Low frequency bulk modulus of partially molten peridotite, KLB-1

https://doi.org/10.1016/j.pepi.2021.106677Get rights and content

Highlights

  • The bulk modulus of partial molten peridotite at mHz frequency have been measured in a multi-anvil apparatus coupled with synchrotron X-ray radiation.

  • The bulk modulus is drastically reduced at the onset of the melting, as predicated by dynamic melting model.

  • Low frequency bulk modulus is important to improve our understanding of how phase transitions affect seismic velocity at seismic frequencies.

Abstract

We report experimental results on the bulk modulus of partially molten peridotite at mantle conditions, using a multi-anvil high pressure apparatus coupled with synchrotron X-ray radiation. A sinusoidal pressure at an amplitude of 180 MPa with period of 360 s is applied to the sample as a function of temperature. The sample volume derived from the X-ray radiograph also demonstrated sinusoidal variation at the same frequency. The derived bulk modulus from the amplitude of the stress and strain shows that the bulk modulus is drastically reduced at the onset of the melting, as predicated by dynamic melting model.

Introduction

Partial melting is one of the most important processes affecting seismic velocity, our primary window into the structure of the Earth's interior. Knowing that the Earth's interior is hot enough in some places to partially melt, we often look to melting as the cause of lowered seismic velocities. There are many regions within the Earth where seismic velocities are reduced that stand as candidates for partial melting. The low velocity zone located at around 100 km depth to the ultra low velocity zone at the core mantle boundary, there are many features that may be associated with partial melting (He and Wen, 2009; Long, 2014; Vinnik and Farra, 2007; Wang and Wen, 2007; Wang et al., 2008; Wang et al., 2010; Yao and Wen, 2014). These different zones represent a wide pressure range, potentially a diverse composition, and significantly different temperatures.

The work by Spetzler and Anderson (1968) demonstrated that even a few percent of melt in a salt-water/ice system significantly lowers the shear modulus stimulating the postulate that partial melting in rocks would create a low velocity region. Models of this phenomena confirmed the possibility of the exaggerated effect of small amounts of fluid on the shear modulus providing that the fluid is present as thin platelets (Faul et al., 2004; Hammond and Humphreys, 2000a; Hammond and Humphreys, 2000b; Jackson et al., 2006; O'Connell and Budiansky, 1977; Schmeling, 1985; Takei, 2000; Walsh, 1969). The consensus of these models is that the bulk modulus is not affected by partial melting. However, this study by Spetzler and Anderson (1968) as analyzed by Weidner et al. (2017) for the salt – water system indicates a reduction of the bulk modulus by 8% with an initial partial melting of 3% and a drop by over 30% with 6% melt, information that contradicts the subsequent models. Thus, even the initial data that was a major stimulus for the models that describe the role of partial melt on seismic velocity is significantly incompatible with these models in regard to the effect on bulk modulus.

Li and Weidner (2013) argue that the effective bulk modulus of a material undergoing melting must include the pressure – volume relation of the melting process in that pressure change induces changes in the percent of melt that in turn affects the total volume of the sample. Fig. 1 illustrates the significance of the melting transformation on the effective bulk modulus. The curves in Fig. 1 are derived from the MELTS (Ghiorso et al., 2001; Smith and Asimow, 2005) program for a peridotite with the composition of KLB-1, with an adaption in which the effect of solid-solid transformations are removed from the calculation. This adaption may change details of the curves, but not the main theme. Fig. 1a illustrates the volume percent melt and density of a peridotite sample as a function of pressure at 1400 °C at thermodynamic equilibrium. The partial melt is over 20 vol% at 1 GPa and nearly vanishing by 2.5 GPa. The melting has induced a density change of about 0.1 g/cm3. The bulk modulus is proportional to the inverse of the slope of the density – pressure curve and the calculated bulk modulus is illustrated in Fig. 1b. As partial melting has introduced a significant change in the slope of the density curve, the resulting bulk modulus demonstrates a considerable change, ranging from about 10 GPa to about 130 GPa. Restricting ourselves to the region below 5% melting, we still find the bulk modulus tripling as the liquid disappears.

This picture is further complicated by considerations of time. Partial melting in peridotite requires atom migration. For example, the melt composition is composed of atoms from all solid phases. Since diffusion consumes time, one concludes that the effective bulk modulus may be a function of time, reflecting the kinetics of melting. Thus, bulk modulus of peridotite at mHz frequency is necessary to compare with the seismic observations. Li and Weidner (2013) obtained an anomalously low Young's modulus in the partially molten region of a peridotite as measured at about 1 mHz. They proposed a dynamic melting mechanism, where the stress field associated with measuring the Young's modulus induced melting and was responsible for this observation. The premise of this model is that the phase transition between the solid and liquid is fast enough that it can keep up with the oscillating stress field associated with the measurement. This would be valid for propagating acoustic waves if the transformation responded to the stress field of the propagating wave. We would expect that 100 s surface waves would provide enough time for the phase equilibria to couple with the wave stress field, but it would be questionable as to whether or not the melting would interact within a 10 ns period of an ultrasonic wave. Thus, it is likely that MHz ultrasonic velocities will not experience a significant bulk modulus softening.

