ELSEVIER
Tectonophysics 307 (1999) 297–312
www.elsevier.com/locate/tecto
Pressure solution compaction of sodium chlorate and implications for
pressure solution in NaCl
Bas den Brok Ł , Mohsine Zahid, Cees W. Passchier
Institut für Geowissenschaften, Johannes Gutenberg-Universität, 55099 Mainz, Germany
Received 6 January 1998; accepted 3 March 1999
Abstract
Sodium chloride (NaCl) has been extensively used as a material to develop, test and improve pressure solution (PS)
rock deformation models. However, unlike silicate and carbonate rocks, NaCl can deform plastically at very low stresses
(¾0.5 MPa). This could mean that NaCl is less suitable for use as an analogue for rocks that do not deform plastically
at conditions where PS is important. In order to test the reliability of NaCl as a rock analogue, we carried out a series
of uniaxial compaction experiments on sodium chlorate (NaClO3 ) at room pressure and temperature (P–T) conditions
and applied effective stresses of 2.4 and 5.0 Mpa. NaClO3 is a very soluble, elastic–brittle salt, that cannot be deformed
plastically at room P–T conditions. The results were compared with experiments on NaCl at similar conditions and show
that NaClO3 behaves in a strikingly similar way to NaCl, despite its brittleness. Like NaCl, it most likely compacts by a
grain boundary diffusion controlled PS mechanism. Mechanical data were fitted to a power law in the form: "P ³ " Þ ¦ n d m
(with volumetric strain rate "P , volumetric strain ", effective stress ¦ and grain size d). A reasonable fit was obtained, with
Þ D 2 to 4, n D 1:6 š 0:5, and m D 2:8 š 0:5. The similarity in mechanical behaviour of the two materials (NaCl plastic,
NaClO3 brittle) suggests that plasticity does not play a key role in PS compaction deformation of NaCl. This means that its
plasticity is not a drawback for its use as a PS analogue for rocks or for deriving PS creep laws for salt from compaction
experiments.  1999 Elsevier Science B.V. All rights reserved.
Keywords: pressure solution; deformation; mechanical properties; diagenesis; sodium chloride; salt tectonics
1. Introduction
Much of the understanding of pressure solution
(PS) as a rock deformation mechanism is based on
experimental work on NaCl (e.g., Bosworth, 1981;
Raj, 1982; Tada and Siever, 1986; Spiers and Schutjens, 1990; Spiers et al., 1990; Hickman and Evans,
Ł Corresponding
author. Present address: Geologisches Institut
ETH, Sonneggstrasse 5, CH-8092 Zürich, Switzerland. Tel.:
C41 1 632 3664; Fax: C41 1 632 1080; E-mail:
[email protected]
1991; Schutjens, 1991; Spiers and Brzesowsky, 1993;
Gratier, 1993). The major reason is that it is much
easier to study PS of NaCl, than that of rock-forming minerals like quartz or feldspar. NaCl has a very
high solubility at room temperature .T / and atmospheric pressure .P/, dissolves and precipitates fast,
has a simple crystal structure, and much is already
known about its physico-chemical and mechanical
behaviour. PS of NaCl has also been studied extensively because of its relevance to rheological problems related to disposal of radioactive waste in salt
domes (e.g., Spiers et al., 1986, 1989; Spiers and
0040-1951/99/$ – see front matter  1999 Elsevier Science B.V. All rights reserved.
PII: S 0 0 4 0 - 1 9 5 1 ( 9 9 ) 0 0 1 0 3 - 1
298
B. den Brok et al. / Tectonophysics 307 (1999) 297–312
Brzesowsky, 1993) and salt tectonics (Spiers et al.,
1990; Carter et al., 1993).
It may be questioned though, whether NaCl is a
good analogue material to model for PS in silicate
rocks since NaCl deforms plastically at very low differential stresses (¾0.5 MPa; e.g., Davidge and Pratt,
1964) even at room P–T conditions. In most, if not all
PS experiments on NaCl reported in the literature, differential stresses are much higher than 0.5 MPa, and
crystal plastic deformation must have taken place. In
nature, by contrast, most rocks do not deform easily by crystal plastic mechanisms under conditions
where PS is important. This may pose a serious problem, since plastic deformation of NaCl may influence
its PS behaviour (Bosworth, 1981; Tada and Siever,
1986), which could therefore differ significantly from
that in silicate rocks (cf. effect of plastic deformation
on PS of calcite, Engelder, 1982).
