PUBLICATIONS
Journal of Geophysical Research: Solid Earth
RESEARCH ARTICLE
10.1002/2016JB012973
Key Points:
• Volumetric and elastic properties of
basalt glass are anomalous and violate
Birch’s law
• Such behavior is attributed to mode
softening due to silicate network
flexibility
• Similar behavior for basaltic melt
enhances the velocity reduction at
crustal and mantle conditions
Supporting Information:
• Supporting Information S1
• Tables S2 and S3
Correspondence to:
A. N. Clark,
[email protected];
[email protected]
Citation:
Clark, A. N., C. E. Lesher, S. D. Jacobsen,
and Y. Wang (2016), Anomalous density
and elastic properties of basalt at high
pressure: Reevaluating of the effect of
melt fraction on seismic velocity in
the Earth’s crust and upper mantle,
J. Geophys. Res. Solid Earth, 121,
doi:10.1002/2016JB012973.
Anomalous density and elastic properties of basalt at high
pressure: Reevaluating of the effect of melt
fraction on seismic velocity in the Earth’s
crust and upper mantle
Alisha N. Clark1,2, Charles E. Lesher1,3, Steven D. Jacobsen4, and Yanbin Wang5
1
Department of Earth and Planetary Sciences, University of California, Davis, California, USA, 2Now at CNRS UMR 7590,
Institut de minéralogie et de physique des milieux condensés, Université Pierre-et-Marie-Curie, Paris, France, 3Department
of Geoscience, Aarhus University, Aarhus, Denmark, 4Department of Earth and Planetary Sciences, Northwestern University,
Evanston, Illinois, USA, 5Center for Advanced Radiation Sources, University of Chicago, Chicago, Illinois, USA
Abstract
Independent measurements of the volumetric and elastic properties of Columbia River
basalt glass were made up to 5.5 GPa by high-pressure X-ray microtomography and GHz-ultrasonic
interferometry, respectively. The Columbia River basalt displays P and S wave velocity minima at 4.5 and
5 GPa, respectively, violating Birch’s law. These data constrain the pressure dependence of the density
and elastic moduli at high pressure, which cannot be modeled through usual equations of state nor
determined by stepwise integrating the bulk sound velocity as is common practice. We propose a
systematic variation in compression behavior of silicate glasses that is dependent on the degree of
polymerization and arises from the flexibility of the aluminosilicate network. This behavior likely persists
into the liquid state for basaltic melts resulting in weak pressure dependence for P wave velocities
perhaps to depths of the transition zone. Modeling the effect of partial melt on P wave velocity reductions
suggests that melt fraction determined by seismic velocity variations may be significantly overestimated
in the crust and upper mantle.
1. Introduction
Received 6 MAR 2016
Accepted 1 JUN 2016
Accepted article online 3 JUN 2016
©2016. American Geophysical Union.
All Rights Reserved.
CLARK ET AL.
Seismic velocities are sensitive to the thermoelastic properties and density of the constituent crystalline
phases, among other factors including grain size and fabric [Anderson and Spetzler, 1970; Birch, 1961a; Faul
and Jackson, 2005] and therefore can be used to constrain the thermal, chemical, and physical structures
of the Earth’s interior. Global seismic velocity profiles generally increase with depth, and abrupt velocity
increases are associated with lithological boundaries (i.e., Moho) or mineral phase transitions (410 and
660 km discontinuities) (e.g., preliminary reference Earth model and AK135-F) [Dziewonski and Anderson,
1981; Kennett et al., 1995]). Velocities that are slower than global average models at a given depth in the
crust and upper mantle are commonly attributed to the presence of partial melt and/or aqueous fluids
(e.g., lithosphere-asthenosphere boundary, Yellowstone, Hawaii, Japan arc) [Anderson and Spetzler, 1970;
Hammond and Humphreys, 2000; Hirschmann, 2010; Karato and Jung, 1998]. The amount of melt causing a
given velocity reduction is not well constrained principally due to uncertainties in elastic properties, density,
and wetting behavior of melts at high pressure.
Laboratory measurements of density and acoustic velocities of silicate melts at high pressure and temperature are notoriously difficult to make, and thus, applications to planetary interiors often rely on tenuous
extrapolations using constitutive relations developed for crystalline solids. Birch’s law [Birch, 1961b] refers
to the linear correlation between longitudinal (P wave) velocity and density for materials of similar mean
atomic weight, even when density changes involve significant structural changes. These relationships
are shown in Figure 1 for the polymorphs of Mg2SiO4 (olivine, wadsleyite, and ringwoodite) and SiO2
(cristobalite and coesite). Birch’s law also holds well for crystalline phases and their vitreous counterparts,
i.e., cristobalite, coesite and SiO2 glass, enstatite and MgSiO3 glass, diopside, and CaMgSi2O6 glass (#1, 2,
and 4 in Figure 1, respectively). Although most of the data in Figure 1 are at standard temperature and
pressure (STP) conditions, the utility of Birch’s law at high pressure and through polymorphic phase transitions is also illustrated by the compression data for orthoenstatite through the high-pressure clinoenstatite
transition [Kung et al., 2004].
BASALT AND HIGH-PRESSURE MELT VELOCITY
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Figure 1. Relationship between density and velocity for silicate crystals (triangles), glasses (squares), and melts (circles).
One-atmosphere and high-pressure data are shown as large and small symbols, respectively. The dashed lines are lines
of constant mean atomic weight (m), the molecular weight divided by the number of atoms in the chemical formula.
Birch’s law states that for a constant m there is a linear relationship between density and velocity. The numbers next to
the symbols indicate composition, which are given with reference below. 1—SiO2 (coesite [Weidner and Carleton, 1977],
β-cristobalite [Bass, 1995], glass [Clark et al., 2014] (high pressure) [Meade and Jeanloz, 1987; Sato et al., 2011; Tsiok et al.,
1998; Weigel et al., 2012], and melt [Polian et al., 2002]), 2—MgSiO3 (orthoenstatite [Weidner et al., 1978] (high pressure)
[Kung et al., 2004], glass [Sanchez-Valle and Bass, 2010], and melt [Rivers and Carmichael, 1987]), 3—CaSiO3 (glass [Bass,
1995] and melt [Rivers and Carmichael, 1987]), 4—CaMgSi2O6 (diopside [Levien et al., 1979], glass [Soga et al., 1976], and
melt [Rivers and Carmichael, 1987]), 5—CaAl2Si2O8 (anorthite [Bass, 1995], glass [Bass, 1995], and melt [Rivers and
Carmichael, 1987; Secco et al., 1991]), 6—NaAlSi3O8 (albite [Bass, 1995] and glass [Bass, 1995]), 7—Mg2SiO4 (olivine [Bass,
1995], wadsleyite [Sawamoto et al., 1984], and ringwoodite [Weidner et al., 1984]), 8—Fe2SiO4 (fayalite [Isaak et al., 1993]
and melt [Rivers and Carmichael, 1987]), 9—andesite (glass [Meister et al., 1980] and melt [Rivers and Carmichael, 1987]),
and 10—basalt (glass [Meister et al., 1980] and melt [Rivers and Carmichael, 1987]).
In contrast to the many examples of Birch’s law highlighted above, some silicate glasses and melts are
anomalous. Figure 1 plots data for a large number of simple and natural silicate glasses and melts spanning
densities from 2.2 to 3.7 g/cm3. These amorphous materials represent a wide range of composition and
structure, i.e., polymerization states, but notably exhibit a relatively restricted range in P wave velocities,
i.e., 5.5–7 km/s for glasses and ~2–3 km/s for melts. Furthermore, compression of silicate glasses (i.e., SiO2
and MgSiO3 glass) show anomalous relationships between density and P wave velocity (Figure 1). In the case
of SiO2 glass, the P wave velocity initially decreases with increasing density reaching a minimum at ~2 GPa,
and while there is a positive density-velocity relationship at higher pressures, the P wave velocity at 6 GPa
is still 5.5% slower than the one atmosphere value. Likewise, MgSiO3 glass shows a similar weak dependence
of P wave velocity on density up to ~8 GPa. At higher pressures the increasing P wave velocity with density
actually exceeds that predicted by Birch’s law between 10 and 29.5 GPa. Thus, Birch’s law appears to have less
clear predictive utility for silicate glasses and melts.
Here we report new experimental results for volumetric measurements by high-pressure X-ray microtomography and acoustic wave travel times measured by GHz-ultrasonic interferometry that constrain the
pressure dependence of density and P and S wave velocities in Columbia River basalt glass up to 5.5 GPa.
CLARK ET AL.
