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Journal of Structural Geology xx (xxxx) 1–15
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Deformation of melt-bearing systems—insight from in situ grain-scale
analogue experiments
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Nicolas P. Walte *, Paul D. Bons , Cees W. Passchier
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Tektonophysik, Institut für Geowissenschaften, Johannes Gutenberg-Universität Mainz, Germany
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Institut für Geowissenschaften, Eberhard Karls Universität Tübingen, Germany
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Received 24 June 2004; received in revised form 7 April 2005; accepted 18 May 2005
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Abstract
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The deformation behaviour of partially molten rocks was investigated using in situ analogue experiments with norcamphorCethanol, as
well as partially molten KNO3CLiNO3. Three general deformation regimes could be distinguished during bulk pure shear deformation. In
regime I, above ca. 8–10 vol.% liquid (melt) fraction (fbulk), deformation is by compaction, distributed granular flow, and grain boundary
sliding (GBS). At fbulk!8–10 vol.% (regime II), GBS localizes in conjugate shear zones. Liquid segregation is inefficient or even reversed
as the dilatant shear zones draw in melt to locally exceed the 8–10 vol.% threshold. At even lower fbulk (regime III), grains form a coherent
framework that deforms by grain boundary migration accommodated dislocation creep, associated with efficient segregation of remaining
liquid. The transition liquid fraction between regimes I and II (fLT) depends mainly on the grain geometry and is therefore comparable in
both analogue systems. The transition liquid fraction between regimes II and III (fGBS-L) varies between 4–7 vol.% for norcamphor–ethanol
and ca. 1 vol.% for KNO3CLiNO3 and depends on system specific parameters. Regime II behaviour in our experiments can explain the
frequently observed small melt-bearing shear zones in partially molten rocks and in HT experiments.
q 2005 Published by Elsevier Ltd.
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Keywords: Analogue experiments; Norcamphor; Magma segregation; Granular flow; Partially molten rocks; Grain boundary sliding
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1. High liquid fraction: crystals are suspended in the
liquid. The mechanical behaviour is controlled
primarily by the liquid viscosity and can be described
as that of a dilute suspension (Einstein, 1906; Ryerson
et al., 1988).
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Liquid-bearing systems range from almost complete
solid grain aggregates with minor amounts of liquid
between grains to almost fully liquid magma in which
isolated crystals are suspended. The amount of liquid is one
of the primary parameters that determines the rheological
behaviour of such composite systems. Three main types of
behaviour can be distinguished:
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1. Introduction
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* Corresponding author. Address: Bayerisches Geoinstitut, Universität
Bayreuth, Germany.
E-mail address: [email protected] (N.P. Walte).
0191-8141/$ - see front matter q 2005 Published by Elsevier Ltd.
doi:10.1016/j.jsg.2005.05.006
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2. Intermediate liquid fraction: crystals form an aggregate
and the rheological behaviour is that of granular flow
and grain boundary sliding (Rutter, 1997; Petford and
Koenders, 1998; Paterson, 2001).
3. Low liquid fraction: grains form an interlocking
load-bearing framework and the mechanics of the
composite system are controlled by the rheology of
the solid phase as follows (Arzi, 1978; Vigneresse
et al., 1996):
(a) The composite system is controlled by the (nonlinear) viscosity of the solid, which deforms by
diffusion or dislocation creep mechanisms (e.g.
Hirth and Kohltstedt, 1995a,b; Gleason et al., 1999;
Mei et al., 2002).
(b) Brittle deformation by intracrystalline fracturing
occurs (e.g. van der Molen and Paterson, 1979;
Dell’Angelo and Tullis, 1988; Rutter, 1997; Renner
et al., 2000; Holyoke and Rushmer, 2002).
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Significant changes in strength and liquid transport are
expected when liquid-bearing systems move from one type
of behaviour to another, for instance during progressive
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2. Experiments
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Two different sets of experiments were performed. In
one set, norcamphor and norcamphor-saturated ethanol
liquid were used as analogues for a monomineralic solid
phase and melt, respectively (cf. Walte et al., 2003).
Norcamphor (C7H10O) is an organic crystalline compound with hexagonal symmetry and crystal–plastic
rheology at room temperature, which has been used as
an analogue for rock-forming minerals such as quartz or
olivine (Bons, 1993; Bons et al., 1993; Herweg and
Handy, 1996; Bauer et al., 2000; Rosenberg and Handy,
2000, 2001; Walte et al., 2003). The ethanol permits fast
diffusion of dissolved norcamphor at room temperature so
that continuous surface-energy driven grain coarsening
(Ostwald ripening or liquid assisted recrystallisation) takes
place as in natural systems at high temperature conditions
(Walte et al., 2003).
The second set of experiments was conducted with a
mixture of 90–95 wt% KNO3 and 5–10 wt% LiNO3. These
nitrates have a eutectic point at 141 8C and therefore are in
the temperature range of in situ analogue experiments. The
LiNO3 is completely molten at the experimental temperature so that the sample consists of a single solid phase
(KNO3) plus a KNO3–LiNO3 melt phase. Nitrates such as
KNO3 are similar to carbonates, such as calcite, in both
crystallography and rheological behaviour (Tungatt and
Humphreys, 1981).
No quantitative measurements of melt and solid phase
viscosities could be made with our experimental setup.
However, the norcamphor crystals are quite weak and the
KNO3 crystals were quite strong at the experimental
conditions, while the viscosity of the two liquid phases
was comparable. The norcamphor–ethanol system and the
partially–molten nitrates therefore represent analogues for
systems with a low and high solid–liquid viscosity ratio,
respectively.