Unfortunately, the effect of crystal plasticity on
PS of NaCl is poorly understood, though evidence
for such effects does exist (Bosworth, 1981; Tada
and Siever, 1986). It is especially in compaction experiments on porous NaCl aggregates that the role
of crystal plastic deformation on PS is not clear (see
discussion in Hickman and Evans, 1991). Yet, compaction experiments are among the most extensively
studied, and document most extensively the PS behaviour of NaCl (Raj, 1982; Spiers and Schutjens,
1990; Spiers et al., 1990; Schutjens, 1991; Spiers
and Brzesowsky, 1993). Spiers and co-workers compacted NaCl aggregates at applied effective pressures
in the range 0.55–4.3 MPa and found that the mechanical behaviour and the deformation microstructures are remarkably consistent with PS models in
which crystal plastic deformation on the grain scale
plays no role (e.g., models from Raj, 1982; Rutter, 1983; Lehner, 1990; Spiers and Schutjens, 1990;
Spiers et al., 1990). However, differential stresses at
the grain-to-grain contacts must have been so high
in these experiments (8–103 MPa according to estimates made by Hickman and Evans, 1991), that
crystal plastic deformation must have taken place.
This may very well have influenced the PS behaviour. Hickman and Evans (1991) suggested that
crystal plastic deformation even might have been
essential in these experiments for PS to take place
at all. They based this on their experience that PS
did not take place between a polished NaCl lens
pressed against an NaCl plate, in a saturated NaCl
solution, at room P–T conditions and average normal contact stresses in the range 1–14 MPa. Instead
of dissolution, neck growth occurred. According to
Hickman and Evans (1991) this occurred because
wetting angles were non-zero. They suggested, that
only very high grain-to-grain contact stresses (up to
¾100 MPa), leading to intense crystal plastic deformation, an increase in free energy and subsequent
contact undercutting by dissolution of the plastically
strained material, would make PS in compaction
experiments on NaCl possible.
We were interested to know whether PS compaction would take place in an elastic–brittle salt
where no plastic deformation at grain-to-grain contacts is to be expected. We therefore performed a
series of PS compaction experiments on aggregates
of sodium chlorate (NaClO3 ) under conditions similar to those of the experiments on NaCl by Spiers
and co-workers. NaClO3 has the advantages of NaCl
as a rock analogue material (high solubility, fast
dissolution–precipitation kinetics), but cannot be deformed by crystal plastic mechanisms at room P–T
conditions (e.g., Ristic et al., 1988). Single crystals can sustain at least 21 MPa differential stress
without any measurable crystal plastic deformation.
At higher stresses, crystals break. It was our aim
to confirm whether PS would occur in this material
and thus to contribute to a better understanding of
the effect of crystal plasticity in PS experiments on
NaCl, and consequently, of PS as a rock deformation
mechanism in general.
2. Materials and methods
2.1. Sodium chlorate (NaClO3 )
NaClO3 is a colourless, highly soluble, cubic salt
(point group 23). At 25ºC and 0.1 MPa, its solubility
.C/ expressed as a molefraction is ¾0.18, compared
with ¾0.11 for NaCl (e.g., Meyer, 1928). Growth
and dissolution rates are extremely high, comparable
to those of NaCl. The interface kinetics coefficient
(i.e., the interface velocity for a thermodynamic driving force of 1 RT joule per mole) of the f100g
face of NaClO3 is ¾30 µm=s (Chen et al., 1979;
Wilcox, 1993), compared to ¾20 µm=s for NaCl
B. den Brok et al. / Tectonophysics 307 (1999) 297–312
(estimated on the basis of growth and dissolution
experiments of Langer and Offerman, 1982). Solute
diffusivities .D/ of NaCl and NaClO3 are similar:
a value of D D 1:5 ð 10 9 m2 =s at 25ºC was calculated for NaCl by Spiers et al. (1986); a value of
D D 1:5 ð 10 9 m2 =s at 30ºC for NaClO3 has been
reported by Wang and Hu (1996). The effective ion
radii of hydrated Cl and hydrated ClO3 at room
P–T conditions are comparable (3.3 Å and 2.5–3.4
Å, respectively; Meyer, 1928). The molar volumes
are 2:7 ð 10 5 m3 =mole and 4:3 ð 10 5 m3 =mole for
NaCl and NaClO3 , respectively.