BASALT AND HIGH-PRESSURE MELT VELOCITY
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From the acoustic wave travel times
we compute acoustic velocities as
a function of pressure, examine
their frequency dependence, and
show that P (and S) wave velocities
decrease with pressure (and density)
up to ~4.5 GPa—opposite to expectations of Birch’s law. We discuss
trends between the elastic properties and compressibility of network
glasses in terms of network flexibility and extend these insights to the
liquid state. In light of these findings, we consider the implications
for seismology, specifically the
quantification of partial melt fraction
in low-velocity regions of the Earth’s
crust and upper mantle.
2. Materials and Methods
2.1. Sample Characterization
Figure 2. (a) Cross section of the HPXMT experimental cell assembly. See text
and the supporting information for further discussion of HPXMT technique.
(b) Radiographs of the basalt sample (dark material—higher X-ray absorption)
loaded in MgO powder (light material—lower X-ray absorption) (left) loaded to
0.3 GPa and (right) compressed to 5.2 GPa.
Experiments were performed on
Columbia River basalt glass (BCR-2
USGS
Geochemical
Reference
Material) with 54.1 wt % SiO2. The
water content (0.35 wt %) was determined by Fourier transform infrared
spectroscopy and is given together
with the bulk composition in the
supporting information. This small
fraction of water is not expected
to significantly affect the physical
properties [Malfait et al., 2011]. The
density for Columbia River basalt
glass at room temperature and oneatmosphere is 2.700 ± 0.002 g/cm3
measured by Archimedes method.
2.2. High-Pressure X-ray
Microtomography (HPXMT)
The density of basalt glass as a function of pressure is determined by
X-ray microtomography utilizing with the rotating anvil apparatus (RAA) on the GeoSoilEnviroCARS
(GSECARS) beamline 13-BM-D at the Advanced Photon Source, Argonne National Laboratory, and methods
described by the present authors [Lesher et al., 2009; Wang et al., 2005, 2011]. To produce a threedimensional rendering of the interior components of the experimental assembly including the sample,
the entire cell is rotated through 180° with radiographs acquired at finite angular increments. This is
accomplished for samples under pressure using the RAA, which consists of two coupler plates mounted
to opposing HarmonicDrive™ units supported by low-profile thrust bearings and driven by stepper motors
through gearboxes. The top and bottom plates of the RAA are advanced onto the experimental assembly
using a 250 t hydraulic press mounted on a computer-controlled positioning stage.
The experimental assembly consists of a boron epoxy (BE) gasket surrounded by a 10 mm i.d., 20 mm OD
containment ring. Two 10 mm × 10 mm tungsten carbide Drickamer-style anvils with 20° tapers truncated
CLARK ET AL.
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Figure 3. Schematic diagrams of the GHz-ultrasonic interferometry experiment (a) room-pressure P wave experiment
and (B) high-pressure S wave experiment. Modified from Clark et al. [2014]. See text and the supporting information for
further discussion.
to 4 mm faces are inserted into the ends of the containment ring and fit flush to the BE gasket. The sample is a
precision ground ~1 mm diameter × 0.5 mm thick disk of Columbia River basalt glass that is inserted into a
1.6 mm cylindrical hole in the BE gasket and surrounded by firmly packed MgO powder. The MgO serves
as the pressure standard and forms a high-contrast interface against the basalt glass sample. Pressure is
determined using the equation of state of MgO (periclase) [Kennett and Jackson, 2009]. Figure 2 shows a cross
section of the experimental assembly and corresponding radiographs displaying the large attenuation
contrast between the basalt glass (dark grey) and periclase pressure standard (light grey).
Data preprocessing involves subtracting the dark and white field intensities from each radiograph, locating
the center of rotation, and performing the Radon transform and grid reconstruction to yield 2-D slices perpendicular to the axis of rotation. All of the above operations are accomplished using the in-house IDL software TOMO_DISPLAY [Rivers and Wang, 2006]. Horizontal slices are imported into Blob3D [Ketcham and
Carlson, 2001], where pixel dimensions and intensity are assigned. The pixel brightness is assigned a value
that ranges from 0 to 255 (in the case of an 8-bit image) with the intensity of 255 for a fully saturated pixel
and 0 for a pixel that received no light signal. These refined 2-D slices are stacked to render the sample in
3-D. Segmentation is performed to isolate the sample (Columbia River basalt glass) from its immediate
surroundings, i.e., periclase. The volume-pixel (voxel) elements of the sample are defined by the range
of intensity values and are isolated during segmentation. Segmented voxels are summed to yield the total
volume occupied by the sample. Additional filters may be applied if voxel elements are isolated or poorly
connected for either exclusion or inclusion into the volume calculation. Further details of the methods are
provided in the supporting information.
2.3. Gigahertz-Ultrasonic Interferometry
The elastic properties of the Columbia River basalt glass are determined by GHz-ultrasonic interferometry [Jacobsen et al., 2002, 2004]. Figure 3 shows schematic cross sections of the ultrasonic interferometry
system at Northwestern University capable of measuring both P and S wave travel times (in different
configurations) over the frequency range of 800–2000 MHz. P wave tone bursts (~101–102 ns duration)
are generated by a thin-film ZnO transducer sputtered onto the end of an acoustic buffer rod (sapphire
and yttrium-aluminum-garnet single crystals for P and S wave buffer rods, respectively), which is tapered to a
200 μm diameter polished face for acoustic coupling by force either directly to the sample, or to the table
CLARK ET AL.
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Journal of Geophysical Research: Solid Earth
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of the diamond-anvil in high-pressure
experiments. Pulse echoes from the
buffer rod-sample interface (diamond
anvil culet—sample interface at high
pressure in the diamond anvil cell
(DAC)) and from the far-end of the
sample are interfered in time, and
when the frequency is scanned, the
resulting acoustic interference spectrum is used to determine the roundtrip travel time (t) by the spacing of
frequency maxima and minima. The
velocity (v) is determined from the
sample thickness (L) related by
Figure 4. Compression curve of basalt from 0 to 6 GPa measured by HPXMT
shown as circles. The densification of basalt can be modeled as a second2
order polynomial up to 6 GPa (dotted curve: y = 0.0022x 0.0369x + 1
2
(R = 0.99284)). The errors in pressure and volume rendering are discussed in
the supporting information. The green field is the predicted volumes
calculated from both the third-order Birch-Murnaghan and Vinet equations
of state using the one-atmosphere KS measured by GHz-ultrasonic interferometry and a range of K0′ = 0 to 10 (solid curve K0′ = 1.8). The diamonds
are density calculated by integrating equation (2). For comparison the
compression curves measured by refractive index for tholeiitic [Kuryaeva
and Kirkinskii, 1997] and alkali [Kuryaeva, 2004] basalts are shown as closed
and open squares, respectively. Also, the compression curve extrapolated
from low-pressure (0–0.8 GPa) MHz-ultrasonic data [Meister et al., 1980] using
a 3BM-EoS is shown as the dashed curve.
v¼
2L
:
t
(1)
In order to obtain high-precision
room-pressure P and S wave velocity measurements, a thick sample
of Columbia River basalt glass
was double polished to ~1 mm
thickness. Following both P and S
wave measurements, a newly developed optical-contact micrometer
[Chang et al., 2014] was used to
measure the sample thickness at
the point of ultrasonic measurements
to within ±0.05 μm. Resulting uncertainties in the STP vP and vS measurements are ±5.8 and 2.2 m/s,
respectively.
For high-pressure measurements in the DAC, we use the interfered echoes from the near and farside of the
sample in contact with the diamond anvil (Figure 3b). Ultrasonic data were collected by measuring the
interfered and reference (diamond culet echo) amplitude as a function of frequency at 4 MHz steps from
0.8 to 1.5 GHz for P waves and 0.7 to 1.3 GHz for S waves. The initial thicknesses of the DAC samples were
calculated from measured travel times at room pressure using the high-precision reference velocities
calculated on thick samples using equation (1). In this way we determine the initial thickness of the
high-pressure samples to within ±0.2 μm. Hydrostatic conditions are maintained in the DAC using a methanol:ethanol:water (16:3:1) pressure medium [Angel et al., 2007], so long as the sample does not bridge the
diamond culets or touch the gasket. Pressure is determined from the shift of ruby florescence [Mao et al.,
1986] for a small ruby sphere placed next to the sample disk surrounded by the methanol:ethanol:water
(MEW) pressure media.
In total, 85 P wave and 62 S wave travel times were measured on compression and decompression (see the
supporting information for data tables). After each pressure adjustment, data were collected at ~10 min intervals for the first half hour, and then, prior to the next pressure adjustment with a minimum of 1 h between
pressure adjustments to evaluate time dependence of the travel time measurements. Additionally, to test for
reversibility P wave data were collected on decompression.
3. Results
3.1. Density by HPXMT
Constraints on the density of Columbia River basalt glass during room temperature compression are provided by the results of our high-pressure X-ray microtomography (HPXMT) experiments. The results are presented in Figure 4, where pressure is determined immediately adjacent to the sample from the lattice
CLARK ET AL.
