Chemical Geology 230 (2006) 232 – 241
www.elsevier.com/locate/chemgeo
Evolution of mineral–fluid interfaces studied at pressure with
synchrotron X-ray techniques
D.K. Dysthe a , R.A. Wogelius b,⁎, C.C. Tang c , A.A. Nield c
b
a
University of Oslo, Physics of Geological Processes, P.O. Box 1048, Blindern, N-0316 Oslo, Norway
University of Manchester, School of Earth, Atmospheric, and Environmental Sciences, Oxford Road, Manchester M13 9PL, UK
c
CLRC Daresbury Laboratory, Daresbury, Warrington, Cheshire, WA4 4AD, UK
Received 3 January 2006; accepted 2 February 2006
Abstract
In situ measurements of mineral surface evolution during the process of pressure solution are possible with the high brightness
of synchrotron X-ray sources. This capability has been explored through the use of newly developed reaction vessels that allow
transmission of the incident and scattered X-ray beam through a low atomic weight piston. Several new vessels are described,
along with details of computational algorithms that are used to simulate X-ray scattering in this unconventional geometry. Results
using calcite (CaCO3) and halite (NaCl) as reactant crystals are presented and compared to other atomic-scale measurements of
surface dissolution processes. Calcite was reacted with an unsaturated fluid at 30 bars of pressure for approximately 24 h. During
reaction the root mean square surface roughness (σ) evolved from 13.7 Å (± 0.5 Å) to 19.5 Å (± 1.0 Å), giving a roughening rate of:
dσ/dt = +6.3 × 10− 5 Å s− 1. This is consistent with other measurements made with free calcite surfaces and is driven almost entirely
by chemical disequilibrium. Analysis of the surface ex situ post-reaction gives an identical σ value, showing that the in situ
measurements are well-constrained. Experiments also at 30 bars but in a saturated solution indicate that the calcite surface does not
significantly roughen, giving the result that pressure solution of calcite at this pressure cannot be monitored in experiments of
several days duration. Experiments with halite, a much more reactive phase, in saturated solutions showed the reflectivity profile to
be dynamic on a time scale of hours. This experiment was left to reach equilibrium over 108 days and then re-analyzed, showing
that σ had increased from 34 Å (±2 Å) to 41 Å (± 2 Å), giving a roughening rate of: dσ/dt ≤ +6.4 × 10− 7 Å s− 1. This is two orders
of magnitude smaller than the calcite roughening rate caused by chemical disequilibrium and provides the first direct in situ
atomic-scale measurement of the rate of surface roughening due to pressure solution.
© 2006 Elsevier B.V. All rights reserved.
Keywords: Synchrotron; Calcite; Halite; Pressure solution; X-ray reflectivity
1. Introduction
Because of the critical importance in understanding
mass transfer processes across the mineral–fluid
⁎ Corresponding author.
E-mail addresses: d.k.dysthe@fys.uio.no (D.K. Dysthe),
Roy.Wogelius@manchester.ac.uk (R.A. Wogelius).
0009-2541/$ - see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.chemgeo.2006.02.028
interface, a large quantity of research has recently
been focussed on directly observing the changes which
occur at the mineral surface during reaction. The
development and use of new techniques and appropriate
in situ cells has been an important part of this effort. Xray reflectivity has proven to be useful at analyzing the
structure of aqueous films on mineral surfaces at
ambient pressure (Chiarello et al., 1993; Fenter et al.,
D.K. Dysthe et al. / Chemical Geology 230 (2006) 232–241
2000; Cheng et al., 2001; Fenter et al., 2001). Effects of
a number of variables have been examined; however, it
has remained extremely difficult to study the evolution
of the surface while under stress. Since pressure is a key
variable in geological systems, we have developed an
experimental approach that has allowed us to directly
measure changes in surface quality at the angstrom scale
for mineral surfaces that are under elevated pressure via
applied normal stress. Our immediate aim is to further
the understanding of the phenomenon of pressure
solution creep (PSC) which is only poorly understood.