Mechanically, the two salts are remarkably different. NaClO3 is brittle at room P–T conditions,
whereas NaCl behaves plastically. The Vickers hardness of NaClO3 on (100) is 117 kg=mm2 , vs. 17
kg=mm2 on (100) of NaCl (von Engelhardt and
Haussühl, 1965; Haussühl, 1983). Not much is
known about the mechanical behaviour of NaClO3
(S. Haussühl, pers. commun., 1997). We have tested
whether NaClO3 could be deformed plastically at
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room P–T conditions. Solution-grown NaClO3 crystals, ¾6 ð 3 ð 3 mm, were axially loaded parallel to
h100i. Samples could not be deformed plastically at
axial stresses of up to 21 MPa. The sample length
was measured during and after loading. No permanent strain could be measured. The resolution of our
measurements was 0.05% strain. At stresses higher
than 15 MPa, small brittle fractures developed at
asperities, near irregularities, and near fluid inclusions that were present in the crystals. At stresses
higher than 21 MPa, samples failed by fracturing.
No optical strain features could be observed around
the fractures. Note, that NaCl crystals loaded at 21
MPa at room P–T conditions instantaneously shorten
permanently by 8–10% (Davidge and Pratt, 1964).
2.2. Experimental procedures
The experimental set up used in the present study
(Fig. 1) was originally designed by C.J. Spiers from
Utrecht University. It is a very simple set up, that al-
Fig. 1. Schematic drawing of the experimental set-up used for wet compaction of NaClO3 and NaCl aggregates. In some experiments
(marked ‘A’ in Table 1) the position of the upper piston and weight was monitored with a linear variable differential transformer (LVDT)
instead of with a dial gauge as depicted in this figure.
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lows easy testing of PS compaction in small samples
of fine-grained soluble salts. De Meer (1995) and De
Meer and Spiers (1997) used this set-up for studying
PS of gypsum aggregates; our set-up and experimental procedure was essentially identical. Aggregates
were uniaxially compacted at constant load in a
capillary glass tube (1.2 mm inner diameter, 6 mm
outer diameter, ¾40 mm long). Steel pistons (1.2
mm diameter) were loaded with dead weights. Aggregate samples are typically ¾30 mm long before
compaction.
The granular aggregates were prepared by sieving
NaClO3 (sodium chlorate pure from Merck, product
number 1.06420) into different grain size fractions
of 75–90 µm, 150–180 µm, 180–212 µm, and
250–500 µm. The grains were used as-received. No
special care was taken to remove very fine particles
adhering on the surface of the grains, to remove
asperities and=or mechanical damage at the grain
surface, or surfacial water present. A typical NaClO3
grain is depicted in Fig. 2. A total of 24 tests were
carried out.
The samples were first compacted dry, at loads
corresponding to calculated nominal stresses (load
divided by tube diameter) of either 5:0 š 0:1 MPa or
4:5 š 0:1 MPa. After 10–30 min of dry compaction,
the load was adjusted for the required (nominal)
stress during wet compaction (2.4, 4.5 or 5:0 š 0:1
MPa). Immediately thereafter, saturated NaClO3 solution was added via the inlet from above, and drawn
through the aggregate by sucking at the solution outlet tube below. The solution entered easily between
the upper piston and the glass tube wall and could
be seen percolating through the sample in seconds.
As soon as the aggregate was filled with solution,
the outlet was closed by a clamp on the outlet tube.
Silicon grease was put onto the solution in the upper
inlet, so that the solution could not evaporate.
In most experiments, displacement of the piston was measured with a dial gauge at different
time intervals (using a stopwatch). In some experiments, displacement of the piston was automatically
registered using a linear variable differential transformer (type ST400 from Solartron metrology with
a Schlumberger OD4 transducer conditioner) and a
computer logging system (LabView version 4.0 from
National Instruments running on a Macintosh PPC
7600). Manually and computer-logged time versus
Fig. 2. Typical example of an NaClO3 grain (¾0.3 mm in diameter) photographed in situ in a relatively loose unloaded aggregate of
NaClO3 . The grains were held in a see-through mini-vessel with a saturated NaClO3 solution present in the pore space.
B. den Brok et al. / Tectonophysics 307 (1999) 297–312
displacement data were processed using commercially available data analysis and graphic presentation software from Abelbeck Software (KaleidaGraph version 2.1.3 for Macintosh). Displacement
values for wet compaction were converted to uniaxial
compaction strains. Uniaxial compaction strain rates
were determined by calculating (with KaleidaGraph)
the time derivative of a smooth curve fitted (also with
KaleidaGraph) to the time versus strain curve (see
for example Fig. 3).
