Dislocation Loops Theory

Dislocation-loop melting theory [30], taking into account entropic effects, introduced two new fixed points on the Ki axis, one stable and the other unstable, where V ==2vj is built-in [28]. As the value of the unstable fixed point is at smaller X, than the stable one, Ki has to be larger than its unstable value for fluctuations to converge to dislocation-loop theory s fixed point [31]. Recent self-consistent one loop calculations by Andereck and Patton [32] and the persistent anisotropy in the critical behavior of have renewed interest in this still mysterious aspect of the N-SmA transition [24]. However, Lubensky emphasizes that the only way theoretically to obtain the larger stable fixed point is by ignoring 1 [28]. If one includes 1, the only stable fixed point is at /sTj = 0 where Vn = y. ... 

Dislocation-mediated melting theories are by far the most popular of the defect-based melting theories, with a correspondingly large literature. The literature on dislocation-mediated melting in 3D up to about 1980 has been reviewed by Cotterill [9,10]. More recently, Edwards and Warner [100] used techniques from polymer physics to treat the statistics of an ensemble of dislocation loops, and found that the interactions between dislocations are screened by a finite density of dislocations,... 

Defect structure of neutron-irradiated Fe-Cr alloys contains free vacancies, SIA, VC, pure dislocation loops, dislocation loops decorated by Cr atoms, and vacancy-Cr complexes as well as Cr precipitates depending on the irradiation regime (Malerba et al. 2008). The CD model in our study is close to the model proposed by Christien and Barbu (2004), where the CD simulations are first performed for the free vacancies, SIAC, and point defect clusters and then for the precipitates, taking into account the steady state values of the free point defects concentrations obtained in the first step. In addition, we take into account the Cr-effect on the SIA diffusivity according to the density functional theory (DFT) calculations (Terentyev et al. 2008). 

The author s theory for the mechanical and electrical fields produced by a continuous distribution of moving dislocations is reviewed with its application to the fields produced by a uniformly moving discrete dislocation-loop. Finally, the author is concerned with the mechanical and electrical fields which are brought about by the influence of the disturbance occured in the electrical field. Special attention is paid to the duality of the formulations for these fields to those given before. 

Films of high misfit such as might lead to dislocation loop formation do not grow as uniform thin layers, but rather form islands on the substrates. The critical thickness analysis does not hold well for such a system, as strain relief can occur both by dislocation formation and by relaxation of the island without dislocations. Relaxation without dislocation formation has been extensively modeled using linear elasticity theory by Johnson and Freimd [10], as in Figure 7.23. The model shows that for moderate misfits and moderate film thicknesses, strain can be maintained in small islands well beyond the critical thickness calculated with Equation 7.30. 

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