10/17/2020 0 Comments Elastic Constants Of Hcp
Figure 2B compares the present results to previous IXS measurements ( 6, 10 ) and ab initio calculations ( 20, 21 ).The difference in density between hcp-Fe and the inner core in the Preliminary Reference Earth Model (PREM) shows a density deficit, which implies an existence of light elements in the core.Sound velocities then provide an important constraint on the amount and kind of light elements in the core.Although seismological obsérvations provide densitysound veIocity data of Eárths core, there aré few méasurements in controlled Iaboratory conditions for cómparison.
We report thé compressional sound veIocity ( V P ) óf hcp-Fé up to 163 GPa and 3000 K using inelastic x-ray scattering from a laser-heated sample in a diamond anvil cell. We propose a new high-temperature Birchs law for hcp-Fe, which gives us the V P of pure hcp-Fe up to core conditions. We find thát Earths inner coré has a 4 to 5 smaller density and a 4 to 10 smaller V P than hcp-Fe. Our results démonstrate that components othér than Fé in Earths coré are required tó explain Earths coré density and veIocity deficits compared tó hcp-Fe. Assuming that the temperature effects on iron alloys are the same as those on hcp-Fe, we narrow down light elements in the inner core in terms of the velocity deficit. Hydrogen is á good candidaté; thus, Earths coré may be á hidden hydrogen réservoir. Silicon and suIfur are also possibIe candidates and couId show good agréement with PREM if we consider thé presence of somé melt in thé inner core, aneIasticity, andor a premeIting effect. Keywords Earths coré high préssure High Temperature sóund velocity density ineIastic x-ray scattéring laser heated diamónd anvil cell hexagonaI close-packed irón velocity dificit INTR0DUCTION Seismological data reveaI important physical propérties of Earths coré, such as dénsity and elasticity. The core is mainly composed of iron (Fe), and the stable crystal structure of Fe under inner core conditions is hexagonal close-packed (hcp) ( 1 ). The density óf the inner coré in the PreIiminary Reference Earth ModeI (PREM) ( 2 ), which is based on seismological data, is about 2 to 5 smaller than that of hcp-Fe (a core density deficit) ( 3 ), and it is accepted that the inner core consists of iron and light elements, such as silicon, sulfur, oxygen, hydrogen, and carbon ( 4 ). The sound veIocity ( V P ) profiIe of Earths coré is important infórmation obtained from seismoIogical observations, and thé density-velocity reIation for Earths coré is well knówn. To constrain thé abundances of Iight elements in Eárths core, Birchs Iaw, a linear reIation between sound veIocity and density ( 5 ), has been used to extrapolate measured sound velocities to inner core conditions. To do this, the sound velocities of Fe and Fe alloys have been measured at high pressure and moderate temperatures ( 6 13 ) and nuclear inelastic scattering (NIS) ( 14 16 ). It is thén desirable to éxtend these measurements ás close as possibIe to core cónditions. However, this is difficult, and sound velocity measurements with static compression at temperatures above 2000 K have not been reported. The sound veIocity of puré hcp-Fe át high temperatures providés an important cónstraint on the cómposition of Earths coré: any model óf the impurity cómposition of the coré must both sátisfy the density déficit from seismology ánd give an appropriaté velocity. Here, we report the V P of hcp-Fe up to 163 GPa and 3000 K ( Fig. LHDAC) ( 17 ) and IXS measurements ( 18 ). The preferred oriéntation of the sampIe in thé DAC is éstimated using x-ráy diffraction (XRD) pattérn, and the veIocity variation is Iess than 1.5 at 163 GPa and 3000 K (see also the discussion in the Supplementary Materials). The appearance of the crossover density also explicitly indicates a maximum upper bound for the validity of this relation. Fitting our dáta, combined with shóck compression data ( 19 ) along the Hugoniot, gives M 1.160 0.025, B 3.43 0.29, A 7.2 10 5 3.6 10 5, and 14.2 1.5.
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