301
Typical tests lasted from one to several days.
Finite uniaxial compaction strains fell in the range
10–27%. Experiments were carried out by varying
the load (i.e., stress) and the grain size independently
(Table 1). The dependence on stress and grain size
could in this way be systematically determined.
The standard relative error in bulk (or average)
linear compaction strains and strain rates was less
than 1%. Due to friction between the sample and the
wall of the glass capillary, strains and strain rates
Fig. 3. Graphs illustrating how compaction data are represented in this paper. (a) Time versus linear compaction strain data points. For
PSM29, data points were obtained by measuring the piston displacement with a dial gauge and manually reading the position at irregular
time intervals. Circles represent the actual measurements. The black line is a smooth curve through the measurements. For PSM50, data
points were obtained by automatic monitoring the piston position using an LVDT and computer logging system. The curve consists of
several thousand measurements that could not be resolved in this graph. (b) Example of the time versus linear compaction strain curves
represented in this paper as smooth curves through the actually measured data. (c) 10-base logarithmic strain versus 10-base logarithmic
strain rate data calculated using data represented in the time versus strain graphs. (d) Representation of the data as best-fit curves through
the data points.
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B. den Brok et al. / Tectonophysics 307 (1999) 297–312
were higher near the upper, and lower near the lower
piston. This appeared to be the major disadvantage
of the experimental set-up and long samples used.
The average stress may be up to 20–30% lower than
the calculated stress 1
NaClO3 aggregates were also compacted dry, and
with ethyl acetate, a liquid in which NaClO3 cannot
dissolve. This was done to test whether crystal plastic
deformation, microfracturing and=or grain boundary
sliding under dry conditions and in the presence
of a non-solvent would contribute to strain. For
comparison, some experiments were also carried out
on NaCl (analytical grade sodium chloride from
Merck, product number 1.06404).
3. Mechanical results
NaClO3 aggregates loaded dry, compacted instantaneously (in seconds) by 1–2%, as soon as the load
was applied. No further measurable compaction occurred thereafter. Aggregates loaded with ethyl ac1
An experiment was carried out to test the role of friction
between the aggregate and the glass-tube wall in the experiments.
To this end we compacted in-line two initially ¾1-cm-long
aggregates separated by an ¾1-cm-long spacer. There appeared
to be a measurable effect of friction. On average, the linear
compaction strain rate in the lower aggregate was roughly 0.5
times the strain rate in the upper aggregate. Assuming a linear to
quadratic dependence of stress on strain rate, the average stress
must have been 0.5 to 0.7 times lower in the lower aggregate
than in the upper aggregate. This means that on average the
friction is about 20–30% of the applied stress in a typical
experiment assuming a linear increase of friction with sample
length. The applied stress of 2.4 MPa may thus effectively fall in
the range of 1.7–2.4 MPa and the stress of 5.0 MPa in the range
of 3.5–5.9 MPa on average. This means that in log-stress versus
log-strain rate space, lines are expected to shift, but not change
slope as friction should depend linearly on the stress. We do
not expect NaCl to behave significantly different from NaClO3
as far as frictional behaviour under wet conditions against an
ideally flat glass wall is concerned, but if there would be a
difference then we would expect the friction of NaClO3 to be
higher because of its higher strength. So, if there is a difference
in frictional behaviour between the two materials, then NaClO3
aggregates should have experienced a somewhat lower effective
applied stress than NaCl. The expected size of this effect should
not significantly affect the conclusions made in this paper. Note
that in experiments reported by Spiers and co-workers, shorter
samples were used and measurements showed friction to be
negligible (De Meer and Spiers, 1997).
etate, in which NaClO3 is insoluble (e.g., Meyer,
1928) behaved the same. No measurable, time-dependent compaction took place after initial instantaneous,
time-independent compaction by 1–2% for ¾1 day.
Aggregates loaded wet started to compact immediately after addition of the saturated solution.
