The analysis of interfaces is crucial for the designing, processing, and application of modern
materials. A variety of phenomena, ranging from mechanical to electronic and from magnetic
to optical, are characterized by the presence of interfaces. The description and modelization of
such interfaces is then critical to exploit the extraordinary properties of nanostructures for the
development of new technologies, such as next-generation electronics, solar cells, and 3D
printing.
This project aims at providing advancements in the understanding of crystal interfaces
by means of the analytical validation of different models introduced in Molecular,
Statistical, and Continuum Mechanics. The main focus is on the justification at the
microscopical level of the crystal Wulff shape and on the morphology of crystal interfaces,
especially grain boundaries, material defects and cavities, and thin-film profiles. Special
emphasis will be given to the fundamental multiscale aspect of the problem by looking for
crystalline ground states at the microscale, showing the emergence of optimal shapes at the
macroscale, and evaluating the fluctuations around the optimal shape at the mesoscale.
Both discrete and elastic continuous models will be investigated. By moving within
the framework of the Calculus of Variations and by combining different techniques from
Combinatorics to Geometry Optimization, from Partial Differential Equations to Geometric
Measure Theory, newly designed methods which have been already tested with promising
preliminary results will be further developed.
The project impact is not only related to the fundamental theoretical questions that
inspire it, but also to technological applications. For example, the mathematical understanding
of thin-film growth is essential to control, in the 3D printing, the energy balance between the
laser-beam power used to melt the material and the energy required to form a desired shape.
Campaigns of experimentshave been here planned to characterize optimum growth
parameters for the synthesis and design of supported nanostructures with an emphasis on
graphene nanoflakes and metal oxide materials. Moreover, an international research network
among Vienna, Italy, and the USA will be strengthened and new partnerships enhanced.