Several recent experimental studies of PSC have shown
that surface morphology evolves with time (Dysthe et al.,
2002, 2003 and references therein). The surface
evolution (for instance, roughening or smoothening) is
crucial to understanding the fundamental mechanisms of
PSC. Small-scale surface evolution is also important to
understand larger scale interface roughening by PSC
called stylolites (Schmittbuhl et al., 2004). There is a
need for in situ studies to follow the evolution and not
only the beginning and end states. PSC is a very slow
process and in order to obtain data in a reasonable time
one should work at small length scales. Studies of the
surface evolution in the sub micrometer range is
important to probe the damping effect of surface tension
in the growth of surface instabilities under pressure
(Koehn et al., 2004). X-ray reflectivity offers the
possibility to study the surface roughness in situ at
length scales between 1 Å and 1 μm for vertically
stressed surfaces with a confined fluid film between the
solid surfaces. It is thus complementary to Surface Force
Apparatus (see Israelachvili and Pashley, 1983; Anzalone et al., 2006-this issue) and other longer wavelengthbased spectroscopies (e.g. Dai et al., 1995). We are
presently also performing AFM studies of calcite
surfaces under lateral stress (no confined fluid film).
233
Fig. 1. Photograph of fixed pressure (a) and adjustable pressure (b)
interfacial analysis cells. Height of each cell is approximately 14 cm.
Fixed pressure cell is set by compressing the spring with a known
mass—the glass piston is then glued in place to fix pressure at a
given value. The variable pressure apparatus uses a calibrated spring
to adjust pressure by rotating the large knurled screw-top. Each
rotation of the screw compresses the spring by a measured amount
to allow pressure to be changed without disturbing the interfacial
region. (c) Sketch of the internal structure of the adjustable pressure
cell to show X-ray beam path.
2. Experimental methods
2.1. Reaction cells
Purpose-built reaction cells were constructed and
experiments were completed at the Daresbury Laboratory Synchrotron Radiation Source. Two types of cells
were developed. The first is a single use cell shown in
Fig. 1a. This design uses a piston-and-spring design to
transfer pressure from a Perspex anvil onto the mineral
surface of interest. Essentially a prepared crystal is
placed facing up onto a metal base within a glass sleeve.
A small hole is drilled in the glass at the height of the
crystal surface to allow X-rays to enter and reflect off the
surface. An X-ray transparent chemically inert (Teflon)
sleeve is placed around the circular crystal and stands
proud of the surface. Fluid is micro-pipetted onto the
surface, and then a Perspex piston is placed face-down
to transfer pressure to the solution/mineral system. An
organic liquid (hexadecane or hexane) is then allowed to
seep into the analytical region to help slow evaporation
of the aqueous interfacial fluid. A brass disk is then
placed over the Perspex piston, followed by a spring and
another disk. A glass rod is then inserted and a known
mass placed on top of the glass rod. This compresses the
spring and thus exerts a known pressure onto the upward
facing mineral. Once the spring system is at equilibrium,
a rapid setting glue is injected into the space between the
glass tube and rod, to fix the entire assembly at the
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D.K. Dysthe et al. / Chemical Geology 230 (2006) 232–241
required pressure. The second design is similar but is
multi-use. Here, instead of using glue to fix a piston in
place, a spring with a calibrated force constant is
depressed by a heavy knurled screw-top. Pressure can be
increased or decreased by turning the screw. This cell
has also been manufactured to maintain thermal
stability, and a temperature controlled fluid may be
passed through the heavy metal base such that
experiments may be completed at above ambient
temperature. A thermal insulating sleeve can be placed
over the entire assembly. As with the single-use cell, a
gap is left in the jacketing so that X-rays may enter and
exit the cell, with fluid kept in place by a thin inert
cylindrical sleeve in which both the mineral and Perspex
anvil are contained. A Perspex anvil was used to
transmit pressure to the mineral surface first of all
because it is a relatively X-ray transparent medium, and
secondly because it is softer than the minerals used and
we did not want solid–solid grinding to occur.
2.2. Reactants and cell preparation
Optical quality disks of single crystal calcite and
halite with 1 cm diameter were purchased. Calcite disks
were Syton polished then sequentially ultrasonically
cleaned first in acetone, then ethanol, then deionized
water (DIW) for at least 2 min in each solvent. They
were then rinsed with flowing DIW and dried at 100 °C.
