JOURNAL OF PETROLOGY
VOLUME 51
NUMBERS 1 & 2
PAGES 9^19
2010
doi:10.1093/petrology/egp043
Stress-driven Melt Segregation in Partially
Molten Feldspathic Rocks
DAVID L. KOHLSTEDT1*, MARK E. ZIMMERMAN1 AND
STEPHEN J. MACKWELL2
1
DEPARTMENT OF GEOLOGY AND GEOPHYSICS, UNIVERSITY OF MINNESOTA, 310 PILLSBURY DR. SE, MINNEAPOLIS,
MN 55455, USA
2
LUNAR AND PLANETARY INSTITUTE, 3600 BAY AREA BLVD., HOUSTON, TX 77058, USA
RECEIVED FEBRUARY 20, 2009; ACCEPTED JUNE 11, 2009
ADVANCE ACCESS PUBLICATION JULY 22, 2009
Not only melt fraction but also melt distribution directly
influence the deformation behavior of a partially molten
rock. The distribution of melt in a viscously deforming,
partially molten rock is, in turn, markedly affected by the
deviatoric stress. Whereas early experimental investigations of the rheological properties of partially molten
rocks emphasized the dependence of viscosity on melt fraction, subsequent studies also explored the coupled phenomena of alignment of melt at the grain scale and
segregation of melt at larger scales during viscous deformation. The latter phenomenon is the focus of this paper.
A number of experimental studies have revealed alignment of melt at the grain scale during viscous deformation
of partially molten peridodites (Bussod & Christie, 1991;
Kohlstedt & Zimmerman, 1996; Daines & Kohlstedt, 1997;
Zimmerman et al., 1999; Zimmerman & Kohlstedt, 2004).
In these samples, a melt preferred orientation developed
with a significant fraction of melt pockets aligned at an
angle of 15^308 to the maximum principal stress, s1. Melt
flowed to extend those pockets that were appropriately
oriented in the applied stress field to produce a minimum
in mean pressure. Subsequent static annealing of deformed
samples resulted in a redistribution of melt dictated by surface tension.
More recent experimental studies explored conditions
under which melt not only aligned in response to an
applied stress but also segregated into melt-rich bands
separated by melt-depleted lenses (Holtzman et al., 2003a,
2003b; Holtzman & Kohlstedt, 2007; King et al., 2009).
A simple yet elegant theoretical model predicted this
behavior (Stevenson, 1989) and careful field observations
anticipated it (Kelemen & Dick, 1995). Although the
theory did not yield a specific length scale for the spacing
*Corresponding author. Fax: 612-25-19. E-mail: [email protected]
ß The Author 2009. Published by Oxford University Press. All
rights reserved. For Permissions, please e-mail: journals.permissions@
oxfordjournals.org
High-strain torsion experiments were performed on a series of samples composed of anorthite plus51 to 12% melt to investigate the formation of melt-rich bands produced by stress-driven melt
segregation. Fine-grained (3^4 m) samples were deformed in
the diffusion creep regime at a temperature of 1450 K and a
confining pressure of 300 MPa at shear strain rates of 1 10^4 to
16 10^4 s^1 and shear stresses of 15^150 MPa to shear strains
between ¼ 19 and 66. The dependence of viscosity, , on melt
fraction, , for these partially molten aggregates can be expressed as
¼ 26 1012 exp (^24 ) Pa s. In each sample, melt-rich bands
develop by a shear strain of ¼ 1, forming a population of bands at
an angle of 5^158 to the shear plane and 40^308 to the applied maximum principal stress. The spacing between and width of the meltrich bands increases as melt fraction increases from 5001 to 006,
then roughly levels off as melt fraction increases to 012. This band
spacing, s, increases linearly with increasing compaction length,
c, according to the relation s ¼ 007 c when the bulk viscosity is
assumed to be twice the shear viscosity. In the Earth, spontaneous
stress-driven segregation of fluids is an important mechanism for
localizing deformation into shear zones.
melt segregation; rock deformation; magma transport;
self-organization; shear zones
KEY WORDS:
I N T RO D U C T I O N
JOURNAL OF PETROLOGY
VOLUME 51
NUMBERS 1 & 2
between melt-rich bands beyond a value lying between the
grain size and the compaction length (i.e. the length scale
over which solid^fluid flow are coupled such that melt
pressure and melt fraction gradients can be sustained), the
experiments indicated a linear increase in band spacing
with increasing compaction length. Furthermore, the
experimental results implied that, even though melt
aligned during deformation of partially molten peridotites,
melt did not segregate because, for these rocks, the sample
thickness was significantly smaller than the compaction
length.
