Full text of DOI:10.1007/s004100100253

Contrib Mineral Petrol #2001) 141: 297±306
DOI 10.1007/s004100100253
Frank R. Schilling á Marcus Hauser
Stanislav V. Sinogeikin á Jay D. Bass
Compositional dependence of elastic properties and density of glasses
in the system anorthite-diopside-forsterite
Received: 3 March 2000 / Accepted: 20 January 2001 / Published online: 11 April 2001
Ó Springer-Verlag 2001
Abstract The compressional #vP) and shear #vS) wave observed increase of Poisson's ratio with increasing
velocities of 20 glasses in the pseudoternary system MgO content may be explained by a reduced bond
anorthite #An)±diopside #Di)±forsterite #Fo) were strength between tetrahedra due to the addition of
measured by Brillouin spectroscopy as a means of MgO.
constraining the e€ect of composition on the elasticity
of glasses. The velocity data together with measured
densities were used to calculate the elastic properties:
Young's modulus #E), adiabatic bulk modulus #KS),
Introduction
shear modulus #G), and Poisson's ratio #r). The data
show that di€erent chemical constituents a€ect the
The density of silicate melts is an important property for
describing the migration of melts in geological settings.
density, velocities and elastic properties in a highly
The ascent and descent of silicate melts in the Earth's
systematic way. All of the properties we examined are
crust and mantle, strati®cation of magma bodies, frac-
well described by ideal mixing of molar properties. The
tionation, and partial melting processes are a€ected by
addition of MgO strongly increases the bulk, Young's
the density contrast between melts and the surrounding
and shear moduli. The results are compared to di€erent
solid rocks #Stolper et al. 1981; Bagdassarov et al. 1999).
models describing the elastic properties of glasses as a
The high compressibility of melts as compared to min-
function of chemical composition. We show that the
erals leads to a greater density increase with increasing
in¯uence of magnesia is underestimated in previous
depth #increasing pressure) for melts than for coexisting
models, in some cases due to a lack of appropriate
minerals. Therefore, the density and compressibility
experimental data. The relatively large values of elastic
of noncrystalline solids are of great importance for
moduli for magnesia-rich glasses can be explained by
understanding melt segregation in the crust and mantle.
the high bonding strength between magnesium and
Although basalts dominate hot-spot volcanism and
SiO4 and AlO4 tetrahedra. The strongest e€ect of
the world's oceanic basins, few experimental data are
magnesium is on the bulk modulus; the shear modulus
available on the elastic properties of basaltic melts and
is less a€ected. Therefore, Poisson's ratio shows a
magnesia-rich compositions. Due to the structural sim-
modest increase with increasing MgO content. The
ilarities between silicate melts and glasses #Stebbins et al.
1995), the physical properties of glasses can often be
related to the physical properties of the corresponding
melts. Knowledge of the properties of magnesia-rich
F.R. Schilling #&) á S.V. Sinogeikin á J.D. Bass
Department of Geology,
University of Illinois at Urbana-Champaign,
1301 W. Green St., Urbana, IL 61801, USA
glasses is therefore a starting point for understanding the
behavior of basaltic melts.
To constrain the e€ect of composition on the elas-
ticity of glasses, we measured the acoustic velocities and
density of 20 di€erent glasses in the pseudoternary
system anorthite #CaAl2Si2O8)±diopside #CaMgSi2O6)±
forsterite #Mg2SiO4), a model basaltic system #Fig. 1).
The velocity and density data were used to calculate the
elastic moduli and Poisson's ratio of the glass samples.
Our results show that di€erent chemical constituents
a€ect the elasticity of these glasses in a highly systematic
way. The results are compared with models describing
M. Hauser
Institut fur Mineralogie, Freie Universitat Berlin,
Takustraûe 6, 14195 Berlin, Germany
F.R. Schilling
Present address: GeoForschungsZentrum Potsdam,
Division 4, Telegrafenberg, 14473 Potsdam, Germany
e-mail: fsch@gfz-potsdam.de
Tel.: +49-331-2881875, Fax: +49-331-2881402
Editorial responsibility: T.L. Grove

298
Fig. 1 Chemical composition of the glass samples in the pseudo-
ternary anorthite-diopside-forsterite system. Liquidus temperatures
are drawn as isotherms #modi®ed after Hauser et al. 1998)
the elastic properties of glasses as a function of their
chemical composition. Possible implications for the
structure and internal forces within these amorphous
materials are discussed.