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Figure 5. The elastic properties of basalt measured as a function of pressure up to 5 GPa for P wave and S wave measurements
shown as circles and squares, respectively. P wave data collected on decompression are shown as black squares. (a) Normalized
P wave travel times, and (b) normalized S wave travel times measured by GHz-ultrasonic interferometry. (c) P wave acoustic
velocity, and (d) S wave acoustic velocity for basalt calculated from equation (1). Length is calculated from the compression
curve of basalt measured by HPXMT for a given pressure. (e) KS and (f) G basaltic glass calculated from velocity and density.
parameters of the periclase surrounding the sample. A small but measurable difference in pressure was found
marginally away from the sample, increasing by <0.2 GPa at a distance of ~100 μm from the edge of the
sample. The uncertainties in pressure shown in Figure 4 reflect this small pressure difference, and it is assumed
here that pressure measured for periclase represents the maximum pressure for the sample. The pressure
calibration data for these experiments are provided as supporting information. As can be seen in Figure 4
the volume of basalt glass decreases monotonically with pressure reaching 85% of its one-atmosphere volume
by 6 GPa corresponding to an increase in density from 2.7 to 3.1 g/cm3. The densification of Columbia River
basalt glass is modeled as a second-order polynomial as function of pressure as shown in Figure 4.
3.2. One-Atmosphere Elastic Properties
One-atmosphere P wave (vP) and S wave (vS) velocities for Columbia River basalt glass derived from equation (1)
are 6024 ± 5.8 and 3497 ± 2.2 m/s, respectively. The adiabatic bulk modulus (KS) and shear modulus (G) are
found using
K s ¼ ρ v 2P 4 3 v 2s ;
(2)
CLARK ET AL.
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and
G ¼ ρv 2s ;
(3)
where the one-atmosphere ρ of Columbia River basalt glass is 2.700 ± 0.002 g/cm3, and vP and vS are as
reported above. For these values, KS0 and G0 are 54.1 ± 0.4 and 32.9 ± 0.1 GPa, respectively.
3.3. High-Pressure Elastic Properties
P and S wave travel time curves normalized to the one-atmosphere travel time (t/t0) for compressed basalt
glass are shown in Figures 5a and 5b. Travel time data are tabulated in the supporting information.
The P wave t/t0 decreases on compression up to 5 GPa, while the S wave t/t0 increases to a maximum at
4–5 GPa. Above 5 GPa, the S wave t/t0 decreases. Although there is a general decrease in P wave t/t0 with
pressure, travel times remain relatively constant in the 1–4 GPa pressure range, and more than half (60%)
of the P wave t/t0 decrease occurs above 4 GPa. Over the entire pressure range investigated, evolution of
the glass sound velocity is fully reversible as demonstrated in Figure 5a by the excellent agreement in P wave
travel times for the compression and decompression paths.
Both vP and vS decrease with increasing pressure, reaching minima at approximately 4.5 and 5 GPa, respectively (Figures 5c and 5d). The minima correspond to vP and vS reductions of 2.8% and 7.2%, respectively,
which is also associated with approximately a 15% increase in density. At high pressure we use equation (1)
to calculate P and S wave velocities, where the sample thickness is derived from the equation of state determined from our HPXMT experiments (Figure 4). The sample thickness at pressure (L(P)) decreases as the cube
root of the volume:
ffi
LðPÞ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
¼ 0:0022P2 0:0369P þ 1;
L0
(4)
with P in GPa and L0 is the initial (one-atmosphere) sample thickness. Acoustic velocities and elastic moduli
derived from our travel time data and equation (4) are plotted as a function of pressure in Figure 5 (see
supporting information for tabulated data). Figure 5e shows that KS increases near-linearly with pressure
(and density) from 54 GPa at one-atmosphere to ~65 GPa at 5.5 GPa, with only small deviations in the vicinity
of the velocity minimum. In contrast, Figure 5f shows that G decreases with pressure by 5% up to 4 GPa,
above which it increases abruptly. The minimum in vS is ~1 GPa higher than the minimum for G.
4. Discussion
4.1. Anomalous Density and Elastic Properties of Basalt Glass
Our new ultrasonic and computed tomography results can be combined to evaluate the constitutive relationships between the elastic properties and density for basalt glass. It is readily apparent from Figure 5 that vP is
weakly dependent on pressure (decreasing by <3% between 0 and ~4.5 GPa), while Figure 4 shows that over
this same pressure interval density increases by 15%. These relationships are in clear violation of Birch’s law
and broadly consistent with the behavior of SiO2 and MgSiO3 glasses shown in Figure 1. Similarly, vS has a
negative pressure dependence reaching a minimum value at ~5 GPa. In contrast, Figures 5e and 5f show
markedly different trends for KS and G. It is not surprising that KS increases with pressure given the increase
in density associated with closer packing of ions of the glass on compression, but at the same time, the G
decreases suggesting an overall weakening of the material under shear forces. Figure 5 shows that vP and
KS are identical within uncertainty along the compression and decompression paths, and likewise, successive
measurements at a given pressure with time are indistinguishable. These observations indicate that the
anomalous density-velocity relationships are fully reversible, similar to vitreous silica under nearly identical
conditions [Clark et al., 2014]. In the case of vitreous silica, the anomalous elastic properties are attributed
to the ability of cross-linked rigid SiO4 tetrahedra that comprise the silicate network to rotate relatively easily
into interstitial void space as the material is compressed and densifies. This buckling of the network does
not involve bond shortening until the collapsed network reaches the point where short-range repulsive
forces are sufficiently large to oppose further collapse [Dove, 1997]. This so-called locking limit may well
correspond to the change in slope in the velocity trend with pressure seen in Figure 5 above which the glass
behaves more normally; i.e., velocity increases with density. The aluminosilicate network is still sufficiently
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Figure 6. One-atmosphere elastic properties of silicate glasses as a function of density and NBO/T measured at GHz frequency (diamonds) with MHz-frequency ultrasonic
and Brillouin spectroscopy measurements from the literature (circles). Numbers next to symbols correspond to different compositions with the references given
below. (a and c) P and S wave velocities shown as open and closed circles, respectively. (b and d) KS0 and G shown as open and grey circles, respectively. The triangles are
KS0 calculated from KT0 measured by HPXMT. 1—SiO2 [Clark et al., 2014; Gerlich and Kennedy, 1978; Meister et al., 1980], 2—MgSiO3 [Sanchez-Valle and Bass, 2010],
3—CaSiO3 [Bass, 1995], 4—CaMgSi2O6 [Soga et al., 1976], 5—CaAl2Si2O8 [Bass, 1995], 6—NaAlSi3O8 [Bass, 1995], 7—Obsidian [Meister et al., 1980], 8—Andesite
[Meister et al., 1980], 9—Basalt [Liu and Lin, 2014; Malfait et al., 2011; Meister et al., 1980], 10—Mg1.63SiO3.63 [Lesher et al., 2009], and 11—Mg2SiO4 [Lesher et al., 2009].
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Table 1. Summary of Compression Behavior and Pressure Dependence of P and S-Wave Velocities for Silicate Glasses
Composition
NBO
T
Pressure of
P Wave Velocity
Minimum
SiO2
NaAlSi2O6
NaAlSi3O8
CaMgSi2O6
MgSiO3
BCR-2 Basalt
SiO2 (He)
MgSiO3 (Ne)
BIR-1 Basalt (Ne)
0
0
0
2
2
0.6
0
2
0.8
2–2.5 GPa
4.5 GPa
5.5 GPa
NA
NA
4.5 GPa
1 GPa
4.2 GPa
1.2 GPa
P wave
Velocity
Change
Pressure of
S Wave Velocity
Minimum
S wave
Velocity
Change
Reference
13%
8%
5.5%
+2.3%
+2.8%
2.8%
3.3%
0%
2%
2–2.5 GPa
6 GPa
7 GPa
1.5 GPa
8 GPa
5 GPa
2.5 GPa
4 GPa
1.5 GPa
13%
7%
4%
1.4%
3.4%
7.2%
5.8%
2.5%
2%
Weigel et al. [2012]
Sakamaki et al. [2014]
Sakamaki et al. [2014]
Sakamaki et al. [2014]
Sanchez-Valle and Bass [2010]
This study
Weigel et al. [2012]
Liu and Lin [2014]
Liu and Lin [2014]
interconnected in basalt glass so that the polymerized network dominates the compression behavior (densification) and elastic properties of the material despite being markedly less polymerized than vitreous silica.
