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Figure 1: (a) Schematic diagram of the sample cell, not drawn to scale. The colloidal suspension is sandwiched between two horizontal glass panes hermetically sealed at the edges and held in place by a retaining bracket. Small reservoirs of mixed ion exchange resin inset into the top pane help to maintain a low ionic concentration in the sample volume. Thin film electrodes are evaporated onto the top plate also, and are contacted with spring-loaded ball bearings. (b) When an electric field is applied across the sample volume, the layer of colloidal microspheres flows past a columnar obstacle which spans the height of the sample volume. In practice, this obstacle is a m irregular grain of glass.

Figure 2: Four stages in the nonequilibrium freezing process. Images in the left column are computer show the distribution of colloidal spheres in one quarter of the experimental field of view. The cylindrical obstruction is hidden by the legends. Voronoi diagrams for the spheres located in these images appear in the right column. Each polygon in these diagrams represents the nearest-neighborhood or Wigner-Seitz cell of a sphere in the corresponding image. (a,b) Square crystal before melting; (c,d) Disordered system at . (e,f) Triangular crystal at seconds after shearing; (g,h) Square crystal reemerging during martensitic transition ( seconds after shearing). The Voronoi diagram shows only those sites in the upper layer for clarity although both layers are visible.

Figure 3: Areal density of spheres in the field of view. The upper horizontal dashed line indicates the measured areal density of m before shear melting. The lower line demarks .

Figure 4: Contour map of the probability density for an individual particle to have a coordination number within of at t seconds after shear melting, as defined by eqn. (7). Contours are at 0.05, 0.10, 0.135, and 0.15.

Figure 5: Population fractions of 4-fold and 6-fold sites as a function of time. Classification is based on the magnitudes of the bond orientational order parameters and calculated for each sphere.

Figure 6: Time dependence of the average self-diffusion coefficient normalized by the free-particle value. Inset: Fits to the Einstein-Smoluchowsky equation at times indicated by the plot symbols in the main figure. The dashed line indicates the free particle result.

Figure 7: In-plane structure factors, at the same times as the images in Fig. 2. The range from the center, , to the edge is 40 m.

Figure 8: Structure factors averaged over angles in reciprocal space, , at and sec. The latter curve is offset upward by 4 for clarity. The first peak, , has already surpassed 2.85 as indicated by the dashed line by .

Figure 9: Detail of the buckled triangular crystal at sec. Larger circles correspond to spheres which are closer to the viewing window. Shaded spheres emphasize a single domain in the buckling superlattice. The superimposed polygons are intended to indicate the six-fold symmetry of the underlying lattice.

Figure 10: Schematic diagrams of six domain boundaries for the edge phonon. (a) blocking boundary, (b) , (c) , (d) Inversion line. Shaded circles represent spheres which are displaced upward.

Figure 11: Detail of a 4-fold domain appearing in an otherwise 6-fold region at t = 160 sec after cessation of shearing. The four frames are from consecutive video images 1/30 sec apart. Light Voronoi polygons are 6-fold coordinated, dark are 4-fold, and the medium gray sites are defects. The displayed field of view is mm.

Figure 12: Rms displacements starting at at 1/30 sec intervals. Inset: Power spectrum of . The diagonal line indicates the power law

Figure 13: Voronoi diagram of the entire polycrystalline structure in the second stage of the martensitic transition at sec. Polygons with 4-fold and 6-fold ordering are differentiated according to the the magnitudes of their orientational order parameters. As in Fig. 11, 6-fold sites are light, 4-fold sites are dark, and disordered sites are medium gray. The central circle represents the extent of the columnar obstacle.

Next: About this document Up: Martensitic Transition in a Previous: Conclusion

David G. Grier
Wed Feb 15 13:32:44 CST 1995