Halite was used as delivered from the manufacturer. The
Perspex anvil surface used to transmit pressure was
gently polished via standard petrographic methods, then
cleaned with detergent and water, next ultrasonically
cleaned in ethanol, then DIW for 2–5 min in each
solvent and finally dried at 100 °C until no visible
water remained.
The calcite undersaturated fluid was simply 18 MΩ
DIW. For the saturated experiment, a DIW solution
that had been in contact with powdered calcite for
2 years was used. A syringe with a 0.2 μm filter was
used to draw off 30 mL of solution. From this sample,
a 5 μL pipette was filled and approximately 0.5 μL of
solution was placed onto the calcite surface before
sealing. A halite saturated solution was produced by
equilibrating DIW with powdered halite for 3 months.
Extraction and loading of the reactant fluid for use in
these experiments was identical to the calcite–solution
methodology, except approximately 0.7 μL was placed
onto the halite surface.
All metal and glass pieces of the cells were rigorously
cleaned first with detergent and water and then with
acetone prior to use. Glass pieces were further
ultrasonically cleaned in ethanol, then DIW.
2.3. Synchrotron analytical conditions
Experiments were completed at the Daresbury
Laboratory Synchrotron Radiation Source, Station 2.3.
These experiments were completed with an incident
beam tuned to a wavelength of between 0.7 and 1.25 Å.
Shorter wavelengths were used to minimize absorption
during in situ measurements. Station 2.3 uses a channel
cut Si(111) monochromator to control the wavelength of
the incident beam. Monochromator resolution is
± 1° × 10− 4. Stepping motors for height adjustment (z)
and adjustment of sample inclination perpendicular to
the beam (c) are available. The diffractometer itself is a
two-circle diffractometer which gives accurate control
of the sample's incident angle (θ, ±2° × 10− 4) and the
detector's position (2θ, ± 1° × 10− 4). Exact alignment of
the sample is completed by adjustments to χ (sample tilt
perpendicular to the X-ray beam), z (sample height), θ,
and 2θ. χ and z adjustments are achieved by a purposebuilt sample stage with stepper motors.
Scattered X-rays are detected with an enhanced
dynamic range scintillation counter mounted on the
extreme downstream end of the 2θ arm. Incident beam is
slitted down to a rectangle 100 μm high and 4 mm wide.
Downstream of the sample, the detector entry slits are
set to the same rectangular size. Between the detector
entry slits and the detector itself, an He-purged flight
path ∼35 cm long is inserted to ensure that the random
noise component entering the detector is minimized.
This configuration ensures the excellent resolution of
angularly dependent scattered intensities by allowing
the detection of only a tight angular range of scattered
photons to be detected for a given geometry. For further
details see Collins et al. (1992) and Tang et al. (1998).
Due to the large range in the intensity of the reflected
beam (over seven orders of magnitude) attenuators must
be placed between the incident beam and the detector.
An attenuator wheel with ports of varying thicknesses of
Al was used for this purpose. A correction for intensity
must therefore be applied to the specular data. Other
corrections for beam-sample geometry and for the slight
decrease in incident intensity over the length of a scan
(due to the degradation of the synchrotron storage ring
over time) must also be applied. A program has been
written to automate the full correction procedure. (For
further details of correction factors and the fundamental
equations describing X-ray reflectivity and diffuse
scatter see Wogelius et al. (1999) and references
contained therein).) Changes in intensity of the
specularly reflected beam and of the diffusely scattered
portion of the beam were monitored. Surfaces of single
crystals of calcite were analyzed under the following
D.K. Dysthe et al. / Chemical Geology 230 (2006) 232–241
conditions: 1) dry and at ambient pressure, 2) dry and at
elevated pressure (either 10 or 30 bars), 3) in contact
with an undersaturated solution at elevated pressure, and
4) in contact with a saturated solution at elevated
pressure. Halite was analyzed under conditions 1), 2),
and 4).
2.4. Reflectivity models
In order to accurately model transmission of X-rays
through a bulk medium with an arbitrary index of
refraction an algorithm for analysis of the data was
formulated based on the Fresnel equations and on the
Cowley and Ryan (1987) surface roughness model.