Experiments were performed in a linear, Urai–Means
see-through deformation apparatus (Fig. 1b), which allows
for continuous observation of the sample with a microscope
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This study presents two sets of analogue experiments
with a single crystalline phase (norcamphor or KNO3)
plus a liquid phase with a well-constrained behaviour as
a melt analogue (ethanol or KNO3–LiNO3 melt) that is
easily observable in situ (Walte et al., 2003). These
systems allow continuous observation of the microstructural processes and changes in deformation behaviour as
a function of a varying liquid fraction within a single
experiment. The experiments show the effect of the
different deformation regimes on melt-segregation. They
also show that the transition between the regimes is not
only a function of melt percentage, but also of the
strength of the solid phase, the strain rate, the melt
pressure and the wetting behaviour of the melt.
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melting, or during crystallisation of a magma (Arzi, 1978;
van der Molen and Paterson, 1979; Vigneresse et al., 1996).
Most attention has been paid to the rheological transition
between melt-dominated behaviour (1C2) and flow
dominated by the solid phase rheology (3) with its
associated change in viscosity over many orders of
magnitude. For this transition Arzi (1978) suggested a
rheologically critical melt percentage (RCMP) that marks a
sharp drop in strength. The RCMP is important to several
systems, such as orogenic belts that contain partially-molten
zones, like the Himalayas. If these partially-molten zones
exceed the RCMP, they will constitute major zones of
weakness that may mechanically detach the overlying crust
from the orogenic root and mantle (Schott and Schmeling,
1998; Arnold et al., 2001). Exceeding the RCMP may also
cause the wholesale mobilization and diapiric ascent of
partially molten rock (Weinberg and Podladchikov, 1994;
Paterson and Vernon, 1995). Strong changes in rheology
with changing melt fraction are also critically important
for porosity waves. These are ascending zones of
increased melt-bearing porosity, which are proposed as
one of the mechanisms of melt ascent beneath, for
example, mid-oceanic ridges (Barcilon and Richter, 1986;
Scott and Stevenson, 1986; McKenzie, 1987; Kelemen et
al., 1997; Holtzman et al., 2003a). Even though the
background melt percentage may be well below the
RCMP, the porosity waves themselves may contain
enough melt to overcome the RCMP, which has to be
considered for numerical models of these processes
(Rabinowicz et al., 2001).
Despite the importance of the change in behaviour from
melt-dominated flow to solid-phase-dominated rheology,
there is still much uncertainty about the nature of this
transition. Experiments have indicated either a dramatic
change in rheology when the RCMP is crossed (Arzi, 1978;
van der Molen and Paterson, 1979), or a gradual transition
(Rutter and Neumann, 1995; Rutter, 1997; Bagdasserov and
Dorfman, 1998; Renner et al., 2000; Rosenberg, 2001).
High-temperature experiments on partial melts are normally
restricted to measurement of stress–strain rate relationships
and post-mortem analyses of the microstructure. Comparison of rheological data for different melt fractions are
complicated by the fact that the melt fraction is most
commonly changed by varying the temperature (e.g. Rutter
and Neumann, 1995) or the water content of a sample (e.g.
van der Molen and Paterson, 1979), both of which may
significantly change the viscosity of the phases. The role of
melt-enhanced embrittlement is also often unclear (Rutter
and Neumann, 1995).
In situ analogue experiments with partially-molten rock
analogues provide a different approach to investigating
these problems (Means and Park, 1994; Park and Means,
1996; Bauer et al., 2000; Rosenberg and Handy, 2000, 2001;
Walte et al., 2003). Instead of focussing on the measurement
of rheology, analogue experiments reveal processes on
the grain-scale when a melt-bearing system is deformed.
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Fig. 1. (a) Setup of the sample. 100-mm-thick sample (norcamphorCethanol or KNO3CLiNO3) is positioned between two glass slides and surrounded by a
barrier of silicone putty (only norcamphorCethanol). (b) Sketch of the Urai–Means linear deformation apparatus. The ca. 100-mm-thick sample is situated
between the glass slides.
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Samples were prepared by sandwiching the desired mix
of fine-grained norcamphor and norcamphor-saturated
ethanol directly between the glass plates and inserting the
assembly into the apparatus. An effectively two-dimensional (only one layer of grains) equilibrated texture forms
within a few hours of static annealing at room temperature.
Grains have smoothly curved boundaries, perpendicular to
the glass plates. At high (O10 vol.%) liquid fractions,
grains that are surrounded by liquid are approximately
spherical in shape without crystal facets. That indicates an
effectively isotropic solid–liquid surface energy of the
norcamphor (Walte et al., 2003). At lower melt fractions,
the grains form a foam texture, with liquid mostly located at
regular triangular inward-curving grain boundary triple
junctions (Fig. 2). The geometry is close to the predicted
equilibrium distribution with a low solid–liquid wetting
angle of about 258 (e.g. von Bargen and Waff, 1986;
Laporte, 1994). However, occasional disequilibrium liquid
pockets, such as larger patches or wetted grain boundaries,
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3.1. Norcamphor–Ethanol experiments
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3. Results
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during an experiment (Urai, 1983; Means, 1989). Approximately, 100-mm-thick samples were sandwiched between
glass slides and positioned in a brass housing, which
contains two heating elements and holes to view the thinsection-like sample. Pure shear deformation was induced by
gluing one thin cover slip as a piston on each glass plate, on
opposite sides, and sliding the upper glass plate relative to
the lower one (Fig. 1a). Sliding of the glass plate was driven
by a motor at a constant displacement rate, resulting in strain
rates between approximately 10K4 and 10K6 sK1 depending
on the motor used and the distance between the pistons. A
barrier of silicone putty (‘Rhodorsil gomme’) encased the
sample to inhibit evaporation of the volatile norcamphor
and ethanol. At the start of the experiments, the barrier was
not in contact with the sample, so that chemical interaction
between the sample and the barrier was inhibited. The
samples were therefore unconfined at the sides during the
deformation and the liquid was free to flow into or out of the
sample as a response to dilation or compaction (Fig. 1a). In
long-term experiments, local dissolution and dilution of the
silicone putty was observed by segregated liquid that came
in contact with the putty barrier. However, no effect of the
interaction between the silicone putty and the sample was
noticed in the observed area. Some loss of liquid and
norcamphor was only noticed in the longest lasting
experiment (O1 week).