In the large-strain torsional shear experiments described
in the present study, stress-driven melt segregation is investigated in samples composed of anorthite plus various
amounts of melt. Because these fine-grained samples
deformed by diffusion creep (i.e. Newtonian viscosity),
compaction lengthçwhich is a function of rock viscosity,
melt viscosity, and permeabilityçwas a function of only
melt fraction, that is, independent of stress (strain rate).
Thus, the relationship between band spacing and
compaction length is not complicated by an evolution in
deformation mechanism and an associated change to a
stress-dependent rock viscosity.
JANUARY & FEBRUARY 2010
two gas-medium apparatuses similar to that described by
Paterson & Olgaard (2000). Two samples were deformed
at the Bayerisches Geoinstitut (BGI) and the remainder
at the University of Minnesota (UMN). Pressure and temperature were maintained constant to 1MPa and 1K,
respectively, with temperature gradients along the sample
of 501K/mm. Torque was measured with an internal
torque cell with a resolution of 02 N m, and angular
displacement was measured with an external rotational
variable differential transformer with a resolution of
0001rad.
Samples were enclosed in a Ni capsule with an inner
diameter of 9 mm, outer diameter of 10 mm, and length of
5 mm. Thin Ni discs separated the sample from the pistons.
This sample assembly, together with alumina and zirconia
pistons, was inserted into an Fe sleeve (see Paterson &
Olgaard, 2000). Each sample was deformed in a series of
constant twist rate steps, yielding shear strain rates of 10^4
to 10^3 s^1 and shear stresses from 15 to 150 MPa at the
outer radius. Fourier transform IR spectra of the deformed
samples revealed no OH-stretching vibrations above background, indicating that the samples were dry.
Data analysis
Torque, M, and angular displacement, h, were measured as
a function of time, t. Angular displacement rate, y_ was calculated directly from the h^t data. The maximum shear
strain rate, g_ R, which occurs at the outer radius of the
sample, R, was then expressed in terms of the angular displacement rate as
E X P E R I M E N TA L P RO C E D U R E S
Sample fabrication
Five samples were fabricated from mixtures of fine-grained
powders of Beaver Bay anorthite (Morrison et al., 1983)
and tholeiitic mid-ocean ridge basalt (MORB) (Cooper
& Kohlstedt, 1984), and two samples were prepared from
Beaver Bay anorthite with no added melt phase. Powders
were obtained by crushing Beaver Bay anorthite (An70)
and then pulverizing this powder in a fluid energy mill.
To reduce the particle size to 2^3 mm, the resulting
powder was Stokes settled, and the finer portion ground
with a mortar and pestle. The MORB was ground using a
mortar and pestle to a particle size of 58 mm. All powders
were dried at 1373 K for 4 h and stored in a vacuum oven.
To form dense samples for deformation experiments,
An70 powders or mechanical mixtures of An70 þ MORB
powders were cold-pressed into Ni capsules and then hotpressed in a gas-medium apparatus at 1473 K, 300 MPa for
3 h. Samples for torsion experiments, 10 mm in diameter
and 5 mm in length, were fashioned from hot-pressed
cylinders with ends flat and parallel to 1 mm. In addition
to specimens of nominally melt-free anorthite, samples
with melt fractions of f ¼ 003, 006, and 012 were fabricated. Grain sizes of the hot-pressed samples were 3^4 mm.
g_ R ¼
R_
y
L
ð1Þ
where L is the length of the sample.
If the rheological behavior of a sample can be described
by a power-law relationship of the form
g_ / tn
ð2Þ
then torque can be converted to shear stress at the outer
radius of the sample, tR, using the relationship
tR ¼
2ð3 þ 1=nÞ M
p
R
ð3Þ
where n is the stress exponent in equation (2). The stress
exponent can then be determined from stepping tests in
which angular displacement rate (or torque) is changed
systematically:
n¼
Deformation experiments
_
d logð_gR Þ
d logðyÞ
:
¼
d logðtR Þ d logðMÞ
ð4Þ
To calculate shear stress, measured values of torque must
be corrected to remove the portion supported by the Fe
jacket and Ni capsule. To do so, we used the above equations with published flow laws for Fe and Ni (Frost &
Seven samples of anorthite MORB were deformed in
torsion at a confining pressure, P, of 300 MPa and a temperature, T, of 1450 K to shear strains of 19 & g & 66 in
10
KOHLSTEDT et al.
