by Mg cations substituting in the octahedral site.

为了计算 Fe-Mg-O 系统中最近发现的高压混合价铁氧化物的热力学性质，需要有关沿着磁铁矿-镁铁氧体连接处的前体反尖晶石相的状态方程的信息。现有的状态方程数据，特别是镁铁氧体的数据，一致性很差，并且不存在中间成分的数据。在这项研究中，几乎纯的镁铁氧体以及中间体\({{\mathrm{Mg}}_{0.5}}^{\vphantom{2+}}\mathrm{Fe}_{0.5}^的可压缩性{2+}{\mathrm{Fe}}_{2}^{3+}{\mathrm{O}}_{4}^{\vphantom{2+}}\)在金刚石压砧室中使用单晶 X 射线衍射首次分别研究了高达约 19 和 13 GPa 的样品。样品在高压合成实验中产生，以促进高水平的阳离子有序化，获得的反演参数大于 0.83。室内压力单元体积V ₀和体积模量K _{T 0}可以使用二阶 Birch–Murnaghan 状态方程充分约束，得到V ₀  = 588.97 (8) Å ³和K _{T 0}  = 178.4 (5) GPa 对于镁铁氧体和V ₀  = 590.21 (5) Å ³K _{T 0} = 188.0 (6) 中间组合物 的 GPa。由于磁铁矿的K _{T 0}  = 180 (1) GPa（Gatta et al. in Phys Chem Min 34:627–635, 2007. https://doi.org/10.1007/s00269-007-0177-3），这意味着与其他几种 Fe-Mg 尖晶石相比，磁铁矿-镁铁氧体固溶体中K _{T 0}的变化明显是非线性的。与两个端元相比，中间成分的更大不可压缩性可能是磁铁矿-镁铁氧体固溶体的特性，这是由取代八面体位置的 Mg 阳离子中断 Fe ²⁺ -Fe ^{3+电子跳跃引起的。}