A Topological Structure Model and a Nonlinear Formation Model of ZnO Tetrapods

Abstract

Objectives. Development of a generalised mathematical model of hierarchical crystalline nanoforms
of zinc oxide tetrapods produced by vapor transport synthesis under the conditions of
chaotic particle dynamics.
Methods and methodology. Topological analysis of nanoscale polymorphic transformations,
nonlinear dynamics of self-assembled structures formation under the conditions of dynamic
chaos. An algorithm to construct an attractor of an affine system of iterated functions with parameters
determined by experimental diagnostic methods: electron microscopy, diffraction studies,
and numerical methods of quantum-chemical calculations for core of hierarchical structure.
Results. The classification of tetrapods as a hierarchical structures was established; nanotechnological
cycle of self-organization of zinc oxide tetrapods chaos - core - percolation system - crystal was determined; the tetrapod structure was mathematically identified as four linked topological
spaces of wurtzite crystal growth; the tetrapod formation modelling method was developed by
constructing an attractor of iterated function systems; the rule of the relation linking a dot in the
nonlinear stochastic dynamic system model attractor with the topological crystallisation space in
the formation of the self-assembled hierarchical crystal structure was established.
A theoretical approach was developed that allows creating and modifying models of three dimensional
space-distributed hierarchical crystal structures characterised by novel physical and
topological properties, as compared to a monocrystal, as well as controlling their form and classifying
the structures by topological and symmetrical properties.
Conclusion. The formation of zinc oxide tetrapods occurs in four linked topological spaces,
modelled as continuous maps of a B4 crystal growth space. The transition from the sphalerite
core growth to the growth of four wurtzite crystals that constitute the tetrapod hierarchical
structure is considered as topological space growth disruption during a polymorphic transformation
of nanoscale. The topological approach involving the affine iterated function systems may
be applied to modelling precrystallisation stages of multipods, as well as dendritic crystal structures
and fractal nanocomposites, and has the capacity to predict their morphology, geometrical
and structural properties.

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