STRESS-DRIVEN MELT SEGREGATION
Ashby, 1982), combined with calibration experiments on Fe
and Ni samples in our laboratory. Corrections for the
strength of the jacket and capsule are relatively small,
1N m, out of a total measured torque of 10 N m.
We report strain, strain rate, and stress as equivalent
values eeq, eeq, and seq, which are related to strain, e,
strain rate, e_, and differential stress, s, determined in triaxial compression tests and to shear strain, g, shear strain
rate, g_, and shear stress, t, obtained from torsion experiments by the relations
eeq
g
¼ e ¼ pffiffiffi
3
g_
e_ eq ¼ e_ ¼ pffiffiffi
3
pffiffiffi
seq ¼ s ¼ 3t:
Table 1: Sample composition and mechanical data for
samples deformed in torsion
Sample no.
f
P-0161
003
P-0155
d (mm)
006
4
4
ð5aÞ
010603b
5001
3
ð5bÞ
ð5cÞ
040603b
5001
3
Microstructural analyses
Microstructural analyses were carried out on two sections
of each deformed sample, a longitudinal tangential section
near the outer edge and a longitudinal axial section
through the center of the sample. These surfaces were
polished on a series of diamond lapping films down to
05 mm, and then finished on a colloidal solution containing 40 nm particles of silica. Samples were then examined
using transmitted and reflected light optical microscopy
as well as scanning electron microscopy (SEM).
g_ R (s–1)
tR (MPa)
gR
Laboratory
10 10–4
43
03
BGI
20 10–4
96
06
32 10–4
141
42
11 10–4
19
02
17 10–4
32
02
36 10–4
63
22
35 10–4
56
03
73 10–4
104
03
149 10–4
149
03
35 10–4
50
28
36 10–4
50
03
78 10–4
103
04
161 10–4
152
04
75 10–4
99
48
BGI
UMN
UMN
100406b
006
4
26 10–4
55
19
UMN
200406b
006
4
11 10–4
29
57
UMN
181103c
012
4
31 10–4
16
66
UMN
BGI, Bayerisches
Minnesota.
Geoinstitut;
UMN,
University
of
and the data for the An70 þ 6% MORB samples yield
values for the stress exponent of n ¼10 01 in the
relationship
e_ / sn :
E X P E R I M E N TA L R E S U LT S
Mechanical data
ð6aÞ
For comparison, a line of this slope was drawn through the
single data point for the sample of An70 þ12% MORB. In
addition, a global fit to the data for all of the samples of
An70 þ MORB to the equation
Melt^rock ratios and mechanical data obtained for all
seven samples are summarized in Table 1. Equivalent
stress vs equivalent strain results are compared for two
samples, one with f ¼ 003 and the other with f ¼ 006,
in Fig. 1. In each case, the equivalent strain rate was
increased sequentially by a factor of 2, from 5 10^5 to
1 10^4 to 2 10^4 s^1. In response, the equivalent
stress increased by a factor of 2 immediately following
each increase in strain rate. Stress begins to decrease at a
shear strain of 1, characteristic of the influence of the
development of a network of melt-rich bands (Holtzman
et al., 2005).
Equivalent strain rate vs equivalent stress results for
samples An70 þ 3%, 6%, and 12% MORB are compared
in Fig. 2. The data for An70 þ 3% MORB are from a
single sample deformed at three different rates (Fig. 1),
whereas the data for An70 þ 6% MORB are from three
samples, one deformed at three different rates (Fig. 1) and
two deformed at a single rate. The sample with 12%
MORB was deformed at only one rate. Linear leastsquare fits to the data for the An70 þ 3% MORB sample
e_ ¼ As expðaÞ
^7 ^1
ð6bÞ
^1
yielded A ¼ (38 03) 10 s MPa and a ¼ 24 1.
The results of this global fit are also presented in Fig. 2.
Data for the two samples without added melt were not
included in this figure because the An70 powders used to
fabricate these samples were taken from a different batch
from that used for the other samples; thus, the grain-size
distribution is different; in addition, the small melt fraction
in these samples is difficult to quantify accurately.
Microstructural observations
Figure 3 presents a scanning electron micrograph of a
sample of An70 þ 6% MORB that illustrates the melt distribution in our samples prior to deformation. Melt wets
some of the grain boundaries and occupies many, if not
all, of the triple junctions. After hot-pressing, the samples
contain 51 vol. % porosity.
