Instabilities of stressed crystal surfaces

1
Instabilities of stressed crystal surfaces in
contact with a fluid
Evolution of surface structures
AGU fall meeting 2002, paper no. NG12C-1039
We present three different experiments. All
experiments were performed with NaClO3 crystals
of height 3 to 4 mm, width 2 to 3 mm and
thickness 2 mm in a saturated solution of NaClO3
at room temperature, 220.001C. The crystals are
stressed vertically with a piston. Experiment one
takes place at the highest stress of about 8 MPa
(a to i) with a crystal that has two notches on
the sides. Experiment two takes place at a lower
stress of about 4 MPa (j to l) and experiment
three takes place without stress (m). The
experiments take one to two weeks. In experiment
one we lower the crystal in the saturated
solution and leave it unstressed for 24 hours.
During these first 24 hours we can observe that
surface tension smoothens the edges of the
crystal. After 24 hours (time 0.0 in a) the
crystal is loaded vertically where upon surface
patterns start to evolve. The evolution of
patterns on the crystal surface takes place in
three different stages. 1. The onset of the
ATG-instability with mostly parallel and
horizontal grooves on the crystal surface. 2.
Upwards travel of grooves on the crystal surface
and coarsening of the pattern. 3. One large
groove travels upwards across the crystal surface
leaving the surface flat again. In experiment two
we use a crystal without notches and reduce the
stress to 4 MPa (j to l). The general evolution
of patterns in experiment one and two are
similar. The main difference to experiment one is
that the crystal in experiment two seems to
develop two wavelengths, one small with grooves
on the surface and one on the scale of the
crystal. Experiment three takes place without
stress (m). After a few days small waves travel
up the crystal and it develops perfect crystal
facets.
Daniel Koehn, Dag Kristian Dysthe, Bjørn Jamtveit
Physics of Geological Processes, University of
Oslo, P.O.box 1048 Blindern, N-0316 Oslo,
Norway Tectonophysics, Department of Geology,
University of Mainz, Mainz, D Germany
We present an experimental investigation on the
dissolution of single stressed crystals of NaClO3
in contact with a reactive fluid. The crystals
are immersed in a saturated fluid, stressed
vertically by a piston and monitored constantly
in situ with a CCD camera. The experiment is
temperature-controlled and the dilation of the
sample is measured with a capacitance
dilatometer. Once the crystal is stressed it
develops a roughness on its free surface with an
almost constant wavelength in accordance to the
Assaro-Tiller-Grinfeld 1,2 instability (ATG).
The initial roughness is composed of parallel
dissolution grooves perpendicular to the
shortening direction. We observe for the first
time a transient evolution of this roughness. The
structures are not stable but grooves on the
crystal surface start to migrate upwards (against
gravity), grow in size and repel each other.
This secondary instability results in a
coarsening of the pattern, which switches from a
one-dimensional geometry of parallel grooves to a
two-dimensional geometry with horizontal and
vertical grooves. At the end of the experiment
one large groove travels across the crystal and
the surface becomes flat again. Pressure solution
creep between the piston and the top of the
crystal only plays a role in the very beginning
of the experiment. . Our experiments suggest that
the crystal-fluid system is driven out of
equilibrium when the crystal is stressed and that
the system goes through transient processes
involving surface energy and elastic energy
effects to come back to a new equilibrium under
stress. During our experiments the processes
operating on the free surface seem to be faster
and of greater importance than pressure solution
at the top of the crystal.
Transient patterns under different stress
conditions
Schematic summary of the surface patterns in the
three performed experiments. In all three
experiments one can observe short-term surface
energy effects that round the crystal edges and
long-term surface energy effects where waves
travel up the crystal and the crystal becomes
flat. The long-term effect of the surface energy
seems to couple with the stress induced grooves
once the roughness has coarsened up to the same
scale as the surface energy waves in the range of
the size of the crystal. The developing patterns
on the crystal surface are a transition towards a
new equilibrium of the system under stress. The
patterns are more pronounced if the system is
driven further out of equilibrium i.e. if the
stress on the crystal is higher.
Coarsening of the roughness
Traveling of grooves
Pressure Solution Creep
Traveling of grooves is probably due to
concentration gradients in the fluid that develop
as an effect of gravity, higher concentration
(and density) at the bottom of the cell. The
upper edge of a groove on the crystal surface
will therefore tend to dissolve and the lower
edge will tend to grow. This effect will result
in a velocity of grooves along the concentration
gradient in the fluid towards the top of the
crystal. Above the velocity of the superstructure
in experiment one is shown. It travels in cycles
with a period of about 25h and an amplitude of
about 8mm/h except when the front crosses the
notches on the middle of the crystal.
The coarsening of the wavelength of the roughness
is recorded for the first 90 hours of experiment
one. During this time the pattern coarsens
progressively with an almost constant velocity of
about 9.10.4 mm per hour. A coarsening with the
same velocity would lead to the wavelength
spanning the crystal (3mm) after 300 hours. This
fits well with the final evolution of the crystal
surface where the grooves disappear and the
surface becomes flat.
Vertical shortening of the crystal versus time
measured with the capacitance dilatometer. The
first 6 hours the crystal is shortened by
pressure solution creep that decays exponentially
with time. Then there is a jump of 7 mm in
crystal height which reinitiates the decay rate.
The inset shows that there is no long time creep.
References 1 R.J. Asaro and W.A. Tiller,
Metall. Trans. 3, 1789 (1972) 2 M.A. Grinfeld,
Sov. Phys. Dokl. 31, (1986)
Electronic address koehn _at_mail.uni-mainz.de