Commercially available programmes for analysis of
reflectivity data do not allow the user to set the medium
of transmission to have a complex index of refraction
unequal to that of a vacuum. Hence, in order to interpret
our experiments, we have had to construct our own data
analysis algorithm. Values for δ and β (the real and
imaginary parts of the complex refractive index) for all
phases that interacted with the X-ray beam were
downloaded in tabular form as a function of wavelength
from the Lawrence Berkeley Laboratory on-line database (http://www.cxro.lbl.gov/optical_constants/). We
have tested our results by comparison with results
from standard reflectivity analysis packages. Fig. 2
gives a comparison between our implementation of the
Fresnel equation and those obtained for exactly the same
235
sample setup from two standard computer packages;
GIXA—a commercially available programme supplied
by Bede Scientific, and REX, a least-squares fitting
package available as freeware (Crabb et al., 1993). The
model calculations are for a halite surface with a 100 Å
thick water film; both the halite and water surfaces are
atomically smooth and the incident radiation wavelength is 1.2 Å. REX allows the user to select either the
Cowley and Ryan (1987) or Nevot and Croce (1980)
roughness models. The computation presented here for
REX is based on the Cowley and Ryan (1987) model—
which is also the formulation we used in our algorithm.
In addition, where possible we completed reflectivity
measurements ex situ as quickly as possible after
surfaces had been analyzed in situ so that we could
further constrain and verify the calculations applied to
the in situ data. In all cases the in situ results agree
closely with the results obtained from ex situ analyses.
Errors quoted for surfaces modelled via our algorithm
are estimated from the sensitivity of the simulation to an
adjustment in the value of the parameter, constrained by
least-squares fitting of identical surfaces using REX. All
reflectivity profiles are presented as log10 of normalized
intensity and are plotted either as a function of incident
angle θ or the scattering vector Q, where:
Q¼
4p
sinh:
k
2.5. Physical parameters determined by the X-ray
scattering experiments
Fig. 2. Benchmark simulations for this study, comparing results of two
standard reflectivity fitting programs, GIXA (open triangles) and REX
(open circles), against the algorithm used in this study (smooth curve).
In this case, the comparison is for specular reflectivity from a perfectly
smooth halite surface with a 100 Å thick zero roughness film of H2O
coating the halite. The incident X-rays in all three cases are modelled
as being transmitted through a medium with a refractive index equal to
unity (vacuum). Our algorithm has been constructed in order to
simulate transmission through Perspex, but here we show that it
functions accurately in this simpler case when compared to standard
programs that cannot model transmission through an arbitrary
medium.
X-ray reflectivity was developed for the study of the
physical structures of atomically smooth surfaces and
has recently been employed in a number of studies on
cleaved and prepared mineral surfaces. The physical
parameters determined by specular reflectivity and
diffuse scatter are explained briefly below. For the
theoretical basis of reflectivity, see Parratt (1954).
Weber and Lengeler (1992) present a full discussion
of diffuse scatter.
For surfaces that are planar and reasonably smooth at
the atomic scale, X-ray reflectivity can determine the
average root mean square roughness of the surface, σ,
defined by the equation:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u L
u1 X
r¼t
ðzi z̄ Þ2
Lt i¼1
where Lt is the total length of the system, zi is the height
of each component i of the surface, and z̄ is the mean
surface height. The symbol used for rms roughness, σ,
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D.K. Dysthe et al. / Chemical Geology 230 (2006) 232–241
reflects the fact that rms roughness defines a statistical
fluctuation of the surface about a reference plane—such
that approximately 95% of the surface will be within
± 2σ of the reference height. Note however that X-ray
reflectivity is relatively insensitive to physical features
that are greater in size than the coherence length of the
X-ray beam (coherence length is a function of
wavelength, distance to source, and beam size, equal
to approximately 1.5 μm in our experiments)—hence it
is useful to think of the reflectivity signal as accurately
measuring angstrom-scale height fluctuations on flat
terraces but relatively insensitive to large steps or other
imperfections.
