Sound velocities and elastic constants of ZnAl2O4 spinel and implications for spinel-elasticity systematics

The pressure dependence of the sound velocities, single-crystal elastic constants, and shear and adiabatic bulk moduli of a natural gahnite (ZnAl 2 O 4 ) spinel have been determined to ~9 GPa by gigahertz ultrasonic interferometry in a diamond anvil cell. The elastic constants of gahnite are (in GPa): C 11 = 290(3), C 12 = 169(4), and C 44 = 146(2). The elastic constants C 11 and C 12 have similar pressure derivatives of 4.48(10) and 5.0(8), while the pressure derivative of C 44 is 1.47(3). In contrast to magnetite, gahnite does not exhibit C 44 mode softening over the experimental pressure range. The adiabatic bulk modulus K S0 is 209(5) GPa, with pressure derivative K S ’ = 4.8(3), and the shear modulus G 0 = 104(3) GPa, with G’ = 0.5(2). Gahnite, along with chromite (FeCr 2 O 4 ) and hercynite (FeAl 2 O 4 ) are the least compressible of the naturally occurring oxide spinels. Evaluation of Birch's Law for isostructural minerals indicates that spinels containing transition metals on both the [4] A and [6] B sites follow a trend about five times more negative than oxide and silicate-spinel phases without any, or only one transition metal.