Post on 08-May-2018
Experimental study of polycrystal growth from an advectingsupersaturated fluid in a model fracture
S. NOLLET, C. HILGERS AND J. L. URAI
Geologie-Endogene Dynamik, RWTH Aachen, Aachen, Germany
ABSTRACT
We present real-time observations of polycrystal growth experiments in transmitted light in an accurately con-
trolled flow system with the analogue material alum [KAl(SO4)2Æ12H2O]. The aim of the experiments is to obtain
a better insight into the evolution of vein microstructures. A first series of experiments shows the evolution of a
polycrystal at supersaturations between 0.095 and 0.263. The average growth rate of the crystals is influenced
by growth competition and the depletion of the solute along fracture length. Growth competition is controlled by
crystallographic orientation, crystal size and crystal location. In addition, the growth rate of an individual crystal
facet also shows variations depending on the facet index, facet size and flow velocity. These variations can influ-
ence the morphology of the grain boundaries and the microstructures. The aim of the second series of experi-
ments is to investigate the growth evolution of rough/dissolved facets in detail. The growth distance required for
the development of facets is around 15 lm. In all the experiments, we observe that the measured growth rates
have a much larger range than predicted by alum single-crystal growth kinetics. This is due to the combined
effect of the facet index and the crystal size. Furthermore, at high supersaturations, the facet growth rate meas-
urements do not fit the same growth rate equation as for the experiments at lower supersaturations (<0.176).
This can be explained by a change in the growth mechanism at high supersaturations with more influence of
volume diffusion, relative to advection of the bulk solution on the growth rate. This effect can also cause a more
homogeneous sealing pattern over fracture length. At high supersaturations, the larger crystals in these experi-
ments incorporate regularly spaced fluid inclusion bands and we propose that these can be used as an indicator
for high palaeo-supersaturation. The final microstructures of the experiments show no asymmetry with respect to
the flow direction.
Key words: advection, crystal growth, supersaturation, veins
Received 8 August 2005; accepted 30 January 2006
Corresponding author: Sofie Nollet, Geologie-Endogene Dynamik, RWTH Aachen, Lochnerstrasse 4-20, D-52056
Aachen, Germany.
Email: s.nollet@ged.rwth-aachen.de. Tel: +49 241 80 95416. Fax: +49 241 80 92358.
Geofluids (2006) 6, 185–200
INTRODUCTION
Dissolved material is transported through rocks by diffusive
or advective mass transfer. Diffusive transport of material
takes place in a stationary fluid, driven by a gradient in
chemical potential (Durney & Ramsay 1973; Fisher &
Brantley 1992). It is a slow process, acting on small-length
scales (cm-scale) and resulting in a rock-buffered chemistry
(Fisher & Brantley 1992; Elburg et al. 2002). In contrast,
advective transport is driven by a hydraulic gradient, can
transport material over large distances, and may induce a
geochemical disequilibrium between the fluid and the host
rock (McManus & Hanor 1993; Sarkar et al. 1995;
Verhaert et al. 2004).
Fluid flow through permeable rocks is described by
Darcy’s law. In fractures, the flow can be described by the
cubic law (Wood & Hewett 1982; Jamtveit & Yardley
1997; Bjørlykke 1999; Taylor et al. 1999):
Q ¼ �a3�g
12�
dh
dL
� �w;
where Q is the volumetric flow rate, a the aperture, q the
density of the fluid, g the acceleration due to gravity, l the
Geofluids (2006) 6, 185–200 doi: 10.1111/j.1468-8123.2006.00142.x
� 2006 Blackwell Publishing Ltd
dynamic viscosity, dh/dL the hydraulic gradient and w the
width.
Fracture networks result in focused fluid flow with fluid
velocities in fractured geological media up to 10)2 m s)1
(Dijk & Berkowitz 1998; Cox 1999; Oliver 2001). Fluid
flow in the upper crust is often episodic and influenced by
fault movements (seismic pumping model and fault-valve
mechanism), resulting in transiently even higher fluid velo-
cities, immediately after seismogenic slip events (Sibson
et al. 1975; Sibson 1990; Jamtveit & Yardley 1997).
Precipitation of material takes place when the fluids
become supersaturated. The resulting veins preserve valu-
able information on the origin of the fluids, the deforma-
tion history and palaeo-overpressures of fluids in the rocks
(Ramsay & Huber 1983; Capuano 1993; Nollet et al.
2005a). When a fluid is flowing through a fracture, there
is an interplay between advection, diffusion and reaction
kinetics (Dijk & Berkowitz 1998). The relative importance
of these processes is expressed by the dimensionless Peclet
number, defined as Pe¼vflowy/Dm, where vflow is the flow
velocity, y the fracture aperture and Dm the molecular dif-
fusion coefficient, and the Damkohler number, defined as
Da¼ky2/Dm, where k is the first-order kinetic reaction rate
coefficient. The Peclet number describes the relative
importance of advection and diffusion, whereas the Dam-
kohler number describes the relative importance of diffu-
sion and reaction kinetics (Lasaga 1998, p. 267). The rate
of precipitation of minerals can be expressed in terms of
supersaturation and the flow velocity (Garside & Mullin
1968; Garside et al. 1975; Rimstidt & Barnes 1980). The
supersaturation ratio S is defined by the ratio between the
solution concentration c and the equilibrium concentration
c* or S ¼ c/c*. The relative supersaturation is defined as
r ¼ S)1.
Calcite precipitation by advective flow was experiment-
ally simulated at room temperature by Lee et al. (1996).
They calculated that an extremely large amount of fluid is
required to precipitate calcite veins in nature (Lee & Morse
1999). Dissolution and precipitation experiments with HCl
and H2SO4 solutions flowing in fractured carbonate rocks
result in calcite dissolution and gypsum precipitation (Sin-
gurindy & Berkowitz 2005). In these experiments, the
overall hydraulic conductivity was measured and it shows
oscillatory behaviour, which is explained by the fluctuating
dominance of precipitation or dissolution (Singurindy &
Berkowitz 2003, 2005).