In addition to determining σ, specular reflectivity can
determine the thickness of well-organized thin films and
also the electron density contrast between the thin film
and the substrate through the analysis of the interference
pattern (Kiessig fringes). Film thickness is inversely
proportional to the peak to peak spacing of the
oscillations when displayed as a function of incident
angle (or the scattering vector, Q). Peak amplitudes are
directly proportional to the electron density contrast
between the two materials. The reflected profile is a
function of the roughness of all of the surfaces which
reflect the beam, and hence the roughness of buried
interfaces can be determined if the film thickness and
electron density allow X-rays to penetrate to the
appropriate depth.
Diffuse scatter monitors the intensity of the scattered
beam in the vicinity of the specular peak. For the
specular reflectivity the scattering vector is kept normal
to the sample surface—therefore the specular profile is
sensitive to structural modification normal to the
surface. In the diffuse case, the scattering vector begins
at an angle to the surface and scans through the surface
normal—hence the diffuse scatter profile is sensitive to
structural modification in the surface plane. A correlation function is typically used to model the diffuse
scatter, and this includes parameters describing the
correlation length (ξ) between features on the surface, a
fractal parameter (h) which describes how smoothly the
correlation function decays as a function of distance,
plus an independent determination of σ. If we assume
that the surface is isotropic we may write the following
correlation function:
2h !
X
C ð X Þ ¼ exp n
where x is distance in the surface plane. The fractal
parameter h may be used to determine the non-integer
dimension (D) of the surface, such that D = 3 − h. The
larger h is, the closer the surface dimension is to 2 and
therefore the closer the surface is to resembling a
Euclidean plane. The smaller h is, the higher the
dimension of the surface. Values of ξ and h are extracted
from mathematical model calculations which use this
correlation function to compute a simulated diffuse
scatter profile.
3. Results
3.1. Perspex anvil
Fig. 3 presents an ex situ reflectivity measurement of
a typical Perspex anvil before use in these pressure
solution experiments (open circles = data, smooth curve = simulation). The simulation of the data indicates
that the Perspex surface has a starting rms roughness of
15 Å (±2 Å). Furthermore, there is a relatively thick
water film 40 Å (± 5 Å) thick on this surface, and the
roughness at the water/air interface is 13 Å (±2 Å). This
implies that the water layer may conform to the Perspex
surface since the two roughness values are so similar.
3.2. Calcite reacted with undersaturated solution
Fig. 4 presents the ex situ reflectivity curve of the
calcite disk before reaction with the undersaturated fluid
(open circles = data with two σ error bars; smooth
curve = simulation). The starting surface roughness is
13.7 Å (± 0.5 Å). Fig. 5 presents, to the best of our
knowledge, the first in situ X-ray reflectivity data
obtained from a mineral surface whilst significantly
above ambient pressure. These data were obtained after
the sample had been at pressure for approximately 1 day.
Fig. 3. Reflectivity profile of the Perspex anvil before use in these
experiments. Shown as the open symbols are the log10 of the reflected
beam intensity; the smooth curve is the simulation of the data, best fit
is for a 15 Å rms rough Perspex surface (σp) covered with a 40 Å thick
atmospheric water layer (zw). The water/air interface is 13 Å rough
(σw). Errors are shown as the vertical bars.
D.K. Dysthe et al. / Chemical Geology 230 (2006) 232–241
Fig. 4. Before reaction reflectivity profile of the calcite surface used in
the undersaturated experiment. Open symbols are reflected beam
intensity; smooth curve is the simulation of the data. The calcite has a
starting roughness of 13.7 Å (σc). Errors same as previous.
Also shown on Fig. 5 is a simulation; these data are most
consistent with a 2050 Å (± 200 Å) gap between the
Perspex anvil and the calcite surface—the separation
between these two surfaces creates the oscillations
apparent in the in situ measurement. The roughness of
this Perspex anvil, a different anvil than shown on Fig.
3, was 67 Å (±7 Å) whilst the calcite has roughened to
19.5 Å (± 2 Å) rms roughness. In order to produce a
simulation that was at all similar to the measurement we
needed to postulate the presence of an additional
interface. When we unloaded the cell, the calcite disk
did not adhere through surface tension to the Perspex
anvil—and hence we infer that an air bubble was caught
within the system during loading. Trapped air would
also account for the large interfacial gap. This additional
interface apparently had a high roughness (40 ± 4 Å).
