View source for Visualizing dislocation nucleation by indenting colloidal crystals

Entry by Haifei Zhang, AP 225, Fall 2009

== Soft matter keywords ==
Colloidal Crystal, Nano-indentation, Defect Nucleation

== Overview ==
The formation of dislocations is central to our understanding
of yield, work hardening, fracture, and fatigue1 of crystalline
materials. While dislocations have been studied extensively in
conventional materials, recent results have shown that colloidal
crystals offer a potential model system for visualizing their
structure and dynamics directly in real space. Although thermal
fluctuations are thought to play a critical role in the nucleation
of these defects, it is difficult to observe them directly. Nanoindentation,
during which a small tip deforms a crystalline film, is
a common tool for introducing dislocations into a small volume
that is initially defect-free. The authors show in the paper that an analogue of
nano-indentation performed on a colloidal crystal provides direct
images of defect formation in real time and on the single particle
level, allowing us to probe the effects of thermal fluctuations. The authors implement a new method to determine the strain tensor of a distorted crystal lattice and the authors measure the critical dislocation
loop size and the rate of dislocation nucleation directly. Using
continuum models, the authors elucidate the relation between thermal
fluctuations and the applied strain that governs defect nucleation.
Moreover, the authors estimate that although bond energies between
particles are about fifty times larger in atomic systems, the
difference in attempt frequencies makes the effects of thermal
fluctuations remarkably similar, so that the results are also
relevant for atomic crystals.

== Experiment ==
[[Image:T6fig1.jpg|300px|thumb|right|Fig. 1. Laser diffraction microscopy images of defect structure.]]

=== Sample preparation ===
The authors grow a 43-mm-thick face-centred cubic crystal in the
[100] direction by slowly sedimenting 1.55-mm-diameter silica
particles onto a patterned [100] substrate11. The silica particles are
suspended in a mixture of water and dimethylsulphoxide (DMSO),
which matches their refractive index. The authors add a small amount of
fluorescein to the solvent so that under fluorescence the particles
appear as dark spots on a bright background.

=== Transmitted beam imaging === 
The authors use the transmitted beam
for imaging the defect structure. LDM exploits the difference in
scattering between the perfect and the distorted crystal lattices near
the dislocation core, and produces a real-space image in which
dislocations appear as dark lines on a bright background. The authors lower
the needle at a rate of 3.4 um/h and record LDM images. Surprisingly, even before the
needle touches the crystal, thermal effects produce local intensity
fluctuations which last several seconds.

Four images of the indented crystal are shown in Fig. 1. About
190 min after starting lowering the needle, it is observed that two dark
regions beneath the needle tip (arrows in Fig. 1b), which is associated
with the strained lattice. Remarkably, these regions exhibit intensity
fluctuations that last several minutes. This suggests that, in the
strained lattice, thermal fluctuations become more spatially correlated,
and persist over longer timescales than in the unstrained lattice.
After 230 min, it is observed that a dark circular spot, about 8 mm in radius,
centred 15 mm below the needle (Fig. 1c). This spot grows in size and
finally detaches from the needle (Fig. 1d). These images show the
nucleation of a dislocation loop and its eventual detachment from
the needle. After the first event, it is observed that nucleation and propagation
of many more loops, which form a complex dislocation
network after 600 min (Fig. 1e). Because of the complexity of this
network, its three-dimensional evolution needs to be explored on the
particle scale.

=== Confocal imaging ===
[[Image:T6fig2.jpg|300px|thumb|left|Fig. 2. Defect formation on the particle scale.]]
[[Image:T6fig3.jpg|300px|thumb|right|Fig. 3. Strain distribution in the indented crystalline film.]]

The authors use confocal microscopy to image individual particles in a
60 mm by 60 mm by 30 mm section of the colloidal crystal (Fig. 2a).
This technique allows us to image the dislocations and to determine
the strain field caused by the indentation.
To determine the full structure of the defects, three dimensional
reconstructions of the unstable and stable defects are shown in Figs 2e–g.

In Fig. 3, Particle colour in a–d indicates the value of the local shear strain (see colour scale).
The distribution of g in Fig. 3c shows that the negative shear strain
regions (blue) inside the dislocation loop almost overlap. Because the
contrast in the LDM images arises from these lattice distortions, this
observation validates our interpretation that small dislocation loops
appear as dark spots in Fig. 1c and d.

== Soft matter details ==
Pushing a sewing needle into a colloidal crystal may seem a crude experiment. On
the contrary, combined with laser diffraction microscopy and confocal microscopy,
it provides a valuable analogy to nanoindentation and promises a deeper
understanding of the mechanical response of crystalline materials.

