Dislocations Volterra process

EDA complex formation, phase transitions 339 edge dislocation, Volterra process 419 effusity, phase transitions 320 Eglington-Glaser reaction, synthesis 99 eigenwaves, SLM 764 Einstein diffusivity-viscosity law 585... 

Both dislocation and disclination can be produced by the well-known Volterra process. Take a cylinder of a medium and do the following operations in sequence on it ... 

The six basic Volterra processes are depicted in Figure 1.20, among them the three intrinsic processes on b produce dislocations while the three intrinsic operations associated with u> produce disclinations. In Figure 1.20, assuming a is the normal of the cut plane,... 

The helical structure of the c-director in the smectic C phase makes the defects different from those in the smectic C phase. As the Volterra process produces a screw dislocation, for example, along the z axis and the Burger vector b = d, it must be accompanied by a parallel wedge disclination in the c-director, in the form... 

The equivalence just demonstrated for screw dislocations versus wedge x disclinations can be extended to edge dislocations (Figure 5.12) versus twist X disclinations and even further, to mixed dislocations and disclinations, for the simple reason that the two corresponding Volterra processes are the same. 

Several examples of the Volterra process in smectic A phases are indicated in Fig. 16 [2, 3]. The symmetry involved can be a translation normal to the layers, in which case the defect is said to be a dislocation. 

Examples of defect lines created in cholesterics according to the Volterra process are shown in Fig. 17. The core structure will be considered below this being replaced by a narrow cylinder. Figures 17 a and b represent translation dislocations in both cases. 

Figure 17. The Volterra process applied to cholesteric phases. The core structure is masked by a cylinder along the line L. (a, b) Edge and screw dislocation, (c-e) A section S limited by L, normal to the cholesteric axis, allows one to build either the edge dislocation (a) or a disclination (d), as in smectics (Fig. 16d and d"). (f, g) Construction of the opposite disclination. (Drawing made in collaboration with F. Livo-lant).

If we now apply the Volterra process, there are two possible ways to obtain a screw dislocation, as indicated in Fig. 22 b and c, when the length of the Burgers vector is p/2, the half-helicoidal pitch. In a simple model it is assumed that the directors... 

Along a circle nm, directors show a definite distribution that is coherent, with a uniform alignment within the horizontal plane (a"). When the Volterra process is applied along the cylinder axis to create screw dislocations (b or c), the rectangles ABA B are transformed into parallelograms (b or c ) and the distributions of the directors are changed along a transverse circle nm. This leads to two different patterns in the core (b" or c") when the molecules are assumed to remain horizontal. (Drawn in collaboration with F. Livolant.)... 

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