Separating the effects on shear modulus and bulk modulus allows one to identify the mechanisms contributing to the change in acoustic velocity. In this study, our focus is to measure the bulk modulus of partial molten peridotite at seismic frequency. We also use the thermodynamic model to assist interpreting the mechanisms.

There are a few studies that demonstrate data that can help resolve the impact of melting on the bulk modulus. Cline and Jackson (2016)) report experiments of both torsional and flexural oscillations on an olivine + basalt sample at 200 MPa during melting with the hope of evaluating both the bulk modulus and the shear modulus. While they concluded that no reduction in the bulk modulus was required, they also concluded that there was poor resolution of the bulk modulus in this data. Furthermore, we evaluated the expected impact of dynamic melting on their sample composition at 200 MPa with the MELTS program and conclude that little or no change in bulk modulus is expected (Weidner et al., 2017). At these conditions the basalt melts over a rather narrow temperature range and the amount of melt changes very slowly outside of this range. Similar calculations at 1–3 GPa are quite different, with the bulk modulus strongly affected by dynamic melting. Analogue materials in addition to the salt-water system described above that can be studied at room pressure have been used to model the effects of melting. (Takei, 2000) measured the P and S velocities in a hydrocarbon system that exhibits eutectic melting at room pressure and about 40 °C and MHz frequency. In this system, the bulk sound velocity did not change on melting from 3% to over 10% melt. This suggests that dynamic melting did not soften the acoustic bulk modulus. One possibility is the kinetics of melting in this hydrocarbon system is too slow for ultrasonic waves to activate the phase transition. (Weidner et al., 2017) measured ultrasonic velocities of partially molten KLB-1. They argue that the deduced bulk modulus of not only their study, but also the experimental study of Chantel et al. (2016) was reduced more than predicted by the model of Hammond and Humphreys (2000b) suggesting that the dynamic melting process was at least partially active at 10 ns.

With propagating elastic waves, dynamic melting can sample an altered bulk modulus with an effect that increases with decreasing frequency. In addition, the thermodynamics of non-hydrostatic stress suggest that the same mechanism will also be active for the shear modulus. In addition, the shear modulus will also be softened by the classical mechanism (Walsh, 1969; Hammond and Humphreys, 2000b). The dynamic melting softening will occur subject to the following conditions. 1) The density of the liquid is different from the density of the solid. In the MELTS calculation for KLB-1, the density of the liquid is generally less than 2.8 g/cm3 while the solid is around 3.3 g/cm3. 2) The period must be longer than the kinetic time for the reaction. Total equilibrium is not required, but volume change is required. Weidner and Li (2015) concluded that the characteristic time constant for the KLB-1 sample is less than a second, while their ultrasonic studies (Weidner et al., 2017) indicated a smaller effect at 10 ns. 3) The assumption is based on the transformation between the liquid and the stable crystalline assemblage. Metastable transformations to glass or to crystalline materials with non-equilibrium compositions will change the size of the effect.

Motivated by the above models, we set on a campaign to experimentally measure the bulk modulus at long periods for the partially molten peridotite, KLB-1, at conditions near to that of the low velocity zone. In particular, we focus on measuring the bulk modulus at low frequency (mHz range) near the solidus where the melt volume is no more than a few percent. Here we report our initial results.

This study was performed at the Advanced Photon Source (APS), a high energy synchrotron located at Argonne National Laboratory, on beamline 6-BMB using a white X-ray beam at a bending magnet source (Li et al., 2020). A solid-pressure media large-volume DDIA device was used to compress the sample to about 1.5 GPa. At this point, pressure is sinusoidally varied at a period of 360 s as the sample is step heated from the subsolidus region into the partial molten zone. After reaching the final temperature of 1545 °C, the temperature was quenched by turning off the furnace. Finally, the sample was slowly decompressed and prepared for SEM observations. Each step was 5 cycles long (30 min). The amplitude of the pressure sine wave was 0.18 GPa for experiment KLB-1_85. The sinusoidal pressure field was generated by sinusoidally driving the motor that pushes the piston in the displacement pump that delivers hydraulic oil into the main ram of the DDIA device. As there was no control on the press force, it rose as the system heated during the 5 h of the experiment from 17 to 18 tons.

The sample, fine ground KLB-1 peridotite powder (Takahashi, 1986) (~5 μm grain size), was cold pressed to 1.5 GPa, then heated to subsolidus conditions (c.a. 850 °C) and annealed for 30 min. The melting relations of this peridotite have been thoroughly studied as a function of pressure (Herzberg et al., 1990; Takahashi, 1986; Takahashi and Scarfe, 1985) as a model mantle composition. A crushable corundum rod is placed above and below the sample (see cell assembly in Fig. 2). A rhenium foil (100 μm thickness) is used to wrap the cylindrical sample (1.2 mm diameter, 2.4 mm long) to serve as the lateral strain marker, in X-ray images. Re discs are also placed above and below the sample. We used 4 sintered diamond anvils as the lateral anvils so that the entire sample is visible in the X-ray beam as demonstrated in Fig. 3.