Compaction creep then decelerated with increasing
volumetric strain (Fig. 4). Finite linear compaction
strains of up to 27% were reached within one to
several days at compaction strain rates decreasing
with time down to 10 6 to 10 7 =s. Wet compaction
appeared to be promoted by increasing stress and by
decreasing grain size (Figs. 4 and 5). The mechanical
data were smoothed and then fitted to a power law
relationship of the form:
"P ¾ "
Þ
¦ nd
m
where is "P the uniaxial compaction strain rate, "
the uniaxial compaction strain, ¦ the uniaxial compaction stress and d the average grain size. Such
a power law accurately describes PS behaviour of
NaCl (e.g., Spiers and Schutjens, 1990; Spiers et al.,
1990; Spiers and Brzesowsky, 1993). The NaClO3
compaction strain rate as a function of compaction
strain under wet conditions can be viewed as roughly
inversed proportional to the compaction strain raised
to the power 2 to 4, proportional to the stress raised
to the power 1 to 2 (the average stress exponent n
is 1:6 š 0:1; the standard deviation is 0.5) and inversed proportional to the grain size to the power ¾3
(the average grain size exponent m is 2:8 š 0:2; the
standard deviation is 0.5) (Figs. 5 and 6).
4. Microstructures
Since it is difficult (but not impossible; see De
Meer and Spiers, 1997) to make thin sections from
the small NaClO3 aggregates compacted in the set-up
used, two experiments (CM3 and CM4, with a grain
size of 180–212 µm) were carried out in a wider,
Vanadium-2a steel vessel (5 mm inner diameter).
Samples were compacted under otherwise identical
conditions. They were first compacted dry at 5.0
MPa nominal stress for 30 min, then saturated solution was added, the stress being held at 5.0 MPa
during the rest of the experiment. Displacement was
monitored using an LVDT and automated logging
B. den Brok et al. / Tectonophysics 307 (1999) 297–312
303
Table 1
Complete set of experiments reported
Material tested
Test=sample number
Grain size
(µm)
Stress ‘dry’
(MPa)
Stress ‘wet’
(MPa)
NaClO3
PSM18
PSM32
PSM50
PSM53
M
M
A
A
75–90
75–90
75–90
75–90
5:0 š 0:1
5.0
4.5
4.5
2:4 š 0:1
2.4
4:5 š 0:1
4.5
NaClO3
PSM27
PSM29
PSM51
PSM52
M
M
A
A
150–180
150–180
150–180
150–180
5:0 š 0:1
5.0
4.5
4.5
2:4 š 0:1
2.4
4:5 š 0:1
4.5
NaClO3
PSM28
PSM30
PSM31
PSM13
PSM16
CM3
CM4
M
M
M
M
M
A
A
180–212
180–212
180–212
180–212
180–212
180–212
180–212
5:0 š 0:1
5.0
5.0
5.0
5.0
5.0
5.0
2:4 š 0:1
2.4
2.4
4:5 š 0:1
4.5
5.0
5.0
NaClO3
PSM17
PSM14
PSM15
M
M
M
250–500
250–500
250–500
5:0 š 0:1
5.0
5.0
2:4 š 0:1
5:0 š 0:1
5.0
NaCl
PSM21
PSM24
PSM57
M
M
A
180–212
180–212
180–212
5:0 š 0:1
5.0
1:0 š 0:1
5:0 š 0:1
2:4 š 0:1
1:0 š 0:1
PSM22
PSM23
PSM25
M
M
M
150–180
150–180
150–180
5:0 š 0:1
5.0
5.0
2:4 š 0:1
2.4
2.4
Experimental conditions: M D manual logging of piston position. A D automatic, computer-aided logging of piston position. Stresses are
nominal, calculated stresses. Stress ‘dry’ D stress during initial ‘dry’ compaction stage. Stress ‘wet’ D stress during and after addition of
saturated solution. All tests were carried out at room temperature (21–23ºC).
system (as described above). Tests were terminated
by reducing the stress to zero, after which the sample
was flushed with ethyl acetate to remove the saturated solution from the pores. The sample was then
slid out of the vessel and immediately impregnated
with Araldite resin at room temperature under vacuum. Sudan blue dye was added to give the resin
a blue colour. Samples were subsequently cut dry
with a wire saw, and polished with corundum polishing powder as well as with polishing paper, using
ethyl acetate for lubrification and as a cooling agent.
Samples were glued on glass sections using Loctite
UV activated glue. Reasonable quality thin sections
could be made in this manner (Figs. 7–9).
Samples CM3 and CM4 were compacted to uniaxial compaction strains of 0.27 and 0.30, respectively. The strain was not homogeneously distributed
over the samples. The aggregates were more dense
in the upper than in the lower parts, presumably due
to friction between the vessel and the sample. In this
way, however, structures formed at a different stage
of compaction could be studied in one thin section.