Hilgers & Urai (2002a) described crystal growth experi-
ments in a transparent see-through cell. They used alum as
an analogue material which allows a microstructural analy-
sis of the growing crystals, in contrast to the experiments
by Lee et al. (1996). A growth rate decrease along the
fracture length is observed when the flow velocity is suffi-
ciently small. This is caused by a depletion of the solution’s
concentration in the flow direction. A numerical model
based on alum growth kinetics confirmed these results and
was applied to quartz. This model predicted that the char-
acteristic length at which the effects of depletion of the
solution’s concentration are manifested is around 1 km
and will not be visible in an outcrop (Hilgers et al. 2004).
It is not clear how a typical microstructure resulting from
advective flow transport at low flow velocities is recognized
and how it differs from a microstructure resulting from dif-
fusional transport, although geochemical arguments, such
as stable isotope chemistry can provide clear evidence (Su-
checki & Land 1983; Verhaert et al. 2004).
Crystal growth in crack-seal veins was numerically simu-
lated based on a kinematic model (Urai et al. 1991; Bons
2001; Hilgers et al. 2001; Nollet et al. 2005b). An open
question with respect to these simulations and the under-
standing of the crack-seal mechanism is how crystal facets
develop on a dissolved or a fractured crystal surface. Until
now, it is unclear how much space is required for crystals
to develop crystal facets (Urai et al. 1991; Nollet et al.
2005b). This aspect is interesting with respect to the evo-
lution of crystals after a crack increment in the crack-seal
model.
In this paper, we present new see-through experiments
with alum in an improved experimental set-up. We investi-
gate the temporal evolution of the microstructures and the
crystal growth rate on a polycrystal scale and on a single-
crystal scale and we analyse the effect of different boundary
conditions, such as flow velocity, supersaturation, flow
direction and facet index on the crystal growth rate.
METHODS AND EXPERIMENTAL SET-UP
Flow and pressure system
The experimental set-up is a modified version of the one
described in Hilgers & Urai (2002a) and Hilgers et al.
(2004). It is a single-path flow unit where a saturated fluid
flows from a reservoir into a transparent reaction cell in
which the temperature is a few degrees lower than in the
reservoir and the fluid thus becomes supersaturated
(Fig. 1A,B). Fluid flow into the reaction cell is driven by a
High Performance Liquid Chromatography (HPLC) pump
at a flow rate of 0.01 ± 0.000019 ml min)1. This flow rate
results in flow velocities in the cell of approximately
0.1 mm s)1, corresponding to flow velocities in natural
fractures. Before running an experiment, we prepared an
equilibrium solution in the reservoir at a temperature of
39 ± 0.05�C, by continuously stirring the solution and
alum crystals over 2–3 days.
A nonmiscible, clean paraffin oil is pumped by the
HPLC pump into the upper part of the reservoir and this
displacement by the oil drives flow of the saturated solu-
tion out of the reservoir into the reaction cell, without
diluting the saturated solution (Fig. 1A). In the fluid reser-
186 S. NOLLET et al.
� 2006 Blackwell Publishing Ltd, Geofluids, 6, 185–200
voir, a small air bubble is present which is used as pressure
indicator. The outflow volume of the fluid at the end of
the reaction cell is measured continuously by a burette
during an experiment. Pressure pulses in the pump have
no significant influence on the flow through the cell.
The reaction cell consists of an upper and a lower glass
plate and two metal plates in between acting as spacers
between the two glass plates (Fig. 1C,D). The metal
plates have a thickness of 0.5 mm and one of them has a
10-mm-long groove where the seed crystals are located
(Fig. 1D). With an average aperture of 1.5 mm and taking
k ¼ 0.008 s)1 and Dm ¼ 5 · 10)10 m2 s)1, the Peclet and
Damkohler numbers are approximately 680 and 36
respectively. This indicates that the dominant transport and
crystal growth mechanisms are advection and reaction kin-
etics respectively.
Pressure is controlled by two pressure valves. The first
valve is located between the pump and the fluid reservoir,
whereas the second valve is located at the end of the sys-
tem and causes a back-pressure (Fig. 2). This system results
in a maximum pressure difference of 0.2 MPa between the
two valves. The first pressure valve (P1 in Fig. 2) prevents
damage to the cell once the fracture is sealed. Shortly
before sealing of the fracture, the pressure rises at the inlet
of the reaction cell and the air bubble in the fluid reservoir
is compressed, until the pressure limit of 0.4 MPa in P1 is
reached (Fig. 2). Based on the cubic law, the aperture of
the fracture is then around 1 lm, which is no longer
observable in the experiment. The back-pressure in P2
minimizes air bubbles in the system.
Temperature
Temperature is controlled by a master–slave Eurotherm
controller system combined with four Pt100 temperature
sensors located at: (i) the reservoir, (ii) the reaction cell,
A
B
C D
Fig. 1. Overview of the experimental set-up. (A) Schematic overview with all components. P1 and P2 indicate the pressure set by the pressure valves. T1, T2,
T3 and T4 indicate the location of the temperature sensors. Details of the reaction cell are given in (C) and (D). (B) Temperature profile in the different com-
ponents of the set-up. The temperature is set 5� higher in the tubes to avoid nucleation. Variations of the temperature difference between the reservoir and
the reaction cell allows different values for the supersaturation. (C) Cross-section view of the reaction cell. (D) Top view of the reaction cell.