11
JOURNAL OF PETROLOGY
VOLUME 51
NUMBERS 1 & 2
JANUARY & FEBRUARY 2010
Fig. 1. Plot of equivalent strain vs equivalent stress for a sample of An70 þ 3 vol. % MORB (P-0161) and a sample of An70 þ 6 vol. % MORB
(P-0155), each deformed in torsion. Each sample was deformed at the three strain rates and at the temperature and pressure conditions indicated
in the figure.
Fig. 2. Log^log plot of equivalent strain rate vs equivalent stress for all of the An70 þ MORB samples deformed in this study. Continuous lines
through the data for samples with 3 vol. % and 6 vol. % melt represent linear least-squares fits to the data at each melt fraction, whereas the
continuous line through the datum for the sample with 12 vol. % melt is the best-fit line with a slope of unity. The dashed lines represent a
global fit of all of the data for samples with 3, 6 and 12 vol. % MORB to equation (6b).
12
KOHLSTEDT et al.
STRESS-DRIVEN MELT SEGREGATION
Fig. 3. Backscattered electron photomicrograph of undeformed sample of An70 þ 6 vol. % MORB. The black spherical features are voids, the
bright areas are melt, and the grey mass is anorthite.
the melt-rich bands in the sample with 12% MORB are
somewhat more closely spaced and about the same width
as those in the samples with 6% MORB.
The photograph in Fig. 4 of a jacketed sample containing
6 vol. % MORB and deformed to a shear strain of g ¼ 35
reveals two sets of striations in the Fe jacket. The first set
of striations, oriented in the shear direction, developed
from vertical creases in the jacket that formed as confining
pressure was applied and then rotated during torsional
deformation. The second set, oriented antithetic to the
shear direction, developed as strain localized in melt-rich
bands. The cause of this second set of striations is evident
in the scanning electron micrograph in Fig. 5a of the
sample of An70 þ 6 vol. % MORB sheared to g ¼ 2.6. The
serrations along the outer edges of this tangential section
formed as strain localized on the melt-rich bands. Highmagnification views of this sample in Fig. 5b and c reveal
the higher melt fraction present in the melt-rich bands
and the lower melt fraction in the melt-depleted lenses
separating the bands.
Spacings and widths of the melt-rich bands for four samples of different melt contents can be compared in Fig. 6.
Melt-rich bands were present even in the samples of An70
with no added melt as 51% melt formed from auxiliary
phases present in the anorthositic rock that was crushed
and ground to produce the anorthite powders. The meltrich bands in the sample with 3% MORB are both more
widely spaced and broader than those in the samples with
51% melt. Likewise, the melt-rich bands in the samples
with 6% MORB are more widely separated and broader
than the bands in the sample with 3% MORB. Finally,
DISCUSSION
Mechanical data
The two samples deformed in torsion at the BGI had previously been deformed in triaxial compression at 1450 K
and 300 MPa (Ginsberg, 2000). The deformation results
from the triaxial compressive creep experiments and
those from the torsion experiments are compared in Fig. 7.
In both cases, at a given differential stress the compressive
creep experiments yield a stress exponent of n ¼1 and a
strain rate that is a factor of 12 faster than obtained in
the torsion experiments. This difference is well within the
uncertainty in the load cell calibration and correction for
jacket strength. Our data are also qualitatively consistent
with previously published results on high-temperature
deformation of fine-grained anorthite, both melt-free samples (Wang et al., 1996) and melt-bearing samples
(Rybacki & Dresen, 2000).
Microstructural observations
Rybacki et al. (2008) also observed melt-rich bands in samples of anorthite plus melt deformed in torsion at experimental conditions similar to those imposed in our
experiments. Their samples of An99 þ53 vol. % of a
13
JOURNAL OF PETROLOGY
VOLUME 51
NUMBERS 1 & 2
JANUARY & FEBRUARY 2010
Fig. 4. Photographs of sample assembly in an iron jacket; sample with top twisted counterclockwise. (a) A lower magnification image showing
the sample (roughened region) between tapered alumina pistons (smooth regions). (b) At higher magnification, two sets of striations are visible
in the jacket. The striations extending from SW to NE developed from vertical creases in the iron jacket that formed when confining pressure
was applied and subsequently deformed into their current orientation as the sample was deformed in torsion; thus, they are strain markers.
The striations running from NW to SE developed at the jacket intruded into offsets in the sample produced by localized deformation on meltrich bands.