=== Probe the mechanical response of surfaces ===
Nanoindentation is much used to probe the
mechanical response of surfaces, thin films
and bulk materials. In this method, a diamond tip is pressed against a surface. The
resulting force and depth of penetration are monitored
at resolutions of micronewtons and nanometres,
respectively, and used to infer the mechanical
properties of the indented material. Nanoindentation
also provides a means to introduce the line defects
known as dislocations into the crystal structure of a
material,allowing defect nucleation and atomic-scale
mechanisms of strength and failure to be studied. 

=== Colloidal crystal as physical analogues for fcc crystals===
[[Image:T6fig4.jpg|400px|thumb|right|(a) Schematic representation of dislocation nucleation in an initially defectfree
crystal. The location of subsurface defect nucleation is marked by the red star. The indentation load P,
and penetration depth h, or equivalently the contact radius a, along with the location of defect nucleation,
provide valuable information about mechanical properties of crystalline materials. (b) During a loadcontrolled
indentation test, a plot of P against h for an initially perfect crystal shows a sudden displacement
burst (known as a ‘pop-in’) during homogeneous defect nucleation.]]

The authors examine defect
nucleation in real time during indentation of colloidal
crystals made of silica spheres. These crystals serve
as physical analogues for face centered cubic atomic crystals. Despite the
complexity in interpreting results, this method could
offer insights into some of the details that we need to correlate atomic-scale
events with macroscopic material properties.
The response of crystals to microindentation
looks like a continuous rise in the plot of force, P,
against indentation depth, h. During nanoindentation,
however, early-stage nucleation of dislocations can
result in discrete jumps and abrupt discontinuities
in the P–h curve (See the figure on right). These correspond to the
moments when, at a fixed load, a sudden displacement
jump takes place or when a sudden drop in load
occurs at a fixed displacement. During homogeneous
nucleation — that is, when nucleation of dislocations
occurs through breaking of the atomic bonds of an
initially perfect crystal — the critical shear stress
needed to activate the first such ‘pop-in’ event in
fcc crystals generally correlates with the theoretical
shear strength. The P–h response extracted from
nanoindentation thus provides insights into the origins
of defect nucleation in initially defect-free crystals.
These studies led to a search for techniques
whereby quantitative nanoindentation could be
combined with real-time imaging of dislocations.
Consequently, several atomic-scale visualization
methods have been pursued. 

In the colloidal crystal method, a rectangular
block of a defect-free crystal, tens of micrometres
along its edges, is obtained by slowly sedimenting silica
microparticles onto a patterned substrate. The crystal is
then indented with a sewing needle whose tip creates a
strain field (the area aff ected by the indentation load in
which the crystal structure becomes distorted) below
the surface. Laser diffraction microscopy is used to
obtain a real-time image of the dislocation loops (the
circular regions inside which the crystal is distorted).

These defects appear in the subsurface region as dark
lines on a light background because of the difference in
the scattering of the laser beam between the perfect and
defective spots in the crystal (See Fig. 1.). Confocal microscopy is then used to image the individual colloidal particles
and to map out the strain field produced by the
indentation. A noteworthy advantage of the colloidal
crystal system is that these dislocation loops and
microscopic strain fields can be obtained along with
the detection of thermal fluctuations of the colloidal
particles over reasonable timescales. Such quantitative
results offer new information about indentation tests
that could be used to develop predictive models of
defect nucleation.

=== Dislocation differences between colloidal crystals and  atomic crystals===
The forces required to nucleate dislocation
loops in the colloidal crystal are orders of
magnitude smaller than those needed for creating
homogeneous dislocations in atomic crystals.
As a result, quantitative estimates of P against
h cannot be obtained from the colloidal crystal
model. Although thermal fluctuations reported
for colloidal crystals are similar to those in atomic
crystals, the bond energies between the colloidal
particles are vastly different from those in atomic
crystals. Despite these limitations, the defect
nucleation criteria proposed in this paper provide opportunities to examine
dislocation dynamics. For example, extensions of
this work could explore how dislocation generation
occurs beyond the first ‘pop-in’ associated with the homogeneous nucleation of dislocations and
how thermal fluctuations and defect interactions
continue to influence multiple ‘pop-in’ events observed in nanoindentation tests on
f.c.c. crystals. Such experiments would also
provide insights for the development of atomistic
computational simulations of nanoindentation
and for formulating theories of defect nucleation
and dynamics in crystalline solids. The colloidal
system could also offer a physical model to
examine how dislocation nucleation at grain
boundaries and grain-boundary sliding might
combine or compete in influencing the strength of
nanocrystalline metals. Such a model might also
provide mechanistic information as to why the
hardness and strength in nanocrystalline metals are
so much more sensitive to the rate of loading than
in microcrystalline metals.

== References ==
[1] P. Schall, Itai Cohen, David A. Weitz, Frans Spaepen, Visualizing dislocation nucleation by indenting colloidal crystals, Nature, 440, 319 – 323, 2006.