Note that the misfit between the data and the simulation
at low angle (< 0.06°) is due to straight-through beam
entering the detector. The simulation algorithm does not
Fig. 5. In situ reflectivity profile of the calcite surface in an
undersaturated aqueous fluid taken at pressure, symbols same as
previous. (Physical parameters used in the simulation are given on the
figure: σ0 is the roughness of the Perspex anvil, z1 is the thickness of
the fluid film, σ1 is the inferred additional roughness at the vapour/
water interface, σ3 is the roughness of the calcite surface.) Errors
shown as vertical bars with end lines.
237
Fig. 6. Ex situ measurement of the calcite surface after reaction.
Symbols same as previous. Inset shows ex situ comparison of
reflectivity profiles before (open symbols) and after (solid line)
reaction. The decrease in reflected intensity corresponds to increased
atomic-scale roughness. The roughness value of the calcite surface (σ)
used to calculate the simulated profile is 19.5 Å. Errors shown as
vertical bars.
account for this geometric effect. (This appears as well
on some of the figures that follow, but some data sets
have been truncated on the low angle side to remove this
feature and enhance clarity.)
After the in situ measurement was completed the
pressure was relieved and the Perspex anvil and Teflon
sleeve removed so that reflectivity data could be
immediately taken from the free calcite surface. Fig. 6
shows the ex situ reflectivity taken after reaction with a
fit to the data—note that the surface has indeed
roughened measurably to 19.5 Å (± 0.5 Å), consistent
with the in situ data. An inset to Fig. 6 compares the
before and after reflectivity result for this sample. The
change in surface roughness (σ) for the calcite surface at
30 bar pressure in an undersaturated solution was:
° s1 :
dr=dt ¼ þ6:3 105 A
This is consistent with previous measurements of
calcite roughening at ambient pressure and can be
accounted for purely by chemical dissolution (Chiarello
et al., 1993) as would reasonably be expected for calcite
in an undersaturated solution—and indeed some of the
trapped vapour phase may have come from the release
of CO2 by the surface.
Reflectivity was used to characterize the calcite
crystal before reaction with the saturated solution and
these data are shown on Fig. 7. This surface was of
poorer quality than that used in the previous experiment,
with a starting roughness of 28 Å (± 1 Å). A water film
can also be resolved on this surface due to atmospheric
water vapour—this is typical. Loading of this sample
apparently was not complicated by trapping of air as was
the case with the previous run, and the in situ data
presented in Fig. 8 show that the Perspex anvil and
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D.K. Dysthe et al. / Chemical Geology 230 (2006) 232–241
Fig. 7. Reflectivity profile of the calcite before reaction in the saturated
experiment, symbols same as previous. σ0 is the roughness of the
water vapour/air interface, z0 is the thickness of the atmospheric water
vapour layer on the surface, σ1 is the roughness of the calcite surface.
Errors equal to symbol size.
calcite surface were far enough apart that the fluid phase
can be dealt with as a bulk fluid rather than a thin film,
and no interference due to a vapour phase occurs.
However these data also indicate that the calcite surface
is not dynamic under these conditions over the time
period of the experiment, i.e. the roughening rate for
calcite in a saturated solution was too small to be
measured over 3.75 days at 30 bars. We decided to also
check whether the in-plane topography was also stable
for this surface by completing diffuse scatter measurements. Fig. 9 presents the diffuse scatter measurement
taken after reaction: the surface roughness is not
significantly greater than that made before reaction
(30 ± 2 Å vs. 28 ± 2 Å, respectively). Correlation length
and the fractal parameter (ξ and h) are also essentially
unchanged. (Unfortunately, due to technical problems
we were not able to measure changes in the diffuse
scatter profile for the calcite reacted at pressure with the
undersaturated fluid.)
Fig. 8. In situ reflectivity for calcite in saturated solution; open
symbols are reflectivity at start of experiment, filled symbols are after a
time lapse of 3.75 days. These data sets are virtually identical,
indicating the change in roughness is too slow to measure over this
time period in a saturated solution. Errors roughly equal to symbol
size.