Experimental
The glass samples are identical to those used for previous viscosity
and electrical conductivity measurements #Hauser et al. 1998;
Hauser 2000). High-purity oxide and carbonate powders were
mixed and melted at 1,500±1,600 °C in Pt/Au and Pt/Rh crucibles,
depending on the glass composition. To insure homogeneity of the
samples, the melt was carefully stirred, and quenched in air by
pouring it onto a liquid N2-cooled Cu block. The obtained glasses
were crushed, mixed, and remelted at least twice. Further details of
the sample preparation are given by Hauser #2000).
Electron microprobe and X-ray ¯uorescence analyses were used
to determine the chemical compositions #Hauser 2000; Table 1;
Fig. 1). For Brillouin spectroscopy optically clear, inclusion-free
samples #ꢀ2´4 mm) were polished plane parallel to a thickness of
0.2±0.4 mm.
A schematic diagram of the experimental setup #Brillouin
spectrometer) is shown in Fig. 2. We used an Ar-ion laser
#k=514.5 nm) as a light source and a 90° symmetric scattering
geometry, where the incident beam and scattering direction are at
45° to the sample surfaces. In symmetric scattering geometry on
plane-parallel samples, uncertainties from the refractive index are
e€ectively eliminated #Whit®eld et al. 1976). The scattered light was
analyzed with a six-pass piezoelectrically scanned Fabry-Perot
interferometer used in combination with a photomultiplier tube
#PMT). Further details of the experimental setup are described by
Sinogeikin et al. #1998). The velocities were determined from the
mean of at least four redundant measurements in which the sample
was turned by 180° to reduce possible errors caused by the devia-
tion from an ideal scattering geometry. The system was periodically
calibrated against a MgO single-crystal standard. In the experi-
ments described here, the elastic velocities are measured in the GHz
range and the reported elastic properties represent unrelaxed
behavior.

299
Fig. 2 Schematic diagram of
the Brillouin spectrometer
used #simpli®ed from Sino-
geikin et al. 1998). BS Beam
splitter, FL focusing lens,
CL collecting lens, L lens, M
mirror, OMM optomechan-
ical modulator, SF spatial
®lter, R re¯ector, PR prism,
PMT photomultiplier tube,
FBC Fabry-Perot controller,
OSC oscilloscope, MCA
multichannel analyzer, PC
personal computer
In a symmetric 90° scattering geometry, the Brillouin shift #Dxi) The density #q) of each glass was measured by the Archimedean
of a particular acoustic mode i does not depend on the refractive method with a Berman microbalance #Berman 1939; Table 2). The
index of the sample. The sound velocities vi #where vi corresponds weight of samples with a mass of at least 80 mg was measured at room
to vS or vP) were calculated according to
Dxi k
temperature in air and toluene, from which the density was calcu-
lated. The resultant densities are accurate to within ‹0.003 g/cm3;
the precision is even better. The accuracy was determined by use of a
quartz standard #q=2.648 g/cm3).
p
vi ˆ
ꢁ1†
2
where k is the wavelength of the laser light #Whit®eld et al. 1976).
To enhance signal-to-noise ratio, the recorded Brillouin spectra
were ®ltered digitally with a low-pass Fourier ®lter #Fig. 3). The
positions of the peaks in the Brillouin spectra were evaluated as the
centers of the full width at half-maximum of the ®ltered peaks
#Fig. 3).