4.2. Compositional and Structural Effects on Elastic Properties of Silicate Glasses at One-Atmosphere
Figure 6 presents a compilation of one-atmosphere velocity and elastic moduli for natural and simple
system silicate glasses plotted as a function of density (Figures 6a and 6b) and the proportion of nonbridging oxygen to total tetrahedral cations, i.e., NBO/T (Figures 6c and 6d) [Mysen et al., 1982]. For reference,
SiO2 glass, Columbia River basalt, and MgSiO3 glass have NBO/T ratios of 0, 0.6, and 2, respectively. Most
of these data come from MHz-frequency ultrasonic studies, which agree well with those obtained in this
study and reported by Clark et al. [2014] at GHz frequencies, as well as one-atmosphere data collected by
Brillouin spectroscopy. A notable feature of this compilation is the similarity of vS over a very large range
of density and composition and, likewise, a very small variation in G0. Larger variations are found for the
KS0 and thus also vP. There is almost a factor of three variations in KS0 between SiO2 and Mg2SiO4 glasses,
while vP varies by less than 15%. The deviation in the increase in KS0 relative to vP can be attributed largely
to the density increase. Figures 6c and 6d also show the velocity and elastic moduli of silicate glasses at
one-atmosphere as a function of NBO/T. The uniformity of vS and G0 for silicate glasses at one-atmosphere
is clear, while there is a positive correlation for vp and KS0 with increasing NBO/T. This positive correlation
is consistent with the density data as, generally at one-atmosphere, polymerization is inversely related
to density.
4.3. Effects of Pressure and Pressure Media
At high pressure, density increase in amorphous silicates is also achieved by reduction in free volume—that is
the space not occupied by aluminosilicate polyhedra or other cations. The high-pressure density-velocity
systematics for a range of silicate glass compositions are listed in Table 1 and shown for vP data in Figure 7.
In previous studies, density is calculated from the elastic properties (KS0 to KT0 conversion, described below),
with the exception of the data for SiO2 glass where the density and vP data are from separate studies [Meade
and Jeanloz, 1987; Sato et al., 2011; Weigel et al., 2012]. For SiO2 glass, the vP and vS minima at 2–2.5 GPa are well
established and correspond to velocity reductions of ~13% for both vP and vS [Kondo et al., 1981; Suito et al.,
1992; Weigel et al., 2012]. NaAlSi2O6 and NaAlSi3O8 glasses (NBO/T = 0) also show minima in vP at 4.5 and
5.5 GPa, respectively, as well as minima in vS at slightly higher pressure for both glasses [Sakamaki et al.,
2014]. The magnitude of the velocity decrease for these glasses is not as large as exhibited by SiO2 glass
(Table 1). Likewise, depolymerized glasses, such as CaMgSi2O6, and MgSiO3 glasses, have vP that are largely
independent of density and pressure (at least to 8–8.5 GPa) [Sakamaki et al., 2014; Sanchez-Valle and Bass,
2010]. For all compositions, vS decreases on compression, while the velocity reduction is greater in the polymerized glasses relative to the depolymerized glasses [Liu and Lin, 2014; Sakamaki et al., 2014; Sanchez-Valle and
Bass, 2010]. Our study, as well as the recent study of Liu and Lin [2014], show that natural basalt glass samples
(NBO/T < 1) display both vP and vS minima. These natural basalt samples are different in composition and
thus do not have the same initial density. The pressure of the velocity minima reported by Liu and Lin [2014]
is at 2 GPa, whereas we find it at ~4.5 GPa (Table 1). As we discuss below these differences can be related to
the pressure medium used in these studies.
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Figure 7. High-pressure density-P wave velocity systematics at high pressure for silicate glasses. Data for glasses and melts
at one-atmosphere from Figure 1 are shown as labeled fields for reference. Density and P wave velocities for BCR-2 basalt
glass are shown as large green circles. High-pressure data for SiO2 (Si) (diamond) [Meade and Jeanloz, 1987; Sato et al., 2011;
Tsiok et al., 1998; Weigel et al., 2012], NaAlSi2O6 (Jd) (plus) [Sakamaki et al., 2014], NaAlSi3O8 (Ab) (triangles) [Sakamaki et al.,
2014], CaMgSi2O6 (Di) (cross) [Sakamaki et al., 2014], MgSiO3 (En) (square) [Liu and Lin, 2014; Sanchez-Valle and Bass, 2010], and
BIR-1 basalt compressed in Ne (small green circles) [Liu and Lin, 2014]. The large symbols are shown when the pressure
medium was either solid [Sakamaki et al., 2014] or MEW (indicated as (S) and (M), respectively). The small symbols are from
studies that used noble glasses (He for SiO2; Ne for MgSiO3 and basalt). The density for the glasses is calculated from the
velocities for previous studies with the exception of the SiO2 data with the combination of data from separate studies (density
from Meade and Jeanloz [1987], Sato et al. [2011], and Tsiok et al. [1998] and velocity from Weigel et al. [2012]).
There are other significant features of the vp-ρ trends in Figure 7 and Table 1. In addition to the minimum for
Iceland basalt glass at 2 GPa shown by Liu and Lin [2014], their results for MgSiO3 glass also show little change
in vp with pressure until ~5 GPa where the pressure dependence increases markedly. For both Icelandic basalt
above 2 GPa and MgSiO3 glass above 5 GPa the vp-ρ trends become subparallel to the slope predicted by
Birch’s law. The same behavior is found for SiO2 glass compressed in a He pressure medium [Weigel et al.,
2012]. What is remarkable is that for all other studies using either MEW as the pressure medium in the
DAC, or where the compression was achieved using a solid-medium apparatus, the anomalous behavior of
silica, albite, jadeite, basalt, diopside, and enstatite glasses extends up to markedly higher pressures before
reaching a minimum. For diopside glass [Sakamaki et al., 2014], there is no clear increase in the density
dependence of vP, even at the highest experimental pressures. Comparisons among the published studies in
Figure 7 and Table 1 illustrate the importance of the pressure medium—experiments using Ne or He as a
pressure medium in the DAC show a narrower pressure interval for anomalous elastic properties compared
to those using MEW or using a solid medium pressure apparatus.
He and Ne gas have been shown to readily permeate silica glass, leading to stiffening of the material and dampening of the anomalous velocities at high pressure [Coasne et al., 2014; Sato et al., 2011; Shen et al., 2011; Weigel
et al., 2012]. These studies further show that as the radius of the noble gas decreases, the stiffness of the glass
increases, which presumably is due to closer packing of smaller ions within the interstices of the silicate network
[Coasne et al., 2014]. We strongly suspect that the principle reason for the difference in the pressure-vP
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relationships for basaltic glass shown in this study and that reported by Liu and Lin [2014] relates to the choice of
pressure media in both studies. MEW used in this study does not easily enter the glass, and while the Ne used in
Liu and Lin experiments more readily permeates the glass. As found for silica, filling interstitial voids with Ne will
lead to stiffening of glass and thus a suppression of the anomalous elastic properties in basalt glass. Further
support for this interpretation comes from studies of MgSiO3 glass where Sanchez-Valle and Bass [2010] found
anomalous behavior extending to at least 8 GPa when MEW was used as the pressure medium, but Liu and Lin
[2014] report that such behavior ceases by about 5 GPa when Ne is used as the pressure medium. Clearly, the
use of pressure media that can occupy the interstitial void space of the glass have a dramatic effect on elastic
properties of network glasses. When network glasses are surrounded by a light gas media, the density-velocity
trends measured are not due solely to the response of the glass. In turn, the apparent sensitivity of elastic properties to identity of the occupants of interstitial voids suggests a strategy for probing the size and distribution of
the void space in network glasses, and perhaps also melts. More systematic examinations of these relationships
are underway.
4.4. Adiabatic (KS0) Versus Isothermal (KT0) Bulk Moduli
In Brillouin and ultrasonic studies of silicate glasses, density and elastic properties are not measured independently, but rather one is calculated from the other assuming that the ratio of adiabatic to isothermal bulk
moduli (KS0 to KT0, respectively) is equal to ~1 [Liu and Lin, 2014; Sakamaki et al., 2014; Sanchez-Valle and
Bass, 2010; Yokoyama et al., 2010]. In this study we utilize HPXMT to constrain the compression curve for
basaltic glass, which directly gives the change in sample length at each pressure to calculate velocity and
elastic moduli from the ultrasonic travel times independently. To illustrate this point, Figure 4 shows the
second-order polynomial fit to our experimental data compared with the family of solutions for the thirdorder Birch-Murnaghan and Vinet equations of state (EoS), assuming KT0 calculated from the value of KS0
we obtained at one-atmosphere and values of K0′ ranging from 0 to 10. For the Birch-Murnaghan EoS fit
achieved for K0′ = 1.8, K0′ from our ultrasonic experiments is clearly a poor match to our experimental measurements. In fact, no reasonable value of K0′ satisfies the observations assuming that KT0 is equal to
~54 GPa, and only would approximate the observations if the value of KT0 is ~38 GPa (KS0 to KT0 > 1). In addition, we calculated density from the acoustic velocities by integrating equation (2), which is the common
method for determining density from high-pressure velocity measurements [Kono et al., 2011; Liu and Lin,
2014; Sakamaki et al., 2014; Sanchez-Valle and Bass, 2010; Yokoyama et al., 2010; Zha et al., 1994] as well as
solving the complete travel time equation of state to integrate the travel time measurements [Spetzler and
Yoneda, 1993] (see supporting information). The density calculated by these methods correlates with the
density calculated from the Birch-Murnaghan EoS for KS0 and K0′ determined by ultrasonic measurements,
but we cannot recover the density measured by HPXMT.