The whole apparatus was mounted on a microscope
stage to observe the microstructural evolution in the thinsection like sample. 756!512 pixel digital colour images
were taken at regular intervals from 2 min to 2 h,
depending on the duration of an experiment that ranged
from a few hours to more than 10 days. Liquid fraction
was determined by directly tracing and measuring the
liquid area from the images with the image analysis
software NIH image and is reported in vol.%. The
precision of the area measurements and the sources of
error due to image resolution are estimated to be G
0.3 vol.%. One drawback of this method is that very low
liquid fractions !1 vol.% cannot be accurately determined because individual liquid pockets can hardly be
distinguished on the digital images.
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Fig. 2. Image of a statically recrystallizing norcamphor–ethanol aggregate.
The grains form an equilibrated foam texture with smoothly curved grain
boundaries. Liquid is situated in triangular three-grain triple junctions
forming dihedral angles of approximately 258 with the norcamphor grains.
Arrows point at disequilibrium features that form due to static grain growth.
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also occur as a result of continuous grain growth (Fig. 2)
(Walte et al., 2003).
Experiments were prepared with an initially high liquid
fraction of O10 vol.% (Fig. 3a). Norcamphor grains in
contact with each other regularly form aggregates with
welded grain boundaries (Fig. 4). This is energetically
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Fig. 3. Deformation of norcamphor crystals plus saturated ethanol liquid by bulk pure shear with a strain rate of w2!10K6 sK1 (vertical shortening direction).
(a) and (b) Grain coarsening accommodated compaction with minor grain boundary sliding. Arrows indicate small grains that disappear and are replaced. (c)
Deformation is accommodated by granular flow. (d) and (e) Localized grain boundary sliding in small shear zones while most of the grains are already locked.
(f) and (g) Locking up of grain boundaries and grain boundary migration accommodated dislocation creep. The liquid fraction at this stage is nearly zero.
Images were taken with partly crossed polarizers. Bottom left numbers indicate time elapsed from the beginning of the experiment, top right numbers indicate
the liquid fraction in vol.%. (h) Mean grain size versus time graph.
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Fig. 4. Interplay of grain boundary welding and grain boundary sliding in a
norcamphorCethanol experiment at a bulk liquid fraction O10 vol.%. The
aggregate in the centre is destroyed as the upper grain is sheared off (see
arrows). Notice the newly formed welded boundary in the lower part of (b)
(lower arrow). Images were taken with partly crossed polarizers.
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favourable for wetting angles above 08 when the ratio of
solid–solid to solid–liquid surface energy is below two, so
that aggregation of grains lowers the total energy of the
system (e.g. Stephenson and White, 1967; Jurewicz and
Watson, 1985).
Experiments were conducted with ‘low’ and ‘high’ bulk
strain rates of approximately 10K6 and 10K5 sK1, respectively. Temperature was held constant at 30G1 8C by room
air conditioning, without additional heating or cooling.
During a single experiment the melt fraction always
decreased within the observed area due to compaction of the
sample and lateral extrusion of liquid that collected at the
sides of the sample. This allowed for a continuous
observation of the transition from high to low liquidfraction behaviour.
3.1.1. ‘Low’ strain rate deformation
The images of Fig. 3 represent more than 8 days of
deformation at a strain rate of w2!10K6 sK1. Initially, the
sample deforms by grain compaction accommodated by a
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Fig. 5. Detail of the low strain rate norcamphorCethanol experiment
showing the development of a single grain (see arrow). Straight sub-grain
boundary in (a) migrates slowly outwards while a new curved sub-grain
boundary develops from below (b). A second sub-grain boundary develops
(c) so that the grain eventually splits into three parts. The lower third
becomes part of a larger bright grain. Images were taken with partly crossed
polarizers. Bulk liquid fraction of (a) 2–3 vol.%.
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Handy, 1996). The grains develop undulose extinction,
which regularly localizes into newly formed sub-grain
boundaries usually oriented parallel to the axis of greatest
compression (Fig. 5). Further rotational recrystallisation
leads to the formation of new grains with high-angle
boundaries (Fig. 5d).
At this stage, grain boundaries become very mobile,
probably because grains are pressed against each other so
that no visible liquid pockets remain between the grains. An
unstable microstructure results as the grain boundaries
begin to sweep other grains and become irregular and
amoeboid in shape (Fig. 3g). The mean grain size increases
rapidly (Fig. 3h). However, this fast grain boundary
mobility is only reached once most of the liquid is expelled
from the sample. As long as liquid can be observed in triple
junctions and between grain boundaries, the boundaries are
prevented from migrating freely. Therefore liquid patches
act as a pinning phase (cf. Evans et al., 2001; Renner et al.,
2002). Small remaining liquid pockets pin mobile grain
boundaries for a limited time before the grain boundaries
sweep over or around them and the liquid remains as round
inclusions within grains (Figs. 6 and 7).
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combination of grain boundary sliding-granular flow and
grain coarsening (Fig. 3a and b). The grain coarsening is
driven by the dissolution of small grains and simultaneous
growth of large grains due to the differences in surface/volume ratio of different sized grains. This process is normally
termed (liquid assisted) ‘static recrystallization’ or ‘Ostwald
ripening’ (e.g. Evans et al., 2001). When a small grain
disappears, a larger grain can slide into the remaining gap
and occupy its space so that the static grain coarsening
facilitates compaction (compare Fig. 3a and b). This
mechanism, coupled with a complex grain rearrangement
and minor grain boundary sliding, dominates the deformation in the beginning of the experiment. The Ostwald
ripening process is responsible for slowly increasing grain
size during the first 140 h of the experiment (Fig. 3h).