The microstructures show unequivocal evidence
for compaction by an indentation mechanism. Almost all the grains show truncated contacts (Figs. 7
and 8). Grain-to-grain contacts are tight, i.e., no evidence for contact undercutting was observed. Where
observation of grain boundary surfaces is possible,
contacts show worm- and tube-shaped fluid inclusion
patterns (Fig. 9). Evidence for newly precipitated
NaClO3 is also present. Many grains have an overall
sub-euhedral shape, and show clear euhedral overgrowth structures (Fig. 9). Grain boundaries in more
intensely compacted areas are remarkably straight
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B. den Brok et al. / Tectonophysics 307 (1999) 297–312
Fig. 4. Time versus linear compaction strain curves obtained in wet compaction experiments on NaClO3 aggregates. (a–d) Graphs
illustrating the effect of varying the nominal compaction stress on linear compaction strain rate for different grain size fractions tested. In
each graph curves are shown for stresses of 2:4 š 0:1 and 5:0 š 0:1 MPa (or 2:4 š 0:1 and 4:5 š 0:1 MPa). (e, f) Graphs showing the
effect of varying the grain size.
B. den Brok et al. / Tectonophysics 307 (1999) 297–312
305
Fig. 5. 10-base logarithmic strain rate versus 10-base logarithmic strain curves calculated for NaClO3 compaction curves represented in
Fig. 4. (a–d) Graphs illustrating the effect of varying the nominal compaction stress on linear compaction strain rate for different grain
size fractions tested. In each graph curves are shown for stresses of 2:4 š 0:1 and 5:0 š 0:1 MPa (or 2:4 š 0:1 and 4:5 š 0:1 MPa). Strain
rate is roughly proportional to strain to the power Þ with Þ in the range of 2 to 4. (e, f) The effects of grain size variations.
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B. den Brok et al. / Tectonophysics 307 (1999) 297–312
B. den Brok et al. / Tectonophysics 307 (1999) 297–312
307
Fig. 7. (a, b) Examples of slight indentation by pressure solution in less compacted areas in sample CM3 compacted wet at 5.0 MPa.
(c–e) Examples of more intense indentation in parts of the sample where more compaction has taken place. The grain size is 180–212
µm; the bulk compaction strain 27%. Black specks are polishing powder. The pore space is filled with resin.
compared with the more irregular shape in less compacted areas (Fig. 8). Healed microfractures are very
common (e.g., Fig. 7a), but the overall impression
is that they did not contribute significantly to compaction strain, since no displacement was seen to be
associated with the fractures.
Fig. 6. (a–d) 10-base logarithmic stress versus 10-base logarithmic strain rate plots for the NaClO3 compaction experiments represented
in Figs. 4 and 5. Stress versus strain rate values were determined for average curves for each stress and grain size fraction, at the different
linear compaction strain values (ε) indicated in the graphs. Strain rate is roughly proportional to stress to the power n with n in the range
1 to 2. (e, f) 10-base logarithmic grain size versus 10-base logarithmic strain rate for a nominal compaction stress of 2:4 š 0:1 MPa, and
4.5 and 5:0 š 0:1 MPa, respectively. Grain size versus strain rate values were determined for average curves for each stress and grain size
fraction, at the different linear compaction strain values (ε) indicated in the graphs. Strain rate is roughly proportional to grain size to the
power m with m in the range of 2 to 3.
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B. den Brok et al. / Tectonophysics 307 (1999) 297–312
Fig. 8. (a, b) Very intense indentation and grain boundary straightening by pressure solution showing presence of 120º ‘equilibrium’
grain boundary triple junctions in sample CM3 (grain size 180–212 µm; bulk compaction strain 27%; wet compaction stress 5 MPa).
Black specks are polishing powder. Pores are filled with resin.
5. Discussion
5.1. NaClO3 compaction mechanism
The experiments demonstrate that wet compaction of NaClO3 aggregates under room P–T
conditions occurs by a water-assisted, time-dependent (i.e., creep) mechanism. No creep was observed
in the dry experiments, nor in experiments with
ethyl acetate as a pore fluid. Time-dependent compaction only occurred immediately after addition
of saturated solution. The deformation microstructures show clear evidence for compaction by a grain
indentation=truncation mechanism. Microfracturing
was relatively unimportant. Brittle processes and
intergranular sliding may have contributed to compaction, but cannot explain the truncation structures.