Values of KT0 and KS0 for basaltic glasses obtained by static (isothermal) measurements and dynamic (adiabatic), respectively, appear to be significantly different. KT0 for Columbia River basalt glass used in the present
study is 38 GPa, agreeing well with KT0 of 40–45 GPa for basalt glass reported by Kuryaeva and coworkers
[Kuryaeva, 2004; Kuryaeva and Kirkinskii, 1997] (Figure 4). Likewise, KS0 for our sample is 54 GPa, broadly consistent with previous studies on basalt glass, where KS0 ranges from 63 to 73 GPa [Liu and Lin, 2014; Malfait
et al., 2011; Meister et al., 1980]. While differences in glass composition can account for the variations in KT0
or KS0 between studies, the available data indicate that KS0 is consistently greater than KT0 by an amount
exceeding the isothermal-adiabatic conversion (see supporting information).
This raises the question to what extent is due to a frequency dependence of the elastic properties and how
this relates to network response to static and dynamic stresses. It is important to consider the effect of
frequency dependence to account for the observed deviation between KT0 and KS0. Due to atomic mobility
in amorphous silicates the measured physical properties can depend on the time scales of experimental
observation. For example, whether the liquid (relaxed) or the glassy (unrelaxed) state is sampled depends
on the frequency of the measurement relative to the time required for the system to reach equilibrium after
perturbation (Maxwell’s relaxation time). While relaxed versus unrelaxed frequency dependence is important for amorphous silicates at elevated temperatures, Maxwell relaxation time for silicate glasses at room
temperature is hundreds of years [Angell, 1995; Dingwell and Webb, 1989], far exceeding the sampling
time for both dynamic and static measurements of K. Moreover, we can show based on our ultrasonic
measurements that there is no frequency dependence over a 500 MHz frequency range at GHz frequencies
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(see supporting information), while previous work on SiO2 glass shows remarkable consistency spanning
104 Hz based on MHz-ultrasonic, GHz-ultrasonic, and Brillouin spectroscopy measurements. These observations taken together suggest that the deviation between KS0 and KT0 is not likely due to dispersion.
While the time scales of the measurements of KS0 and KT0 do not appear to account for the observed differences, what may be important are the length scales of the sample probed by dynamic versus static stresses.
A possible explanation is that network flexibility permits the silicate glass to reduce volume (long scale—
rotation of tetrahedra in interstitial voids—static stress) without an equivalent elastic response (short scale
—compression of interatomic bonds—dynamic stress) consistent with the observation that when a static
stress is applied the sample appears softer than when a dynamic stress is applied. However, what is clear
from Figure 4 is that neither the Birch-Murnaghan and Vinet EoS captures the compression behavior of
basaltic glass over the pressure range of the crust and upper mantle, a conclusion that has been previously
reached for basaltic liquids [Sakamaki et al., 2013]. Also, integrating the acoustic velocities calculates a
compression curve that is stiffer than the independently measured density. This decoupling of the volumetric and elastic properties is consistent with the violation of Birch’s law exhibited by amorphous materials, where density values are greater than would be predicted based on vP (Figure 1). This result also
suggests caution in extrapolating the properties of amorphous materials to high pressure or recovering
elastic properties from acoustic velocities in the absence of independent constraints on density.
5. Geophysical Applications
5.1. Glass Versus Melt Properties
We attribute the anomalous elastic properties of vitreous silicates shown in Figure 7 to their polymerized
structure and the manner in which the network flexes when strained. Here we present several lines of evidence suggesting that such behavior is a universal feature of amorphous silicates, including melts at low
to moderately high pressure. Our findings suggest that P wave velocities for basaltic glass depend weakly
on pressure, and hence, density, up to 4–5 GPa, provides an upper limit on the pressure dependence of
P wave velocities at all frequencies for basaltic liquid. Furthermore, since silicate melts are more compressible
than their corresponding glasses, it follows that melts will similarly deviate from Birch’s law.
In both silicate glasses and melts, cation-anion associations are similar in that high-valence (e.g., Si4+ and Al3+)
cations form a tetrahedral framework while most of the remaining cations are in octahedral coordination or
occupy interstitial positions. These short-range configurations are fairly resilient to changes in temperature
and pressure, although there is abundant evidence that the average coordination number of network formers
increases with temperature and pressure, most significantly for Al+3 beginning at 2–4 GPa and for Si+4 above
15–20 GPa [e.g., Allwardt et al., 2005; Gaudio et al., 2008, 2015; Lee, 2010; Sakamaki et al., 2013; Sanloup et al.,
2013; Wang et al., 2014]. Likewise, many of these studies have shown that T-O bond distances also are relatively unaffected by pressure in advance of coordination changes, unlike inter-tetrahedral (T-O-T) bond
angles reflecting the high degree of flexibility of the network of rigid polyhedra during compression and
thermal expansion. Examples of the similarities in densification mechanism between silicate glasses and
melts on compression include the regions of increasing densification on loading and Si coordination
changes in the same pressure range for SiO2 glass and basalt melt [Bridgman, 1939; Sakamaki et al., 2013;
Sanloup et al., 2013].
Where glass and melt diverge, it is the translational degree of freedom available in melts that give access to
more structural configurations at a given pressure and temperature than the glass. This is perhaps the most
important difference between melts and glasses, and critical when considering the extent to which knowledge about the elastic properties of glasses has applicability to melts. Melts sampled at seismic frequencies
by definition are in thermodynamic equilibrium and thus possess a “relaxed” structure, which can be sampled
by passing through the glass transition either on cooling or by shortening the observational timescales. The
glass structure corresponds to the “fictive” pressure and temperature structure of the liquid minus the translational degree of freedom possessed by the melt. An important question is how critical is the translational
degree of freedom for the elastic properties? Clearly, it is critical for the shear modulus, which for a liquid that
cannot support a shear stress; thus, G approaches zero at temperatures above the glass transition. On the
other hand, ultrasonic studies of silicate liquids at one-atmosphere have shown that the bulk modulus KS0
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Figure 8. Basalt melt velocity at high pressure modeled using a BM3-EoS
from the data of Agee [1998] and Ohtani and Maeda [2001] (grey curve),
velocity of basalt melt modeled using a BM3-EoS from Ueki and Iwamori
[2016] (dotted curve), and the velocity of basalt/mafic melt modeled on
the magnitude of the dvP/dρ observed in the silicate glasses at high pressure
(red field). Velocity models at high pressure for AK135-F global 1-D model
[Kennett et al., 1995] for reference (blue curve). One-atmosphere basalt/mafic
melt velocity is from Rivers and Carmichael [1987] for all models.
10.1002/2016JB012973
for relaxed liquid is only ~5–10 GPa
lower than that for unrelaxed liquid
[Askarpour et al., 1993; Webb, 1991].
More important for this study is the
pressure (and density) dependence
of KS or similarly its dependence on
density. What is clearly shown in
Figure 7 is that for a range of silicate
glasses, and we submit also melts,
the negative or weakly varying P wave
velocities with density trends reflect
the anomalous pressure dependence
of KS (and also G in the case of the
glass). As we have noted earlier this
behavior is in direct conflict with the
expectations of crystalline materials
obeying Birch’s law.
Like glasses, network flexibility in
melts is not without limit, and eventually, further collapse will be impeded
by repulsive interatomic forces—the
so-called packing limit or saturation
pressure [Dove, 1997; Greaves et al.,
2011; Wang et al., 2014]. To the extent
that the pressure required to reach this locking limit depends on the interstitial void space initially present,
it seems reasonable to expect that a high-temperature melt will exhibit anomalous behavior over a larger
pressure range than compositionally equivalent glass at room temperature. Moreover, the translational
and rotational degrees of freedom available to the melt presumably will permit further densification before
the onset of normal behavior.