Results
The elastic moduli and Poisson's ratio are calculated
from the wave velocities and density using the relations:
Fig. 3 Brillouin spectrum and
evaluation procedure. The inset
shows both raw spectrum and
spectrum after applying a low-
pass ®lter. The Brillouin shifts
corresponding to vP and vS
velocities are deduced as the
center of the width of the
®ltered peak at half-maximum.
The velocities are calculated
according to Eq. #1)

300
Shear modulus
G ˆ v2s q
2
2
4
Adiabatic bulk modulus Ks ˆ vq q À = vs q
3
9KS G
ꢁ2†
Young's modulus
E ˆ
3KS ‡G
ꢀ
ꢁ
3KS À2G
1
1
2
P =vS † À1
Poisson's ratio
r ˆ 1 À ꢁv
ˆ
2ꢁ3KS ‡G†
2
The velocities, densities and elastic properties are listed
in Table 2. Note that the adiabatic bulk modulus KS is
systematically larger than the isothermal #KT) modulus
by a small amount #Table 2). However, the di€erence is
smaller than the experimental error. Therefore, our
discussion of systematic relationships based on KS
should also be valid for KT, at least near ambient con-
ditions.
When the acoustic velocities of the glasses are plotted
as a function of diopside content #Fig. 4), it is seen that
variation of the anorthite-diopside ratio has a minor e€ect
on the acoustic velocities. The data suggest that the shear
#vS) velocity may decrease slightly with increasing diop-
side content, whereas the compressional #vP) velocity is
virtually independent of the An/Di ratio. The major fea-
ture displayed by Fig. 4 is a pronounced increase in vP and
vS velocities with increasing forsterite content.
The minor changes in vP and vS with variable com-
position are more clearly resolved in Poisson's ratio
#Fig. 5). With increasing diopside and forsterite con-
tents, Poisson's ratio increases.
Figure 6 shows the variation of density as a function
of the anorthite/diopside ratio. With increasing diopside
content, an increase in density is observed. Samples with
low forsterite content have lower densities than samples
with high forsterite content.
Fig. 4 Longitudinal #vp) and shear wave #vS) velocity as a function
of the diopside content. Lines connect samples with approximately
similar forsterite #Fo) content. For comparison the velocities
measured for glasses with anorthite and diopside compositions by
Askapour et al. #1993) are indicated by open symbols. The mean
standard deviation #bar) out of at least four measurements #2r) on
each sample is less than 1%

301
Velocity and Poisson's ratio
The small change observed in the vP and vS velocities
with increasing diopside content #Fig. 4) is in good
agreement with previous observations #Vo-Thanh et al.
1996). From Fig. 4 it would appear that vP and vS are
insensitive to the Al2O3 content, but this inference is
misleading. The in¯uence of Al2O3 in isolation, and the
other oxide components will be discussed below.
Although the variations in the velocities with anorth-
ite/diopside ratio are relatively small, they result in the
observed increase in Poisson's ratio with increasing
diopside content #Fig. 5). Poisson's ratio is measured ac-
curately, because it involves the ratio of vP/vS #Eq. 2), and
any small systematic errors a€ecting the velocity mea-
surements tend to cancel. The resulting uncertainty in
Poisson's ratio #‹0.0009ꢀ‹0.3%) is calculated as the
mean standard deviation from repetitive measurements
on each sample. With increasing MgO/#CaO+MgO)
content, the glasses show a higher Poisson's ratio #Fig. 7),
as well as an increase in both the shear and bulk moduli
#Fig. 8, Table 2). This is in excellent agreement with ab
initio simulations #Hauser et al. 1998; Hauser 2000),
which indicate that magnesium is more strongly bonded in
the glass structure than is calcium.
Fig. 5 Poisson's ratio versus anorthite to diopside ratio. A line
connects samples with approximately similar forsterite #Fo) content
An interesting secondary e€ect, which is suggested
by these same simulations, is that the strength of the Si-
O-Si bonds within the glass structure decreases due to
the addition of magnesium #Hauser et al. 1998; Hauser
2000). This tendency to weaken the tetrahedral frame-
work is greater for Mg than for Ca. To the extent that
the shear rigidity depends on the strength of Si-O-Si
bonding, MgO may increase the shear modulus G and
shear velocity vS of a glass by a lesser amount than it
would in the absence of such an interaction. Therefore,
vS and G increase with the addition of MgO, but by a
lesser amount than the vP and bulk modulus, and so
Fig. 6 Variation of the density of glasses with composition. A line
connects samples with approximately similar forsterite #Fo)
content. Filled symbols this study. Open symbols Askapour et al.