Fig. 9. The diffuse scatter data for the calcite in a saturated solution
measured ex situ and post-reaction. Open circles are the diffuse scatter
intensity, smooth curve is the simulation of the data. In-plane
mathematical descriptors correlation length (ξ) and fractal parameter
(h) can be evaluated along with roughness and other parameters in this
type of scan; however the in plane nature of the surface has not
significantly changed in this experiment. (Simulation parameters are as
follows: σ0 is the roughness of the water thin film/air interface, z0 is the
thickness of the water film on the surface, σ1 is the roughness of the
calcite surface.) Errors equal to symbol size.
3.3. Halite
Reactivity of halite with a saturated solution was also
explored with the expectation that the faster reaction
rates and higher solubilities of this phase would present
a more dynamic system for study than calcite.
Characterization of the halite surface before reaction is
shown in Fig. 10, where the surface starting roughness is
determined to be 35 Å (± 2 Å) and halite displays a 57 Å
(± 3 Å) thick film of adsorbed water, apparently more or
less conforming to the roughness of the primary surface
Fig. 10. Reflectivity profile of the halite surface before reaction
(symbols same as previous). Halite's high solubility makes it
impossible to polish with Syton as was done for calcite, hence the
starting surface roughness is high; sample parameters are a surface
roughness of halite equal to 35 Å (σ1) with 57 Å of atmospheric water
vapour adsorbed onto the halite (z0). The water film/air interface is also
quite rough with an estimated roughness equal to 26 Å (σ0). Errors
equal to symbol size.
D.K. Dysthe et al. / Chemical Geology 230 (2006) 232–241
Fig. 11. In situ reflectivity for halite in a saturated solution. Curve “a”
is at the start of the experiment, and four curves progressively
darkening on a grey scale present the slight change in reflectivity of the
halite surface over six hours of reaction, finishing with the curve
labelled “b.” Our synchrotron allocation ended after collection of curve
“b.” We stored the reaction vessel at ambient temperature and left
pressure constant until our next allocation period 108 days later and
repeated the reflectivity measurement after checking the station
alignment with gold on silicon standard. The heavy curve labelled
“c” represents the reflectivity after an extended period at pressure and
this is significantly different from the other curves. Errors shown as
vertical lines.
(26 Å rough). Fig. 11 shows the evolution of the in situ
reflectivity for this sample, with each of the four upper
curves collected approximately 1.5 h apart. Fig. 12
presents a simulation of the curve on Fig. 11
corresponding to 6 h of reaction (curve b). This is
consistent with the starting surface roughness of 35 Å,
implying that another parameter besides surface roughness was probably dominating the slight change in the
reflected signal over the initial reaction period. The cell
239
Fig. 13. Reflectivity after 108 days (symbols same as previous): using
constant roughness for the Perspex anvil, the best fit to the data
indicates that the halite surface has roughened and the fluid-filled gap
between the Perspex and the halite has significantly decreased. This is
interpreted to be the result of large surface features decreasing in size
due to pressure solution. (σp is the roughness of the Perspex anvil, σH
is the roughness of the halite crystal, z is the final thickness of the
solution layer between the anvil and the mineral.) Errors not shown.
was set aside and stored in a heated laboratory at the
University of Manchester for 108 days, and then realigned and re-analyzed with exactly the same beam
conditions. The lowermost curve on Fig. 11 compares
this measurement with the short-term reaction data and
indicates that a large change in the system has resulted
from the long re-equilibration time. Fig. 13 presents a
simulation to this data, which shows that much of the
change in the profile results from the gap between the
Perspex and the halite decreasing from 250 to 60 Å.
However, in this long term experiment for halite in a
saturated solution at 30 bar, it also appears that the
mineral surface has roughened only slightly from 35 Å
(± 2 Å) to 41 Å (± 3 Å), giving a roughening rate of: dσ/
dt ≤ + 6.4 × 10− 7 Å s− 1. This is two orders of magnitude
smaller than the chemically driven rate measured for
calcite roughening in the undersaturated experiment,
and represents the first long term estimate of the rate of
surface roughening caused by pressure solution.
4. Conclusions
Fig. 12. This presents the reflectivity for curve “b” (solid symbols) and
our best simulation (smooth curve) uses an unchanged starting
roughness of the halite plus an aqueous fluid layer 250 Å thick
between the Perspex anvil and the halite surface. The roughness of the
Perspex anvil must be high in order to produce a reasonable simulation
of these data, and other geometric factors have been changed relative to
the in situ calcite data. Errors not shown.