5.2. Calculation of Mafic Melt Velocity at High Pressure
To constrain the possible range of velocities for mafic melts (NBO/T = ~1–2) we use the dvP/dρ determined for
basaltic glass to place limits based on dvP for basalt melt, where
dv PðliquidÞ
v PðliquidÞ ðPÞ ¼ v PðliquidÞ;0 þ dρ
;
dρ
(5)
and vP(liquid),0 is from Rivers and Carmichael [1987] (see Table 1 for other parameters). In Figure 8 calculations are
shown assuming a third-order Birch-Murnaghan equation of state (BM3-EoS) of the liquid where KS0/KT0 ~ 1
[e.g., Ueki and Iwamori, 2016], and those for a weak pressure dependent on velocity reported in this study
reflecting that KS0/KT0 > 1. The models extend to pressures up to 16 GPa (i.e., reaching the transition zone)
and are compared to the global 1D AK135-F velocity model [Kennett et al., 1995]. Our model predicts that vP
for mafic melt in the upper mantle and well into the transition zone are between 2 and 3 km/s, assuming that
the density of the melt increases by ~30% over this depth interval [Ohtani and Maeda, 2001; Sanloup et al.,
2013]. This is in contrast to the Birch-Murnaghan EoS model assuming a near equivalence of KS0 and KT0 that
predicts that vP increases from 2.6 km/s at 0.01 GPa to 5 km/s at 15 GPa [e.g., Hammond and Humphreys,
2000]. It is noteworthy that vP predicted at the base of the lithosphere by our model is 20% lower than
the velocity when assuming the Birch-Murnaghan EoS, while it is more than 40% lower on reaching the top
of the transition zone. If this is the case, the effects of melt on seismic velocities have been grossly underestimated, implying an overestimation of melt fraction associated with low-velocity regions in the Earth’s mantle.
5.3. Calculation of Aggregate Velocity
We can estimate the minimum effect of partial melt on aggregate mantle seismic properties using a simple
additive model. First, we use the mantle structure and properties of the AK135-F 1D global model, providing
CLARK ET AL.
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Figure 9. Normalized P wave velocity (Voigt limit) as a function of melt fraction for 1, 5, and 10% melt (red, green, and blue,
respectively). The solid curves are calculated from the velocity envelope calculated for basaltic (mafic) melts in Figure 8. The
dashed curves are from the velocity calculated from a BM3-EoS calculated from the isothermal bulk modulus. The grey
boxes are for reported P wave velocity reductions. See text for discussion.
vP as a function of pressure for the crystalline component of the mantle. Second, we use the melt velocity calculated by equation (5) (and shown in Figure 8) for mafic silicate melts based on the pressure dependence
exhibited in glasses (here after referred to as the current model) and for velocities calculated using the
BM3-EoS model. Finally, to calculate vP of partially molten mantle, the proportions of crystalline and silicate
melt are summed as a function of both melt fraction and depth (the Voigt limit). In these calculations, melt
is assumed to be homogenously distributed through the mantle and the velocity reduction is due solely to
the proportion of melt present. The Voigt limit is calculated to constrain the minimum reduction of the aggregate velocity due to the presence of partial melt; that is, these calculations provide a maximum estimate of
melt fraction (the Ruess limit and Hill average are given in the supporting information). Consideration of realistic melt geometry—as tubes and films organized along grain boundaries, and at triple junctions—leads to
larger velocity reductions for a given melt fraction, requiring less melt to account for an observed velocity
perturbation than calculated from an additive model [Hammond and Humphreys, 2000; Mavko, 1980;
Schmeling, 1985; Takei, 2002]. However, it instructive to use a simple additive model to evaluate the relative
effect of the pressure dependence of silicate melts on the elastic properties because estimates of absolute
melt fraction determined for realistic melt geometry can vary significantly depending on the methods and
model parameters.
Figure 9 shows the normalized vP as a function of pressure up to 16 GPa for 1, 5, and 10% melt. In general,
increasing the melt fraction leads to a reduction in the normalized vP for both models. Aggregate velocities
for the current model decrease monotonically up to 16 GPa. In contrast, while the aggregate velocities using
the BM3 EoS are lower than the average 1-D mantle, the aggregate velocity increases with pressure (after an
initial decrease in velocity up to 0.5 GPa). The difference in the calculated melt fraction between the two models increases as a function of pressure. For example, the recent work of Stern et al. [2015] reports 8% P wave
velocity reduction at 70–80 km depth. As stated above, the Voigt limit provides a maximum for the melt
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fraction, so what is important here is not the absolute melt fractions but the relative estimates of melt fraction. The melt fraction calculated by the current model and the BM3 EoS model differs by 16% at 2.5 GPa.
In contrast, the global tomography study of Montelli et al. [2004] reports more modest P wave velocity reductions of 1.5–2.5% for many hot spots between 300 and 600 km depth (Figure 9). The melt fraction calculated
by the current model and the 3BM EoS model differs by a factor of 1.5 and 2 at 10 and 16 GPa, respectively, for
the given P wave velocity reductions. These considerations of the P wave velocity reductions of partially
molten aggregates show that extrapolation of the 3BM EoS can result in a significant overestimation of melt
fraction. Furthermore, the magnitude of this overestimation increases with pressure. These findings need to
be considered when interpreting the significant of low-velocity anomalies in the crust and upper mantle.
6. Conclusions
The high-pressure P and S wave velocities of basalt glass have been calculated from density determined by
HPXMT and travel times measured by GHz-ultrasonic interferometry. The main conclusions from our study
are as follows:
Acknowledgments
This research was supported in part by
U.S. National Science Foundation grants
EAR-1215714 to C.E.L. and EAR-1452344
to S.D.J, EAR-1214376 to Y.W., and a grant
from the UC Lab Fees Research Program
(12-LR-237546) to C.E.L. C.E.L. also wishes
to acknowledge support from the Danish
National Research Foundation for the
Niels Bohr Professorship at Aarhus
University, DK, and S.D.J. acknowledges
support from the Carnegie/DOE Alliance
Center, the David and Lucile Packard
Foundation, and the Alexander von
Humboldt Foundation. High-pressure
tomography experiments were carried
out at the beamlines of GSECARS, which
is supported by the National Science
Foundation - Earth Sciences (EAR1128799) and Department of EnergyGeoSciences (DE-FG02-94ER14466). The
use of the Advanced Photon Source, an
Office of Science User Facility operated
for the U.S. Department of Energy (DOE)
Office of Science by Argonne National
Laboratory, was supported by the U.S.
DOE under Contract DE-AC0206CH11357. The data used in this study
are available in the supporting information, figure captions, and references.
CLARK ET AL.
1. P and S wave velocities for basalt glass are shown to decrease with increasing density and pressure up to
4.5 GPa. This behavior violates Birch’s law.
2. Independent volume and elasticity measurements show that basaltic glass undergoes density-velocity
changes, which result in erroneous elastic moduli at high pressure if the density at high pressure is
obtained by integration of the bulk sound velocity, as is commonly done in Brillouin scattering experiments of silicate glasses.
3. The anomalous elastic properties of silicate glass at high pressure are attributed to mode softening arising
from the flexibility of the silicate network during compression.
4. Composition, and hence polymerization, has a significant effect on the anomalous elastic properties of
silicate glasses.
5. Comparison of our results with previous studies demonstrates the influence of pressure media for the
elastic response of glass on compression. The glass is stiffened when void space is occupied by noble
gases.
6. We find for basalt glass, KS0 > KT0. This is unexpected and attributed to network flexibility that allows the
silicate glass to densify without compressing the interatomic bonds. This means that the correlation
between KS0 and KT0 is less direct than in crystalline systems leading to the failure of crystalline EoS to
replicate amorphous silicate behavior at high pressure.
7. If mode softening occurs in silicate melts as well, P wave velocities will have much weaker pressure dependence than commonly assumed (as we have shown for their glassy counterparts). Given this likelihood,
the presence of silicate melt will have greater influence on seismic velocities, which, in turn, will reduce
the amount of melt required to account for a given velocity reduction at crustal and upper mantle
conditions.
References
Agee, C. B. (1998), Crystal-liquid density inversions in terrestrial and lunar magmas, Phys. Earth Planet. Inter., 107(1–3), 63–74.
Allwardt, J. R., B. T. Poe, and J. F. Stebbins (2005), Letter. The effect of fictive temperature on Al coordination in high-pressure (10 GPa) sodium
aluminosilicate glasses, Am. Mineral., 90(8–9), 1453–1457.
Anderson, D. L., and H. Spetzler (1970), Partial melting and the low-velocity zone, Phys. Earth Planet. Inter., 4(1), 62–64, doi:10.1016/0031-9201
(70)90030-0.
Angel, R. J., M. Bujak, J. Zhao, G. D. Gatta, and S. D. Jacobsen (2007), Effective hydrostatic limits of pressure media for high-pressure
crystallographic studies, J. Appl. Crystallogr., 40, 26–32, doi:10.1107/s0021889806045523.
Angell, C. A. (1995), Formation of glasses from liquids and biopolymers, Science, 267(5206), 1924–1935.
Askarpour, V., M. H. Manghnani, and P. Richet (1993), Elastic properties of diopside, anorthite, and grossular glasses and liquids: A Brillouin
scattering study up to 1400 K, J. Geophys. Res., 98, 17,683–17,689, doi:10.1029/93JB01558.