#1993)
Discussion
General compositional trends
Density
The increase in glass density with increasing forsterite
#MgSiO4)anddiopside #CaMgSi2O6) contents #Fig. 6) can
be attributed to the increasing concentration of magnesia
in the glass. This result is in accord with previous obser-
vations #Stebbins et al. 1984; Wang 1989) The molar mass
of magnesium #24.3 g/mol) is much smaller than that of
calcium #40.1 g/mol), but the ionic radius #Pauling radius)
of magnesium #0.65 A) is much smaller than the radius
of calcium #1.14 A). Therefore, the molar density of
magnesium is higher than that of calcium, and, as a result,
an increase in magnesium content leads to an increase in
the density.
Fig. 7 Poisson's ratio as a function of the MgO content. The values
of the ``end-member'' compositions are indicated by An #anorthite)
and Di #diopside)

302
Poisson's ratio #Eq. 2) and the vP/vS ratio increase.
Under the assumption of an ideal mixing model
Thus, a possible structural interpretation is that the #Stebbins et al. 1984; Fig. 9), molar densities were de-
increase in Poisson's ratio with increasing MgO content duced from the measured values by a least-squares re-
may be correlated with a reduced bonding strength gression analysis #Table 3). Figure 9 shows a comparison
between network-forming tetrahedra. Regardless, our between the measured densities and densities calculated
results show that the dominant e€ect on the elastic with Eq. #3). The scatter of the data #approximately
properties of the glasses is the strength of Mg-O 0.003 g/cm3) corresponds to the experimental uncer-
bonding, resulting in comparatively large, positive tainty in the density measurements.
partial molar moduli.
For the compositions examined in this study, the
assumption of ideal mixing between simple oxide
constituents is also satisfactory for velocities, Poisson's
ratio, and elastic moduli #Figs. 10, 11, 12). As for the
density, the molar velocities, moduli and Poisson's ratios
#Table 3) were deduced from the measured values by a
least-squares regression.
Mixing models
Ideal molar mixing model
The elastic properties, density, and sound velocities of
glasses and liquids are often expressed in terms of an molar volumes Vi, and all related properties such as
Under the assumption of a simple ionic model the
P
et al. 1984). A bulk property P #e.g., density, velocity, the glass) or the compressibility dV/dP, will mix ideally
ideal mixing of molar properties of oxides #e.g., Stebbins the densityq ˆ Vi=M #where M is the molar mass of
moduli) is calculated by
X
#e.g., Makishima and Mackenzie 1973). An ionic model
may also explain ideal mixing of partial molar shear
moduli. If q, K, and G mix ideally, the resultant veloci-
ties #Fig. 10) and Poisson's ratio #Fig. 11) should display
nonlinear behavior #Eq. 2). However, over the restricted
range of velocities and Poisson's ratios measured in this
P ˆ
xiPi
ꢁ3†
i
where xi is the molar fraction of component i, and Pi is
the corresponding molar property. These empirical
molar properties can be ®tted to observed data by least-
square algorithms.
The elasticity and density of glasses and melts con-
taining MgO have been measured previously #Loewen-
stein 1961; Soga et al. 1976; Rivers and Carmichael
1987; Wang 1989; Askapour et al. 1993; Vo-Thanh et al.
1996). Nevertheless, model calculations are heavily
weighted by a small number of points representing high
MgO contents. Therefore, the existing database may not
suce to accurately represent the molar properties of
chemically complex high-MgO glasses.
Fig. 9 Modeled versus measured density. The densities were
modeled according to an ideal mixing of molar properties #Eq. 3).
