Bubble raft model

VTi. Keenan E. Dungey, George MJII Lisensky, and S. Michael Condren, "Kixium Monolayers A Simple Alternative to the Bubble Raft Model for Close-Packed Spheres," /. Chem. Educ., Vol. 76, 1999, 618-619. 

Fig. 6.39. Images of dislocation nucleation in a bubble raft model of a single crystal subjected to surface indentation. In the case of the smallest surface roughness (a), dislocation nucleation occurs at the peaks of the asperities where they contact the indenter. At the intermediate scale (b), dislocation nucleation occurs at the reentrant corners at the bases of the asparities. Finally, for the largest scale asperity (c), the stress level near the stress concentrations has been reduced geometrically, and dislocations nucleated homogeneously at an interior point where the shear stress is the largest. Each bubble in this raft is 1 mm in diameter and it represents an atom which is approximately 0.3 nm in diameter. Reproduced with permission from Gouldstone et al. (2001).

Another limitation of the approach of Ewers and Sutherland [38] is that it is essentially qualitative. However, there have been some attempts to put it on a quantitative basis [5, 45, 46]. The first such attempt was due to Shearer and Akers [5], who were concerned with the antifoam effect of PDMSs on lube oils. Here the effect of antifoam on a monolayer raft of bubbles is modeled theoretically and the results compared with experiment. 

Early in the history of crystal dislocations, the lack of resistance to motion in pure metal-like crystals was provided by the Bragg bubble model, although it was not taken seriously. By adjusting the size of the bubbles in a raft, it was found that the elastic behavior of the raft could be made comparable with that of a selected metal such as copper (Bragg and Lomer, 1949). In such a raft, it was further found that, as expected, the force needed to form a dislocation is large. However, the force needed to move a bubble is too small to measure. 

Several experiments with this bubble model confirmed the fact that the constraint factor, described in Section 1.4.1.1, is dependent on the angle at the indenter tip. By measuring the force transmitted to the frame at the bottom of the substrate raft, the tensile stress generated on indenter removal, and the rate at which these stresses decayed, were monitored and were shown to follow the theoretical paths calculated for the indentation process in Section 5.2. 

Dislocations may be demonstrated by means of a soap bubble analogy. This consists of a raft of small bubbles, all the same size, generated on the surface of a soap solution. The bubbles represent atoms and are subjected to two forces just as the atoms in a metal are. Surface tension causes the bubbles to attract each other and form a dense array, while pressure within the bubbles prevents them from approaching each other closer than a characteristic distance. When a raft of bubbles is formed on a fluid surface, grain boundaries are evident as well as dislocations (Fig. 8.10). When such a raft of bubbles is sheared, deformation is seen to occur as dislocations move across the crystal. While the forces at work are not identical to those associated with atoms, the soap bubble model is a useful analogy. A film has been produced by Sir Lawrence Bragg who devised the soap bubble analogy, and this film lends considerable credibility to the relatively sophisticated dislocation concept. 

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