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Publication# Thermal transport beyond Fourier, and beyond Boltzmann

Abstract

Crystals and glasses exhibit fundamentally different heat conduction mechanisms: the periodicity of crystals allows for the excitation of propagating vibrational waves that carry heat, as first discussed by Peierls in 1929, while in glasses the lack of periodicity breaks Peierls' picture and heat is mainly carried by the coupling of vibrational modes, often described by a harmonic theory introduced by Allen and Feldman in 1989.

In this thesis we derive a unified microscopic equation that describes on an equal footing heat conduction in crystals, glasses, and anything in-between. In particular, such an equation predicts correctly and in agreement with experiments the thermal conductivity in crystals, glasses, and most importantly in the mixed regime of complex crystals with glasslike conductivity. This formulation is relevant for several technological applications, as it will potentially allow to predict and engineer the ultralow thermal conductivity of, for example, target materials for thermoelectric energy conversion and for thermal barrier coatings.

We also show how in the crystalline regime such a microscopic transport equation can be coarse grained into a set of "viscous heat equations", which generalize the macroscopic heat equation formulated by Fourier in 1822. These viscous heat equations account for both diffusion and heat hydrodynamics, and rationalize the recent discovery of heat transfer via temperature waves in graphitic devices.

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Related concepts (4)

Heat transfer

Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species (mass transfer in the form of advection), either cold or hot, to achieve heat transfer.

Crystal

A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography.

Boltzmann equation

The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of equilibrium; it was devised by Ludwig Boltzmann in 1872. The classic example of such a system is a fluid with temperature gradients in space causing heat to flow from hotter regions to colder ones, by the random but biased transport of the particles making up that fluid.