Polycrystal growth from an advecting supersaturated fluid 187
� 2006 Blackwell Publishing Ltd, Geofluids, 6, 185–200
(iii) the connecting tube between the reservoir and the
reaction cell and (iv) the connecting tube between the
reaction cell and the outflow reservoir (Fig. 1A). In the
tubes, the temperature is set up to 5�C higher than in the
reservoir to avoid nucleation. The temperature was meas-
ured with a high-precision thermometer (PREMA 3040
box), which has both a Pt100 temperature sensor and a K-
type thermocouple. The Pt100 temperature sensor was cal-
ibrated by the manufacturer to a precision of 0.03�C and
is used as reference thermometer. The ultra-thin K-type
thermocouple (0.25 mm diameter and 0.05�C precision) is
calibrated against the reference thermometer in an isother-
mal block and is used to measure the temperature inside
the reaction cell and the fluid reservoir in dummy flow
experiments (Fig. 3A). In these calibrations, the tempera-
ture in the reaction cell was measured at three different
positions (in, mid and end in Fig. 1D) at flow rate of
0.01 ml min)1 to characterize the temperature profile
across the reaction cell. Figure 3B shows the measured
temperature profile at four different set-points and verifies
that the higher temperature in the inlet tubing has no
influence on the temperature at the in section of the frac-
ture at a flow rate of 0.01 ml min)1. In the middle of the
reaction cell, the temperature can be 0.2�C lower than
at the outer parts, with only a minor influence (0.006) on
supersaturation. The temperature difference at the three
different positions is due to the heating system of the cell,
which allows more heating at the outer parts of the cell
and cooling of the glass by air in the middle part. A valid-
ation of the calibration was carried out by an experiment
with settings corresponding to zero supersaturation, con-
firming that no growth or dissolution takes place.
Fig. 2. Pressure and flow rate evolution over time at different positions in
the experimental set-up at the start of an experiment, shortly before seal-
ing, when the limit pressure in the first pressure valve is reached (with aper-
ture of 1 lm according to the cubic law) and when the crystals have sealed
the open space and further flow through the cell is impossible. (P ¼ pres-
sure, Q ¼ flow rate, Q1 ¼ flow rate at the pump, Q2 ¼ flow rate at the
end of the system, P1 ¼ pressure at the first pressure valve, P2 ¼ pressure
at the back-pressure valve at the end of the system).
Fig. 3. Temperature calibration in the reaction cell. (A) Measured tempera-
ture in the reaction cell plotted against set-point temperature of the tem-
perature controller. This set-point is the difference between the reservoir
temperature and the reaction-cell temperature. The plotted values are the
average of the three measured positions. (B) Deviation of the measured
temperature in the reaction cell from the average values (over time) plotted
for three different positions: inlet (in), middle (mid) and outlet (end) of the
cell. All temperature measurements are done during fluid flow through the
cell at a flow rate of 0.01 ml min)1. (DT ¼ temperature difference between
reservoir and reaction cell, room temperature ¼ 25�C).
188 S. NOLLET et al.
� 2006 Blackwell Publishing Ltd, Geofluids, 6, 185–200
Material characterization
In the experiments presented here, alum [KAl
(SO4)2Æ12H2O, Roth ‡97.5% quality] is used as the min-
eral analogue. This highly soluble material was chosen
because of its well-known growth kinetics and high growth
rates at temperatures between 30 and 40�C. At room tem-
perature, the crystal structure of potash alum is cubic with
eight {111} facets, but crystals commonly show an octa-
hedral habit with the {111}, {100} and {110} facets as
main habit facets (Bhat et al. 1992) (Fig. 4). When a dis-
solved crystal starts to grow, minor {221}, {112} and
{012} facets grow in the initial growth stages (Klapper
et al. 2002) (Fig. 4A). Because of their higher growth rate,
these are rapidly outgrown. The occurrence of the octa-
hedral crystal habit for the alum used in the experiments
was confirmed in single-crystal growth experiments.
Seed crystals of alum for the reaction cell are prepared
by melting alum powder, after adding approximately 1%
volume of water, and pouring this melt in between the
two metal spacers. This is followed by pressing the melt
quickly into the fracture shape to a thin plate with a
thickness of 0.5 mm. Before we run an experiment, we
flow slightly undersaturated solution through the cell
for 15 min to remove alum nuclei in the set-up and
slightly dissolve the seed crystals. In all experiments
presented here, the same seed crystals were used by
dissolving the grown crystals each time after an experi-
ment.
To calculate the supersaturation in the experiments,
the solubility data for alum in H2O are required. The
solubility of the alum was measured by adding a con-
trolled mass to H2O at a constant temperature until no
more alum could dissolve over a period of 1 day, indica-
ting that saturation of the solution has taken place. The
solution was permanently stirred to achieve equilibrium.
The results are compared with solubilities given in Syno-
wietz & Schafer (1984), Mullin (2001) and Barrett &
Glennon (2002) and correspond very well to these
(Fig. 5). However, the solubility of hydrated alum with
12 molecules of H2O (which we used in the experi-
ments) was only measured directly by Barrett & Glennon
(2002) whereas the other authors measured the dehy-
Fig. 4. Single crystal of alum. (A) Development of cubic alum crystal with
{111} facets, starting from a crystal with high index facets. Relative growth
rates of the crystal facets are {111}: 1.0, {110}: 4.8, {001}: 5.3, {221}: 9.5
and {112} 11.0 (after Klapper et al. 2002). The faster growing facets are
outgrown by the slower growing facets. (B) Single alum crystal in 3D, with
the commonly observed {100}, {110} and {111} facets.
Fig. 5. Solubility of alum in mol/100 g H20 as a function of temperature
according to different authors and measured in this study. The data from
Synowietz & Schafer (1984) and Mullin (2001) are based on measurements
of dehydrated alum whereas the data from Barrett & Glennon (2002) and
in this study are based on hydrated alum with 12 molecules of H2O. The
melting point (90�C) of alum is indicated.
Polycrystal growth from an advecting supersaturated fluid 189
� 2006 Blackwell Publishing Ltd, Geofluids, 6, 185–200
drated type of alum. Therefore, solubilities are calculated
based on an equation derived from the data from Barrett
& Glennon (2002).
According to Garside & Mullin (1968), the overall
growth rate of alum depends on the supersaturation and
the flow velocity; both these parameters are controlled pre-
cisely in this set-up.
Image analysis
During an experiment, the transparent reaction cell is
placed under the microscope, which is connected to a
high resolution digital camera. Images of 748 · 576 pix-
els were grabbed every 2 min over a period of around
20 h. Image analysis of the experiments is done by trac-
ing the grown distance orthogonal to the crystal facet
and tracing the grown area in a specific time interval.
The latter measurements are followed by dividing the
measured area by the crystal surface length. The
grown area for the whole experiment was also divided
into three parts (in, mid and end section) to compare
the average growth rate evolution along the fracture
length.