The scatter of the data #‹0.003 g/cm3) corresponds to the
experimental error. The solid line represents ideal mixing behavior.
The measured and calculated densities would be equal on this line
Table 3 Molar properties of glasses in the system anorthite-
diopside-forsterite. An ideal mixing law is assumed #Eq. 3)
Molar property
SiO2
Al2O3
MgO
CaO
Density #g/cm3)
vP #m/s)
vS #m/s)
Poisson's ratio
E #GPa)
2.523
6,029
3,419
0.2667
70.0
2.507
7,921
4,421
0.2719
127.11
94.5
3.247
8,166
4,369
0.305
154.0
125.2
59.4
3.167
6,681
3,791
0.2602
116.8
83.8
Fig. 8 Adiabatic bulk #KS) and shear #G) modulus versus MgO
content. The values of the ``end-member'' compositions are
indicated by An #anorthite) and Di #diopside). The size of the
symbols represents the experimental error
KS #GPa)
G #GPa)
47.4
27.8
49.9
46.1

303
Fig. 12 Modeled G, K and E moduli compared to measured ones.
The moduli were calculated according to an ideal mixing of molar
properties #Eq. 3, Table 3). The scatter of the data is in agreement
with the precision of the modulus determination and is smaller than
‹1%. The solid line represents ideal mixing behavior
Fig. 10 Modeled versus measured vP and vS velocities. The
velocities were calculated according to an ideal mixing of molar
properties #Eq. 3). The scatter of the data is in agreement with the
precision of the measurements and is smaller than ‹0.5%. The
solid line represents ideal mixing behavior
compressional velocity and shear velocity of Al2O3 are
much higher than the corresponding molar properties of
SiO2 #Table 3). As discussed above, MgO #3.247 g/cm3)
shows a higher molar density than CaO #3.167 g/cm3).
The molar moduli and velocities of MgO are much
higher than those of CaO #Table 3). The minor changes
in vP and vS velocities with variable anorthite to diopside
ratio #Fig. 4) are the result of the Al2O3 to MgO ex-
change in this pseudobinary system, whereas both oxides
have comparable molar velocities #Table 3). The higher
#MgO+Al2O3)/#CaO+SiO2) ratio with increasing for-
sterite content leads to the observed increase in vP and
vS, in which MgO and Al2O3 have higher molar veloci-
ties than CaO and SiO2 #Table 3).
Structural related models
Makishima and Mackenzie #1973) presented a structure-
based mixing model by taking into account the dissoci-
ation energy of the oxide constituents per unit volume
and the packing density. Their theoretical model is based
on ideal ionic bonding within the structure. These
authors assume that the Young's modulus #E) of a
crystalline or noncrystalline solid is given by
Fig. 11 Modeled Poisson's ratio as a function of the measured one
#Eq. 3, Table 3). The solid line represents ideal mixing behavior
study, we ®nd empirically that an ideal mixing approx-
imation describes the observations well, even if it cannot
be valid over a larger compositional range, and despite
the fact that there is no theoretical basis for applying
ideal mixing to nonvolumetric properties such as veloc-
ities. Additional empirical justi®cation for our approach
aU
E ˆ 2
ꢁ4†
r03
is provided by the results of Rivers and Carmichael where a is a Madelung constant, U is the attractive
#1987) who obtained partial molar velocities for the electrostatic energy, and r0 the interatomic distance. In a
oxide constituents of silicate melts. These authors simi- disordered glass structure the Madelung constant is not
larly cautioned against extrapolating the results of such well de®ned. Makishima and Mackenzie #1973) consid-
an analysis far from the compositional range of their ered the product of the dissociation energy per unit
experiments. volume Gt and a relative packing density Vt instead of
SiO2 and Al2O3 have similar molar densities #2.523 the Madelung constant. The packing density Vi for each
and 2.507 g/cm3, respectively) but the molar moduli, oxide component MexOy is linked to the Pauling ionic

304
radius of the component #Makishimna and Mackenzie The deviation #Fig. 14) between observed and mod-
1973). The Young's modulus in the Makishima and eled values ± calculated using the ideal mixing approach
Mackenzie model is expressed by
and the data set of Wang #1989) ± can be attributed to
the lack of appropriate data for magnesia-rich compo-
sitions. The older data #Loewenstein 1961; Soga et al.
