The Equation Of State Of Fe₃C Under High Temperature And High Pressure

The compostion and state of Earth's inner core are closely related to the accretion process of the primitive Earth,the anisotropy of the inner core,the generation and evolution of Earth's magnetic field,and the deep cycle of the carbon.After more than 60years of investigation,it has been confirmed that the main composition of the inner core is iron-nickel alloy with a small amount of light elements.As an important candidate of light elements,carbon?C?has attracted wide attention of geophysicists and geochemists.Although the equation of state and sound velocity of Fe-C alloys have been studied extensively using static compression techniques,the content of C in the inner core is still controversial.Compared with the static compression technique,the dynamic compression technqiue can reach higher temperature and pressure,which is closer to the environment of the inner core.In order to accurately constrain the content of C in the inner core,the equation of state for Fe₃C along Huogniot was measured by dynamic compression device?two-stage light gas gun?.Comparing our results with those obtained by static compression technqiue,we constrain the thermodynamic parameters of Fe₃C at high pressure and tempeature.Based on the Hugoniot data,we calculated the equation of state of Fe₃C and Fe under the conditions of inner core,and constrained the content of C in the inner core.The main contents and innovations in this paper are as follows:1.Using multi-anivil compressor,we successfully sintered the bulk,small porosity and high purity Fe₃C samples.We investigated the effects of sintering temperature,pressure and particle size.It was found that the optimum sintering conditions are 4 GPa,1000K,and size of the particle ranging from 1.3 to 9?m.Based on the density measurements,XRD diffraction patterns,electron probe elemental analysis and ultrasound analysis,we confirmed the Fe₃C samples have uniform composition,high purity and small porosity.The average bulk density of the samples is 7.53?0.07?g/cm³,which is slightly less than that of the single crystal density of7.68 g/cm³.2.Using two-stage light gas gun,the equation of state for Fe₃C were measured up to 250 GPa.The fitted Hugoniot parameter are C₀=4.669?0.088?km/s and?=1.68?0.037?.Compared with the static compression data,we disscuss the thermodynamic parameters of Fe₃C.It is found that when the lattice Grüneisen parameter is?_l=2.8?7.86/??^0.8,and the electronic Grüneisen parameter?_e=2,the calculated equation of state agrees with static compression data.It proves that the thermodynamic parameters adopted in this paper are correct.3.According to the thermodynamic parameters of Fe and Fe₃C and the Grüneisen equation of state,we estimated the densities of Fe and Fe₃C under the conditions of the inner core.The densities of Fe₃C are lower than those of the inner core,while the densities of pure iron are higher than those of the inner core.Based on the ideal additive law,the density of the mixture of Fe and Fe₃C is calculated.It is found that when the weight percent of Fe₃C is 36%,that is,when the content of C is2.4 wt%,the density of Fe-2.4 wt%C matches the density of the inner core.Assuming that C is the sole light element in the inner core,its amount is no more than2.4 wt%.