MICROSTRUCTURAL EVOLUTION OFPOLYCRYSTALS
A series of polycrystal growth experiments at different flow
velocities and supersaturations is carried out (Fig. 6). In all
experiments, the flow rate is constant and is set at
0.01 ml min)1. The initial flow velocity, determined based
on the initial fracture morphology, varies between 0.12
and 0.27 mm s)1 in the individual experiments. The super-
saturation in the different experiments varies between
0.095 and 0.263 (±0.006), depending on the temperature
difference between the fluid reservoir and the reaction cell
(2.5 and 6.3 ± 0.12�C).
All experiments start with a rough, irregular surface com-
posed of dissolved alum seed crystals. Faceted crystals are
well established after about 15 min of growth (Fig. 6A). In
the initial stages of the experiments, numerous seed crystals
grow, whereas at the final stages, fewer crystals grow
(Fig. 6A). Most of this growth competition occurs at the
initial stage of the experiment, when the crystals are small
(e.g. experiment 4 in Fig. 6). Growth competition is the
result of different factors. First of all, the crystallographic
orientation plays an important role. This can be seen in A
Fig. 6. Series of polycrystal growth experiments. Four experiments are run with the same flow rate and different supersaturation. The identical seed crystals
are used in the different experiments. (A) Evolution of the microstructures over time. (B) Growth rate evolution shown by traced grain boundaries in time
intervals of 60 min in experiment 1 and 30 min in experiments 2, 3 and 4. The arrow indicates a facet that changes its orientation during the evolution,
because of the influence of high-index facets which are outgrown in the latest stages. In area A, growth competition because of crystallographic orientation
can be observed. This area is enlarged in Fig. 7. In area B, the influence of crystal location on growth competition can be observed. The crystal which is
located on the ridge outgrows the crystal located in a depression.
190 S. NOLLET et al.
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in Fig. 6A, where crystals initially have the same size. The
only difference between the different crystals is the crystal-
lographic orientation, which is indicated by the orientation
of the developed facets. After 2 h, the central crystal is out-
grown and the growth competition in this example is influ-
enced mainly by the crystallographic orientation (Fig. 7).
Secondly, crystals, which are located on ridges on the
fracture surface, have a better chance to survive, whereas
crystals located in the depressions or at the back with
respect to the flow direction hardly grow, independent of
their orientation (B in Fig. 6A).
The crystals themselves also undergo a microstructural
evolution over time. This is visible in Fig. 6B, where the
evolution of the crystals can be analysed in the traced ima-
ges. In the first stages, the crystals have developed numer-
ous facets, including high-index facets. After 60 min of
growth, it can be seen that some facets are outgrown in
the larger crystals (e.g. the central crystal in the mid sec-
tion in experiments 2 and 3) whereas others are preserved.
We also observe that the direction of a facet can evolve,
indicating that minor high-index facets are not completely
outgrown yet. This is visible in the largest crystal of the in
section in experiment 2, which has at first a stable orienta-
tion after 150 min. The surviving facets are the slower
growing low-index facets ({100}, {110}, {111}) and their
length can show variations during their further evolution.
FACET GROWTH RATE MEASUREMENTS
The growth rate of individual facets in the polycrystal
growth experiments is analysed by measuring the grown
distance, orthogonal to the facet, in a specific time interval.
Because identical crystals grow in the different experiments,
this method allows a comparison of the growth rate of
identical facets under different supersaturation conditions
(Figs 8 and 9). We observed that the growth rate of identi-
cal facets increases with increasing supersaturation, as
expected according to the growth kinetics of alum (Garside
& Mullin 1968).
Variations and trends over time
The growing crystals have not only developed cubic {111}
facets, but also octahedral {100} and {110} facets, which
Fig. 7. Details of area A in Fig. 6, showing the
growth competition caused by crystallographic
orientation in experiment 4 after (A) 60 min, (B)
after 1 h 50 min and (C) after 3 h 40 min.
A
B
C
D
Fig. 8. Final stages of the four experiments, with indication of the meas-
ured facets. (A) Experiment 1 (supersaturation ¼ 0.095), (B) experiment 2
(supersaturation ¼ 0.135), (C) experiment 3 (supersaturation ¼ 0.176) and
(D) experiment 4 (supersaturation ¼ 0.263). Growth sector boundaries and
60 min isochrons are indicated. The growth sector boundaries are mostly
irregular, indicating that growth rate variations occur.
Polycrystal growth from an advecting supersaturated fluid 191
� 2006 Blackwell Publishing Ltd, Geofluids, 6, 185–200
will subsequently be referred to as non-{111} facets
(Fig. 8, see also Ristic et al. 1996). In all experiments, the
growth rate of {111} facets is more constant over time
than the non-{111} facets, which show large amplitude
variations in growth rate (up to 5 · 10)5 mm s)1)
(Fig. 9). This is especially clear for facets 5 and 6 in experi-
ments 2 and 3 (Figs 8B,C and 9B,C). In both experi-
ments, facet 5 is a non-{111} facet which initially grows
slowly. After 175 min in experiment 2 and after 225 min
in experiment 3, the growth rate increases suddenly and
the facet tends to disappear. In contrast, facet 6 ({111}
facet) grows in both experiments steadily over time.
In experiments 2, 3 and 4, flow is blocked when facet 6
grows until it meets the opposing metal plate. This facet is
oriented parallel to the metal plate and the aperture of the
fracture decreases significantly over time at this position,
resulting in an increase in flow velocity, up to 2 mm s)1
shortly before sealing. According to alum growth kinetics,
growth rate increases with increasing flow velocity (Garside
& Mullin 1968). Therefore, we would expect an effect on
the growth rate of this facet, especially at the latest growth
stages, but this is not observed (Fig. 9B–D).
Dispersion growth rate of different facets: orientation
effects?
The results of the facet measurements show that in all
experiments, except in experiment 1, the growth rates of
the different {111} facets display a relatively large scatter in
a range of 5 · 10)5 mm s)1 (Fig. 9B–D). One aspect which
can result in variations of growth rate between the different
measured facets is the facet orientation with respect to the
flow direction. According to Prieto et al. (1996), facets
which are oriented perpendicular to the flow direction can
grow faster than facets oriented parallel with the flow direc-
tion. Facets, which are located in the shade position with
respect to the flow direction, have the lowest growth rates.
