Dislocation unbinding

Defects in crystals are known to have a potentially major influence on phase behavior. For instance, dislocation unbinding is believed to be central to the 2D melting transition, while in 3D there is evidence to suggest that defects can act as nucleation centers for the liquid phase [105]. In superconductors, defects can pin vortices and influence vortex melting [106]. 

Halperin and Nelson [53,54] and Young [55] recognized that the vector character of dislocations must be taken into account in calculating the melting temperature, and also recognized that the dislocation-unbinding transition results in a sixfold bond orientationally ordered fluid phase, the hexatic phase, and that a second, discliriatiori- mbm mg transition is required to obtain an isotropic fluid. 

The description of the Chen-Lubensky model is reasonably well borne out by experiment [50,51] the universal topology of the phase diagram and the existence of a Cx=0 line in particular are well established. An interesting possibility pointed out by Grinstein and Toner [52] with a model of dislocation unbinding is the existence of a biaxial nematic phase if the N-SmA and SmA-SmC lines are second order with XT critical exponents, the N-SmA-SmC point should be tetracritical [53] and a mixed phase (i.e. a biaxial nematic) should show up. It has however not been observed so far. 

However, there is a small bump in the specific heat above [85], representing the entropy associated with unbinding dislocation pairs. This feature may be unobservably small, however, because the density of such pairs is assumed to be small. 

It is interesting to contrast this melting model with the KTHNY theory. In the KTHNY theory, 2D melting is associated with the unbinding of a dilute gas of thermally generated, bound dislocation pairs,... 

At this point we also note the relation to the Halperin-Nelson (1978)-Young (1978) theory of continuous melting in two dimensions via an unbinding of dislocation pairs. Writing the Hamiltonian in terms of the strain tensor afi = J[dtip/dxa -(- < Uq/... 

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