1
Auxiliary Material for
2
Abnormal Acoustic Wave Velocities of Basaltic and (Fe,Al)-Bearing Silicate Glasses at
3
High Pressures
4
Jin Liu1, Jung-Fu Lin1
5
1
6
at Austin, Austin, Texas, USA
7
Corresponding author: Jin Liu (jinliu@utexas.edu)
Department of Geological Sciences, Jackson School of Geosciences, The University of Texas
8
Geophysical Research Letters, 2014
9
10
Introduction
11
Here we provide additional information for experimental and modeling results.
12
1. The file of Auxilliary_Material.doc includes related mathematical formulas, two supplemental
13
tables, and four supplemental figures:
14
1.1 Table S1. Chemical compositions of the basaltic glass and synthetic silicate glasses.
15
1.2 Table S2. Acoustic velocities and density of the glasses at high pressure.
16
1.3 Table S3. Bulk and shear modulus of the glasses at ambient conditions and the pressure
17
derivatives of the moduli.
18
1.4 Figure S1. Representative Brillouin spectra of the glasses at ambient conditions.
19
1.5 Figure S2. Bulk sound velocities of the glasses as a function of pressure.
20
1.6 Figure S3. Velocity differences using MgSiO3 glass as the standard at high pressure.
21
1.7 Figure S4. Density and relative change in density of the glasses at high pressure.
22
Mathematical formulas
23
The bulk sound velocity (VΦ) and Poisson’s ratio (ν) are directly calculated from measured
24
acoustic velocities using the following equations:
25
4
V2  VP2 - VS2 ,
3
26
1 (VP /VS )2 -2
and  
,
2 (VP /VS )2 -1
27
where VP and VS are compressional and shear wave velocities, respectively. The density (ρ) of
28
the glasses under high pressure is calculated using the following equation:
29
   0   1 / (VP2 - VS2 )dP,
30
where ρ0 is the density at ambient conditions and P0 is the pressure at ambient conditions
31
[Sanchez-Valle and Bass, 2010]. Details of the integration method used here have been reported
32
and discussed previously [Sanchez-Valle and Bass, 2010]. With the calculated density, the
33
experimental bulk (K) and shear (G) modulus are derived from the following equations:
34
4
K   (VP2 - VS2 ) ,
3
35
P
P0
4
3
2
and G  VS .
36
37
Following the modeling procedure reported by Sanchez-Valle and Bass [2010], we have also
38
used the third-order finite strain equations to model the compressional acoustic and equation of
39
state behavior of the glasses at high pressures [Davies and Dziewonski, 1975]. The finite-strain
40
equations used here are expressed in the following equations [Davies and Dziewonski, 1975]:
41
VP2  (1  2 )5 2 ( L1  L2 ) ,
2
42
VS2  (1  2 )5 2 ( M 1  M 2 ) ,
43
P  (1  2 )5 2 (C1  C2 2 2) ,
44
where the strain ε is given by:
45
  [1  (
46
and the coefficients are defined as:
47
L1  K0  4G0 / 3 ,
48
L2  5L1  K0 (3K '  4G ' ) ,
49
M1  G0
50
M 2  5G0  3K0G '
51
C1  3L1  4 M 1 ,
52
C2  3L2  4 M 2  7C1 ,
53
where K0, G0, K’ and G’ are the adiabatic bulk modulus and shear modulus at ambient pressure
54
and their pressure derivatives, respectively. We note that the slight mismatch between our fitting
55
and the high-pressure data is attributed to the inadequacy of the third-order finite strain equations
56
in describing the anomalous velocities of the glasses in Figure 2. Future results on the density of
57
the glasses as function of pressure will help improve the misfits here and add to a better
58
understanding of the acoustic behavior of the glasses at high pressures.
1
2
 23
) ],
0
3
59
References
60
Davies, G. F., and A. M. Dziewonski (1975), Homogeneity and constitution of the Earth's lower
61
mantle and outer core, Phys. Earth Planet. Inter., 10(4), 336-343, doi:10.1016/0031-
62
9201(75)90060-6.
63
Sanchez-Valle, C., and J. D. Bass (2010), Elasticity and pressure-induced structural changes in
64
vitreous MgSiO3-enstatite to lower mantle pressures, Earth Planet. Sci. Lett., 295(3–4), 523-530,
65
doi:10.1016/j.epsl.2010.04.034.
