Anomalous energy transfer in crystalline materials from the viewpoints of discrete mechanics and continuum theory

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This project focuses on theoretical and experimental studies of anomalous energy transfer by heat conduction in crystalline lattices. At the nanoscale materials exhibit special thermomechanical properties mostly related to the discreteness of the atomic structure of the medium. An understanding of the energy transfer by heat conduction at that level is essential to obtain a link between the microscopic and the macroscopic descriptions of solids. Latest developments in technology made it possible to investigate properties of low dimensional objects, such as nanotubes, graphene, or fullerenes. During the last decades it was shown that in low dimensional structures, where the phonon mean free path is small compared to the structural size, the nature of heat propagation is ballistic rather than diffusive. Electrical and mechanical properties of low dimensional crystalline structures became of interest during the last decades due to applications in microelectronic devices. Problems of energy transport by heat conduction are of great importance due to problems of cooling and designing innovative thermal devices. Miniaturization of electronic devices and circuits has led to the emergence of self-heating as a critical bottleneck to the performance and reliability of newly developed microelectronic circuits and systems. In order to address heat transfer physics at the single device level, more advanced models of energy transport by heat conduction should be considered. This motivates recent interest in investigating thermal properties of the structures, such as graphene and carbon nanotubes, where such anomalies are most prominent. The aim of this proposal is to investigate anomalous energy transport by heat conduction in low dimensional structures using analytical approaches and simulations, which will help to design and interpret experiments to be performed in order to validate theoretical model predictions.The following will be investigated:- Formulation of discrete and continuous models of anomalous energy transfer in 1D and quasi-1D crystalline materials.- Description of anomalous energy transfer in 2D materials of simple structure.- Development of 2D lattice and continuum models. - Simulation of the energy transfer by heat conduction in such systems using discrete and continuum approaches.- Analogous experiments for the transient case.- Performing experiments determining thermal parameters of nano-structures (graphene) in the non-steady regime using Raman spectroscopy and AFM thermosensors.- Comparison and interpretation of experimental data with results of simulation and analytical studies.Our main objectives:- Create a theory of energy propagation by heat conduction in crystals based on first principles.- Investigate its consistency with extended thermodynamics and phenomenological theories. - Test the models in custom designed experiments