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Next: Conclusion Up: Martensitic Transition in a Previous: The Buckled Triangular

The Martensitic Transition

The time evolution of both the distribution of coordination numbers and also the structure factor point to a dramatic change in symmetry from a buckled triangular crystal to a two-layer square crystal beginning at sec. This transition occurs without spheres having to exchange places with their neighbors. Rather, unit cells of the triangular crystal shear to square symmetry through local elastic distortions. Such diffusionless phase transitions are called martensitic transitions [21] and are known to be strongly first order. Martensitic transitions occur in a wide range of conventional materials including high carbon steels.

Microscopically, the martensitic transition in the confined colloidal suspension is characterized by domains of the minority symmetry rapidly growing and shrinking in a background of the other symmetry. The brief burst of diffusivity at evident in Fig. 6 could be the signature of the onset of these fluctuations. A typical 4-fold fluctuation early in the transition appears in the sequence of Voronoi diagrams shown in Fig. 11. Although the overall transition from to symmetries is monotonic when averaged over the entire field of view (see Figs. 4 and 5) local and short time fluctuations are very large.

The internal stresses set up by local shearing generate topological defects such as dislocations and grain boundaries which propagate rapidly through the crystal. In conventional materials, such defect propagation results in audible clicks known as Barkhausen noise which often are associated with martensitic transitions. The distribution of click intensities and timings in these systems has been found to display a -noise spectrum.

The small size of our observation volume precludes all but a qualitative search for noise in our system. To monitor the magnitude and frequency of sudden local rearrangements we measure the rms displacement between consecutive frames,

 

where sec. Fig. 12 shows over 1280 consecutive frames starting at together with its power spectrum,

 

The dashed line indicates the scaling law while the horizontal line at indicates the minimum noise signal we can detect given the 50 nm errors in our single sphere coordinates.

Fig. 5 suggests that the martensitic transition enters a second phase at roughly sec, not long after squares have become the majority symmetry. The rate at which 6-fold coordinated sites are converted to 4-fold order decreases abruptly by about 60 percent at this time. Similar slowing is observed in conventional materials' martensitic transitions [21] and is apparently generic to this class of structural transformations. Analysis of the microscopic dynamics in the present system provides direct evidence for the microscopic origins of this effect.

Once symmetry predominates, islands of 6-fold order can become trapped between 4-fold crystallites which are misaligned with respect to each other and poorly lattice matched to the triangular crystal. Misaligned domains can form even within a single crystal if the local shearing follows different triangular lattice directions. An included domain can be frustrated in attempts to shear into registry with any of its neighbors by the elastic energy needed to form misfitting boundaries with the others. This competition presumably stabilizes the domains. Interfaces between misoriented grains characteristically include a large number of topological defects many of which are 6-fold coordinated. These relax away by the transfer of single spheres from one grain to another and by the sudden rotation of entire domains. The first is the usual process of grain coarsening and is responsible for the microstructure of conventional materials such as metals. The second may only be possible in the unusually soft lattices of colloidal suspensions, and generates large scale ripples which propagate throughout the system. These are the largest spikes in . Fig. 13 shows both inclusions and grain boundaries at sec.



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Next: Conclusion Up: Martensitic Transition in a Previous: The Buckled Triangular



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