66
Gladney, E. S., and I. Roelandts (1988), 1987 compilation of elemental concentration data for
67
USGS BIR-1, DNC-1 and W-2, Geostandard. Newslett., 12(1), 63-118, doi:10.1111/j.1751-
68
908X.1988.tb00044.x.
4
69
Table S1. Chemical compositions of the Icelandic basaltic glass and synthetic silicate glasses.
70
The compositions listed are based on electron microprobe analyses, with the unit of wt% in the
71
table.
72
Icelandic Basalt
MgSiO3
Mg0.9Fe0.1SiO3 Mg0.79Fe0.10Al0.10Si0.96O3
Glass*
Glass
Glass
Glass
SiO2
47.96
59.89
57.82
56.25
Al2O3
15.50
4.97
CaO
13.30
MgO
9.70
40.11
34.92
31.05
FeO
8.34
4.90
1.57
Fe2O3
2.06
2.33
6.16
Na2O
1.82
TiO2
0.96
MnO
0.18
K2O
0.03
*Obtained from Gladney and Roelandts [1988].
5
73
Table S2. Acoustic Velocities and Density of the Glass Samples at High Pressure
Pressure (GPa)
ambient
0.8 (±0.1)
1.3 (±0.1)
1.9 (±0.1)
2.4 (±0.1)
2.8 (±0.2)
3.3 (±0.1)
4.2 (±0.1)
4.7 (±0.1)
5.2 (±0.2)
5.7 (±0.2)
6.3 (±0.2)
6.9 (±0.2)
7.4 (±0.3)
8.1 (±0.2)
8.9 (±0.3)
9.6 (±0.2)
10.5 (±0.3)
11.3 (±0.3)
12.2 (±0.3)
13.0 (±0.3)
13.9 (±0.3)
15.0 (±0.3)
VP (km/s)
VS (km/s)
MgSiO3 Glass
7.22 (±0.03)
4.00 (±0.03)
7.19 (±0.04)
3.99 (±0.03)
7.21 (±0.04)
3.96 (±0.03)
7.19 (±0.05)
3.94 (±0.04)
7.20 (±0.05)
3.89 (±0.05)
7.19 (±0.05)
3.90 (±0.04)
7.13 (±0.05)
3.90 (±0.04)
7.20 (±0.05)
3.92 (±0.03)
7.25 (±0.05)
3.92 (±0.03)
7.37 (±0.05)
3.92 (±0.05)
7.41 (±0.05)
3.94 (±0.03)
7.53 (±0.05)
3.95 (±0.03)
7.61 (±0.05)
3.96 (±0.03)
7.68 (±0.06)
3.99 (±0.03)
7.79 (±0.05)
4.01 (±0.04)
7.89 (±0.05)
4.07 (±0.04)
8.02 (±0.05)
4.14 (±0.03)
8.18 (±0.05)
4.19 (±0.03)
8.28 (±0.05)
4.23 (±0.03)
8.43 (±0.05)
4.29 (±0.04)
8.59 (±0.06)
4.36 (±0.03)
8.77 (±0.05)
4.44 (±0.04)
8.95 (±0.07)
4.51 (±0.05)
Density (g/cm3)
2.75 (±0.01)
2.78 (±0.01)
2.79 (±0.01)
2.81 (±0.01)
2.83 (±0.01)
2.84 (±0.01)
2.86 (±0.01)
2.89 (±0.01)
2.90 (±0.01)
2.92 (±0.01)
2.93 (±0.01)
2.95 (±0.01)
2.97 (±0.01)
2.98 (±0.01)
3.00 (±0.01)
3.02 (±0.01)
3.03 (±0.01)
3.06 (±0.01)
3.07 (±0.01)
3.09 (±0.01)
3.11 (±0.01)
3.13 (±0.01)
3.15 (±0.01)
Mg0.9Fe0.1SiO3 Glass
ambient
0.9 (±0.1)
2.2 (±0.1)
3.6 (±0.1)
5.1 (±0.1)
5.9 (±0.1)
6.7 (±0.1)
7.2 (±0.1)
8.6 (±0.2)
8.9 (±0.2)