Dissolution–precipitation processes such as ‘contact melting’ as reported by Means and Park (1994) were not
observed and are probably of minor importance. One reason
for this is the different grain shape in our experiments
compared with the older experiments. It is easier for more
equant grains in our samples to change position by grain
boundary sliding than for the elongated grains of Means and
Park (1994), so that stress concentrations are reduced. Grain
boundary sliding is either distributed throughout the sample
(granular flow) at a high liquid fraction exceeding ca. 8–9%
or is localized in small, short-lived, often conjugate shear
zones that occur at lower liquid fractions. During their
activity, the shear zones have a locally stable liquid fraction
as grains slide past each other (Fig. 3c–e). A shear zone can
become de-activated during deformation e.g. by rotation
towards the shear plane. A de-activated shear zone often
compacts by redistribution of the melt in the surrounding
matrix or to the edge of the sample. Welding of several
grains into coherent clusters between the shear zones is
another characteristic of this deformation/melt fraction
stage (Figs. 3d and e and 4).
During progressive pure shear, the liquid fraction
decreases slowly due to an overall compaction of the grains
and lateral expulsion of liquid towards the sides of the
sample. The grain-scale liquid distribution at this stage is
governed by opening and closing gaps between sliding
grains, by liquid redistribution due to disappearing grains,
and growing grains that slide into cavities. As the grain size
increases and the liquid fraction decreases, the relative
effect of grain coarsening as an accommodation process for
compaction decreases.
Below about 8 vol.% liquid fraction, the deformation
becomes more localized into shear zones and grain
boundary sliding is more and more inhibited by welded
grain boundaries and the formation of larger grain clusters.
Once the liquid fraction drops below 3–4 vol.%, there is a
dramatic switch in microstructure and deformation mechanism (Fig. 3f and g). Grain boundary sliding is absent as all
grains are locked into one single framework. The grains are
now deforming internally by crystal plastic deformation,
probably dislocation creep (Bons, 1993; Herweg and
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3.1.2. ‘High’ strain rate deformation
The deformation behaviour and microstructure in the
experiments with a ‘high’ strain rate (w10K5 sK1) is
generally similar to the ‘low’ strain rate behaviour described
above. At a liquid fraction above ca. 8 vol.% deformation is
accommodated by grain rearrangement during compaction
and granular flow (Fig. 8a–c). Because of the higher strain
rate, the surface energy driven grain coarsening described
above is negligible as an accommodation mechanism
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(Fig. 8f). At a lower liquid-fraction, the aggregate deforms
by grain boundary migration accommodated dislocation
creep with welded non-sliding grain boundaries (Fig. 8).
The transition between the granular flow regime and the
dislocation creep regime is more abrupt between about 6–
8 vol.%, compared with the low strain rate experiments,
with less development of localized shear zones.
3.2. KNO3–LiNO3 experiments
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In the second type of experiment, the samples were
prepared by complete melting of a KNO3–LiNO3 mixture at
300 8C and subsequent cooling and crystallising between
the glass plates, down to 200 8C, at which temperature it was
left to anneal for 24 h. At this temperature all LiNO3 is
completely molten and the solid phase is only composed of
KNO3 grains. Due to a temperature gradient of about 10 8C
between the centre of the observation window (colder) and
the metal housing (hot) most of the nitrate melt migrates out
of the centre during static grain coarsening (Lesher and
Walker, 1988) and collects at the side of the sample, so that
the observed area of the sample has a low starting melt
fraction of approximately 1 vol.% (Fig. 9a). Because of the
low melt fraction and the temperature gradient, the wetting
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angle is difficult to measure accurately but appears to be
well below 608.
Experiments were carried out in pure shear, at a ‘high’
strain rate of about 10K5 sK1 and at a constant temperature
of 200 8C. At this temperature non-molten NaNO3, a
compound similar to KNO3 in its behaviour, displays
rotational recrystallisation and grain boundary migration
recrystallisation in the experiments of Tungatt and
Humphreys (1981). However, since the KNO3 grains in
our experiments are comparably rigid, deformation is
dominated by grain boundary sliding and internal deformation of the grains was only observed at a very low melt
fraction !1 vol.% (see below). During progressive deformation small conjugate shear zones develop throughout the
sample (Figs. 9–11). Because of the initially low melt
fraction the grain boundary sliding depends on a geometrical accommodation process. However, no diffusion or
contact melting (cf. Means and Park, 1994) accommodation
of the grain boundary sliding was observed but the sliding of
grain boundaries was rather accommodated by local dilation
and creation of new dynamic porosity in the shear zones.
The newly created porosity is filled with melt that is drawn
in from the matrix and from the edge of the sample. In this
way the segregated melt originally located at the side is
redistributed within the sample and the bulk melt-fraction of
the sample is dynamically increased (Figs. 10 and 12c).
Shear zones rotate towards the shear plane and become
inactive, as new shear zones develop to take up the strain.
