Elasticity of franklinite and trends for transition-metal oxide spinels

Abstract

The pressure dependence of single-crystal elastic moduli of a natural Mn-rich franklinite, (Mn 0.40 Fe 2+ 0.16 Zn 0.37 Mg 0.03 )(Fe 3+ 1.94 Al 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 (ZnAl 2 O 4 ), franklinite exhibits pressure-induced mode softening of C 44 similar to magnetite (Fe 3 O 4 ). Between end-member compositions ZnFe 2 O 4 (franklinite) and MnFe 2 O 4 (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.