10.1 (±0.2)
11.3 (±0.2)
12.9 (±0.2)
14.0 (±0.2)
14.7 (±0.2)
6.91 (±0.03)
6.93 (±0.03)
6.90 (±0.03)
6.81 (±0.02)
6.95 (±0.03)
7.15 (±0.05)
7.31 (±0.03)
7.38 (±0.07)
7.61 (±0.07)
7.65 (±0.08)
7.89 (±0.07)
8.09 (±0.07)
8.38 (±0.07)
8.56 (±0.08)
8.66 (±0.08)
3.80 (±0.02)
3.80 (±0.03)
3.79 (±0.02)
3.78 (±0.03)
3.79 (±0.02)
3.82 (±0.02)
3.87 (±0.03)
3.89 (±0.03)
3.99 (±0.03)
4.04 (±0.03)
4.11 (±0.03)
4.17 (±0.03)
4.24 (±0.04)
4.32 (±0.04)
4.39 (±0.04)
6
2.84 (±0.01)
2.87 (±0.01)
2.92 (±0.01)
2.97 (±0.01)
3.02 (±0.01)
3.04 (±0.01)
3.07 (±0.01)
3.08 (±0.01)
3.12 (±0.01)
3.13 (±0.01)
3.16 (±0.01)
3.19 (±0.01)
3.23 (±0.01)
3.25 (±0.01)
3.27 (±0.01)
16.4 (±0.2)
17.9 (±0.2)
19.6 (±0.2)
22.2 (±0.3)
24.7 (±0.4)
8.95 (±0.08)
9.09 (±0.09)
9.32 (±0.07)
9.53 (±0.08)
9.74 (±0.09)
4.45 (±0.04)
4.52 (±0.04)
4.65 (±0.05)
4.74 (±0.05)
4.83 (±0.05)
3.30 (±0.01)
3.33 (±0.01)
3.36 (±0.01)
3.40 (±0.01)
3.44 (±0.01)
Mg0.79Fe0.10Al0.10Si0.96O3 Glass
ambient
0.8 (±0.1)
1.3 (±0.1)
1.9 (±0.1)
2.4 (±0.1)
2.8 (±0.2)
3.3 (±0.1)
4.2 (±0.1)
4.7 (±0.1)
5.2 (±0.2)
5.7 (±0.2)
6.3 (±0.2)
6.9 (±0.2)
7.4 (±0.3)
8.1 (±0.2)
8.9 (±0.3)
9.6 (±0.2)
10.5 (±0.3)
11.3 (±0.3)
12.2 (±0.3)
13.0 (±0.3)
13.9 (±0.3)
15.0 (±0.3)
6.99 (±0.03)
6.98 (±0.03)
6.96 (±0.02)
6.96 (±0.04)
6.96 (±0.04)
6.91 (±0.05)
6.90 (±0.05)
6.87 (±0.04)
6.96 (±0.05)
7.01 (±0.05)
7.04 (±0.05)
7.08 (±0.05)
7.24 (±0.04)
7.31 (±0.04)
7.36 (±0.05)
7.48 (±0.05)
7.59 (±0.05)
7.67 (±0.05)
7.88 (±0.05)
7.96 (±0.05)
8.01 (±0.05)
8.14 (±0.05)
8.27 (±0.06)
3.82 (±0.02)
3.81 (±0.02)
3.77 (±0.02)
3.77 (±0.02)
3.78 (±0.02)
3.78 (±0.03)
3.75 (±0.02)
3.74 (±0.03)
3.75 (±0.03)
3.74 (±0.03)
3.77 (±0.03)
3.79 (±0.03)
3.81 (±0.03)
3.84 (±0.03)
3.87 (±0.03)
3.91 (±0.04)
3.94 (±0.04)
3.98 (±0.03)
4.05 (±0.03)
4.09 (±0.03)
4.11 (±0.03)
4.19 (±0.03)
4.25 (±0.04)
2.81 (±0.01)
2.84 (±0.01)
2.85 (±0.01)
2.87 (±0.01)
2.89 (±0.01)
2.91 (±0.01)
2.92 (±0.01)
2.95 (±0.01)
2.97 (±0.01)
2.99 (±0.01)
3.00 (±0.01)
3.02 (±0.01)
3.04 (±0.01)
3.06 (±0.01)
3.08 (±0.01)
3.10 (±0.01)
3.12 (±0.01)
3.14 (±0.01)
3.16 (±0.01)
3.19 (±0.01)
3.21 (±0.01)
3.23 (±0.01)
3.25 (±0.01)
Icelandic Basalt Glass
ambient
0.8 (±0.1)
1.2 (±0.1)
1.7 (±0.1)
