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

• Applicant: Professor Dr. Wolfgang H. Müller
• Subject Area: Mechanics
• Term: from 2019 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 405631704

• Final Report Year: 2023

Final Report Abstract

The project aimed at developing novel continuum constitutive models in order to describe anomalous heat conduction in dielectric solids based on microscopic considerations. At the macroscale and at room temperature heat conduction is described by the Fourier’s law. At lower temperature and/or smaller scales (micro/nano meters) heat conduction deviates for Fourier’s law. Despite several existing models to explain this phenomenon, numerous competing theories and paradoxes still exist. In this project we proposed novel theoretical concepts which led us to develop a ballistic heat conduction model which was implemented to solve a series of important classical initial-boundary value problems. The advantage of this model lies in its analytical derivation and the ability to obtain analytical solutions for crucial problems. Therefore this model can serve as a benchmark for other models, particularly in the limiting case. Furthermore, it is applicable to the ballistic heat regime of heat conduction, such as in crystals at very short length scales. We benchmarked existing theories in the limiting ballistic regime with this model in the Transient Thermal Grating (TTG) geometry to find an excellent agreement. TTG is the crucial experimental measurement method able to capture transient response in exotic regimes. Furthermore, we designed the setup and performed Raman optothermal measurements of single- and bilayer graphene thermal conductivity and benchmarked other novel models. Our project aims at addressing the increasing global energy demand and the negative impact on the environment by developing new methods of energy harvesting, storage, and transfer. One of the major challenges in this endeavor is the excess waste heat generated by miniaturized electronic devices and circuits, which affects their performance and reliability. Therefore novel simulation tool and methods for effective thermal management are needed. We specifically focus on developing heat conduction models to contribute to improving the efficiency of electrical components used in various industries, such as electric vehicles and spacecraft, to enhance performance, reduce emissions, and contribute to solving the global energy crisis.

Publications

• Change of entropy for the one-dimensional ballistic heat equation: Sinusoidal initial perturbation. Physical Review E, 99(4).
  Sokolov, Aleksei A.; Krivtsov, Anton M.; Müller, Wolfgang H. & Vilchevskaya, Elena N.
  
• Geometrically nonlinear dynamic model for a hexagonal lattice. Physical Review E, 102(2).
  Porubov, A. V.; Krivtsov, A. M.; Antonov, I. D.; Müller, W. H. & Sokolov, A. A.
  
• Strain localization in two-dimensional lattices. Journal of Physics: Conference Series, 1686(1), 012036.
  Porubov, A.V.; Antonov, I.D.; Sokolov, A.A. & Müller, W.H.
  
• Heat conduction in 1D harmonic crystal: Discrete and continuum approaches. International Journal of Heat and Mass Transfer, 176, 121442.
  Sokolov, Aleksei A.; Müller, Wolfgang H.; Porubov, Alexey V. & Gavrilov, Serge N.
  
• Signatures of Transient Purely Ballistic Heat Conduction: Theory and Experimental Investigation. Advanced Structured Materials, 613-632. Springer International Publishing.
  Sokolov, Aleksei A.; Müller, Wolfgang H.; Krivtsov, Anton M. & Porubov, Alexey V.
  
• “On the wave nature of thermal transport in low-dimensional lattices: from the atomistic to the continuum perspective”, Ph.D. thesis in TU Berlin DepositOnce, 2023.
  A.A. Sokolov