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2002, Archives of Mechanics
We consider phase transitions in solids due to heat propagating through crystalline materials at low temperatures. These are considered in a steady state context where, at the transition temperature, the specific heat becomes singular and the heat conductivity has a maximum. Several consequences are found for the heat capacity having finite or infinite jump discontinuities.
SIAM Journal on Applied Mathematics
Phase Transitions and Change of Type in Low-Temperature Heat Propagation2006 •
2006 •
Classical heat pulse experiments have shown heat to propagate in waves through crystalline materials at temperatures close to absolute zero. With increasing temperature, these waves slow down and finally disappear, to be replaced by diffusive heat propagation. Several features surrounding this phenomenon are examined in this work. The model used switches between an internal parameter (or extended thermodynamics) description and a classical (linear or nonlinear) Fourier law setting. This leads to a hyperbolic-parabolic change of type, which allows wavelike features to appear beneath the transition temperature and diffusion above. We examine the region around and immediately below the transition temperature, where dissipative effects are insignificant.
2017 •
The purpose of this work is simply to present the thermodynamic theory of the structural phase transition in solids. Second-order phase transition will be described in detail as well as the evaluation of entropy and the specific heat of a physical system when undergoing a structural transition. It was found that lowering the temperature from higher temperature (above Curie temperature) the entropy decreases continuously, indicating a decreasing of number of accessible states in this specific thermal condition and structure rearrangement. The specific heat has showed to be discontinuously in and increase linearly with temperature.
The Journal of chemical physics
Physical origins of temperature continuity at an interface between a crystal and its melt2018 •
We justify and discuss the physical origins for the assumption of temperature continuity at crystal/melt interfaces by performing atomistic simulations. We additionally answer why the crystal/melt interfaces differ from the typical solid/liquid interfaces, which usually exhibit dissimilarities and a resulting temperature drop. We present results for pure silver modeled using the embedded-atom method and Lennard-Jones potential function and contrast the results with each other. We find that the temperature continuity at an interface between a crystal and its melt originates from the perfect vibrational coupling, which is caused by the interfacial structural diffusivity. This study provides fundamental insights into the heat transfer for cases of extremely large heat flux and thermal gradients occurring during rapid melting and solidification. The findings additionally determine the role of rough surfaces in manipulating the thermal conductance in nanodevices.
2019 •
For 200 years, Fourier’s law has been used to describe heat transfer with excellent results. However, as technology advances, more and more situations arise where heat conduction is not well described by the classical equations. Examples are applications with extremely short time scales such as ultra fast laser heating, or very small length scales such as the heat conduction through nanowires or nanostructures in general. In this thesis we investigate alternative models which aim to correctly describe the non-classical effects that appear in extreme situations and which Fourier’s law fails to describe. A popular approach is the Guyer-Krumhansl equation and the framework of phonon hydrodynamics. This formalism is particularly appealing from a mathematical point of view since it is analogous to the Navier-Stokes equations of fluid mechanics, and from a physical point of view, since it is able to describe the physics in a simple and elegant way. In the first part of the thesis we use p...
Kramers' theory frames chemical reaction rates in solution as reactants overcoming a barrier in the presence of friction and noise. For weak coupling to the solution, the reaction rate is limited by the rate at which the solution can restore equilibrium after a subset of reactants have surmounted the barrier to become products. For strong coupling, there are always sufficiently energetic reactants. However, the solution returns many of the intermediate states back to the reactants before the product fully forms. Here, we demonstrate that the thermal conductance displays an analogous physical response to the friction and noise that drive the heat current through a material or structure. A crossover behavior emerges where the thermal reservoirs dominate the conductance at the extremes and only in the intermediate region are the intrinsic properties of the lattice manifest. Not only does this shed new light on Kramers' classic turnover problem, this result is significant for the design of devices for thermal management and other applications, as well as the proper simulation of transport at the nanoscale. Thermal transport is an important process in micro-and nano-scale technologies. It is often in a precarious position: On the one hand, thermal management strategies, including the engineering of low-resistance interfaces, become increasingly important as elements in electronic devices approach the atomic level. On the other hand, phononics – phonon analogues of electronics – seek tunability and inherently nonlinear behavior to make functional devices 1. Thermal transport is thus at the forefront of nanotechnology research. Its impact in a broad array of applications has sparked advanced methods of the fabrication, control, and measurement of transport in, e.g., carbon nanotubes and single-molecule junctions 1–3. Moreover, thermal transport is at the center of one of the major unresolved puzzles in theoretical physics , the absence of a derivation of Fourier's law of heat conduction from a microscopic Hamiltonian 4–9. This is related to the seminal work of Fermi, Pasta and Ulam (FPU) 10–12 , which demonstrated that non-linearity does not always lead to thermalization. The considerations of FPU also apply to the emergence of a well-defined thermal conductivity. The role of nonlinearity – in addition to the description of the thermal reservoirs and interfacial regions – is thus the central topic of many studies examining thermal transport (see refs 5,13,14 for recent reviews). In this work, we demonstrate that thermal transport goes through three physically distinct regimes as the coupling to the surrounding environment – the reservoir that supplies the heat – changes. For weak coupling, energy input from the reservoir limits the heat current through the entire system. For strong coupling, the lattice dynamics are distorted by the presence of the reservoir and this dominates the
Solid State Communications
Observation of a two level thermal conductivity in the low-dimensional materials2010 •
The recent theoretical one-dimensional models display invariably anomalous thermal conductivity. Thermal conductivity of several low-dimensional crystalline systems has been investigated using our new techniques. The results show that for most of the measured materials in the high temperature range the thermal conductivity is composed of two extremes: a low- and a high-conductive state. The effective thermal conductivity jumps abruptly between these two states giving rise to apparent discontinuities or “spikes”.
Journal of Integral Equations and Applications
Phase Transition Problems in Materials with Memory1993 •
2023 •
In this review, we discuss a nonequilibrium thermodynamic theory for heat transport in superlattices, graded systems, and thermal metamaterials with defects. The aim is to provide researchers in nonequilibrium thermodynamics as well as material scientists with a framework to consider in a systematic way several nonequilibrium questions about current developments, which are fostering new aims in heat transport, and the techniques for achieving them, for instance, defect engineering, dislocation engineering, stress engineering, phonon engineering, and nanoengineering. We also suggest some new applications in the particular case of mobile defects.
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