The pressure dependence of single-crystal elastic moduli of a natural Mn-rich franklinite, (Mn0.40Fe2+0.16Zn0.37Mg0.03)(Fe3+1.94Al0.08)O4, has been determined by GHz-ultrasonic interferometry in a diamond-anvil cell to 9.8 GPa. The room-pressure elastic constants of franklinite are C11 = 244(3) GPa, C12 = 142(4) GPa, and C44 = 77(2) GPa. Linear pressure derivatives of C11 and C12 are 4.3(3) and 3.8(3), respectively, whereas the C44 modulus exhibits softening, fitted in the P ≤ 10 GPa pressure range to C44 = 77(2) + 0.29(2)P – 0.018(2)P2 GPa. The average of Hashin-Shtrikman bounds on the adiabatic bulk modulus (KS0) of franklinite is 175(3) GPa, with pressure derivative KS′ = 4.3(3), and the shear modulus G0 = 66(2) GPa with G′ = 0.09(3). The isothermal compressibility of franklinite was determined from a separate high-pressure, single-crystal X-ray diffraction experiment to 7.8 GPa, yielding KT0 = 173.5(7) GPa fitted with a fixed pressure derivative of KT′ = 4. When K′ is fixed to the ultrasonic value of 4.3, we obtain KT0 = 172.2(7) GPa. In contrast to iron-free gahnite (ZnAl2O4), franklinite exhibits pressure-induced mode softening of C44 similar to magnetite (Fe3O4). Between end-member compositions ZnFe2O4 (franklinite) and MnFe2O4 (jacobsite), the bulk modulus decreases linearly with increasing %Mn, however we observe non-linear behavior in other elastic moduli, especially C44, which displays a pronounced negative anomaly for the mid-range Mn composition. Applying Birch’s law to AB2O4-type spinels reveals that oxide spinels containing transition metals on both A and B sites follow a distinct trend from other spinels.

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