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 (ZnAl₂O₄) spinel have been determined to ∼9 GPa by gigahertz ultrasonic interferometry in a diamond anvil cell. The elastic constants of gahnite are (in GPa): C₁₁ = 290(3), C₁₂ = 169(4), and C₄₄ = 146(2). The elastic constants C₁₁ and C₁₂ have similar pressure derivatives of 4.48(10) and 5.0(8), while the pressure derivative of C₄₄ is 1.47(3). In contrast to magnetite, gahnite does not exhibit C₄₄ mode softening over the experimental pressure range. The adiabatic bulk modulus K_SO is 209(5) GPa, with pressure derivative K_S'=4.8(3), and the shear modulus G₀ = 104(3) GPa, with G¹ = 0.5(2). Gahnite, along with chromite (FeCr₂O₄) and hercynite (FeAl₂O₄) 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.