1976; Wang 1989) underestimate the e€ect of magnesia
on the E modulus #Table 3).
q
E ˆ 2 DtVt
M
X
X
i
ꢁ5†
q
E ˆ 2
Dixi
Vixi
M
i
The increasing discrepancy for glasses with increasing
ionic strength #high magnesia content) is plotted in
Fig. 14 as a function of the number of nonbridging
oxygens divided by the number of #SiO4+AlO4) tetra-
hedra #NBO/T). The NBO/T ratio is not independent of
the magnesia content in the system. Therefore, two
explanations are possible to interpret the observations.
The deviation between the measured and modeled
E modulus might result from the increasing number of
NBO/T. This would imply that the higher strength of
these glasses compared to the calculated value is due to
the lower degree of polymerization. On the other hand,
ꢁ6† depolymerization ± disruption of the framework ± leads
where Di is the molar dissociation energy, q is the bulk
density, and xi the molar fractions.
The Makishima and Mackenzie model was extended
by Rocherulle et al. #1989) to describe the elastic moduli
of high-strength glasses, especially oxynitride glasses.
They modi®ed the packing density by an additional
parameter Z ± the number of formula units per ``unit
volume'' #referred as ``unit cell'' by Rocherulle et al.
1989) ± which is ®tted to the data.
Following the model of Rocherulle et al. #1989), the
Young's modulus is expressed as
X
i
X
i
E ˆ 2
Gixi
Cixi
where Ciˆ V iꢁq=M†Z is the packing factor.
The bulk modulus KS is approximated in both models
by a linear relationship between K and E.
K ˆ bVtE
ꢁ7†
with b=1.2 for the Makishima and Mackenzie model
and 1.08 for the modi®ed model of Rocherulle et al.
#1989). The latter authors used a slightly di€erent Gi
value for alumina than Makishima and Mackenzie
#1973). The Gi, Vi, and Ci values for both models are
listed in Table 4.
Elastic properties
In Fig. 13 the measured elastic properties are compared
to the theoretical model of Makishima and Mackenzie
#1973), Rocherulle et al. #1989), and the empirical rela-
tion #ideal mixing Eq. 3) by Wang #1989). A better
correlation between the measured and modeled E moduli
is observed for glasses with low magnesia content
#anorthite dominated). With increasing forsterite and
diopside #Mg) contents, deviations between modeled
and observed E moduli increase. Therefore, the in¯uence
of magnesium on the strength of glasses is underesti-
mated in all three models.
Fig. 13 Measured E modulus compared to moduli calculated from
di€erent models. The solid line represents an ideal model, where
measured and calculated E modulus would be equal
Table 4 Gi, Vi, and Ci values for the models after Makishima and
Mackenzie #1973), and Rocherulle et al. #1989). Value in paren-
theses GI value used by Rocherulle et al. #1989)
Compound
Gi
Vi
Ci
#mJ/m3)
#mm3)
SiO2
64.4
14.0
21.4
9.4
0.6174
0.8333
0.5530
0.6750
Al2O3
CaO
MgO
133.8 #120)
63.8
83.6
Fig. 14 Di€erence between measured and calculated E moduli as a
function of the number of nonbridging oxygen divided by the
number of tetrahedra #NBO/T)
7.6

305
to a decrease in the fraction of strong bonds between in the elastic moduli with increasing MgO content for
tetrahedra and, therefore, should lead to a lower melts as well. Due to the stronger bonding, lower
Young's modulus, which is in contradiction to the temperature and pressure derivatives of the elastic
observation #Fig. 14). Makashima and Mackenzie #1973) moduli would be expected. The limited database for
and Rocherulle #1989) showed for various compositions glasses with high MgO content already shows a strong
with variable NBO/T that the ionic models work ®ne for in¯uence of MgO on the elastic properties #e.g., Steb-
alkaline glasses and even for oxynitride glasses, inde- bins et al. 1995). Marginal support for this model
pendent of the NBO/T ratio. Therefore, the assumption comes from the results of Rivers and Carmichael #1987)
of a dominating in¯uence of NBO/T to Young's mod- who found that the molar #dV/dP)T for MgO is approxi-
ulus cannot explain the observed behavior.
