Influence of octahedral site chemistry on the elastic properties of biotite

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 natural 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 well-known Brillouin equation with refractive indices and phonon frequencies obtained from the Becke line test and spectral peak positions, respectively. In general, these velocities increase with decreasing iron content, approaching those of muscovite at low iron concentrations. Twelve of thirteen 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, while the remaining constant was estimated under the approximation of hexagonal symmetry. Elastic constants \(C_{11}\), \(C_{22}\), and \(C_{66}\) are comparable to those of muscovite and show little change with iron concentration due to the strong bonding within layers. In contrast, nearly all of the remaining constants show a pronounced dependence on iron content, a probable consequence of the weak interlayer bonding. Similar behaviour is displayed by the elastic stability, which exhibits a dramatic decrease with increasing iron content, and by the elastic anisotropy within the basal cleavage plane, which decreases as the amount of iron in the crystal is reduced. This systematic dependence on iron content of all measured elastic properties indicates that the elasticity of biotite is a function of octahedral site chemistry and provides a means to estimate the elastic constants and relative elastic stability of most natural biotite compositions if the iron or, equivalently, magnesium, concentration is known. Moreover, the good agreement between the elastic constants of Fe-poor (Mg-rich) biotite and those of phlogopite obtained from first-principles calculation based on density functional theory indicates that the latter approach may be of use in predicting the elastic properties of biotites.