Dislocation evolution in epitaxial multilayers and graded composition buffers

This paper presents models to describe the dislocation dynamics of strain relaxation in an epitaxial uniform layer, epitaxial multilayers and graded composition buffers. A set of new evolution equations for nucleation rate and annihilation rate of threading dislocations is developed. The dislocation interactions are incorporated into the kinetics process by introducing a resistance term, which depends only on plastic strain. Both threading dislocation nucleation and threading dislocation annihilation are characterized. The new evolution equations combined with other evolution equations for the plastic strain rate, the mean velocity and the dislocation density rate of the threading dislocations are tested on GexSi1-x/Si(100) heterostructures, including epitaxial multilayers and graded composition buffers. It is shown that the evolution equations successfully predict a wide range of experimental results of strain relaxation and threading dislocation evolution in the materials system. Meanwhile, the simulation results clearly signify that the threading dislocation annihilation plays a vital role in the reduction of threading dislocation density.

Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments.

Self-assembly processes resulting in linear structures are often observed in molecular biology, and include the formation of functional filaments such as actin and tubulin, as well as generally dysfunctional ones such as amyloid aggregates. Although the basic kinetic equations describing these phenomena are well-established, it has proved to be challenging, due to their non-linear nature, to derive solutions to these equations except for special cases. The availability of general analytical solutions provides a route for determining the rates of molecular level processes from the analysis of macroscopic experimental measurements of the growth kinetics, in addition to the phenomenological parameters, such as lag times and maximal growth rates that are already obtainable from standard fitting procedures. We describe here an analytical approach based on fixed-point analysis, which provides self-consistent solutions for the growth of filamentous structures that can, in addition to elongation, undergo internal fracturing and monomer-dependent nucleation as mechanisms for generating new free ends acting as growth sites. Our results generalise the analytical expression for sigmoidal growth kinetics from the Oosawa theory for nucleated polymerisation to the case of fragmenting filaments. We determine the corresponding growth laws in closed form and derive from first principles a number of relationships which have been empirically established for the kinetics of the self-assembly of amyloid fibrils.