With significant recent advancements in thermal sciences—such as the development of new theoretical and experimental techniques, and the discovery of new transport mechanisms—it is helpful to revisit the fundamentals of vibrational heat conduction to formulate an updated and informed physical understanding. The increasing maturity of simulation and modeling methods sparks the desire to leverage these techniques to rapidly improve and develop technology through digital engineering and multi-scale, electro-thermal models. With that vision in mind, this review attempts to build a holistic understanding of thermal transport by focusing on the often unaddressed relationships between subfields, which can be critical for multi-scale modeling approaches. For example, we outline the relationship between mode-specific (computational) and spectral (analytical) models. We relate thermal boundary resistance models based on perturbation approaches and classic transmissivity based models. We discuss the relationship between lattice dynamics and molecular dynamics approaches along with two-channel transport frameworks that have emerged recently and that connect crystal-like and amorphous-like heat conduction. Throughout, we discuss best practices for modeling experimental data and outline how these models can guide material-level and system-level design.

Thermal transport in defective and disordered materials

High speed dislocations have long been identified as the dominant feature governing the plastic response of crystalline materials subjected to high strain rates, controlling deformation and failure...

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The mechanics and physics of high-speed dislocations: a critical review

In this paper, the method of discrete dislocation plasticity (DDP) is extended to include explicitly the thermal effects of moving dislocations. In this manner, localization of heat during fast deformation can be calculated exactly. The thermal effects included are the thermal dissipation due to dislocation drag, the temperature dependence of the drag coefficients themselves and a temperaturedependent obstacle strength through a simple Arrhenius-type dependence. An analytical solution is presented and the temperature distribution is calculated using a time-dependent Galerkin finite-element solution. The two solutions are compared to provide a mutual validation. Then, the stress-strain curves are calculated for Al under simple shear for constant temperatures of 100, 298 and 900 K. The stress-strain curves reflect the temperature dependence of the drag coefficients, since the deformation takes place at a strain rate of 106s−1, which is well within the drag-controlled regime. Finally, the temperatur...

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Temperature rise due to fast-moving dislocations

https://pure.rug.nl/ws/files/3629071/2001CompMaterSciRoos2.pdf

High-speed dislocations in high strain-rate deformations

Simultaneous measurements of the thermal conductivity and specific heat of copper-aluminum (2, 5, 8, and 12 at.%) alloy crystals have been done by the temperature-wave method at 1.4–7.5 K. Specimens containing dislocations of medium (10 10 cm -2 ) and high (10 12 cm -2 ) densities were used. In the case of crystals of medium dislocation density, the lattice thermal conductivity data were well explained by the mechanism of the strain-field scattering of phonons, and the numerical results agreed with those recently calculated by the authors. The lattice specific heat of the crystals was found to be strongly decreased by the introduction of dislocations, and the results were interpreted by considering the effect of atmosphere of alloying atoms. Anomalous behaviors of the specific heat and thermal conductivity were found in crystals of high dislocation density. The origin was assumed to be quasi-local phonon modes around dislocations, and the analysis of the data along this idea gave reasonable results.

Effect of Dislocations on Low-Temperature Thermal Conductivity and Specific Heat of Copper-Aluminum Alloy Crystals

General method to treat the scattering of lattice waves by static strain fields in anisotropic solids was applied to the calculation of thermal conductivity of crystals containing dislocations. The...

Lattice Thermal Conductivity of Crystals Containing Dislocations

The thermal conductivity and thermal diffusivity of lithium fluoride single crystals have been measured simultaneously by the temperature wave method at 1.5–20 K. The specimens were successively deformed by compression and dislocations with densities of 10 6 –10 8 cm -2 were introduced. The diffusivity data were used to analyze the scattering of phonons by dislocations. The analysis was made with the Callaway's method, and the empirical representation of the relaxation rate for the dislocation scattering was found to be a sum of two rates with different dependences on phonon frequency: τ F -1 ∝ω -1 and τ A -1 ∝ω 2 . The former corresponds to the phonon scattering by the fluttering of dislocations, while the latter represents other unknown scattering mechanism effective at high temperatures. Specific heat of the crystals was also determined from the conductivity and diffusivity data. The Debye temperature was found to decrease or the specific heat to increase by fairly large amount when dislocations were i...

Thermal Conductivity, Thermal Diffusivity and Specific Heat of Lithium Fluoride Crystals Containing Dislocations

Computer simulation has been carried out for visualizing solitons and phonons propagating in one-dimensional mass-spring model crystals using the molecular dynamics method. Lattice anharmonicity up to the fourth order in interatomic potential was taken into account. Two kinds of experiments were performed: multiple-pulse input applied to an isolated linear crystal, and single-pulse input applied to a circular crystal. The kinetic energies or displacements of atoms in the crystals were computed after the pulse application. In the first case, phonons were mainly produced together with a preceding soliton, while in the second case, solitons of opposite sign with small tails composed of phonons were produced. The propagation velocities were different for solitons and phonons, and were respectively quite stable and unstable for mutual collisions. The velocity of solitons was determined for various input pulse amplitudes and amounts of lattice anharmonicity. The velocity was found to be enhanced by the increase of the pulse amplitude and the strength of anharmonicity of crystal lattice.

Computer Experiment on Solitons in One-Dimensional Anharmonic Crystals

Molecular dynamics computer simulation has been performed in order to excite solitons in the two-dimensional mass-spring square-lattice model crystals. Central forces were considered between the nearest neighbor atoms in the crystal, and a lattice anharmonic potential up to the fourth order was taken into account. An input pulse displacement was given to the atomic rows in the crystal and the displacements of all the atoms were computed. When the applied input pulse was large, multiple solitons were produced. Collisions of the solitons with homogeneous and inhomogeneous rows of mass defects were simulated in order to investigate the characteristics of the defect-soliton interaction in the two-dimensional crystal. Collisions of solitons and phonons with a single mass defect were also simulated in order to investigate the differences in the characteristics of the two kinds of excitations.

Computer Experiments on Collisions of Solitons with Defects in Two-Dimensional Model Crystals

The meaning and importance of ultrasonic experiments under high pressure were pointed out, and some examples of sound velocity and sound attenuation measurements in solids under hydrostatic pressure were briefly cited. Special emphasis was put on explaining details of our attenuation experiment by a pulse reflection method for a solid in pressurized fluid, and origins of sound losses other than true energy loss in the specimen solid were fully discussed. An experiment to determine the pressure dependence of damping of dislocation motion in crystals was referred as an illustration.

Yoshio Hiki

Papers

Lattice Thermal Conductivity of Crystals Containing Dislocations

Thermal Conductivity, Thermal Diffusivity and Specific Heat of Lithium Fluoride Crystals Containing Dislocations

Computer Experiment on Solitons in One-Dimensional Anharmonic Crystals

Computer Experiments on Collisions of Solitons with Defects in Two-Dimensional Model Crystals

Ultrasonic Measurements Under Extreme Conditions. Part II. –Measurements under High Pressure