These aspects were observed in KDP (KH2PO4) crystals
under laminar flow conditions, where growth rates of well-
oriented facets can be twice as high as growth rates of unfa-
vourable oriented facets (Prieto et al. 1996).
In experiment 1, facets 9 and 10 both belong to the same
crystal, have approximately the same size and are both {111}
facets. The only difference between these two facets is their
orientation with respect to the flow direction. In contrast to
A B
DC
Fig. 9. Growth rate based on facet measurements for the four experiments. (A) Experiment 1 (supersaturation ¼ 0.095), (B) experiment 2
(supersaturation ¼ 0.135), (C) experiment 3 (supersaturation ¼ 0.176) and (D) experiment 4 (supersaturation ¼ 0.263). Results are plotted against time. Fac-
ets are at first measured when they are completely established and when they show no more influence of small high-index facets. The {111} facets grow at
more uniform rates over time than the non-{111} facets. A wide variation in growth rates between the different facets is observed for all experiments and
can be explained by a combination of the facet index, the facet size and the flow direction with respect to the facet orientation.
192 S. NOLLET et al.
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the results of Prieto et al. (1996), the growth rates of facets
9 and 10 show no significant dependence on orientation.
If we compare facets 5 and 7, both non-{111} facets, we
see that before 200 min, facet 7 grows faster than facet 5,
in contrast to what is expected according to their orienta-
tion in relation to the flow direction (Fig. 9B). After
200 min, the growth rate of facet 5 is significantly higher
than that for facet 7. A similar trend is observed for facets
5 and 7 in experiment 3 (Fig. 9C).
Based on these observations, we conclude that we do
not observe a significant influence of the facet orientation
with respect to the flow direction on the growth rate in
our experiments. It is more likely that the variation in
growth rates between the different facets is caused by the
length of the facets (larger facets grow faster), the facet
index and the irregular seed crystal morphology. It is poss-
ible that there are effects of the flow direction but these
are probably overwhelmed by the other effects.
OVERALL GROWTH RATE MEASUREMENTS
Variations and trends over time
We observe in all experiments that the average growth
rate is not constant but shows variations over time,
keeping in mind the errors in measurements of growth
rate (±2.9–6.8 · 10)6 mm s)1) (Fig. 10). This could be
due to an influence of growth competition on the growth
rate. This is visible in experiment 4, where growth com-
petition between equal-sized crystals is visible near the
end of the experiment. Shortly before a crystal is out-
grown, the average growth rate of the measured area
shows a decrease (Fig. 11). The outgrown crystal itself is
no longer able to integrate new material at that time,
because it is almost completely enclosed by the two
neighbouring crystals. After the enclosed crystal is out-
grown, the growth rate of the neighbouring crystals
increases again.
In experiments 2, 3 and 4, we observe that the growth
rate at the in sector decreases over time (Fig. 10B–D).
The initial aperture was large in this sector and, there-
fore, there is no significant influence of increasing flow
velocity with time in this sector. On the other hand, out-
growth of crystals and disappearance of fast-growing,
high-index facets, on the scale of individual crystals, can
result in a decrease of the growth rate over time and
these are, therefore, negative effects on the growth rate
evolution.
In experiments 2 and 3, the average growth rate at the
mid section increases slightly over time (Fig. 10B,C). This
can be explained by the decreasing aperture and increasing
flow velocity over time. The fact that this effect is only vis-
ible in the mid sector is due to the fracture morphology
with initially the smallest aperture (1.2 mm) in this sector.
In the mid sector, the negative effects (e.g. outgrowth of
fast-growing facets) on the growth rate are also expected
to occur but cannot be recognized because the increase
because of the increasing flow velocity is larger. In experi-
ment 4, where the initial aperture of the mid section was
even smaller, we also expect an increase in growth rate over
time but observe a slight decrease (Fig. 10D).
In all experiments, the growth rate shows no decreasing
or increasing trend at the end sector. The above-described
positive and negative effects on the growth rate also occur
in this sector, but presumably the combination of these
results in a constant growth rate over time.
A B
DCFig. 10. Growth rate calculated based on grown
area measurements. The growth rates are plotted
against time and for three different sectors: inlet
(in), centre (mid) and outlet (end) of the
reaction cell. (A) Growth rate for experiment 1
(supersaturation ¼ 0.095), (B) experiment 2
(supersaturation ¼ 0.135), (C) experiment 3
(supersaturation ¼ 0.176) and (D) experiment 4
(supersaturation ¼ 0.263). Error bars are based
on the error measured in the area measure-
ments, followed by error propagation for the fur-
ther calculations.
Polycrystal growth from an advecting supersaturated fluid 193
� 2006 Blackwell Publishing Ltd, Geofluids, 6, 185–200
Trends between the different areas
After comparing the growth rate evolution over time, we
will now analyse the growth rate evolution along fracture
length. In experiments 2 and 3, the growth rate at the in
section and mid section is initially clearly larger than at the
end section and thus, the growth rate decreases along the
fracture length (Fig. 10B,C). During the further evolution
of the experiment, this trend is less apparent, because of
influences of other effects, which cause decreases and
increases in growth rate over time.
In experiment 1, at very low supersaturations, the differ-
ences in growth rate between the in, mid and end sections
are initially also visible but are significantly smaller
(Fig. 10A). This was already shown in Hilgers & Urai
(2002a) and can be explained by the exponential relation
between supersaturation and growth rate, which results in
less growth rate decrease along fracture length for low
supersaturation.
In experiment 4, at very high supersaturations, there is
initially no trend of decrease in growth rate over fracture
length. In the final stage of the experiments (after
Fig. 12. Fluid inclusions in the experimentally grown alum crystals in (A)
experiment 3 (supersaturation ¼ 0.176) and (B) experiment 4 (supersatura-
tions ¼ 0.263). The inclusions are regularly spaced and contain one fluid
phase. In experiment 3, inclusions show a band spacing of 50–150 lm,
whereas in experiment 4, the band spacing is around 20 lm.