The most important result of this study is that
interface structure can be analyzed with X-ray scattering
under pressure. The new method has been proven by in
situ experiments on both calcite and halite. This method
will be especially valuable when studying slowly
reacting minerals such as quartz and other highly
polymerized silicates. The surface dynamics of such
materials are extremely sluggish and should be studied
at atomic length scales that are inaccessible by optical
methods.
240
D.K. Dysthe et al. / Chemical Geology 230 (2006) 232–241
Results for calcite indicate that undersaturation of the
fluid is a much larger driving force for surface
roughening than pressure. In saturated solution the
small driving force of stress is either too small to
overcome the surface tension at these length scales or the
growth time scale is too large for our experiment. These
findings are consistent with AFM studies of free surfaces
of calcite under tangential stress (Bisschop et al., in
press). For halite however, there is marked change with
time in both fluid film thickness and roughness.
Several recent studies have been performed on
surface roughening under stress and during dissolution.
Schmittbuhl et al. (2004) studied stylolites where
normal stress on a horizontally infinite solid acts to
stabilize the surface roughness, only disorder in the
dissolving crystal destabilizes the surface and leads to
growth of stylolites. The analysis of Schmittbuhl et al.
is not directly applicable to this study since the
roughness measured here is smaller than the fluid film
thickness. It is clear that one cannot assume homogenous normal stress over the surface in this case, the
confined fluid of varying thickness as a stress
transmitter must be taken into account, not only elastic
solids. The Asaro–Tiller–Grinfeld (ATG) instability
(Asaro and Tiller, 1972; Grinfeld, 1986) is driven by
stress parallel to the surface. For a finite size sample the
vertical compression acts also as a horizontal stretching
that destabilizes the surface (Gal et al., 1998) and
causes onset of the ATG instability. The length scales in
this study are, however, far below the ATG length scale
for calcite and halite (Misbah et al., 2004) and therefore
this model can not be applied directly to predict the
surface evolution observed in confinement, it must be
combined with the dynamics of a thinning film (Dysthe
et al., 2003). But the fact that there are measurable
changes on sub-micron length scales is analogous to the
exponential growth of roughness leading to the
characteristic length scale from the linearized ATG
analysis. A recent study at similar length scales of the
dynamics of polished calcite surfaces stressed parallel
to the surface (but with free water) shows that the effect
of parallel stress is very subtle (Bisschop et al., in
press). The thermodynamic driving force of the normal
stress in our study is, however, 3 to 4 orders of
magnitude larger than that of similar parallel stress. It is
too early to draw conclusions about implications for
pressure solution creep from a preliminary X-ray
reflectivity study, but what we observe seems to be a
precursor to surface roughening during pressure
solution creep that has been observed at different scales
by several authors (Den Brok, 1998; Dysthe et al.,
2002; Karcz et al., 2006).
It goes beyond the scope of this study to develop new
models of how the confined fluid film coevolves with
the roughening solid surface. The confined fluid film
response to solid surface change, to our knowledge, has
hardly been studied in detail. The surface forces
apparatus and molecular dynamics simulations have
long seemed to be the tools of choice for studies of
confined fluids of static interfaces. We have now shown
that X-ray reflectivity is a powerful and useful technique
to study dynamic, confined interfaces. Some methodological issues clearly remain. We have chosen to use
Perspex as a piston because its low electron density
makes it fairly transparent to X-rays. Using a nonwetting polymer such as this will clearly affect the
stability and dynamics of the confined fluid under study.
Future studies should preferably use other materials
with surface properties more similar to those of the
minerals of interest. Also, because this is a new
application of X-ray reflectivity and therefore comparable data do not exist, it is important to be able to
constrain in situ measurements with ex situ before and
after profiles. For this reason, the sealed “fixed pressure”
cell (Fig. 1a) is not optimal, because unloading risks
destroying the sample surface.
Acknowledgments
RAW would like to thank the diffraction group at
Daresbury Laboratory for all of their help with this
project, both in terms of cell design and synchrotron
access. [DR]
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