Scaling band spacing from laboratory to
Earth conditions
silica-rich melt were fabricated from powders obtained by
crystallizing a synthetic anorthite glass. The nature of the
bands in their samples differs substantially from those
formed in our experiments. Cavities nucleated, grew and
coalesced into bands at an angle similar to that observed
for the melt-rich bands in our study. Glass concentrated in
these shear bands. In some cases, catastrophic rupture
occurred as cavitation progressed, even at high temperatures for which plastic flow occurs at differential stresses
well below the confining pressure, a situation not anticipated based on the Goetze criterion (Kohlstedt et al.,
1995). The major difference between the experiments of
Rybacki et al. (2008) and those performed in this study is
the viscosity of the melt phase. In our experiments on
An70 þ MORB, the melt viscosity is 10 Pa s, whereas in
the experiments on An99 þ silica-rich melt, the melt viscosity is orders of magnitude larger. As local stresses build up
at the grain scale during deformation, a low-viscosity melt
is able to flow sufficiently quickly to relax stress concentrations before voids nucleate and/or grow and to blunt incipient cracks before they can propagate (Hier-Majumder
et al., 2004; Kohlstedt & Holtzman, 2009). Therefore, the
difference between the melt-rich bands formed in our
experiments and those developed in the experiments of
Rybacki et al. (2008) is attributed to the difference in melt
viscosity between these two sets of experiments.
Analyses of band spacing in terms of compaction length
suggest a linear relationship (Holtzman et al., 2003a;
Holtzman & Kohlstedt, 2007). Compaction length, dc, can
be expressed in terms of the permeability, k, melt viscosity,
m, and rock shear and bulk viscosities, Z and , as
s
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
k
4
ð7Þ
þ & :
c ¼
3
For our samples of An70 þ MORB, at a fixed temperature and pressure, the shear viscosity is a function of
melt fraction only, Z(f) ¼ Z(0) exp(^af) with Z(0) ¼
(26 03) 1012 Pa s and a ¼ 24 1, based on values for
the shear viscosity obtained early in each experiment,
prior to the formation of melt-rich bands. We assume that
the bulk viscosity is twice the shear viscosity, ¼ 2Z
(Takei & Holtzman, 2009a). Grain size is the same from
sample to sample in our experiments on An70 þ MORB.
Therefore, at fixed temperature and pressure,
k(f) ¼ fmd2/b is also a function of melt fraction only with
the geometrical constant b ¼1 103 and the melt fraction
exponent m ¼ 2 (Holtzman et al., 2003a). Therefore, in our
experiments at T ¼1450 K and P ¼ 300 MPa, dc is a function of f alone.
14
KOHLSTEDT et al.
STRESS-DRIVEN MELT SEGREGATION
Fig. 5. Backscattered electron photomicrographs of a tangential section of a sample of An70 þ 6 vol. % MORB (P-0155) deformed in torsion to a
shear strain of g ¼ 26. (a) At low magnification, a number of melt-rich bands are visible along the height of the sample. In addition, a
number of serrations are observable along the contact between the sample and the Ni sleeve. These serrations develop as strain localizes along
melt-rich bands. (b) At intermediate magnification, three melt-rich bands are aligned parallel to one another at an angle of 158 to the shear
plane, 308 to the maximum principal stress. (c) At higher magnification, the melt fraction in the melt-rich band is 15 vol. %, whereas the
melt fraction in the melt-depleted regions between melt-rich bands is 1 vol. %. The black spherical features are voids, the bright areas are
melt, and the gray mass is anorthite.
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JANUARY & FEBRUARY 2010
Fig. 6. Transmitted-light optical photomicrographs of four samples deformed in torsion, sheared top to the right. (a) Melt-rich (dark) bands are
present even in the nominally melt-free samples prepared from crushed and ground Beaver Bay anorthosite. This sample contains 51 vol. %
melt. (b) Melt-rich (dark) bands align from NW to SE in this sample at an angle of 158 to the shear plane. A few bands lie close to 08, connecting the higher-angle melt-rich bands. (c) Melt-rich (dark) bands aligned at 158 from the shear plane extend from NW to SE. (d) Melt-rich
(dark) bands aligned near both 158 and 08 to the shear plane are visible, with the lower angle bands appearing to connect the higher
angle bands.
The plot of steady-state band spacing, ds , as a function of
compaction length in Fig. 8 suggests a systematic scaling
relationship. A linear least-squares fit yields ds ¼ 007 dc.
To compare our results with those of Holtzman et al.