A B
C
Fig. 11. Details of growth competition and effects on the growth rate in
three examples in the end section of experiment 4. (A) Image of the final
situation of the experiment. (B) Growth rate evolution shown by traced
grain boundaries in time intervals of 10 min. (C) Growth rate versus time
for the end section of the experiment. Shortly before a crystal is outgrown,
the average growth rate decreases. After the crystal is outgrown, the aver-
age growth rate of the surviving crystals increases again.
194 S. NOLLET et al.
� 2006 Blackwell Publishing Ltd, Geofluids, 6, 185–200
175 min), the growth rate is even higher at the end section
than at the in and mid section (Fig. 10D). The initial seed
crystal morphology with a significantly smaller aperture
and higher flow velocity at the mid section, compared to
the in and end section can explain the observed trend in
the first growth stages. However, this cannot explain the
trend at the final stage of the experiment. In the traced
images of the experiment, we also observe that the growth
rate is more constant over fracture length at the final stages
of the experiment (Fig. 6B).
FLUID INCLUSION GENERATION INCRYSTALS
Fluid inclusions are formed in experiments 3 and 4, at high
supersaturations (0.176 and 0.263 respectively) (Fig. 12).
They are only visible in the largest crystals and are present
in both the {111} and non-{111} sectors, at different ori-
entations with respect to the flow direction. The inclusions
contain one fluid phase, have a rounded shape and are
arranged in regular bands. The band spacing is around 50–
150 lm in experiment 3 and 20 lm in experiment 4
(Fig. 12). Based on the measured facet growth rate, this
corresponds to a time interval of around 10 min in experi-
ment 3 (vgrowth ¼ 7.16 · 10)5 mm s)1) and 3.5 min in
experiment 4 (vgrowth ¼ 9.5 · 10)5 mm s)1). The differ-
ence in band spacing in the same crystal facet in the two
experiments, carried out at different supersaturation, sug-
gest that it is related to the supersaturation and that spa-
cing decreases with increasing supersaturation.
FACET DEVELOPMENT OF SINGLE CRYSTALSWITH A ROUGH SURFACE
Flow experiments were run at two different supersatura-
tions and at a constant flow rate of 0.01 ml min)1, focus-
ing on the evolution of a single dissolved crystal with a
diameter of 500 lm (Fig. 13).
In the first experiment, with a supersaturation of 0.095,
the first facet develops at the front with respect to the flow
direction after 5 min of growth (Fig. 13A). After 6 min,
facets develop at the back of the crystals and after 7 min,
the crystal has clearly evolved from a rounded, dissolved
crystal to a faceted crystal. The grown band has at that
time a thickness of 18 lm. This indicates that the growth
rate in this time interval was around 4.44 · 10)5
(±0.5 · 10)5) mm s)1. Compared with the facet growth
rate and area growth rate measurements at the same super-
saturation, this growth rate is very high, suggesting that
growth on an irrational crystal surface occurs extremely
rapidly in the first stages.
In the second experiment, the supersaturation was set at
0.263 and the same crystal as in the first experiment was
observed (Fig. 13B). Facets again develop at first at the
front and later at the back with respect to the flow direc-
tion. The difference with the first experiment is that the
evolution to a completely faceted crystal happens faster
(5 min) and the crystal needs only to grow 12 lm to
evolve from a dissolved crystal surface to a faceted crystal.
The growth rate in this time interval is 7.69 · 10)5
(±0.5 · 10)5) mm s)1, which corresponds to the highest
range of the facet growth rate measurements and is higher
than the area growth rate measurements.
DISCUSSION
Comparison of growth rate data with literature
We can compare the growth rates of individual facets and
the measured average growth rate with the growth rate
predicted by the alum growth kinetics (Mullin 2001; Hil-
gers & Urai 2002a) (Fig. 14). The alum growth kinetics is
A
B
Fig. 13. Detailed analysis of facet development
in the same crystal after dissolution. (A) Facet
development at a supersaturation of 0.095. The
crystal has grown a band of 18 lm before it has
become faceted. (B) Facet development at
supersaturation of 0.264. The crystal has only
grown a band of 12 lm before it has become
faceted.
Polycrystal growth from an advecting supersaturated fluid 195
� 2006 Blackwell Publishing Ltd, Geofluids, 6, 185–200
based only on the growth of {111} facets and these facets
normally have a slower growth rate than the other ({110}
and {100}) main habit facets (Ristic et al. 1996; Klapper
et al. 2002). These non-{111} facets are still present in the
final stages of the experiments. The minor facets ({221},
{112} and {012}), which are outgrown during the experi-
ment grow much faster (up to 10 times faster than {111}
facets (Klapper et al. 2002).
When the supersaturation is lower than 0.176, the
growth rate measured in the experiments is lower than the
growth rate predicted by the alum growth kinetics equa-
tion for the same supersaturation (Fig. 14). When the
supersaturation is increased up to 0.263, the growth rate
increases, as described in the literature, but shows a totally
different gradient for both the facet and the area measure-
ments (Fig. 14). This suggests that the growth kinetics
equation which was valid for the lower supersaturations is
not valid for supersaturations higher than 0.176.
Variations in growth rate over time are observed in both
the facet growth rate measurements and the area growth
rate measurements. We will now compare these variations
with effects described in the literature and discuss how
these variations could influence natural vein microstruc-
tures.
Growth rate oscillations with an amplitude of
8 · 10)6 mm s)1 have been described in alum crystals over
a period of 50 min (Gits-Leon et al. 1978; Zumstein &
Rousseau 1987; Bhat et al. 1992; Ristic et al. 1996; Tre-
ivus 1997). The growth sectors of the {111}, {100} and
{110} facets were analysed by X-ray topography in Bhat
et al. (1992) and Ristic et al. (1996), and they concluded
that the growth rates of {100} and {110} facets vary con-
siderably over time with respect to the growth rate of the
{111} facets. Bhat et al. (1992) and Ristic et al. (1996)
explain these variations by a dislocation flux from the non-
{111} sectors towards the finally surviving {111} sectors.