2.2 (±0.1)
2.6 (±0.1)
3.1 (±0.1)
3.8 (±0.1)
4.3 (±0.1)
4.8 (±0.1)
5.3 (±0.1)
5.8 (±0.1)
6.68 (±0.02)
6.59 (±0.04)
6.55 (±0.03)
6.57 (±0.04)
6.58 (±0.03)
6.70 (±0.03)
6.79 (±0.03)
6.89 (±0.04)
7.00 (±0.03)
7.11 (±0.03)
7.20 (±0.03)
7.27 (±0.04)
3.73 (±0.02)
3.68 (±0.02)
3.65 (±0.03)
3.66 (±0.03)
3.68 (±0.04)
3.75 (±0.03)
3.77 (±0.02)
3.79 (±0.04)
3.83 (±0.04)
3.86 (±0.04)
3.89 (±0.02)
3.92 (±0.02)
7
2.79 (±0.01)
2.82 (±0.01)
2.84 (±0.01)
2.86 (±0.01)
2.88 (±0.01)
2.89 (±0.01)
2.91 (±0.01)
2.94 (±0.01)
2.95 (±0.01)
2.97 (±0.01)
2.99 (±0.01)
3.00 (±0.01)
6.3 (±0.2)
6.9 (±0.2)
7.5 (±0.2)
8.2 (±0.2)
8.8 (±0.2)
9.7 (±0.2)
10.1 (±0.2)
11.0 (±0.2)
12.2 (±0.2)
13.0 (±0.2)
14.1 (±0.3)
15.0 (±0.3)
16.1 (±0.3)
16.9 (±0.3)
17.9 (±0.3)
19.3 (±0.3)
20.7 (±0.3)
7.34 (±0.04)
7.43 (±0.04)
7.57 (±0.05)
7.63 (±0.04)
7.77 (±0.05)
7.89 (±0.03)
7.99 (±0.05)
8.07 (±0.04)
8.22 (±0.05)
8.35 (±0.04)
8.46 (±0.04)
8.59 (±0.05)
8.73 (±0.06)
8.85 (±0.05)
8.99 (±0.06)
9.12 (±0.05)
9.27 (±0.05)
3.96 (±0.04)
3.98 (±0.02)
4.02 (±0.04)
4.07 (±0.02)
4.09 (±0.05)
4.12 (±0.05)
4.15 (±0.04)
4.18 (±0.04)
4.26 (±0.05)
4.30 (±0.03)
4.35 (±0.04)
4.38 (±0.04)
4.43 (±0.04)
4.48 (±0.04)
4.52 (±0.03)
4.58 (±0.04)
4.65 (±0.06)
74
8
3.02 (±0.01)
3.03 (±0.01)
3.05 (±0.01)
3.07 (±0.01)
3.09 (±0.01)
3.11 (±0.01)
3.12 (±0.01)
3.14 (±0.01)
3.17 (±0.01)
3.19 (±0.01)
3.21 (±0.01)
3.23 (±0.01)
3.25 (±0.01)
3.27 (±0.01)
3.29 (±0.01)
3.31 (±0.01)
3.34 (±0.01)
75
Table S3. Modeled Bulk and Shear Moduli of the Glasses at Ambient Conditions and Their
76
pressure derivatives.
K0 (GPa)
84.2
(±1.3)
Low-Pressure State
K’
G0 (GPa)
1.5
(±0.2)
43.5
(±1.5)
G’
K0 (GPa)
MgSiO3 Glass
0.1
61.2
(±0.1)
(±2.4)
Mg0.9Fe0.1SiO3 Glass
0.3
57.6
(±0.1)
(±1.8)
81.0
(±0.8)
1.3
(±0.2)
41.0
(±0.7)
83.3
(±1.5)
0.4
(±0.1)
40.7
(±1.2)
72.8
(±0.6)
-0.6
(±0.2)
38.9
(±0.9)
High-Pressure State
K’
G0 (GPa)
G’
6.8
(±0.7)
32.9
(±1.7)
2.0
(±0.4)
6.9
(±0.6)
33.1
(±1.1)
2.0
(±0.3)
Mg0.79Fe0.10Al0.10Si0.96O3 Glass
0.1
60.0
5.7
(±0.1)
(±2.1) (±0.5)
32.6
(±1.3)
1.7
(±0.2)
35.8
(±0.9)
1.8
(±0.3)
Icelandic Basalt Glass
-0.4
56.4
(±0.1)
(±1.4)
77
9
6.5
(±0.4)
BLS Spetra of Glass
A
VP
MgSiO3
VP
VS
VS
Rayleigh
Intensity (a.u.)
