Most of the shock wave methods used for preheated experiments are described in this chapter. The determination of the molten Mg2SiO4 (forsterite) EOS is presented in Chapter III, together with revised EOS parameters for CaMgSi2O6 (diopsite), CaAl2Si2O8 (anorthite) [Asimow and Ahrens, 2010] and MgSiO3 (enstatite) melts [Mosenfelder et al. , 2009]. This new set of end-member EOS, including fayalite, is used to determine the isentropic temperature profile of a fully molten magma ocean of two hypothetical bulk mantle compositions, chondrite [Andrault et al., 2011] and peridotite [Fiquet et al., 2010], using the isentropic mixture model presented in Chapter II.
In our model, a magma ocean from the entire mantle would first crystallize in the middle lower mantle, or at the base of the mantle, if it were composed of peridotite or. Earth's early history may have included one or more deep ocean events with magma that may have extended to the core–mantle boundary (CMB) [ Labrosse et al ., 2007 ]. Furthermore, changes in chemical equilibria with increasing pressure are defined by the molar volume, the pressure derivative of the Gibbs free energy [ Asimow and Ahrens , 2010 ].
In addition, the detection of ultra-low velocity zones (ULVZ) [ Garnero and Helmberger , 1995 ] at the base of the mantle may indicate the presence of partial silicate melts [ Lay et al ., 2004 ; Mosenfelder et al., 2009; Williams et al., 1998] or more specifically iron-bearing melts [Labrosse et al., 2007]. We have performed new equation of state measurements of molten fayalite (Fe2SiO4) using the following techniques: (i) Archimedean two-bob method for melt density and thermal expansion at ambient pressure (University of Michigan), (ii) ) multiple anvil Sink/float technique to measure melt density at 4.5 GPa (University of New Mexico), and (iii) P-V-E equation of state shock wave measurements at 161 GPa (Caltech).
The latest sink/float measurements are shown in Figure 4 next to two third-order Birch-Murnaghan isotherms (dashed and dotted lines). The isotherms correspond to ρo from this study, the bulk modulus from ultrasonic experiments (KT = 19.4) [Ai and Lange, 2004], and K' from the slope of the latest restricted linear Hugoniot (K'=5.33) (dashed in Figure 4) or K' of the 3rd order Birch-Murnaghan/Mie-Grüneisen (3BM/MG ) (K'=7.28) from this study (dashed in Figure. The details of the 3BM/MG fit are given below in the Thermal equation of the state adjustment section. The geometric arrangement of these spheres gives the contribution of entropy to the compression of the fluid [Jing and Karato, 2011a].
All EOS parameters for each of these compositions, corrected (see above) or recommended by the original authors, are given in Table 5. The revised EOS are discussed in detail in the next chapter (Tables 3 and 4). Karato (2011a), A new approach to the equation of the state of silicate melts: an application of the theory of hard sphere mixtures, Geochim. Estimated shock temperatures are from Chen et al. a) Static image of the back of the molybdenum sample holder, inverted 90 degrees clockwise so that the top is on the left.
The most central circle is the sample chamber or "top hat"; the type wire poles are the smaller circles on the left and right. The yellow vertical lines correspond to the part of the drivers (outer two lines) and top hat (central line) that are sampled for shock wave arrival discontinuities. The dashed blue lines are the 4th order polynomial extrapolation of the shock front shape from the drivers.
Gray arrows indicate the direction of change of liquid composition with partial crystallization of Pv. disregarding Fe partitioning). a) EOS parameters used for En and Fo are given in Table 5 and Fa 3BM parameters in Table 4. b) EOS parameters used for En and Fa are given in Table 4 and Fo 3BM parameters in Table 3 of Chapter III.
Figure 9
This latter idea is partly based on the simplified modeling of the mantle as an isochemical MgSiO3 system [Mosenfelder et al., 2009], which would begin crystallization in the midmantle of a full-mantle magma ocean. Asimow and Ahrens , 2010 ]. The boards were also cut with a slot from the center hole to the bottom including two separate inch-deep slots at the top (a Y shape) to relieve mechanical stresses caused by thermal expansion of the board while at high temperatures. The procedure for the selection of cutoffs and the calibration of the streak velocity is described in Thomas et al.
The 95% confidence interval for the fit was used as the upper and lower bounds for the location of the shock front and was the largest source of error in the calculated final shock state—that is, the error bars for the shock pressure shock (PH), shock density (ρH), particle velocity (up) and shock wave velocity (Us). However, this idea is contrary to the previous assumption that silicate minerals require such great fluid overpass that partial melting does not occur [Akins et al., 2004]. However, only excluding these points does not resolve the inconsistent behavior obtained by simultaneously fitting the lowest pressure points of Ridgen et al., the high pressure data of Asimow and Ahrens, and the bulk sound speed of 1 bar [Lange and Carmichael, 1990].
Although several plausible explanations can be put forward for the seemingly unusual character of the Ridgen et al. Second, it has been shown that crystallization during the experiment is unlikely, since the rise time of the shock wave in the sample is much shorter than the time required for crystallization [Rigden et al., 1988]. Using the 3BM/MG EOS fit (calculated in Section 3.3 ), Figure 6 shows that even for the highest temperature estimates of the Mg2SiO4 liquidus curve [ de Koker et al ., 2008 ; Ohtani and.
2009] (which includes the static data from Saxena et al. [1999]), the density of Pv at each intersection can be calculated to determine whether the first formed crystals would sink or float. To calculate the densities of the mantle solids, (Mg,Fe)SiO3 perovskite (MgPv) and (Mg,Fe)O ferropericlase (Fp), we used the EOS given in Mosenfelder et al.[2009] too clean. The solid lines represent curves of constant density contrast for the melt and the residue, where positive percentages are a partial melt density and negative percentages are a residue denser than the melt. The ULVZ density range is delimited by dashed lines representing a density 6 -14% denser than PREM kg/m3).
These new data enable a revision of the previous liquid Mg2SiO4 EOS [Mosenfelder et al., 2009]. Behavior of the Grüneisen parameter for liquid Mg2SiO4 (dense, solid green) compared to the previously reported value (dashed) [Mosenfelder et al., 2009]. The estimated path of the T-P Hugoniot (dashed line) and lightning #1077 (diamond) (see Table 1) lie within the fluid field.
XMg/(XFe+XMg). The density of the ULVZ is the blue area bounded by dashed lines. An estimate for the ambient mantle composition of 80% MgPv +20% Fp (fpv =0.8) with a Mg# of 0.85 is given with its calculated aggregate density (agg ρ) with 30% volume fraction of partial melt.. The unphysical area on the graph indicates where the Mg# of the partial melt is negative and therefore represents total densities unattainable with the given amount of Fe in the system). For a full description of the thermal EOS equations and fitting procedures, the reader is referred to Asimow and Ahrens [2010] and Thomas et al.
In the VB model, the Ca would have a larger “share” of the O valence due to the.
