Ab initio calculations of elastic constants of plagioclase feldspars

Plagioclase feldspars comprise a signification portion of the Earth's crust, thus their elastic properties are essential for understanding the Earth's seismic structure. However, the accuracy of existing elastic constants for plagioclase feldspars is uncertain. Alexandrov & Ryzhova (1962, Bull Acad Sci USSR Geol Ser, 10) and Ryzhova (1964, Bull Acad Sci USSR Geol Ser, 7) measured the elastic constants for a series of natural plagioclase feldspars but were unable to measure all crystallographic directions for the triclinic symmetry. In addition, the exact chemical composition, degree of twinning, and imperfections of their samples were not well characterized. More recent experiments on albite were performed by Brown et al. (2006, Phys Chem Minerals, 33) whose values vary considerably from the earlier measurements. We calculated elastic constants for three members in the plagioclase solid solution family in order to compare and improve upon elastic constants using density functional theory (DFT) as implemented in the Vienna Ab-initio Simulation Package (VASP) (Kresse and Hafner, 1993, Phys Rev B, 47). Starting from the experimentally determined crystal structures of low albite, labradorite, and anorthite, we relaxed the geometries at constant volume. Then we strained the unit cell, calculated the corresponding stresses, and derived elastic constants from the finite differences, C_ij=(Δσ_i)/(Δɛ_j) where indices are given in Voigt notation. Our calculated values for albite fall in between those of Ryzhova (1964) and Brown et al. (2006), but are more similar to Brown et al. (2006). Our labradorite results are similar to Alexandrov and Ryzhova (1962) and Ryzhova (1964), but more similar to the latter. Anorthite elastic constants have not yet been measured, but our calculated results for anorthite follow a trend of increasing C₁₁ and C₂₂ and decreasing C₄₄ with increasing Ca content. P-wave velocities for albite are between 486-798 km/s while velocities for labradorite are 582-784 km/s, and for anorthite, 583-794 km/s, suggesting that seismic anisotropy decreases with Ca content. This study provides more reliable elastic constants for determining elastic properties of plagioclase-bearing rocks for seismic applications.