Most of the compaction and notably its rate therefore must have taken place by a PS mechanism.
The deformation microstructures show no evidence
for grain-to-grain contact undercutting. So it seems
most likely, that grain boundary diffusional type PS
(Spiers et al., 1990; Spiers and Brzesowsky, 1993)
did occur. This is consistent with the elastic–brittle
nature of NaClO3 .
The mechanical data (Þ-, n- and m-values) are
consistent with grain boundary diffusional PS models as published in the literature (e.g., Rutter, 1983;
Spiers and Schutjens, 1990; Spiers et al., 1990;
Spiers and Brzesowsky, 1993). The relatively high
m-value suggests that the PS compaction rate is
controlled by grain boundary diffusion (e.g., Spiers
and Schutjens, 1990). Calculations show that as for
NaCl, the dissolution=precipitation rates of NaClO3
are too high to be the rate-controlling factor of PS.
5.2. Comparison with experiments on NaCl
The mechanical results obtained for NaCl during this study are presented in Fig. 10. There is
good agreement with the data reported by Schutjens (1991) (Fig. 10a) and by Spiers and Schutjens
(1990) despite differences in experimental procedures. These authors compacted aggregates in rubber
B. den Brok et al. / Tectonophysics 307 (1999) 297–312
309
Fig. 9. Typical structure of a grain boundary in experiment CM3 (27% finite strain) showing irregular distribution of worm-like fluid
inclusion arrays. Note the euhedral shape of the overgrowth at the left side of the grain. The grain size is approximately 50 µm.
baloons in an oil medium pressure vessel. Friction,
unlike in our experiments, did not play a role. In addition, Schutjens (1991) loaded samples dry at a rate
of about 0.1 MPa=min, from 0.1 to 2.15 MPa (i.e.,
in about 20 min), whereas we loaded our samples
instantaneously (in seconds) from 0.1 to 5:0 š 0:1
MPa. Apparently, loading history does not play a
very important role during PS in NaCl. There is also
good agreement between our mechanical results on
NaCl and those of Spiers et al. (1990; e.g., Fig. 7a)
obtained in uniaxial compaction experiments.
Comparison of our results and those of Spiers
and co-workers, on NaCl, with the NaClO3 data
(Fig. 10b–d) shows that the mechanical compaction
behaviour of both materials is remarkably similar.
The most important similarities are the following. (1)
Similarity of Þ-values (Fig. 10b–d). Spiers and coworkers found Þ-values for NaCl in the range of 2
to 5, compared with our Þ in the range of 2 to 4 for
NaClO3 . (2) Compaction strain rates as a function of
strain are about half an order of magnitude slower
for NaClO3 than for NaCl. (3) Average stress and
grain size exponents for NaCl are n ¾ 1 and m ¾ 3,
respectively (Spiers et al., 1990), and n D 1:2 and
m D 2:8 (Schutjens, 1991) compared with average
values of n D 1:6 š 0:1 (standard deviation 0.5) and
m D 2:6 š 0:2 (standard deviation 0.5) for NaClO3
determined here. The similarity in mechanical com-
paction behaviour suggests that the PS compaction
mechanism for both materials is the same, i.e., a diffusion-controlled PS mechanism at room P–T conditions (Spiers and Schutjens, 1990; Spiers et al., 1990;
Schutjens, 1991; Spiers and Brzesowsky, 1993).
Following existing PS compaction laws (e.g.,
Spiers and Schutjens, 1990; Spiers et al., 1990;
Spiers and Brzesowsky, 1993), NaClO3 should compact about three times faster than NaCl, because its
solubility is almost two times and its molar volume one and a half times higher than that of NaCl.
We found, however, that in the present experiments
NaClO3 deformed about half an order of magnitude
slower than NaCl. The reason for this is not understood. Possible explanations are: (i) existing flow
laws are not adequate for PS of NaClO3 , (ii) the
grain boundary structure (like the thickness) is different for the two materials leading to a difference in
the effective grain boundary diffusivity.
5.3. Role of plasticity during PS of NaCl
The close agreement in behaviour of NaCl and
NaClO3 suggests that the plasticity of NaCl does not
play a key role in making PS possible, such as might
be concluded from experimental results of Hickman
and Evans (1991). This idea is supported by the
following observations.
