Measurements of Elastic Constants of Chromian spinel Single-Crystal by Resonant Ultrasound Spectroscopy

Chromian spinel grains in mantle xenoliths usually contain fluid inclusions whose residual pressure (fluid density) can provide us the origin depth of the xenoliths. The precise estimation of the origin depth needs elastic properties of chromian spinel. We thus have studied elastic constants of a chromian spinel single-crystal via the resonance method. Chromian spinel grains were taken from mantle xenoliths, which were collected from Sveyagin, Far East Russia (Yamamoto et al., 2009, Island Arc). One crystal grain was selected in terms of the uniformity of crystallographic orientation examined by SEM-EBSD. The selected grain was shaped into a rectangular parallelepiped (0.517×0.417×0.412 mm³). The density is 3.83(1) × 10³ kg/m³, which is estimated from the chemical composition and the lattice parameter. Lower 16 oscillation modes were observed in the frequency range from 4.000 MHz to 9.000 MHz. Measurements were conducted for different specimen-holding forces. The resonance frequency of a free vibration was estimated by the extrapolation of measured resonance frequencies to the specimen-holding force of zero. In order to precisely take into account the specimen shape, the FEM was employed to calculate resonance frequencies for a given set of elastic constants. By comparing calculated and measured resonance frequencies, C₁₁, C₁₂ and C₄₄ were determined to be 264(3) GPa, 154(3) GPa, and 142.6(2) GPa, respectively. Chromian spinel is a solid solution of spinel (MgAl₂O₄) and hercynite (FeAl₂O₄). Elastic constants of the specimen are compared with those of spinel (Yoneda, 1990) and hercynite (Wang and Simmons, 1972). Determined elastic constants are lower than the values expected from the tie-line between spinel and hercynite. We suggested that the relatively low elastic constants of chromian spinel are attributed to the divalent and trivalent cation-disorder in octahedral and tetrahedral sites.