The effect of nickel on the strength of iron nickel alloys: Implications for the Earth’s inner core
Introduction
The Earth’s inner core, located 5150–6370 km within the planet, is subjected to extreme pressure and temperature conditions that range from 330 to 364 GPa and ∼4000–7000 K (Antonangeli, 2016). It is primarily composed of iron with 5–15% nickel, and a certain amount of light element(s) (Birch, 1952, Birch, 1964, Hirose et al., 2013). At inner core conditions, iron-rich FeNi alloys likely crystallize in an hexagonal close packed (hcp) phase (e.g., Lin et al., 2002, Liu et al., 2016; Mao et al., 2006; Tateno et al., 2010, Tateno et al., 2012, Sakai et al., 2011), although one recent theoretical study suggests that the stable phase may be body centered cubic (bcc) (Belonoshko et al., 2017). The Earth inner core exhibits a complex structure with seismic anisotropy, where seismic waves travel ∼3% faster in the polar than the equatorial direction (Creager, 1992, Morelli et al., 1986, Shearer, 1994, Song and Helmberger, 1993, Tromp, 1993, Woodhouse et al., 1986), and lateral and hemispherical variations (Bréger et al., 2000, Cao and Romanowicz, 2004, Creager, 1999, Deuss et al., 2010, Irving, 2016, Song and Helmberger, 1995, Sun and Song, 2002, Vinnik et al., 1994). Gleason and Mao (2013) extrapolated the shear strength of pure iron to inner core conditions and determined it was weaker than previously thought, supporting that dislocation creep may be the dominant creep mechanism in the inner core. Pure Fe has been used as a proxy to understand the nature of the inner core including numerous studies on materials properties at high pressure and high temperature conditions (e.g. Struzhkin et al., 2004, Shen et al., 2004, Mao et al., 2008, Lin et al., 2005, Mao et al., 2001, Merkel et al., 2013, Tateno et al., 2010). There is a measured velocity-density profile discrepancy between the values of pure Fe and the those of the inner core, together with cosmochemical and geochemical observations, indicting the presence of Ni and other light elements (Birch, 1964), thus quantifying the effects of the addition of Ni on the geophysical properties of Fe is important. We examined the effect of varying nickel content on the strength of pure iron by studying Fe0.88Ni0.12 and Fe0.8Ni0.2 up to 70 GPa.
We define strength, t, as the maximum shear stress a material can withstand before undergoing plastic deformation. All values were calculated by anisotropic linear elasticity theory using the following methodology developed by Singh and Balasingh, 1994, Singh et al., 1998a, Singh et al., 1998b. Non-hydrostatic pressure conditions produce lattice strains in a sample loaded into a diamond-anvil cell (DAC) that can be measured using radial X-ray diffraction, where the X-ray beam is nearly perpendicular to the compression axis. The geometry of a radial X-ray diffraction experiment is shown in Fig. 1. Samples in a DAC experience two stresses: axial stress, σ3, and radial stress, σ1. The deviatoric stress component is given by t = σ3 − σ1, equivalent to the lower bound of the shear strength, which we refer to as t. Line shifts in the diffraction pattern provide a measure of the deviatoric strain relative to the hydrostatic strain for a crystallographic orientation and lattice plane. The d-spacing measured under non-hydrostatic compression, dm (hkl), is given bywhere dp (hkl) is the d-spacing under hydrostatic condition, ψ, is the angle between the compression direction and the diffraction vector, and Q (hkl) is the differential strain. When ψ = 54.7° gives dp (hkl), the d spacing equals that of hydrostatic conditions. Eq. (1) is valid for all crystal systems. The deviatoric strain produced by d(hkl) for a given ψ is given by
A material’s strength can be related to its shear modulus, G, and the average value of the differential strain, <Q(hkl)>, for all observed reflections by
Section snippets
Methods
The Fe0.88Ni0.12 and Fe0.8Ni0.2 starting materials were synthesized with Fe and bbNi nanopowders, along with a small amount (1.7 vol%) of Si nanopowder (supplier, Alfa Aesar). Two different powder mixes were made, one with 80%Fe-20% Ni and the other with 88%Fe-12% Ni atomic abundances. The nanopowder mix was ultrasonicated in ethanol for several hours to mix thoroughly and dried in air. The powder mix was placed in a silica glass crucible, which was then inserted into a larger silica glass
Results and discussion
Strength measurements were collected up to 47 GPa for Fe0.88Ni0.12 and 70 GPa for Fe0.8Ni0.2. Fe0.88Ni0.12 completed a transition to the hcp structure at 20 GPa and steadily increased in strength from 2.0 GPa to 2.8 GPa between 21 and 47 GPa. Fe0.8Ni0.2 made a complete transition to hcp at 35 GPa. Strength measurements were collected up to 70 GPa and are seen to increase from 1.6 to 4.2 GPa (Table 1). Fig. 3 shows a comparison of the different strength measurements for Fe0.88Ni0.12, Fe0.8Ni0.2,
Acknowledgements
M.M. Reagan, A.E. Gleason, and W.L. Mao are supported by the NSF Geophysics Program (EAR-1446969); and LANL LDRD for Gleason. M. J. Krawczynski was supported by NASA grant NNX15AJ25G. We thank Changyong Park (APS), Martin Kunz (ALS), and Jinyuan Yan (ALS) for their assistance with the synchrotron experiments. Portions of this work were performed at beamline 12.2.2 of ALS, LBNL. ALS is supported by the Director, Office of Science, Office of Basic Energy Sciences (BES), of the U.S. Department of
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