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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: [email protected]. 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


(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).



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.



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.



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.



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.



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.



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.



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.



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.



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.



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



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’.

REFERENCES

Babel M (2002) Brine palaeocurrent analysis based on oriented

selenite crystals in the Nida Gypsum deposits (Badenian, south-

ern Poland). Geological Quarterly, 46, 435–48.

Barrett P, Glennon B (2002) Characterizing the metastable zonewidth and solubility using Lasentec FBRM and PVM. ChemicalEngineering Research and Design, 80, 799–805.

Bhat HL, Ristic RI, Sherwood JN, Shripati T (1992) Dislocation

characterization in crystals of potash alum grown by seededsolution growth under conditions of low supersaturation. Jour-nal of Crystal Growth, 121, 709–16.

Bjørlykke K (1999) An overview of factors controlling rates ofcompaction, fluid generation and flow in sedimentary basins. In:

Growth, Dissolution and Pattern Formation in Geosystems (eds

Jamtveit B, Meakin P), pp. 381–404. Kluwer Academic Publish-

ers.Bons PD (2001) Development of crystal morphology during unit-

axial growth in a progressively widening vein. I. The numerical

model. Journal of Structural Geology, 23, 865–72.

Capuano RM (1993) Evidence of fluid flow in microfractures ingeopressured shales. AAPG Bulletin, 77, 1303–14.

Cox S (1987) Antitaxial crack-seal vein microstructures and their

relationship to displacement paths. Journal of Structural Geology,9, 779–87.

Cox S (1999) Deformational controls on the dynamics of fluid

flow in mesothermal gold systems. In: Fractures, Fluid Flow andMineralization: Geological Society of London Special Publica-tions Vol. 155 (eds McCaffrey KJW, Lonergan L, Wilkinson JJ),

pp. 123–40. Geological Society of London.

Dijk P, Berkowitz B (1998) Precipitation and dissolution of

reactive solutes in fractures. Water Resources Research, 34,457–70.

Durney DW, Ramsay JG (1973) Incremental strains measured by

syntectonic crystal growth. In: Gravity and Tectonics (eds de

Jong KA, Scholten R), pp. 67–96. John Wiley & Sons, NewYork.

Elburg MA, Bons PD, Foden J, Passchier CW (2002) The origin

of fibrous veins: constraints from geochemistry. In: DeformationMechanisms, Rheology and Tectonics: Current Status and FuturePerspectives (eds De Meer S, Drury M, De Bresser JHP, Penn-

ock GM), pp. 103–18. Geological Society Special Publication,

200.Geological Society of London, UK.Fisher DM, Brantley SL (1992) Models of quartz overgrowth and

vein formation: deformation and episodic fluid flow in an

ancient subduction zone. Journal of Geophysical Research, 97,

20043–61.

Garside J, Mullin JW (1968) The crystallization of aluminiumpotassium sulphate: a study in the assessment of crystallizer

design data. Part III. Growth and dissolution rates. TransactionsInstitution Chemical Engineers, 46, T11–8.

Garside J, Janssen-Van Rosmalen R, Bennema P (1975) Verifica-tion of crystal growth rate equations. Journal of Crystal Growth,29, 353–66.

Gits-Leon S, Lefaucheux F, Robert MC (1978) Effect of stirringon crystalline quality of solution grown crystals – case of potash

alum. Journal of Crystal Growth, 44, 345–55.

ten Have T, Heijnen W (1985) Cathodoluminescence activation

and zonation in carbonate rocks: an experimental approach.Geologie en Mijnbouw, 64, 297–310.

Hilgers C, Urai JL (2002a) Experimental study of vein growth

during lateral flow in transmitted light: first results. Journal ofStructural Geology, 24, 1029–43.

Hilgers C, Urai JL (2002b) Microstructural observations on nat-

ural syntectonic fibrous veins: implications for the growth pro-

cess. Tectonophysics, 352, 257–74.Hilgers C, Koehn D, Bons PD, Urai JL (2001) Development of

crystal morphology during unitaxial growth in a progressively

widening vein. II. Numerical simulations of the evolution of antit-

axial fibrous veins. Journal of Structural Geology, 23, 873–85.Hilgers C, Dilg-Gruschinski K, Urai JL (2004) Microstructural

evolution of syntaxial veins formed by advective flow. Geology,32, 261–4.

Jamtveit B, Yardley WD (1997) Fluid flow and transport in rocks:an overview. In: Fluid Flow and Transport in Rocks. Mechanismsand Effects (eds Jamtveit B, Yardley BWD), pp. 1–14. Chapman

& Hall, London.Janssen-van Rosmalen R, Bennema P (1975) The influence of vol-

ume diffusion on crystal growth. Journal of Crystal Growth, 29,

342–52.

Janssen-van Rosmalen R, Bennema P (1977) The role of hydrody-namics and supersaturation in the formation of liquid inclusions

in KDP. Journal of Crystal Growth, 42, 224–7.

Klapper H, Becker RA, Schmiemann D, Faber A (2002) Growth-

sector boundaries and growth-rate dispersion in potassium alumcrystals. Crystal Research Technology, 37, 747–57.

Lasaga AC (1998) Kinetic Theory in the Earth Sciences. Princeton,

New Jersey.

Lee Y-J, Morse JW (1999) Calcite precipitation in synthetic veins:implications for the time and fluid volume necessary for vein fill-

ing. Chemical Geology, 156, 151–70.

Lee Y-J, Morse JW, Wiltschko DV (1996) An experimentally veri-fied model for calcite precipitation in veins. Chemical Geology,130, 203–15.