The elevated porosity of an inactive shear zone is quickly
destroyed by compaction and redistributed into newly
formed shear zones (e.g. Fig. 10b and c). As the melt
fraction rises during the experiment, the shear zones widen
and deformation thereby becomes less localized and
progress towards distributed granular flow (e.g. lower left
region in Fig. 10d with a local melt fraction flocalz9–
10 vol.%). However, this progressive increase in melt
fraction is only possible if a sufficiently large melt reservoir
is available at the side of the sample that can be sucked into
the aggregate during deformation. If the melt fraction
cannot increase freely, deformation stays localized in GBS
shear zones and the compacting regions are often
characterised by a flattening of the crystals, possibly by
diffusional creep, or by anomalous fast grain growth
(Fig. 11). This stage of framework deformation at which
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Fig. 6. ‘Regular pinning’ in the grain boundary migration stage of a ‘low’ strain rate norcamphorCethanol experiment. (a) and (b) A moving grain boundary
(arrows) is pinned by a small liquid bubble. (c) Eventually, the boundary detaches and leaves a round liquid inclusion (arrow). Images were taken with partly
crossed polarizers. Bulk liquid fraction /1 vol.%.
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Fig. 7. ‘Irregular pinning’ in a ‘low’ strain rate norcamphorCethanol
experiment. The sweeping boundary cannot detach from a larger fluid patch
as in Fig. 6. The sides swing around and leave a small island grain
connected to a liquid inclusion (see arrows). Images were taken with partly
crossed polarizers. Bulk liquid fraction /1 vol.%.
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deformation can be explained by the strong grains
combined with the low wetting angle of the melt that
inhibits grain welding and clustering and favours the
formation of dilatant shear zones.
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grains lock and the onset of internal crystal plastic
deformation is only observed in compacting areas of the
samples with a very low melt-fraction !1 vol.%. The
very low melt fraction for the onset of framework
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Fig. 8. Deformation of norcamphor crystals plus ethanol liquid by bulk pure shear with a ‘high’ strain rate of ca. 10K5 sK1 (vertical shortening). (a) and (b)
Deformation is mainly by grain boundary sliding accommodated compaction. (c) Onset of the locking stage of the grains into one coherent cluster suppressing
GBS. Beginning of framework compaction. (d) GBM starts in the liquid-poor central region while liquid pockets still pin the grain boundaries in the other parts.
(e) Further compression and liquid removal allows free grain boundary migration. The grain size is now significantly larger than during grain boundary sliding.
Images were taken with partly crossed polarizers. Bottom left numbers indicate time elapsed from the beginning of the experiment, top right numbers indicate
the liquid fraction in vol.%. (f) Mean grain size versus time graph.
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Fig. 9. Nitrate deformation experiment with a bulk pure shear of approximately 10K5 sK1 (vertical compression) Binary images trace the liquid evolution,
bottom right numbers give the melt vol.%. (a) Potassium nitrate aggregate before deformation with low porosity. (b)–(d) Deformation localizes into a small
shear zone that deforms by GBS. Opening gaps are filled with melt that is drawn in from the outside. The dynamic porosity in the shear zone has now
significantly increased to approximately 10%, while the matrix has retained a low porosity. Images were taken with partly crossed polarizers. Bottom left
numbers indicate time elapsed from the beginning of the experiment.
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Fig. 10. Nitrate deformation experiment, continued from Fig. 9 with a lower magnification. Observed area of Fig. 9 is marked in (a). Binary images trace the
liquid evolution, top right numbers give the melt vol.%. Aggregate deforms by conjugate GBS shear zones. The melt-fraction in the observed area rises during
progressive deformation, and the deformation develops from localized shear zones towards distributed granular flow. Bottom left numbers indicate time
elapsed from the beginning of the experiment.
similar liquid fractions of w10 vol.% and the shortening
was calculated in relation to these starting images. The
curves of the low strain rate (Fig. 12a) and the high strain
rate (Fig. 12b) experiment show a very similar liquid versus
strain evolution in the norcamphor–ethanol system. In the
beginning, deformation is dominated by compaction, until
at around 8–9 vol.% liquid fraction (10% shortening) the
deformation is dominated by liquid assisted granular flow.
The subsequent flattening of the liquid curve until a bulk
shortening of 30–35% represents temporary inefficient
liquid segregation during granular flow. At that stage,
below a liquid fraction of ca. 8 vol.%, liquid segregation
picks up again when norcamphor grains reach partial
locking combined with localized grain boundary sliding
(Fig. 12a and b). Although the described departure from
linearity of the liquid evolution in Fig. 12 appears not to
be very pronounced, it should be noted that it is within
measurement precision and that the curve coincides very
well with the described microstructural transitions.
The liquid fraction and the microstructural evolution of
the nitrate experiments and the norcamphor–ethanol
experiments display opposite trends during the experiments.
While the latter evolve from high to low liquid-fraction
during progressive deformation, the nitrate experiments
evolve from low to high liquid-fraction. Thus the
norcamphor experiments start with granular flow, which
evolves to localized GBS and finally reach framework
deformation, while the nitrates start deforming by localized
GBS and progress towards granular flow. It is interesting to
note that despite these differences the transitions from
localized GBS deformation to granular flow is similar for
both systems (8–10 vol.%).
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Fig. 12 shows the evolution of the liquid fraction as a
function of the bulk shortening of the norcamphor–ethanol
experiments (Fig. 12a and b) and the KNO3–LiNO3
experiments (Fig. 12c). For the analysis of the norcampor
experiments starting images were chosen that contain
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3.3. Evolution of the liquid-fraction in the analogue
experiments
Fig. 11. Nitrate deformation experiment with a low bulk melt fraction
(estimated to be !3 vol.%). Black bodies are rigid ‘micro boudins’ made
out of 0.1-mm-thick metal foil. Deformation is by localized GBS with a
small shear zone that separates the two ‘boudins’. Melt fraction in the shear
zone is raised, while the matrix compacts, probably by dislocation creep.
Fast, anomalous grain growth (see arrow) overgrows large parts of the finegrained matrix. Width of view is approximately 1 cm.
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‘moderate’ liquid-fraction (fbulk !8–10 vol.%) deformation is by localized GBS with compacting grain clusters
in between (regime II), and at a ‘low’ liquid-fraction (fbulk
varies depending on the system) an interlocking granular
framework is deformed (regime III). The following sections
discuss the implications of these observations for the
deformation behaviour of partially-molten rocks and for
the small-scale distribution of liquid in general.