With respect to naturally occurring vein minerals,
growth rate variations in individual facets are described in
experimentally grown calcite and dolomite (ten Have &
Heijnen 1985; Nordeng & Sibley 1996). The results of
ten Have & Heijnen (1985) suggest that cathodolumines-
cence patterns in calcite are caused by changes in the crys-
tal growth rate, independent of variations in the pore fluid
chemistry. Penniston-Dorland (2001) observed similar pat-
terns in natural hydrothermal quartz. In halite grown
under stable evaporitic conditions, the varying spacings
observed for growth striations also suggest variations in
growth rate (Warren 1999; Schleder & Urai 2005).
Based on the arguments outlined above, we suggest that
natural crystal growth in open fractures can vary over time,
even under constant flow rate and supersaturation condi-
tions.
We can now model a microstructure with crystals grow-
ing at a constant growth rate and compare it with a micro-
structure with crystals growing at a variable growth rate
(Fig. 15). At constant growth rate, the grain boundaries
and the crystal facet boundaries are straight lines. The
grain boundary changes its direction only when a crystal is
consumed (Fig. 15A). In contrast, when the growth rate
of one facet is increased in one time increment, the grain
boundary and the crystal facet boundary is no longer a
straight line but changes its direction. The final grain
boundary then becomes serrated instead of a straight line
in the case of a constant growth rate (Fig. 15B–D). Differ-
ent microstructures can be modelled, depending on varia-
tions in the growth rate for different facets. With respect
to naturally growing polycrystals, we can conclude that
irregular or serrated grain boundaries (e.g. Cox 1987) can
be the result from small variations in growth rate in at least
one neighbouring crystal facet, although they can also be
the result of grain boundary migration during deforma-
tion.
On a larger scale, we observed in most experiments that
the average growth rate decreases along the fracture length
(in the flow direction) in the initial growth stages. During
further evolution of the experiment, this trend is also influ-
enced by the growth competition, the increasing flow velo-
city and the outgrowth of high-index facets. Hilgers &
Fig. 14. Facet growth rate data (average over time) and average growth
rate data (initial values at in section), as measured in the four experiments
plotted against supersaturation. Facets 5 and 7 are non-{111} facets,
whereas the others are {111} facets. The abnormal trend of facet 8 can be
explained by the smaller size of this facet in experiment 4. The growth kin-
etics equation according to Hilgers & Urai (2002a) and Mullin (2001) is also
plotted for a flow velocity of 0.15 and 0.3 mm s)1, measured in {111} fac-
ets. Literature data are only available for supersaturations <0.18. At super-
saturations ‡0.176, the measured growth rates show a different slope.
196 S. NOLLET et al.
� 2006 Blackwell Publishing Ltd, Geofluids, 6, 185–200
Urai (2002a) described that it will never be possible to seal
a fracture homogeneously by advective flow under the con-
ditions of low constant flow rate in relation with the reac-
tion kinetics. However, in the experiment with the highest
supersaturation, we observed that there is no trend of
decreasing growth rate along the flow direction indicating
that more homogeneous sealing of the fracture is obtained,
especially at the final stages of the experiment (Fig. 10D).
The growth rate of crystals depends on two steps: (1)
the volume diffusion in the bulk solution and (2) a surface
integration step when a new crystal layer is formed (Gar-
side et al. 1975). At low supersaturations (<0.10), the
growth rate of alum is determined mainly by the second
step, whereas at high supersaturations, the volume diffu-
sion will be the rate-limiting step and has more influence
on the growth rate (Garside et al. 1975; Janssen-van
Rosmalen et al. 1975). This implies that the Damkohler
number will be decreased (<3). According to Dijk & Ber-
kowitz (1998), homogeneous sealing of fractures is only
possible in two cases: (i) at extremely high Peclet number,
at high vflow) and (2) at extremely low Damkohler (<3),
when the molecular diffusion on the solute transport
becomes more dominant. In the case of our experiments,
only the supersaturation was changed and, therefore, the
more homogeneous sealing trend at high supersaturations
could be explained by the second case. A more homoge-
neous sealing in the final stages of all experiments can be
explained by the decreasing aperture over time, causing a
higher flow velocity and a higher Peclet number.
Facet development of crystals and implications for the
crack-seal model
Fibrous veins with host rock solid inclusions are commonly
thought to have formed by incremental crack-seal events
(Ramsay 1980). Numerical simulations of this process
show that completely fibrous crystals are only formed when
the crystal growth rate is higher than the opening rate of
the fracture and if the fracture surface is sufficiently rough
(Urai et al. 1991; Hilgers et al. 2001; Nollet et al.
2005b). Transitional structures between fibrous and elon-
gate-blocky microstructures are formed when the crystal
growth rate is lower than the opening rate of the fracture
(Nollet et al. 2005b). Until now, the critical growth dis-
tance at which facets develop is unknown (Urai et al.
1991; Nollet et al. 2005b). In the experiments presented
here, we have demonstrated that the transition between
dissolved and faceted alum crystals occurs very rapidly. At
supersaturation of 0.263, crystals can develop facets and
nonparallel grain boundaries when crack increments are lar-
ger than 12 lm. This distance is comparable with the crit-
ical distance required to simulate a natural fibrous vein
(Hilgers et al. 2001). In the initial stages of crystal growth
on a rough surface, we observed that the growth rate is
much higher than predicted by the growth kinetics. It is
very likely that this also occurs when the crystals are frac-
tured, as in the crack-seal mechanism. The crystal growth
kinetics which is valid for large, faceted crystals is, there-
fore, not always valid for the initial stages of growth, after
fracturing or dissolution.
Palaeo-supersaturation indicator
In this work, we present for the first time alum polycrystal
growth experiments at high supersaturations (>0.176). The
experiments are characterized by epitaxial overgrowth of
seed crystals but the crystals have incorporated primary
fluid inclusions, in contrast to the clear inclusion-free crys-
tals grown at lower supersaturations. Prieto et al. (1996)
described the occurrence of fluid inclusions in single KDP
crystals at the back of the crystal with respect to the flow
direction, because of ‘eddy’ currents. The inclusions that
are observed in the experiments presented here are
observed in all crystal sectors, irrespective of the relation
between their orientation and the flow direction. There-
fore, it is not very likely that the generation of the inclu-
sions is related to the hydrodynamic environment. It
would be interesting to be able to compare the supersatu-
ration range used in the experiments with values of super-
saturation in nature. However, there is some discussion in
the literature about the degree of supersaturation in natural
Fig. 15. Modelled microstructure with four crystals to show the variability
of microstructures depending on the growth rate of the individual facets
over time. (A) All facets of the four crystals are growing with a constant
growth rate. The grain boundaries are very regular and only change their
orientation when a crystal is outgrown. (B)–(D) Some facets show an
increase or a decrease of the growth rate at specific time intervals, causing
more irregular grain boundaries.