B
VP
Mg0.9Fe0.1SiO3
VS
C
VS
VP Mg0.79Fe0.10Al0.10Si0.96O3 V
VS
D
VP
Icelandic Basalt
VP
-5
P
VS
VS
VS
-10
VP
0
5
10
Velocity (km/s)
78
Figure S1
79
Figure S1. Brillouin spectra of the silicate glasses at ambient conditions. (a) MgSiO3 glass; (b)
80
Mg0.9Fe0.1SiO3 glass; (c) Mg0.79Fe0.10Al0.10Si0.96O3 glass; (d) Icelandic basalt glass with a
81
chemical composition of Na0.06Ca0.26Mg0.26Fe0.16Al0.33Si0.88O3. Open symbols: experimental data;
82
red solid lines: fitted results.
10
7
A
6
Bulk Sound Velocity (km/s)
MgSiO3
8
B
7
6
Mg0.9Fe0.1SiO3
5
C
6
Mg0.79Fe0.10Al0.10Si0.96O3
7
D
6
Icelandic Basalt
5
0
83
5
10
15
20
25
Pressure (GPa)
84
Figure S2. Bulk sound velocities (VΦ) of the glasses as a function of pressure. (a) MgSiO3 glass;
85
(b) Mg0.9Fe0.1SiO3 glass; (c) Mg0.79Fe0.10Al0.10Si0.96O3 glass; (d) Icelandic basalt glass. Open
86
symbols: experimental bulk sound velocities obtained directly from measured VP and VS. Errors
87
are smaller than the symbols and are not shown in the plots for clarity. The shaded zone
88
represents the approximate pressure range of the abnormal velocity behavior.
Figure S2
11
0
A Mg0.9Fe0.1SiO3
-2
VS
(Vel-VelMgSiO3)VelMgSiO3 (%)
-4
V
VP
-6
-2
B Mg0.79Fe0.10Al0.10Si0.96O3
-4
-6
C Icelandic Basalt
0
-4
-8
0
5
10
15
20
25
Pressure (GPa)
89
Figure S3
90
Figure S3. Velocity differences using MgSiO3 glass as the standard at high pressure. (a)
91
Mg0.9Fe0.1SiO3 glass; (b) Mg0.79Fe0.10Al0.10Si0.96O3 glass; (c) Icelandic basalt glass. Diamonds:
92
compressional wave velocity (VP); squares: shear wave velocity (VS); circles: bulk sound velocity
93
(VΦ); vertical ticks: representative errors (±1σ) calculated using standard error propagations.
12
A
Density (g/cm3)
3.4
3.2
MgSiO3
3.0
Mg0.9Fe0.1SiO3
Mg0.79Fe0.10Al0.10Si0.96O3
Icelandic Basalt
Mg0.96Si1.02O3, SB2010
2.8
B
(0)
0.15
0.10
MgSiO3
Mg0.9Fe0.1SiO3
0.05
Mg0.79Fe0.10Al0.10Si0.96O3
Icelandic Basalt
0.00
94
0
5
10
15
20
25
Pressure (GPa)
95
Figure S4. Density and relative change in density of the glasses at highFigure
pressure. S4
(a) Density; (b)
96
The relative change in the density ((ρ-ρ0)/ρ). Circles and dash-dotted line: MgSiO3 glass;
97
diamonds and dashed line: Mg0.9Fe0.1SiO3 glass; squares and dash-dot-dotted line:
98
Mg0.79Fe0.10Al0.10Si0.96O3 glass; triangles and dotted: Icelandic basalt glass; pluses (+):
99
Mg0.9Fe0.1SiO3 glass, Sanchez-Valle and Bass [2010]; solid lines: modeled results.
13