Bass, J. D. (1995), Elasticity of minerals, glasses, and melts, in Mineral Physics & Crystallography: A Handbook of Physical Constants, edited by
T. J. Ahrens, pp. 45–63, AGU, Washington, D. C., doi:10.1029/rf002.
Birch, F. (1961a), Composition of the Earth’s mantle, Geophys. J. R. Astron. Soc., 4, 295–311.
Birch, F. (1961b), The velocity of compressional waves in rocks to 10 Kilobars, part 2, J. Geophys. Res., 66, 2199–2224, doi:10.1029/
JZ066i007p02199.
Bridgman, P. W. (1939), The high pressure behavior of miscellaneous minerals, Am. J. Sci., 237, 7–18.
Chang, Y.-Y., S. D. Jacobsen, M. Kimura, T. Irifune, and I. Ohno (2014), Elastic properties of transparent nano-polycrystalline diamond
measured by GHz-ultrasonic interferometry and resonant sphere methods, Phys. Earth Planet. Inter., 228, 47–55, doi:10.1016/
j.pepi.2013.09.009.
BASALT AND HIGH-PRESSURE MELT VELOCITY
15
Journal of Geophysical Research: Solid Earth
10.1002/2016JB012973
Clark, A. N., C. E. Lesher, S. D. Jacobsen, and S. Sen (2014), Mechanisms of anomalous compressibility of vitreous silica, Phys. Rev. B, 90(17),
174110.
Coasne, B., C. Weigel, A. Polian, M. Kint, J. Rouquette, J. Haines, M. Foret, R. Vacher, and B. Rufflé (2014), Poroelastic theory applied to the
adsorption-induced deformation of vitreous silica, J. Phys. Chem. B, 118(49), 14,519–14,525, doi:10.1021/jp5094383.
Dingwell, D. B., and S. L. Webb (1989), Structural relaxation in silicate melts and non-newtonian melt rheology in geologic processes,
Phys. Chem. Miner., 16(5), 508–516.
Dove, M. T. (1997), Theory of displacive phase transitions in minerals, Am. Mineral., 82(3–4), 213–244.
Dziewonski, A. M., and D. L. Anderson (1981), Preliminary Earth reference model, Phys. Earth Planet. Inter., 25(4), 297–356, doi:10.1016/
0031-9201(81)90046-7.
Faul, U. H., and I. Jackson (2005), The seismological signature of temperature and grain size variations in the upper mantle, Earth Planet. Sci.
Lett., 234(1–2), 119–134, doi:10.1016/j.epsl.2005.02.008.
Gaudio, S. J., S. Sen, and C. E. Lesher (2008), Pressure-induced structural changes and densification of vitreous MgSiO3, Geochim. Cosmochim.
Acta, 72(4), 1222–1230, doi:10.1016/j.gca.2007.12.005.
Gaudio, S. J., C. E. Lesher, H. Maekawa, and S. Sen (2015), Linking high-pressure structure and density of albite liquid near the glass transition,
Geochim. Cosmochim. Acta, 157, 28–38, doi:10.1016/j.gca.2015.02.017.
Gerlich, D., and G. C. Kennedy (1978), Second pressure derivative of the elastic moduli of fused quartz, J. Phys. Chem. Solids, 39, 1189–1191.
Greaves, G. N., A. Greer, R. Lakes, and T. Rouxel (2011), Poisson’s ratio and modern materials, Nat. Mater., 10(11), 823–837.
Hammond, W. C., and E. D. Humphreys (2000), Upper mantle seismic wave velocity: Effects of realistic partial melt geometries, J. Geophys.
Res., 105, 10,975–10,986, doi:10.1029/2000JB900041.
Hirschmann, M. M. (2010), Partial melt in the oceanic low velocity zone, Phys. Earth Planet. Inter., 179(1–2), 60–71, doi:10.1016/j.pepi.2009.12.003.
Isaak, D., E. Graham, J. Bass, and H. Wang (1993), The elastic properties of single-crystal fayalite as determined by dynamical measurement
techniques, Pure Appl. Geophys., 141(2–4), 393–414, doi:10.1007/BF00998337.
Jacobsen, S. D., H.-J. Reichmann, H. A. Spetzler, S. J. Mackwell, J. R. Smyth, R. J. Angel, and C. A. McCammon (2002), Structure and elasticity of
single-crystal (Mg,Fe)O and a new method of generating shear waves for gigahertz ultrasonic interferometry, J. Geophys. Res., 107(B2),
2037, doi:10.1029/2001JB000490.
Jacobsen, S. D., H. Spetzler, H. J. Reichmann, and J. R. Smyth (2004), Shear waves in the diamond-anvil cell reveal pressure-induced instability
in (Mg,Fe)O, Proc. Natl. Acad. Sci. U.S.A., 101(16), 5867–5871, doi:10.1073/pnas.0401564101.
Karato, S.-i., and H. Jung (1998), Water, partial melting and the origin of the seismic low velocity and high attenuation zone in the upper
mantle, Earth Planet. Sci. Lett., 157(3–4), 193–207, doi:10.1016/S0012-821X(98)00034-X.
Kennett, B. L. N., and I. Jackson (2009), Optimal equations of state for mantle minerals from simultaneous non-linear inversion of multiple
datasets, Phys. Earth Planet. Inter., 176(1–2), 98–108, doi:10.1016/j.pepi.2009.04.005.
Kennett, B. L. N., E. R. Engdahl, and R. Buland (1995), Constraints on seismic velocities in the Earth from traveltimes, Geophys. J. Int., 122(1),
108–124, doi:10.1111/j.1365-246X.1995.tb03540.x.
Ketcham, R. A., and W. D. Carlson (2001), Acquisition, optimization and interpretation of X-ray computed tomography imagery: Application
to the geosciences, Comput. Geosci., 27, 381–400.
Kondo, K., S. Lio, and A. Sawaoka (1981), Non-linear pressure-dependence of the elastic moduli of fused quartz up to 3 GPa, J. Appl. Phys.,
52(4), 2826–2831.
Kono, Y., A. Yamada, Y. Wang, T. Yu, and T. Inoue (2011), Combined ultrasonic elastic wave velocity and microtomography measurements at
high pressures, Rev. Sci. Instrum., 82(2), 023906, doi:10.1063/1.3552185.
Kung, J., B. Li, T. Uchida, Y. Wang, D. Neuville, and R. C. Liebermann (2004), In situ measurements of sound velocities and densities across the
orthopyroxene → high-pressure clinopyroxene transition in MgSiO3 at high pressure, Phys. Earth Planet. Inter., 147(1), 27–44, doi:10.1016/
j.pepi.2004.05.008.
Kuryaeva, R. (2004), Effect of high pressure on the refractive index and density of natural aluminosilicate glasses of alkali basalt composition
in the SiO2-Al2O3-TiO2-Fe2O3-P2O5-FeO-MnO-CaO-MgO-Na2O-K2O system, Glass Phys. Chem., 30(6), 523–531.
Kuryaeva, R., and V. Kirkinskii (1997), Influence of high pressure on the refractive index and density of tholeiite basalt glass, Phys. Chem.
Miner., 25(1), 48–54.
Lee, S. K. (2010), Effect of pressure on structure of oxide glasses at high pressure: Insights from solid-state NMR of quadrupolar nuclides,
Solid State Nucl. Magn. Reson., 38(2), 45–57.
Lesher, C. E., Y. Wang, S. Gaudio, A. Clark, N. Nishiyama, and M. Rivers (2009), Volumetric properties of magnesium silicate glasses and
supercooled liquid at high pressure by X-ray microtomography, Phys. Earth Planet. Inter., 174(1), 292–301.
Levien, L., D. Weidner, and C. Prewitt (1979), Elasticity of diopside, Phys. Chem. Miner., 4(2), 105–113, doi:10.1007/BF00307555.
Liu, J., and J.-F. Lin (2014), Abnormal acoustic wave velocities in basaltic and (Fe,Al)-bearing silicate glasses at high pressures, Geophys. Res.
Lett., 41, 8832–8839, doi:10.1002/2014GL062053.
Malfait, W. J., C. Sanchez-Valle, P. Ardia, E. Médard, and P. Lerch (2011), Compositional dependent compressibility of dissolved water in
silicate glasses, Am. Mineral., 96(8–9), 1402–1409.
Mao, H. K., J. Xu, and P. M. Bell (1986), Calibration of the ruby pressure gauge to 800 kbar under quasi-hydrostatic conditions, J. Geophys. Res.,
91, 4673–4676, doi:10.1029/JB091iB05p04673.
Mavko, G. M. (1980), Velocity and attenuation in partially molten rocks, J. Geophys. Res., 85, 5173–5189, doi:10.1029/JB085iB10p05173.