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Fig. 12. Evolution of the liquid fraction in the norcamphor–ethanol
experiments and the KNO3-LiNO3 experiment versus bulk strain. (a)
Development of the liquid fraction in the low strain rate experiment. Time
displayed is 80 h. (b) Liquid evolution in the ‘high’ strain rate experiment.
Approximate positions of microstructural transitions (fLT and fGBS-L) are
marked with stippled lines. The bulk shortening is calculated in relation to
the initial stage at approximately 10% liquid. Time displayed is 5 h. (c)
Melt-fraction evolution in the nitrate experiment shown in Figs. 9 and 10.
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4. Discussion
949
The deformation behaviour of all described analogue
systems can be classified into three deformation regimes: at
a ‘high’ liquid-fraction (fbulkR8–10 vol.%) deformation is
by compaction and distributed granular flow (regime I), at a
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The term grain boundary sliding (GBS) is used here to
characterize the grain-scale deformation mechanism of
grains moving relative to each other. The experiments have
shown that GBS is the dominant deformation mechanism at
a high to moderate liquid fraction above about 4–6 vol.% in
the norcamphor–ethanol experiments and above ca. 1 vol.%
in the KNO3–LiNO3 experiments. GBS-dominated deformation behaviour was subdivided into two regimes based on
the degree of strain localization. If deformation is
distributed throughout the aggregate without or with only
minor strain localization, we use the term granular flow
(deformation regime I). Granular flow was observed in both
sets of analogue experiments and in the analogue
experiments of Park and Means (1996) at a liquid fraction
of R8–10 vol.%. At a lower liquid fraction GBS deformation is localized in shear zones in our experiments, which
we call localized GBS (deformation regime II).
Granular flow and grain boundary sliding of partiallymolten rocks is considered as a potentially important
deformation mechanism in nature (e.g. Rutter, 1997;
Paterson, 2001; Rosenberg, 2001; Mecklenburgh and
Rutter, 2003). Theoretical models for GBS consider
diffusional creep and reactions as rate limiting parameters
and therefore predict Newtonian flow behaviour (Paterson,
2001). However, experimental investigations generally
result in a higher strain rate sensitivity, such as nz3.5 for
quartz plus albite–quartz melt (Rutter and Neumann, 1995;
Mecklenburgh and Rutter, 2003). This power-law behaviour
indicates that another mechanism than diffusion is rate
controlling. Mecklenburgh and Rutter (2003) suggested
fracturing and intra-grain microcracking for higher strain
rates and the destruction of welded grain boundaries (intergrain microfracturing) for low strain rates as alternative
mechanisms. The latter process is also observed in our
experiments. In our norcamphor–ethanol experiments, grain
boundaries are continuously welded and separated (Fig. 4).
Although the opening of welded grain boundaries may be
the rate-controlling mechanism for GBS deformation, a
freely moving liquid is required to provide the geometric
porosity for grains to slide past each other. This process is
evident from our experiments and explains the degree of
deformation localization observed. At a bulk liquid fraction
R8–10 vol.% GBS deformation can occur as non-localized
granular flow (deformation regime I). At a lower liquid
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4.1. Deformation regime I (granular flow) and regime II
(localized grain boundary sliding)
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fraction there is insufficient liquid to let the whole aggregate
deform by GBS and deformation is localized into GBS shear
zones (regime II, e.g. Fig. 10). Similar relatively meltenriched shear zones have been observed in olivine- and
feldspar-melt deformation experiments (Holtzman et al.,
2003a,b) and in norcamphor–benzamide analogue experiments (Rosenberg and Handy, 2000).
Natural examples of regime II behaviour could be the
small melt-filled shear zones or shear bands that are
frequently observed in natural partially molten rocks (e.g.
Brown, 1994; Brown and Rushmer, 1997; Brown and Solar,
1998). Brown and Rushmer (1997) proposed melt-induced
local fracturing and cataclastic flow to explain the increased
porosity. Alternatively, if the systems deformed in regime
II, small initial melt fraction fluctuations would naturally
cause small shear zones with a raised melt fraction that
deform by GBS.
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4.3. Deformation regime III: grain boundary migration
accommodated dislocation creep
4.2. The localization threshold (fLT)
Because of the importance of the liquid fraction for
determining the localization of GBS deformation, we
Deformation regime III is characterized by the welding
of all grain boundaries into a coherent cluster at a liquid
fraction below ca. 4–7 vol.% in the norcamphor–ethanol
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Fig. 13. Schematic representation of the observed deformation regimes. (a) At high liquid fraction (fbulkOfLT) a solid–liquid aggregate deforms by
compaction and granular flow (regime I). At a lower liquid fraction (fbulk!fLT) a solid–liquid aggregate can either deform by localized grain boundary sliding
(b) (regime II, fbulkOfGBS-L) or by framework deformation (c) (regime III, fbulkOfGBS-L). Note that knowledge of the initial microstructure and liquid
fraction is not sufficient for determining the deformation regime.
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suggest calling the liquid fraction that separates regime I
from regime II the localization threshold (fLT). If the bulk
liquid fraction of a liquid-bearing aggregate exceeds fLT for
a given system (fbulkOfLT), flow is by pervasively
distributed granular flow with or without compaction
(regime I, Fig. 13a). If the bulk liquid fraction is lower
than fLT (fbulk!fLT), GBS shear zones with a locally
raised liquid fraction are formed (regime II, Fig. 13b). fLT is
a transition zone at about 8–10 vol.% in the case of twodimensional (2-D) analogue experiments. In three-dimensional (3-D) reality, fLT is expected to be higher, probably
around 25–30 vol.%. This can be derived from comparing
the pore area fraction of a closest circle packing in 2-D to
the pore volume fraction of closest sphere packing in 3-D,
which is ca. 9 and 26 vol.%, respectively.