(2003a), who did not include the bulk viscosity in their calculation of compaction length, we also calculated the compaction length using only the shear viscosity (i.e.
effectively setting ¼ 0 Pa s). This approach yields
ds ¼ 014 dc , a value in good agreement with that of
Holtzman et al. (2003a), who obtained ds ¼ 0.15 dc.
independent of strain, at an angle of 10^258 to the shear
plane, 35^208 to the maximum compressive stress. In our
experiments, melt-rich bands develop at somewhat lower
angles of 5^158 to the shear plane, again antithetic to the
shear direction. In models based on two-phase flow
theory of the formation of melt-rich bands during simple
shear, four factors have been identified as coupling deformation and melt distribution, thus affecting band angle.
First, if the dependence of viscosity on melt fraction leads
to band formation, the band angle is predicted to be 458
to the shear plane (Spiegelman, 2003; Rabinowicz
&Vigneresse, 2004). Second, if viscosity is also strongly
stress dependent, the band angle is reduced, approaching
a value of 15^208 for a stress exponent of n ¼ 6 (Katz
et al., 2006). Third, the non-linear coupling produced by
Steady-state band angle
In previously reported experiments (Holtzman et al.,
2003a, 2003b; Holtzman & Kohlstedt, 2007; Rybacki et al.,
2008; King et al., 2009), melt-rich bands emerge and persist,
16
KOHLSTEDT et al.
STRESS-DRIVEN MELT SEGREGATION
Fig. 7. Log^log plot of equivalent strain rate vs equivalent stress comparing results obtained in torsion from this study with those acquired in
triaxial compression experiments by Ginsberg (2000). The results from the two different types of experiments are in good agreement.
Fig. 8. Plot of band spacing vs compaction length for the samples deformed to high strain in torsion in this study. Compaction lengths were calculated using equation (7), and band spacings were obtained from two-dimensional autocorrelation analyses of transmitted-light optical micrographs, such as those in Fig. 6, of our deformed samples.
17
JOURNAL OF PETROLOGY
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partitioning of strain between networks of melt-rich bands
and melt-depleted lenses influences not only macroscopic
deformation behavior but also the band angle, leading to
angles near 208 (Holtzman et al., 2005). Finally, the anisotropic viscosity that develops as a result of grain-scale
alignment of melt pockets couples the shear and normal
components of the stress tensor, thus influencing segregation and organization of melt at a larger scale and resulting in a maximum growth rate of melt-enriched bands at
an angle of 158 (Takei & Holtzman, 2009b). In our
experiments, viscosity is independent of stress (i.e. n ¼1),
demonstrating that a stress-dependent viscosity is not an
essential element in band formation.
JANUARY & FEBRUARY 2010
system in which strain rate is greatest as a result of corner
flow (Phipps Morgan, 1987; Katz et al., 2006). Deformation
produces networks of melt-rich and thus low-viscosity
channels that facilitate rapid extraction of melt from the
mantle (Holtzman & Kohlstedt, 2007; Holtzman &
Kendall, in press; Kohlstedt & Holtzman, 2009). Such
melt-rich shear zones reduce the effective viscosity of the
asthenosphere near the LAB to a value smaller that associated with a homogeneously distributed melt. The LAB is
then defined by the direct effect of melt segregating into
melt-rich bands, thus weakening the asthenosphere
(Holtzman & Kohlstedt, 2005; Kawakatsu et al., 2009;
Kohlstedt & Holtzman, 2009; Takei & Holtzman, 2009b),
combined with the indirect effect of partitioning of water
from the peridotite into the melt, thus strengthening the
lithosphere (Karato, 1986; Hirth & Kohlstedt, 1996;
Phipps Morgan, 1997).
Implications
To extrapolate experimental results on the influence of
stress on melt distribution to mantle conditions, both a
thermodynamic and a kinetic criterion must be met
(D. J. Stevenson, personal communication; Kohlstedt &
Holtzman, 2009). Thermodynamically, the differential
stress driving melt alignment and spontaneous segregation
must exceed the surface tension restoring force, that is, s/
(/r) must be 41, where is the surface energy and r is
the radius of curvature of the melt pocket. The surface tension can be rewritten as /r 3/df1/2. The condition
s/(/r)41 must hold under laboratory conditions, as melt
segregation occurs. It should also hold under geological
conditions because the increase in grain size more than offsets any decrease in differential stress in going from the
laboratory to the Earth. Kinetically, the rate at which
melt-filled pockets are distorted by straining a rock must
be greater than the rate at which they recover their equilibrium shape by diffusion; that is, e_ /(cD/d2) must be
greater than unity, where c and D are the concentration
and the diffusivity, respectively, of the slowest diffusing
component of the solid in the melt. Because melt segregation occurs, e_ /(cD/d2) must be 41 in our laboratory experiments. The large grain size in natural rocks compared
with that in our deformation samples (3 mm vs 3 mm)
roughly offsets the decrease in strain rate in going from
laboratory to geological conditions. Because both the thermodynamic and the kinetic criterion are met in the Earth
as well as the laboratory, melt alignment and segregation
produced are expected to occur not only under laboratory
conditions but also under geological conditions (Kohlstedt
& Holtzman, 2009).
