Andrey S. Mysovsky | Searcharxiv

arXiv2019

Simple algorithm for correction of a finite matrix group known approximately

In this paper we have considered a finite unitary matrix group with exact elements being unknown and only approximate elements available. Such a group becomes inconsistent with its own multiplication table. We found simple correction formula for such group. When applied iteratively this formula gives fast convergence of the group elements and allows to perform the group reconstruction. Next we considered small unitary rotation of entire group which makes the group consistent with a set of additional conditions. For example, we might demand that group elements act on certain set of vectors in a predefined manner. Again, iterative procedure based on this correction shows fast convergence. All algorithms developed in this paper were implemented in a Python library which is available as open source software.

math.GR↗

arXiv2013

Local structure and defect segregation on the tilt grain boundaries in silicon

We present the results of atomistic and ab initio simulation of several different tilt grain boundaries (GB) in silicon. The boundary structures obtained with genetic algorithm turned out to have no coordination defects, i.e. all silicon atoms restored their tetrahedral coordination during the structure optimisation. That concerns previously known symmetric Σ 5 (130), Σ 3 (211) and Σ 29 (520) boundaries as well as previously unknown asymmetric Σ 9 (-255)/(-211), Σ 3 (-255)/(211) and Σ 13 (790)/(3 11 0) structures. We have performed an extensive study of defect segregation on the boundaries, including neutral vacancy and carbon, phosphorus and boron impurities. A clear correlation between the segregation energy of the defect and local geometry of the boundary site where the defect is segregated has been revealed. We suggest a simple purely geometric model for evaluation of approximate segregation energies of the listed defects.

cond-mat.mtrl-sci↗