Elasticity of franklinite and trends for transition-metal oxide spinels

The pressure dependence of single-crystal elastic moduli of a natural Mn-rich franklinite, (Mn0.40Fe0.162+Zn0.37Mg0.03)(Fe-1.Al-3+(94)0.08)O-4, has been determined by GHz-ultrasonic interferometry in a diamond-anvil cell to 9.8 GPa. The room-pressure elastic constants of franklinite are C-11 = 244(3) GPa, C-12 = 142(4) GPa, and C-44 = 77(2) GPa. Linear pressure derivatives of C-11, and C-12 are 4.3(3) and 3.8(3), respectively, whereas the C-44 modulus exhibits softening, fitted in the P <= 10 GPa pressure range to C-44 = 77(2) + 0.29(2)P - 0.018(2)P-2 GPa. The average of Hashin-Shtrikman bounds on the adiabatic bulk modulus (K-S0) of franklinite is 175(3) GPa, with pressure derivative K-S' = 4.3(3), and the shear modulus G(0) = 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 K-T0 = 173.5(7) GPa fitted with a fixed pressure derivative of K-T' = 4. When K' is fixed to the ultrasonic value of 4.3, we obtain K-T0 = 172.2(7) GPa. In contrast to iron-free gahnite (ZnAl2O4), franklinite exhibits pressure-induced mode softening of C-44 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 C-44, which displays a pronounced negative anomaly for the mid-range Mn composition. Applying Birch's law to AB(2)O(4)-type spinels reveals that oxide spinels containing transition metals on both A and B sites follow a distinct trend from other spinels.