Meade, C., and R. Jeanloz (1987), Frequency-dependent equation of state of fused-silica to 10 GPa, Phys. Rev. B, 35(1), 236–244.
Meister, R., E. C. Robertson, R. W. Werre, and R. Raspet (1980), Elastic moduli of rock glasses under pressure to 8-kilobars and geophysical
implications, J. Geophys. Res., 85, 6461–6470, doi:10.1029/JB085iB11p06461.
Montelli, R., G. Nolet, F. Dahlen, G. Masters, E. R. Engdahl, and S.-H. Hung (2004), Finite-frequency tomography reveals a variety of plumes in
the mantle, Science, 303(5656), 338–343.
Mysen, B. O., D. Virgo, and F. A. Seifert (1982), The structure of silicate melts: Implications for chemical and physical properties of natural
magma, Rev. Geophys., 20, 353–383, doi:10.1029/RG020i003p00353.
Ohtani, E., and M. Maeda (2001), Density of basaltic melt at high pressure and stability of the melt at the base of the lower mantle,
Earth Planet. Sci. Lett., 193(1–2), 69–75.
Polian, A., V.-T. Dung, and P. Richet (2002), Elastic properties of a-SiO 2 up to 2300 K from Brillouin scattering measurements, Europhys. Lett.,
57(3), 375.
Rivers, M. L., and I. S. E. Carmichael (1987), Ultrasonic studies of silicate melts, J. Geophys. Res., 92, 9247–9270, doi:10.1029/JB092iB09p09247.
Rivers, M. L., and Y. B. Wang (2006), Recent developments in microtomography at GeoSoilEnviroCARS, paper presented at Developments in
X-Ray Tomography V, San Diego, Calif.
CLARK ET AL.
BASALT AND HIGH-PRESSURE MELT VELOCITY
16
Journal of Geophysical Research: Solid Earth
10.1002/2016JB012973
Sakamaki, T., A. Suzuki, E. Ohtani, H. Terasaki, S. Urakawa, Y. Katayama, K.-i. Funakoshi, Y. Wang, J. W. Hernlund, and M. D. Ballmer (2013),
Ponded melt at the boundary between the lithosphere and asthenosphere, Nat. Geosci., 6, 1041–1044.
Sakamaki, T., Y. Kono, Y. Wang, C. Park, T. Yu, Z. Jing, and G. Shen (2014), Contrasting sound velocity and intermediate-range structural
order between polymerized and depolymerized silicate glasses under pressure, Earth Planet. Sci. Lett., 391, 288–295, doi:10.1016/
j.epsl.2014.02.008.
Sanchez-Valle, C., and J. D. Bass (2010), Elasticity and pressure-induced structural changes in vitreous MgSiO3-enstatite to lower mantle
pressures, Earth Planet. Sci. Lett., 295(3–4), 523–530, doi:10.1016/j.epsl.2010.04.034.
Sanloup, C., J. W. E. Drewitt, Z. Konopkova, P. Dalladay-Simpson, D. M. Morton, N. Rai, W. van Westrenen, and W. Morgenroth (2013),
Structural change in molten basalt at deep mantle conditions, Nature, 503(7474), 104–107, doi:10.1038/nature12668.
Sato, T., N. Funamori, and T. Yagi (2011), Helium penetrates into silica glass and reduces its compressibility, Nat. Commun., 2, 345,
doi:10.1038/ncomms1343.
Sawamoto, H., D. J. Weidner, S. Sasaki, and M. Kumazawa (1984), Single-crystal elastic properties of the modified spinel (beta) phase of
magnesium orthosilicate, Science, 224(4650), 749–751, doi:10.1126/science.224.4650.749.
Schmeling, H. (1985), Numerical models on the influence of partial melt on elastic, anelastic and electric properties of rocks. Part I: Elasticity
and anelasticity, Phys. Earth Planet. Inter., 41(1), 34–57, doi:10.1016/0031-9201(85)90100-1.
Secco, R. A., M. H. Manghnani, and T. C. Liu (1991), The bulk modulus-attenuation-viscosity systematics of diopside-anorthite melts,
Geophys. Res. Lett., 18, 93–96, doi:10.1029/90GL01711.
Shen, G., Q. Mei, V. B. Prakapenka, P. Lazor, S. Sinogeikin, Y. Meng, and C. Park (2011), Effect of helium on structure and compression behavior
of SiO2 glass, Proc. Natl. Acad. Sci. U.S.A., 108(15), 6004–6007, doi:10.1073/pnas.1102361108.
Soga, N., H. Yamanaka, C. Hisamoto, and M. Kunugi (1976), Elastic properties and structure of alkaline-earth silicate glasses, J. Non-Cryst.
Solids, 22(1), 67–76, doi:10.1016/0022-3093(76)90008-9.
Spetzler, H., and A. Yoneda (1993), Performance of the complete travel-time equation of state at simultaneous high pressure and
temperature, Pure Appl. Geophys., 141(2–4), 379–392, doi:10.1007/BF00998336.
Stern, T. A., S. A. Henrys, D. Okaya, J. N. Louie, M. K. Savage, S. Lamb, H. Sato, R. Sutherland, and T. Iwasaki (2015), A seismic reflection image for
the base of a tectonic plate, Nature, 518(7537), 85–88, doi:10.1038/nature14146.
Suito, K., M. Miyoshi, T. Sasakura, and H. Fujisawa (1992), Elastic properties of obsidian, vitreous SiO2, and vitreous GeO2 under high pressure
up to 6 GPa, in High-Pressure Research: Application to Earth and Planetary Sciences, pp. 219–225, AGU, Washington, D. C.
Takei, Y. (2002), Effect of pore geometry on Vp/Vs: From equilibrium geometry to crack, J. Geophys. Res., 107(B2), 2043, doi:10.1029/
2001JB000522.
Tsiok, O. B., V. V. Brazhkin, A. G. Lyapin, and L. G. Khvostantsev (1998), Logarithmic kinetics of the amorphous-amorphous transformations in
SiO2 and GeO2 glasses under high-pressure, Phys. Rev. Lett., 80(5), 999–1002.
Ueki, K., and H. Iwamori (2016), Density and seismic velocity of hydrous melts under crustal and upper mantle conditions, Geochem. Geophys.
Geosyst., doi:10.1002/2015GC006242.
Wang, Y., T. Uchida, F. Westferro, M. L. Rivers, N. Nishiyama, J. Gebhardt, C. E. Lesher, and S. R. Sutton (2005), High-pressure X-ray tomography
microscope: Synchrotron computed microtomography at high pressure and temperature, Rev. Sci. Instrum., 76(7), 073709.
Wang, Y., et al. (2011), In situ high-pressure and temperature X-ray microtomographic imaging during large deformation: A new technique
for studying mechanical behavior of multi-phase composites, Geosphere, 7(1), 40–53.
Wang, Y., T. Sakamaki, L. B. Skinner, Z. Jing, T. Yu, Y. Kono, C. Park, G. Shen, M. L. Rivers, and S. R. Sutton (2014), Atomistic insight into viscosity
and density of silicate melts under pressure, Nat. Commun., 5, 3241, doi:10.1038/ncomms4241.
Webb, S. L. (1991), Shear and volume relaxation in Na2Si2O5, Am. Mineral., 76(9–10), 1449–1454.
Weidner, D. J., and H. R. Carleton (1977), Elasticity of coesite, J. Geophys. Res., 82, 1334–1346, doi:10.1029/JB082i008p01334.
Weidner, D. J., H. Wang, and J. Ito (1978), Elasticity of orthoenstatite, Phys. Earth Planet. Inter., 17(2), P7–P13, doi:10.1016/0031-9201(78)90043-2.
Weidner, D. J., H. Sawamoto, S. Sasaki, and M. Kumazawa (1984), Single-crystal elastic properties of the spinel phase of Mg2SiO4, J. Geophys.
Res., 89, 7852–7860, doi:10.1029/JB089iB09p07852.
Weigel, C., A. Polian, M. Kint, B. Ruffle, M. Foret, and R. Vacher (2012), Vitreous silica distends in helium gas: Acoustic versus static
compressibilities, Phys. Rev. Lett., 109(24), 245504, doi:10.1103/PhysRevLett.109.245504.
Yokoyama, A., M. Matsui, Y. Higo, Y. Kono, T. Irifune, and K. Funakoshi (2010), Elastic wave velocities of silica glass at high temperatures and
high pressures, J. Appl. Phys., 107(12), 123530, doi:10.1063/1.3452382.
Zha, C. S., R. J. Hemley, H. K. Mao, T. S. Duffy, and C. Meade (1994), Acoustic velocities and refractive-index of SiO2 glass to 57.5 GPa by
Brillouin-scattering, Phys. Rev. B, 50(18), 13,105–13,112.
CLARK ET AL.
BASALT AND HIGH-PRESSURE MELT VELOCITY
17