Stress-driven melt segregation provides a natural mechanism for localizing strain into a shear zone. This possibility
has been recognized in ophiolites where localized deformation and focused melt flow are temporally and spatially
juxtaposed (Kelemen & Dick, 1995). Recently, it has been
suggested that the lithosphere^asthenosphere boundary
(LAB) beneath a mid-ocean ridge is determined by stressdriven melt segregation away from the ridge axis
(Holtzman & Kohlstedt, 2007), in the region of the ridge
AC K N O W L E D G E M E N T S
This research was supported by the NSF through grant
OCE-0648020. Experiments at BGI were carried out
while D.L.K. was the recipient of an Alexander von
Humboldt Senior Award. The authors are grateful for the
superb help of Julian Mecklenburgh and Iona Stretton in
carrying out the torsion experiments at BGI. Constructive
and insightful reviews by Georg Dresen, Julian
Mecklenburgh, Erik Rybacki, and Jean-Louis Vigneresse
resulted in significant improvements to the manuscript.
This paper is LPI Contribution 1473.
R E F E R E NC E S
Bussod, G. Y. & Christie, J. M. (1991). Textural development and melt
topology in spinel lherzolite experimentally deformed at hypersolidus conditions. Journal of Petrology, Special Lherzolite Issue 17^39.
Cooper, R. F. & Kohlstedt, D. L. (1984). Sintering of olivine and
olivine^basalt aggregates. Physics and Chemistry of Minerals 11, 5^16.
Daines, M. J. & Kohlstedt, D. L. (1997). Influence of deformation on
melt topology in peridotites. Journal of Geophysical Research 102,
10257^10271.
Frost, H. J. & Ashby, M. F. (1982). Deformation-mechanism Maps: The
Plasticity and Creep of Metals and Ceramics. New York: Pergamon
Press, 167 pp.
Ginsberg, S. B. (2000). Deformation experiments on natural and synthetic diabasic aggregates, with application to the tectonics of
Earth and Venus. Doctoral dissertation, University of Minnesota,
Twin Cities, 135 pp.
Hier-Majumder, S., Leo, P. H. & Kohlstedt, D. L. (2004). On grain
boundary wetting during deformation. Acta Materiala 52,
3425^3433.
Hirth, G. & Kohlstedt, D. L. (1996). Water in the oceanic upper
mantle: implications for rheology, melt extraction and evolution of
the lithosphere. Earth and Planetary Science Letters 144, 93^108.
Holtzman, B. K. & Kohlstedt, D. L. (2007). Stress-driven melt segregation and strain partitioning in partially molten rocks: the evolution of melt distribution. Journal of Petrology 48, 2379^2406.
Holtzman, B. K., Groebner, N. J., Zimmerman, M. E., Ginsberg, S. B.
& Kohlstedt, D. L. (2003a). Stress-driven melt segregation in
18
KOHLSTEDT et al.
STRESS-DRIVEN MELT SEGREGATION
partially molten rocks. Geochemistry, Geophysics, Geosystems 4, 8607,
doi:10.1029/2001GC000258.
Holtzman, B. K., Kohlstedt, D. L., Zimmerman, M. E.,
Heidelbach, F., Hiraga, T. & Hustoft, J. (2003b). Melt segregation
and strain partitioning: implications for seismic anisotropy and
mantle flow. Science 301, 1227^1230.
Holtzman, B. K., Kohlstedt, D. L. & Phipps Morgan, J. (2005).
Viscous energy dissipation and strain partitioning in partially
molten rocks. Journal of Petrology 46, 2569^2592.
Karato, S. (1986). Does partial melting reduce the creep strength of
the upper mantle? Nature 319, 309^310.
Katz, R. F., Spiegelman, M. & Holtzman, B. K. (2006). The dynamics
of melt and shear localization in partially molten aggregates.
