Colloidal Crystals as Model Systems
to Study Solid State Phenomena


First of all, have a look at that video, please:



What you see there looks a bit like high-resolution transmission electron microscopy (HRTEM) of a metal. You might recognize single crystal grains separated by grain boundaries. You might recognize a lot of features from a solid state physics textbook: a dislocation line moving around, vacancies jumping from one lattice site to the next. But this is not electron microscopy - it is not even a metal sample. What you see here are small silica (glass) beads in a fluorescent suspension, imaged by a confocal microscope. Although there is no attractive interaction between the particles (hard sphere), driven by entropy, they form closed packed crystals. These crystals behave very much like metals on the atomic scale. For the physicist, however, they offer the advantage of convenient time and length scales. As the clock at the bottom right tells you, the things you see in the movie happened over the course of one hour. The individual particles have a diameter of 450nm and can be seen with a modern confocal microscope like ours. Larger particles can be used of course. They move even more slowely.

There are many techniques to study metals on the atomic scale, but none of them allow you really to watch what you see in the video above. HRTEM doesn't show individual atoms and only works for very thin samples, not for the bulk. X-ray  diffraction (XRD) averages over the whole sample volume and gives you reciprocal space information only. Scanning electron, tunnel or atomic force microscopy (SEM, STM, AFM) are surface techniques and not bulk sensitive. Tomographic atom probe (TAP) is destructive and allows post-mortem analysis only. Computer simulations have become a very important tool during the last years, but the number of particles that can be simulated and the time period over which they can be studied will always be limited by computer power.

Most of the time we prefer to work not with polycrystals like the sample shown in the video above, but with a single crystal. Single crystals of colloids can be grown by preparing a template [1], using photolithography. The templates we fabricate ourselves at the CNS-Facility here at Harvard are just hole patterns in PMMA films on a microscopy slide:


Photo of Template

Both pictures show the same slide held at slighty different angles to the light source and the observer. Depending on the orientation, constructive interference causes the pattern to shine brightly in different colors. As shown in the cartoon inset, the sedimenting particles in the first layer settle into the hole pattern and act as a seed to direct the formation of a single crystal in the subsequent layers. In this way, we can grow large crystals in various crystallographic orientations:

Confocal Microscopy of a (100) FCC crystalConfocal Microscopy of a (110) FCC Crystal

The left image shows a crystal grown on top of a (100) template, the right one a crystal grown on a (110) template. The lattice is face centered cubic (FCC), although the free energy of a stacking fault is negligibly small. The particles used here have a diameter of about 1.5 µm.

With crystals like these we can now do all kind of fun stuff [2,3] (see also Peter Schall and Claudia Friedsam's work). An example is shown below, where we induced the collapse of a stacking fault by locally disordering the crystal. The video has been generated from real data by identifying all particle positions in (x,y,z) and rendering images using only select particles. All white beads belong to a stacking fault, all yellow beads have a disordered neighborhood and are not part of the crystal. The particles of the perfect crystal are are not shown.



There are more than 20,000 particles in the imaged volume, as many as in state-of-the-art numerical simulations. However, unlike in simulations, we don't have to worry about boundary effects, since our image volume is part of a crystal that is an order of magnitude larger in both x and y.




Literature

[1] A.van Blaaderen, R.Ruel and P.Wiltzius: Template directed colloidal crystallization. Nature 385 (1997) 321-324
[2] P.Schall, I.Cohen, D.Weitz and F.Spaepen: Visualization of Dislocation Dynamics in Colloidal Crystals. Science 305 (2004) 1944-1948
[3]
P.Schall, I.Cohen, D.Weitz and F.Spaepen: Visualizing dislocation nucleation by indenting colloidal crystals. Nature 440 (2006) 319-323

I am doing this work at Harvard University with Prof. Frans Spaepen and Prof. David Weitz