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Below fLT there is a second transition (fGBS-L) from
(localized) grain boundary sliding to crystal–plastic framework deformation, when the framework gets locked. Unlike
fLT, fGBS-L is sharp in our experiments.
A critical question for the GBS-L transition concerns the
conditions under which a locked framework is established
that can support the applied stress without or with only
minor grain-boundary sliding. To better characterize the
magnitude and variation of fGBS-L for different systems, we
have to consider the parameters of our analogue experiments that determine and influence fGBS-L. In the
norcamphor–ethanol GBS regime spontaneous welding
and clustering between adjacent norcamphor grains is
energetically favourable and might act as a rate limiting
mechanism for GBS deformation as discussed in Section
4.1. Thus, the total work necessary for continuous grain
boundary sliding in addition to overcoming frictional forces
is the work necessary to locally break one solid–solid grain
boundary times the total number of boundaries. The number
of welded grain boundaries and the ratio of the solid–solid to
solid–liquid boundary area in a sample directly depend on
the liquid fraction, so that the work per strain increment of
GBS increases with decreasing liquid fraction. Thus, fGBS-L
occurs at that liquid fraction at which the strain energy rate
for maintaining GBS equals or exceeds the strain energy
rate for framework deformation. Several parameters should
influence the magnitude of fGBS-L (see also Fig. 13):
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4.4. The grain boundary sliding–grain boundary locking
(GBS-L) transition
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very low liquid fraction might enhance grain boundary
mobility. Similar conclusions were drawn by Renner et al.
(2002) for static systems.
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experiments and below about 1 vol.% in the nitrate
experiments. A common observation from both sets of
experiments was the anomalous grain growth, which
occurred during framework deformation and led to a
significant increase of the grain size. This increase of
grain size during deformation appears to be different from
previously described processes of abnormal or discontinuous grain growth (cf. Atkinson, 1988; Evans et al., 2001, and
references therein) or exaggerated grain growth (cf. Vernon,
1976), in which single larger grains grow at the expense of
smaller matrix grains, since the latter occurred during static
recrystallisation.
The microstructures observed during grain boundary
migration in the norcamphor experiments correspond to the
dislocation creep regime 3 of Hirth and Tullis (1992) and
the GBM regime of Stipp et al. (2002a,b) that are
characterized by grain boundary migration accommodated
dislocation creep with only minor sub-grain rotation
recrystallisation. Although these regimes have been defined
for non-molten deforming quartzite, our observation that the
strong grain boundary migration only starts when nearly all
melt has been removed from the sample fits well with the
description of regime 3, especially since a very low melt
fraction !1% was reported for some of the experiments of
Hirth and Tullis (1992). However, the very high mobility of
the grain boundaries and the dramatic increase of the grain
size in our experiments are unusual for the unmolten GBM
regime of Hirth and Tullis (1992). The sudden grain growth
that was observed in some of the nitrate experiments (e.g.
Fig. 11) was even more pronounced than in the norcamphor
experiments. This grain size increase is probably the result
of a similar process as in the norcamphor, since the
temperature of deformation (200 8C) in our experiments lies
within the range of GBM recrystallisation in NaNO3
reported by Tungatt and Humphreys (1981).
Liquid-enhanced grain boundary mobility has been
reported in other materials, such as wet bischofite (Urai,
1983) and norcamphor plus norcamphor–benzamide melt
(Rosenberg and Handy, 2001). In a natural example, Stipp et
al. (2002b) reported an unexplained dramatic increase in
grain size of a deformed quartzite adjacent to the contact of
the Adamello pluton (Italian Alps). Although the quartzite
layers do not contain visible traces of melt, the pluton and
the surrounding rocks were partially molten during the
deformation (Stipp, personal communication, 2004). It is
therefore possible that small traces of melt were present in
the quartzite layers during deformation, which lead to a
similar dynamic grain-size increase, as observed in our
experiments. A very large grain size is also a characteristic
of high-temperature quartz ribbon mylonites (e.g. Hippert et
al., 2001), which could similarly be connected to the
presence of a low percentage of melt or metamorphic fluid
during crystal plastic deformation. The results of our
analogue experiments and of the examples given above
indicate that while macroscopic liquid or melt pockets tend
to inhibit grain boundary mobility by pinning (Figs. 6 and 7), a
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1. Solid strength and liquid viscosity: A strong solid phase
with a relatively low viscosity liquid facilitates GBS and
therefore lowers fGBS-L (e.g. nitrate experiments),
compared with a system with a weaker solid phase
with a relatively higher viscosity liquid which facilitates
framework deformation and thereby raises fGBS-L (e.g.
norcamphor experiments). The solid–liquid viscosity
ratio can change in a system as a function of strain rate
(the strain rate sensitivity) and temperature, thereby
changing fGBS-L.
2. The bonding strength of grain boundaries: This is
probably a function of the solid–solid surface energy, the
wetting angle, and the relative liquid pressure. A wellwetting liquid will facilitate dynamic wetting and
breaking of grain boundaries so that fGBS-L is lowered
compared with a similar system with a poorly-wetting
liquid. Furthermore, the relative liquid pressure is of
importance for breaking of grain boundaries and
creating dynamic porosity. Liquid overpressure facilitates breaking of grain boundaries, thereby lowering
fGBS-L.