mately zero for silicate melts, although the value of this
If we assume that the di€erence in strength between property was generally small for most of the oxide
modeled and measured properties is due to the increased constituents. Additional support comes from the results
magnesia content, we can conclude that the in¯uence of of Lange #1997) who found a smaller molar #dV/dT)P
magnesium on the strength of the glass is underesti- for MgO compared to other alkaline or earth-alkaline
mated and that MgO has a signi®cant in¯uence on the oxides for silicate melts.
structure of the glass.
Therefore, all inferences about the behavior of
Because all of the glasses we studied are transparent basaltic melts which are based on the properties of
and poor electrical conductors, metallic bonding in these MgO-poor melts may need to be reevaluated. If MgO-
glasses may be neglected. As pointed out above, mo- rich melts have lower temperature and pressure de-
lecular simulations indicate strong bonding of magne- rivatives of elastic properties, then basic or ultrabasic
sium to the adjacent clusters of tetrahedra. Similar to the melts would experience a larger buoyancy force at
explanation for AlN components in glasses #Rocherulle depth due to pressure, but a smaller buoyancy force
et al. 1989), the di€erence between the observed and due to the high temperatures of the interior. Which of
measured E modulus may be explained by a higher these e€ects will dominate is uncertain. Because the
strength of Mg++-related bonds compared to simpli®ed pressure and temperature derivatives of basaltic melts
ionic models. This is in good agreement with the result are rarely known, all models that include the buoy-
of ab initio simulations #Hauser et al. 1998; Hauser ancy forces of basaltic melts are highly speculative.
2000), which show that Mg2+ is more strongly bonded Therefore, this study on the elastic properties of glasses
within the glass structure than is Ca2+. This can be can only be the starting point of a more detailed study
taken into account in the ionic model of Rocherulle et al. of the elastic properties at elevated temperatures and
#1989) by an increased packing density and, therefore, pressures.
higher Z value for MgO. An increase in the observed
As the velocity and elasticity systematics of basaltic
E-modulus with increasing magnesia content can thus melts are fairly uncertain, conclusions drawn from
be explained by increasingly stronger bonding and a extrapolated elastic properties for basaltic melts may be
resultant higher packing density due to magnesium misleading. Therefore, systematic investigations are
ions. In other words, MgO does fundamentally change necessary to understand in more detail the elastic and
the structure.
rheological properties of basaltic melts at elevated
Our results indicate that an extrapolation of molar temperatures. Atomic-level simulations and spectro-
properties to vastly di€erent chemical compositions may scopic investigations could give additional information.
result in a signi®cant error #Fig. 14, high MgO-contents).
Acknowledgements We express our gratitude to Prof. Dr. J. Arndt
As the glass structure may strongly depend on di€erent
constituents, the use of molar properties over a wide
range of composition could be misleading. This is clearly
for the support of this work. The helpful and constructive com-
ments of two anonymous reviewers are gratefully acknowledged.
Financial support from the Deutsche Forschungsgemeinschaft
demonstrated by silica glass, for which the inferred
molar density #2.523 g/cm3), KS #47.4 GPa), and G
#27.8 GPa) of a virtual SiO2 component compare poorly
with the measured values for silica glass #q=2.204 g/
cm3; KS=36.5 GPa; G=31.2 GPa; values taken from
Bass 1995).
#grant SFB 267 ``Deformation processes in the Andes'', Heisenberg
grant Schi545/1) and the National Science Foundation is gratefully
acknowledged.
References
Due to the structural similarities between silicate
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