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B. den Brok et al. / Tectonophysics 307 (1999) 297–312
Fig. 10. (a) 10-base logarithmic strain versus 10-base logarithmic strain rate graphs for wet compaction experiments on NaCl and
NaClO3 . (a) Comparison of results obtained on NaCl in the present study (black lines; PSM21, 24 and 57) with results on NaCl from
Schutjens (1991) (grey lines; E1 and H1). Grain size was 180–212 µm; temperature 21–23ºC. Wet compaction stresses as well as dry
compaction stresses (between brackets) are indicated for each test. Note the good agreement between the different results. For further
explanation see text. (b–d) Comparison of present results obtained on NaCl (grey lines) and NaClO3 (black lines) for different applied
compaction stresses and grain size fractions. NaCl appears to consistently compact about half an order of magnitude faster than NaClO3 .
(1) NaClO3 cannot be deformed plastically at room
P–T conditions, and intracrystalline hydrolytic weakening of NaClO3 cannot have taken place. ‘Weakening’ occurred instantaneously, as soon as a solution
was added and water had no time to diffuse into the
grains (see also De Meer and Spiers, 1997).
(2) During plastic deformation of NaCl single
crystals, strain hardening occurs (e.g., Davidge and
Pratt, 1964). All of the crystal plastic deformation
should therefore take place during the initial stages
of a compaction experiment of the type such as
carried out in this study and of Spiers and co-workers. During on-going wet compaction, grain-to-grain
contact stresses steadily decrease, and, at the lower
stresses, the deformed material should not deform
plastically any more. This means, that after initially
loading the aggregate dry at e.g. 5 MPa, there should
be no difference in compaction rate between further
wet compaction at different stresses lower than 5
MPa. No extra crystal plastic strain will be induced.
B. den Brok et al. / Tectonophysics 307 (1999) 297–312
Yet, our experiments show, that samples loaded dry
at 5 MPa and then wet at 2.4 MPa deform much
slower in the wet state than samples loaded dry
and then wet at 5 MPa (Fig. 10), even though the
amount of crystal plastic deformation should be the
same in both. The same effect is found in all other
compaction experiments on NaCl (e.g., Spiers and
Schutjens, 1990). All differences in strain rate must
therefore be due to differences in stress.
(3) Results of stress stepping experiments on
NaCl: lowering the stress during a compaction experiment should have no effect on the strain rate if
plasticity plays an important role. No extra plastic
strain is produced nor plastic strain recovered. Yet,
results of Schutjens (1991) and Spiers and Brzesowsky (1993) show, that stress stepping to lower
stresses results in lower strain rates, compatible with
conventional grain boundary diffusional PS laws.
This means that the stress and not the plastic strain
controls the strain rate. We did a single stress stepping experiment on NaCl (PSM57, 180–212 µm,
see Table 1) in which we increased the stress during
compaction. At a bulk compaction strain of 16% the
stress was increased from 1:0 š 0:1 to 4:5 š 0:1 MPa.
No instantaneous compaction took place, indicating that the grain-to-grain contact stresses remained
below values reached during the initial compaction
stage. Yet, the strain rate increased by roughly half
an order of magnitude, consistent with the idea that
stress and not plastic strain controls the PS compaction rate.
(4) A significant contribution of plastic deformation creep to PS compaction creep in NaCl may also
be ruled out by the low stress exponent (e.g. experiments by Spiers and co-workers). For deformation
by dislocation glide of cubic NaCl single crystals
at room P–T conditions, the stress exponent n falls
within the range of 10 to 12 (Wanten et al., 1996).
6. Conclusion
At room temperature and pressure, stresses of 2.4
and 5 MPa, and grain sizes in the range of 75–
500 µm, NaClO3 aggregates compact by a diffusioncontrolled PS mechanism, like NaCl. The NaClO3
compaction rate is about half an order of magnitude lower than that of NaCl (at similar conditions).
311
Since NaClO3 cannot be deformed by crystal plastic
mechanisms at room temperature and pressure, the
similarity in PS compaction behaviour observed in
these two materials means that crystal plastic deformation does not play a key role in making PS
of NaCl possible. Hence, the plastic nature of NaCl
does not seem to be a serious drawback for using this
material as an analogue for silicate rocks. Moreover,
existing data on PS in NaCl are inferred to offer a
description of the PS rheology which is not significantly influenced by any plastic deformation effects
or driving forces.
Acknowledgements
This research was supported by the Volkswagen
Stiftung and the Deutsche Forschungsgemeinschaft.
The comments and advice of Chris Spiers and Terry
Engelder contributed significantly to the final version
of this paper.
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