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Efficient melt segregation at melt-fractions above the
RCMP is predicted to occur by compaction and filter
pressing, whereas only restricted segregation occurs below
the RCMP once a solid framework is established (Arzi,
1978). Interestingly, our results indicate the opposite. The
liquid-fraction evolution of the experiments show that
segregation of liquid per strain increment is significantly
slower or even reversed (in the nitrate experiments) during
granular flow and grain-boundary sliding (regimes I–II),
while liquid segregation is most efficient during regime III
framework deformation (Fig. 12). The reason is that grain
boundary sliding can only occur with a sufficient liquid
fraction (fGSP) and local dilation and compaction will
shuffle liquid around, rather than expel it. Efficient filter
pressing can only occur in regime III where the deforming
framework can effectively exert a pressure on the lowviscous liquid to expel it to any available sinks.
5. Conclusions
Experiments performed with the liquid-bearing norcamphor–ethanol system and the partially molten KNO3–LiNO3
system give information on a range of deformation
mechanisms that potentially act in partially molten and
fluid-bearing rocks from high to very low liquid fractions.
The deformation behaviour of the analogue systems is
characterised by three different deformation regimes
(quoted liquid fractions are for 2-D experiments, and are
probably higher for 3-D systems).
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Arzi (1978) suggested the existence of a rheological
critical melt percentage (RCMP), which marks a transition
between essentially solid behaviour to much weaker meltdominated behaviour. The RCMP concept predicts a sharp
drop in strength at a bulk melt fraction of about fbulkz20G
10% melt. Vigneresse et al. (1996) and Vigneresse and
Tikoff (1999) extended and modified the concept by arguing
that there is a difference between a progressively melting
system (increasing melt fraction) and a crystallising system
(decreasing melt fraction) and defined four thresholds by
utilizing percolation theory. In the crystallising case they
defined the rigid percolation threshold (RPT) at fbulkz45 vol.% and the particle locking threshold (PLT) at
fbulkz25–28 vol.%. The PLT is analogous to the RCMP.
All authors have in common that they base their theory on
the consideration that once a geometric stress-supporting
framework of rigid grains has been established, the rheology
of the system should change dramatically. The melt-fraction
at the transition between solid- and liquid-dominated
behaviour is argued to depend mainly on melt fraction and
particle shape.
Although the existence of a RCMP is not undisputed
(e.g. Bagdasserov and Dorfman, 1998; Renner et al.,
2000; Rosenberg, 2001), our observations, and those of
Park and Means (1996), support a microstructural
transition from liquid-dominated (regimes I–II) to framework-dominated (regime III) behaviour, comparable
with the rheological RCMP. Whereas previous authors
(Vigneresse et al., 1996; Vigneresse and Tikoff, 1999) set
the RCMP exactly at the liquid fraction where the solid
phase forms a connecting framework, we show that
redistribution of the liquid may significantly lower the
transition to regime III behaviour.
An indication of the transition from regime II to III
(fGBS-L) in nature may be derived from the careful mapping
of grain-scale melt pseudomorphs in migmatites that was
presented by Sawyer (2001). His fig. 2 (p. 294) shows an
elongate melt-enriched zone, with about 25 vol.% melt, in a
matrix with only 6–13 vol.% melt. The microstructure, with
a bulk melt fraction about 12.5 vol.% melt, is similar to our
regime II, suggesting that fGBS-L lies below 12.5 vol.% in
this partially molten pelite.
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4.5. Relation to other threshold models (RCMP, RPT, PLT)
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4.6. Segregation of liquid
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3. Grain size: In grain-size sensitive framework deformation (liquid-assisted diffusional creep), fGBS-L is
raised by a decreasing grain size.
4. Permeability and viscosity: To create localized shear
zones, liquid has to move a certain distance along a
hydraulic head into the shear zones. This migration from
the matrix into the shear zones is a function of liquid
viscosity and matrix permeability (see Holtzman et al.,
2003a).
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5.1. ‘High’ liquid fraction R8–10 vol.%: compaction and
granular flow
1322
At liquid fraction O10% deformation is dominated by
compaction. Strain is accommodated by grain rearrangement, GBS, and, at sufficiently low strain rate, by the
disappearance of small grains due to grain coarsening whose
space is taken up by larger grains. At a liquid fraction of
about 8–10 vol.% (fLT) deformation of the norcamphor–
ethanol and the KNO3–LiNO3 experiments is by distributed
granular flow. In the norcamphor–ethanol experiments,
liquid segregation is least efficient at liquid fractions just
above fLT. In the KNO3–LiNO3 experiments, liquid
segregation is even reversed by drawing in melt to enable
GBS.
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5.2. ‘Moderate’ liquid fraction: localized grain boundary
sliding
1338
Below 8–10 vol.% (fLT) the ‘low’ strain rate norcamphor–ethanol experiments and the nitrate experiments often
exhibit conjugate shear zones that deform by GBS. The
areas in between form grain clusters that compact slightly
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Acknowledgements
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We thank Daniel Koehn, Marlina Elburg, and Jochen
Arnold for help and fruitful discussions. The reviewers J.
Tullis and E. Rutter are thanked for constructive reviews
that helped to improve and clarify the manuscript. N. Walte
acknowledges funding by the DFG-Graduiertenkolleg
‘Composition and Evolution of Crust and Mantle’.
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The grains of the solid–liquid systems form a stresssupporting framework that deforms internally by a
mechanism of framework deformation such as dynamic
recrystallisation accommodated dislocation creep (norcamphor–ethanol experiments). The grains recrystallise by very
mobile grain boundaries that sweep highly strained areas of
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sliding–grain boundary locking threshold (fGBS-L). In
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norcamphor–ethanol experiment) and ca. 1% (KNO3–
LiNO3 experiments). Earlier threshold models (e.g. the
RCMP; Arzi, 1978) considered the geometric formation of a
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5.3. ‘Low’ liquid fraction: framework deformation by
dislocation creep
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Bulau et al. (1979).
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and thereby loose liquid to the shear zones (flocal!fbulk) or
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