McManus KM, Hanor JS (1993) Diagenetic evidence for massive

evaporite dissolution, fluid flow, and mass transfer in the Louisi-ana Gulf Coast. Geology, 21, 727–30.

Mullin JW (2001) Crystallization. Butterworth-Heinemann,

Oxford.

Newhouse WH (1941) The direction of flow of mineralizing solu-tions. Economic Geology, 36, 612–29.

Nollet S, Hilgers C, Urai JL (2005a) Sealing of fluid pathways in

an overpressure cell – a case study from the Buntsandstein inthe Lower Saxony Basin (NW Germany). International Journalof Earth Sciences, 94, 1039–55.

Nollet S, Urai JL, Bons PD, Hilgers C (2005b) Numerical simula-

tions of polycrystal growth in veins. Journal of Structural Geol-ogy, 217, 217–30.

Nordeng SH, Sibley DF (1996) A crystal growth rate equation for

ancient dolomites: evidence for millimeter-scale flux-limited

growth. Journal of Sedimentary Research, 66, 477–81.



Oliver NHS (2001) Linking of regional and local hydrothermalsystems in the midcrust by shearing and faulting. Tectonophysics,335, 147–61.

Penniston-Dorland SC (2001) Illumination of vein quartz textures

in a porphyry copper ore deposit using scanned cathodolumines-cence: Grasberg Igneous Comples, Irian Jaya, Indonesia. Ameri-can Mineralogist, 86, 652–66.

Prieto M, Paniagua A, Marcos C (1996) Formation of primaryfluid inclusions under influence of the hydrodynamic environ-

ment. European Journal of Mineralogy, 8, 987–96.

Putnis A, Prieto M, Fernandez-Diaz L (1995) Fluid supersatura-

tion and crystallization in porous media. Geological Magazine,132, 1–13.

Ramsay JG (1980) The crack-seal mechanism of rock deformation.

Nature, 284, 135–9.

Ramsay JG, Huber MI (1983) Techniques in Modern StructuralGeology. Volume 1. Strain Analysis. Academic Press, London.

Rimstidt JD, Barnes HL (1980) The kinetics of silica–water reac-

tions. Geochimica et Cosmochimica Acta, 44, 1683–99.Ristic RI, Shekunov B, Shewood JN (1996) Long and short per-

iod growth rate variations in potash alum crystals. Journal ofCrystal Growth, 160, 330–6.

Roedder E (1984) Fluid Inclusions. BookCrafters Inc., Virginia.Sarkar A, Nunn JA, Hanor JS (1995) Free thermohaline convec-

tion beneath allochthonous salt sheets: an agent for salt dissolu-

tion and fluid flow in Gulf Coast sediments. Journal ofGeophysical Research, 100, 18085–92.

Schleder Z, Urai JL (2005) Microstructural evolution of deforma-

tion modified primary halite from the Middle Triassic Rot For-

mation at Hengelo, the Netherlands. International Journal ofEarth Sciences, 94, 941–55.

Sibson RH (1990) Faulting and fluid flow. In: MAC Short Courseon ‘Crustal Fluids’ (ed. Nesbitt BE), pp. 93–132. Mineralogical

Association of Canada.Sibson RH, Moore JM, Rankin AH (1975) Seismic pumping – a

hydrothermal fluid transport mechanism. Journal of the Geologi-cal Society, 131, 653–9.

Singurindy O, Berkowitz B (2003) Evolution of hydraulic conduc-tivity by precipitation and dissolution in carbonate rock. WaterResources Research, 39, 1016.

Singurindy O, Berkowitz B (2005) The role of fractures on cou-pled dissolution and precipitation patterns in carbonate rocks.

Advances in Water Resources, 28, 507–21.

Suchecki RK, Land LS (1983) Isotopic geochemistry of burial-

metamorphosed volcanogenic sediments, Great Valley Sequence,northern California. Geochimica et cosmochimica Acta, 47,

1487–99.

Sunagawa I (1984) Growth of crystals in nature. In: Material Sci-ence of the Earth’s Interior (ed. Sunagawa I), pp. 63–105. Terra

Scientific Publishing Company.

Synowietz C, Schafer K (1984) Chemiker-Kalender. Springer,

Berlin.Taylor WL, Pollard DD, Aydin A (1999) Fluid flow in discrete

joint sets: field observations and numerical simulations. Journalof Geophysical Research, 104, 28983–9006.

Treivus EB (1997) The oscillations of crystal growth rates at theirformation in the regime of free convection of a solution: statisti-

cal investigation. Crystal Research Technology, 32, 963–72.

Urai JL, Williams PF, Roermond HLM (1991) Kinematics of crys-tal growth in syntectonic fibrous veins. Journal of StructuralGeology, 13, 823–36.

Verhaert G, Muchez P, Sintubin M, Similox-Tohon D, Vandycke

S, Keppens E, Hodge EJ, Richards DA (2004) Origin of palaeo-fluids in a normal fault setting in the Aegean region. Geofluids,4, 300–14.

Walther JV, Wood BJ (1986) Mineral-fluid reaction rates. In:

Fluid-rock Interactions during Metamorphism (eds Walther JV,Wood BJ), pp. 194–211. Springer, Berlin.

Warren J (1999) Evaporites: Their Evolution and Economics. Black-

well Publishers, Oxford.Wood JR, Hewett TA (1982) Fluid convection and mass transfer

in porous sandstones – a theoretical model. Geochimica et Cos-mochimica Acta, 46, 1707–13.

Zumstein RC, Rousseau RW (1987) Growth rate dispersion byinitial growth rate distributions and growth rate fluctuations.

AIChE Journal, 33, 121–9.



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