Polycrystal growth from an advecting supersaturated fluid 197
� 2006 Blackwell Publishing Ltd, Geofluids, 6, 185–200
fluid systems. Walther & Wood (1986) suggest that the
required supersaturation for nucleation is relatively small,
whereas the variety of growth habits in nature suggests the
existence of a wide range of supersaturations (Sunagawa
1984; Putnis et al. 1995). The spacing of primary fluid
inclusion bands in natural vein crystals can be around
50 lm (Roedder 1984), similar as in the alum crystals.
Because the fluid inclusions are observed only in experi-
ments at high supersaturations (>0.176), we suggest that
this type of regularly spaced primary inclusions in natural
crystals could be used as an indicator for high supersatura-
tions.
Palaeo-flow direction
We can now discuss whether the microstructures in experi-
ments presented here contain indicators for the flow direc-
tion and advective material transport. In single-crystal
growth literature, it is described that there is an influence
of the flow direction on the growth rate of facets located
at the downstream side of crystals (Janssen-van Rosmalen
& Bennema 1977; Prieto et al. 1996). In natural systems,
it was suggested that crystals grown by advective flow show
a shape-preferred orientation (Newhouse 1941; Babel
2002). In the polycrystal growth experiments presented
here, we could not observe any preferred crystal orienta-
tion or facet development related to the flow direction.
A second aspect which could indicate the flow direction
is the effect of depletion of the fluid over fracture length,
as shown by Hilgers & Urai (2002a). However, in experi-
ments presented here, this effect is only visible in the initial
stages of the experiments with moderate supersaturation.
During further evolution of the crystals, we observed that
effects on the crystal scale (outgrowth of crystals and crys-
tal facets) and the increasing flow velocity, which are not
included in the numerical model used in Hilgers & Urai
(2002a), significantly influenced the growth rate trends.
On the other hand, the rough fracture morphology did
not result in more sealing at the inlet of the fracture.
Therefore, there is no clear evidence for the effect of
depletion of the fluid based on the microstructures only.
A third aspect that could indicate the palaeoflow direc-
tion is the location of fluid inclusions (Prieto et al. 1996).
As already outlined above, we only observed fluid inclu-
sions at high supersaturations (>0.176) and these are not
related to a specific direction.
These aspects indicate that the final microstructures of
the experiments do not contain indicators for the palaeo-
flow direction. The crystal size with respect to the aperture
size of the simulated fracture is in good agreement with
natural veins, suggesting that the crystal-scale effects, as
seen in the experiments, will also occur in natural veins. A
rough fracture morphology is also observed in natural veins,
but is commonly less rough than the one used in the
experiments (Hilgers & Urai 2002b). The aspects discussed
above suggest that the microstructure will not contain sig-
nificant evidence for the palaeo-flow direction in natural
fracture sealing systems, when the flow velocity was low.
CONCLUSIONS
Our experiments with the mineral analogue material alum
result in a better understanding of natural fracture sealing
because the parameters that we can control in our experi-
ments are the flow velocity and the supersaturation. These
are key parameters that control natural fracture sealing.
Polycrystal growth experiments result in elongate-blocky
microstructures with epitaxial growth on existing seed crys-
tals at supersaturations in a range between 0.095 and
0.263 and flow rates of 0.01 ml min)1 along the fracture.
On an individual crystal scale, a variation of growth rate
in different facets is due to the size of the individual facets,
their orientation with respect to the flow direction and dif-
ferences in the flow velocity. Individual facets also show
variations in growth rate over time.
Variations in the average growth rate over time are
explained by growth competition, which is influenced by
crystallographic orientation, crystal size and the fracture
roughness.
All of these factors are likely to influence the growth of
natural elongate-blocky veins. During the growth of nat-
ural veins, at constant flow rate and supersaturation condi-
tions, growth rates are likely to be variable.
A detailed observation of single-crystal growth indicates
that the critical distance to grow facets is very small (12–
18 lm). This indicates that fibrous alum veins would only
form under crack-seal conditions when opening increments
are smaller than 12 lm. The initial growth stages on a
rough surface are characterized by very high growth rates.
The growth rates measured in our experiments are lower
and show a slightly different trend with respect to the
supersaturation, when compared with the alum growth
kinetics described in the literature. At high supersaturations
(‡0.176), the growth rate changes its slope, indicating that
there is a change in crystal growth kinetics. This change in
crystal growth kinetics, with volume diffusion becoming
more dominant, could induce homogeneous sealing along
fracture length.
At high supersaturations (‡0.176), fluid inclusions form
parallel to the crystal facets and with regular spacing of
20 lm, similar to natural primary fluid inclusions. There-
fore, we propose that it is possible that natural crystals in
elongate-blocky veins also grow under high supersatura-
tions and that the fluid inclusions are an indicator of these
conditions.
The final microstructures of the experiments are not
influenced by the flow direction. Therefore, we suggest
that the microstructure cannot be used as a tool to derive
198 S. NOLLET et al.
� 2006 Blackwell Publishing Ltd, Geofluids, 6, 185–200
flow direction in natural veins when the flow velocity was
small.
ACKNOWLEDGEMENTS
We thank Dipl.-Ing Hanz-Dietrich Scherberich and his
workshop at the Institute of Crystallography (RWTH
Aachen) for the design of parts of the experimental set-up.
Daniel Koehn and Stephen Cox are acknowledged for their
very constructive reviews. This project is funded by the DFG
(Hi 816/1–2) and is part of the SPP 1135 project ‘Dynam-
ics of Sedimentary Systems under varying Stress Conditions
by Example of the Central European Basin System’.
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