The axial ratio of hcp Fe and Fe – Ni – Si alloys to the conditions of Earth ’ s inner core 1 " 2 "

10" The Earth’s iron-rich inner core is seismically anisotropic, which may be due to the 11" preferred orientation of Fe-rich hexagonal close packed (hcp) alloy crystals. Elastic anisotropy in 12" a hexagonal crystal is related to its c/a axial ratio; therefore, it is important to know how this 13" ratio depends on volume (or pressure), temperature, and composition. Experimental data on the 14" axial ratio of iron and alloys in the Fe–Ni–Si system from 15 previous studies are combined here 15" to parameterize the effects of these variables. The axial ratio increases with increasing volume, 16" temperature, silicon content, and nickel content. When an hcp phase coexists with another 17" structure, sample recovery and chemical analysis from each pressure-temperature point is one 18" method for determining the phase’s composition and thus the position of the phase boundary. An 19" alternate method is demonstrated here, using this parameterization to calculate the composition 20" of an hcp phase whose volume, temperature, and axial ratio are measured. The hcp to hcp+B2 21" phase boundary in the Fe–FeSi system is parameterized as a function of pressure, temperature, 22" and composition, showing that a silicon-rich inner core may be an hcp+B2 mixture. These 23"