X-ray diffraction patterns were gathered with our 10 element conical slit system in which each element simultaneously collects a diffraction pattern, but are arrayed in a circular pattern to yield constraints on the deviatoric stress field (Weidner et al., 2010). In each 30 degrees of the sine wave, one diffraction data set and one image are gathered, the diffraction alternating between the sample and the corundum end-plug. This yields six diffraction data sets for the sample and six for the corundum during a single cycle along with twelve images. The diffraction is used to define pressure (and possible stress) variations and the images are designed to yield the strain field of the sample. In total, nearly 8000 individual diffraction spectra and 800 images were collected in this run.

The data collection protocol yields about 23 s to gather the energy dispersive diffraction signal. This coupled with the absorption of X-rays through the Re foil affected the quality of the diffraction data and led us to collect data from the corundum end plugs since there is no Re around them. Furthermore, the diffraction data from the KLB-1 sample suffers from recrystallization at temperatures where melting begins to be present. All in all, the diffraction patterns of the sample are fairly poor, but with two or three strong olivine peaks still resolvable and one peak (112) being present at most diffraction spectra. Temperature was calibrated with separate experiments for the same cell assembly. Based on the wattage of the furnace, temperature reached 1545 °C in the run KLB-1_85 in steps of 25o over the last 5 steps, with larger temperature steps at lower temperature.

The SEM image of the entire sample is illustrated in Fig. 4a. Several insets show expanded images for illustration. Fig. 4b illustrates long thin rivers of fluid radiating from the center of the cylindrical sample. Here the melt has gathered into these zones that are much larger than the individual grain size. This is probably the hottest region of the sample as it is in the axial center, but closest to the outside of the cylindrical sample and closest to the furnace. Along the axis of the cylinder (Fig. 4c), there is less visible melt. Towards the ends of the cylinder, there is less melt, eventually merging into regions that have no obvious melt texture (Fig. 4d), suggesting that this region remains subsolidus throughout the experiment. At the end of the run the sample was 2.4 mm long. According to the results of (Raterron et al., 2013), this size of sample will have a temperature variation of 230 °C from the center to the end. By comparison a 1 mm long sample will exhibit a temperature range of only 40 °C. In our sample, at peak temperature of 1545 °C in the center should be at about 1300 °C on the ends. This is subsolidus for KLB-1 using the MELTS program at 1.5 GPa (our estimated pressure). We used long samples so that we could resolve the strain, but at the cost of such high temperature variations in the sample.

In examining the quenched sample center, we are looking at a sample that is about 200 degrees hotter than our target sample, one near the solidus. The MELTS program predicts about 30% melting at the higher temperature, at which we would expect the melt pockets to be quite interconnected and draining the solid sample. The sample texture that we are more interested in lies towards the end of the sample, where melt is just appearing. This represents the texture that we would find in the center at about 1350 °C. There the texture is dominated by multiple solid phases with small intergranular melt pockets.

Section snippets

Results

We use diffraction and image measurements in this study, ultimately giving us two measurements of strain. The image-strain is the strain defined by the outline of the rhenium capsule that holds the sample. As we view only two dimensions of the sample, corresponding to the axial and one radial direction, we need to assume that the other radial strain is the same as the observed one. Then the volume strain is the sum of the three linear strains. Diffraction yields spacing between lattice planes.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Acknowledgements

This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357 on beamline 6BMB with the support of Haiyan Chen. The research was supported by the U.S. National Science Foundation (NSF) grant EAR 1809165. This research was partially supported by COMPRES, the Consortium for Materials Properties Research in Earth Sciences under

References (31)

  • C.J. Cline et al.

    Relaxation of the bulk modulus in partially molten dunite?

    Geophys. Res. Lett.

    (2016)
  • U.H. Faul et al.

    Shear wave attenuation and dispersion in melt-bearing olivine polycrystals: 2. Microstructural interpretation and seismological implications

    J. Geophys. Res.-Solid Earth

    (2004)
  • M.S. Ghiorso et al.

    The pMELTS: a revision of MELTS for improved calculation of phase relations and major element partitioning related to partial melting of the mantle to 3 GPa

    Geochem. Geophys. Geosyst.

    (2001)
  • W.C. Hammond et al.

    Upper mantle seismic wave attenuation: effects of realistic partial melt distribution

    J. Geophys. Res.-Solid Earth

    (2000)
  • W.C. Hammond et al.

    Upper mantle seismic wave velocity: effects of realistic partial melt geometries

    J. Geophys. Res.-Solid Earth

    (2000)
  • Cited by (1)

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