Influence of octahedral site chemistry on the elastic properties of biotite

Abstract

Brillouin light scattering spectroscopy was used along with detailed composition information obtained from electron probe microanalysis to study the influence of octahedral site chemistry on the elastic properties of biotite crystals. Elastic wave velocities for a range of directions in the AC and BC crystallographic planes were obtained for each crystal by application of the Brillouin equation with refractive indices and phonon frequencies obtained from the Becke line test and spectral peak positions, respectively. In general, velocities increase with decreasing Fe content, approach those of muscovite at low Fe concentrations. 12 of the 13 elastic constants for the full monoclinic symmetry were obtained for each crystal by fitting analytic expressions for the velocities as functions of propagation direction and elastic constants to corresponding experimental data, with the remaining constant estimated using hexagonal symmetry. Elastic constants C11, C22, and C66 are comparable to those of muscovite and show little change with Fe concentration due to strong bonding within layers. In contrast, nearly all remaining constants show a pronounced dependence on Fe content, likely due to the weak interlayer bonding. Similar behaviour is shown by elastic stability, which falls greatly as Fe concentration increases, and elastic anisotropy within the basal cleavage plane, which decreases with Fe content. This consistent dependency of all measured elastic constants on Fe content suggests that biotite elasticity is a function of octahedral site chemistry and gives a method to determine the elastic constants and elastic stability of most biotite compositions provided, Fe or Mg concentrations are known. Moreover, the good agreement between elastic constants of Fe-poor biotite and those of phlogopite obtained from DFT simulations indicate a method to predict elastic properties of biotites.