Nature 442, 676^679.
Kawakatsu, H., Kumar, P., Takei, Y., Shinohara, M., Kanazawa, T.,
Araki, E. & Suyehiro, K. (2009). Seismic evidence for sharp lithosphere^asthenosphere boundaries of oceanic plates. Science 324,
499^502.
Kelemen, P. B. & Dick, H. J. B. (1995). Focused melt flow and localized
deformation in the upper mantle: Juxtaposition of replacive dunite
and ductile shear zones in the Josephine Peridotite, SW Oregon.
Journal of Geophysical Research 100, 423^438.
King, D. S., Kohlstedt, D. L. & Zimmerman, M. E. (2009). Stressdriven melt segregation in partially molten olivine-rich rocks
deformed in torsion. Journal of Petrology 50, 000^000.
Kohlstedt, D. L. & Holtzman, B. K. (2009). Shearing melt out of the
Earth: An experimentalist’s perspective on the influence of deformation on melt extraction. Annual Review of Earth and Planetary
Sciences 37, 16.1^16.33, doi:10.1146/annurev.earth.031208.100104.
Kohlstedt, D. L. & Zimmerman, M. E. (1996). Rheology of partially
molten mantle rocks. Annual Review of Earth and Planetary Sciences
24, 41^62.
Kohlstedt, D. L., Evans, B. & Mackwell, S. J. (1995). Strength of the
lithosphere: Constraints imposed by laboratory experiments.
Journal of Geophysical Research 100, 17587^17602.
Morrison, D. A., Ashwal, L. D., Phinney, W. C., Shih, C.-Y. &
Wooden, J. L. (1983). Pre-Keweenawan anorthosite inclusions
in the Keweenawan Beaver Bay and Duluth Complexes,
northeastern Minnesota. Geological Society of America Bulletin 94,
206^221.
Paterson, M. S. & Olgaard, D. L. (2000). Rock deformation tests to large
shear strains in torsion. Journal of Structural Geology 22,1341^1358.
Phipps Morgan, J. (1987). Melt migration beneath mid-ocean spreading centers. Geophysical Research Letters 14, 1238^1241.
Phipps Morgan, J. (1997). The generation of a compositional lithosphere by mid-ocean ridge melting and its effect on subsequent offaxis hotspot upwelling and melting. Earth and Planetary Science
Letters 146, 213^232.
Rabinowicz, M. & Vigneresse, J.-L. (2004). Melt segregation under
compaction and shear channeling: application to granitic magma
segregation in a continental crust. Journal of Geophysical Research
109, B04407, doi:10.1029/2002JB002372.
Rybacki, E. & Dresen, G. (2000). Dislocation and diffusion creep of
synthetic anorthite aggregates. Journal of Geophysical Research 105,
26017^26036.
Rybacki, E., Wirth, R. & Dresen, G. (2008). High-strain creep of feldspar rocks: Implications for cavitation and ductile failure in the
lower crust. Geophysical Research Letters 35, L04304, doi:10.1029/
2007GL032478.
Spiegelman, M. (2003). Linear analysis of melt band formation by
simple shear. Geochemistry, Geophysics, Geosystems 4, 8615, doi:10.1029/
2002GC000499.
Stevenson, D. J. (1989). Spontaneous small-scale melt segregation in
partial melts undergoing deformation. Geophysical Research Letters
16, 1067^1070.
Takei, Y. & Holtzman, B. (2009a). Viscous constitutive relations of
solid^liquid composites in terms of grain boundary contiguity I:
Grain boundary diffusion-control model. Journal of Geophysical
Research 114, B06205, doi:10.1029/2008JB005850.
Takei, Y. & Holtzman, B. (2009b). Viscous constitutive relations of
solid^liquid composites in terms of grain boundary contiguity III:
causes and consequences of viscous anisotropy. Journal of
Geophysical Research 114, B06207, doi:10.1029/2008JB005852.
Wang, Z., Dresen, G. & Wirth, R. (1996). Diffusion creep of finegrained polycrystalline anorthite at high temperature. Geophysical
Research Letters 23, 3111^3114.
Zimmerman, M. E. & Kohlstedt, D. L. (2004). Rheological properties
of partially molten lherzolite. Journal of Petrology 45, 275^298.
Zimmerman, M. E., Zhang, S., Kohlstedt, D. L. & Karato, S. (1999).
Melt distribution in mantle rocks deformed in shear. Geophysical
Research Letters 26, 1505^1508.
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