The colloidal suspensions used in this study consist of polystyrene sulfate spheres 0.654 0.009 m in diameter (Catalog # 5065, Duke Scientific, Palo Alto, CA), dispersed in deionized water. These spheres develop strongly negative surface charges due to dissociation of their ionic surface groups. Pair interaction measurements indicate an effective surface potential of meV . An aqueous suspension of these spheres was purified by 3 months of dialysis against deionized water followed by tumbling with mixed-bed ion exchange resin. Samples of the cleaned suspension were filled into sample chambers at volume fractions and . Both suspensions crystallized into face-centered cubic (FCC) structures. The remainder of this Article concerns the properties of these two crystals.
The sample container depicted schematically in Fig. 1 is created by hermetically sealing the edges of a #1 glass coverslip to a glass microscope slide with a high-purity UV curing adhesive (Norland Optical Adhesive Type 88, Norland Products, New Brunswick, NJ). The enclosed volume has a visible area of and is roughly m thick. Access to the sample volume is provided by two glass tubes extending from holes drilled through the slide. All parts were thoroughly cleaned before assembly  and the finished sample cells were flushed with deionized water in a nitrogen-purged glove box before filling. After filling, the tubes serve as reservoirs of colloid and contain mixed bed ion exchange resin to maintain the chemical purity of the interior. The ends of the tubes are continually flushed with water-saturated Ar to prevent the suspension from becoming acidified by absorbing CO2 from the air. Applying an alternating pressure difference across the tubes causes the colloid to flow back and forth through the sample cell and past the ion exchange resin, and further lowers the ionic strength of the suspension. Filled sample cells were allowed to equilibrate for several weeks before the measurements we describe below were performed.
Observations were made with an Olympus IMT-2 inverted optical microscope. A combination of a 100 N.A. 1.4 oil immersion objective and a 10 video eyepiece provides a total magnification of 172 nm/pixel on the attached charge-coupled device camera, so that a single sphere's image subtends an area of roughly square pixels. At this magnification, the 615470 pixel field of view corresponds to a visible area of 10682 m2. The 100 nm depth of focus of the optical system is comparable to the diameter of a sphere so that only a single crystal layer is resolved at a given focal depth. We record the spheres' motions at 1/30 second intervals using a SONY EVO-9650 Hi-8 computer-controlled video deck. The video tapes are then digitized with a Data Translation DT-3851A frame grabber before being analyzed. Figures 2(a) and (c) show typical digitized images of the two crystals' (111) planes in the layer closest to the glass wall.
Each sphere in Fig. 2 appears as a bright blur
on a dark background.
We use precision image analysis techniques 
to locate the spheres' centroid to within 20 nm in the plane.
Their locations in a sequence of
video frames are then linked into trajectories
using a maximum likelihood algorithm .
The data for this study consists of the time-resolved sphere
Small variations in atmospheric pressure cause the crystals to drift slightly relative to the imaging volume during data acquisition. To avoid artifacts introduced by this secular drift, we subtract off the mean displacement over the field of view at each time step. Typical trajectory sequences appear in Figs. 2(b) and (d).
Once the spheres' centroids have been located in the field of view, we apply computational geometry techniques  to analyze their distribution. In particular, we use the Delaunay triangulation to uniquely identify the set of nearest neighbors for each sphere in a snapshot. Given the nearest-neighbor connectivity, we then calculate lattice descriptors such as the mean nearest-neighbor separation and the principal reciprocal lattice vectors. For the relatively dilute crystal shown in Fig. 2(a), the mean separation is m. Focusing up through the crystal reveals a m interlayer spacing. This is consistent with the FCC structure and is inconsistent with a body-centered cubic (BCC) lattice whose equivalent interlayer spacing would be only half as big in this projection. The corresponding lattice constant in the FCC crystal's (111) plane is m. By an equivalent analysis, the dense crystal also adopts the FCC structure, with m and m.
The extent of the crystals' ordering can be measured with
the time-averaged pair correlation function
The angle-averaged structure factor,
Hansen and Verlet  observed that the structure factor's first peak at q = q0 reaches the universal value S(q0) = 2.85 when fluids freeze to FCC crystals. Figure 4 reveals that both suspensions are crystallized according to the Hansen-Verlet criterion.
The spheres' dynamics further allow us to assess the crystal's
Building upon a suggestion by Lindemann ,
Gilvarry  postulated that crystals melt when
the ensemble averaged r.m.s. lattice displacement
Having established the crystals' states, we are in a position to probe the interactions responsible for their structure and dynamics. This is a useful goal in itself since measuring particle interactions is an important component in process control for a wide range of industrial applications . Direct imaging is almost entirely noninvasive and nonperturbative and so offers possible benefits over electrokinetic and mechanical methods commonly used.