Search Results

Properties of Solids at Low Temperatures

Jack W. Ekin

in Experimental Techniques for Low-Temperature Measurements: Cryostat Design, Material Properties and Superconductor Critical-Current Testing

This chapter discusses the physics of the properties of material used in cryostat construction and presents tables of data for cryostat design. The order of presentation of the first four properties ... More

This chapter discusses the physics of the properties of material used in cryostat construction and presents tables of data for cryostat design. The order of presentation of the first four properties (specific heat; thermal expansion; electrical resistivity; and thermal conductivity) has been chosen because the underlying physics of each one logically flows into the next. The last two properties, magnetic susceptibility and mechanical properties, are not always included in treatments of material properties, but they are absolutely crucial to the selection of materials for cryostat design.Less

ELECTRONIC CONDUCTION IN METALS

J. M. Ziman

in Electrons and Phonons: The Theory of Transport Phenomena in Solids

This chapter discusses the electrical conductivity of metals. Topics covered include the transport properties of metals, residual resistance in alloys, the resistance-minimum phenomenon, residual ... More

This chapter discusses the electrical conductivity of metals. Topics covered include the transport properties of metals, residual resistance in alloys, the resistance-minimum phenomenon, residual resistance from crystal imperfections, the Bloch theory, lattice resistivity, electrical resistivity of transition metals, thermal conductivity, thermopower, phonon drag, and electron-electron scattering.Less

Electrical and Thermal Conductivity

Takamichi Iida and Roderick I.L. Guthrie

in The Thermophysical Properties of Metallic Liquids: Volume 1 — Fundamentals

This chapter discusses some of the important electronic transport properties of metallic liquids: their electrical conductivities or electrical resistivities, and thermal conductivities. Topics ... More

This chapter discusses some of the important electronic transport properties of metallic liquids: their electrical conductivities or electrical resistivities, and thermal conductivities. Topics covered include theoretical equations for the electrical and thermal conductivities of metallic liquids; the relationship between electrical conductivity and thermal conductivity of metallic liquid (the Wiedemann–Franz–Lorentz law); methods of electrical conductivity/resistivity and thermal conductivity measurement; and experimental data for the electrical resistivity and thermal conductivity of metallic liquids.Less

The thermal diffusion equation

Stephen J. Blundell and Katherine M. Blundell

in Concepts in Thermal Physics

This chapter looks at solving problems involving the thermal conductivity of matter using a technique developed by mathematicians in the late 18th and early 19th centuries. The key equation describes ... More

This chapter looks at solving problems involving the thermal conductivity of matter using a technique developed by mathematicians in the late 18th and early 19th centuries. The key equation describes thermal diffusion, i.e., how heat appears to 'diffuse' from one place to the other, and much of the chapter presents techniques for solving this equation. The thermal diffusion equation for a sphere, Newton's law of cooling, the Prandtl number, sources of heat, and particle diffusion are discussed.Less

Transport properties in gases

Stephen J. Blundell and Katherine M. Blundell

in Concepts in Thermal Physics

This chapter describes how a gas can transport momentum, energy, or particles from one place to another. It considers non-equilibrium situations, but still in the steady state, i.e., so that the ... More

This chapter describes how a gas can transport momentum, energy, or particles from one place to another. It considers non-equilibrium situations, but still in the steady state, i.e., so that the system parameters are time-independent, but the surroundings will be time-dependent. The phenomena examined are called transport properties and the following are considered: (i) viscosity, which is the transport of momentum; (ii) thermal conductivity, which is the transport of heat; and (iii) diffusion, which is the transport of particles.Less

Transport properties

E. R. DOBBS

in Helium Three

This chapter examines the transport properties of 3He-4He mixtures. It outlines the theory for the transport coefficient over a wide range of temperatures and then discusses experiments that measure ... More

This chapter examines the transport properties of 3He-4He mixtures. It outlines the theory for the transport coefficient over a wide range of temperatures and then discusses experiments that measure that viscosity coefficient. It also presents further measurements of the thermal conductivity coefficient, including the propagation of heat pulse, and discusses diffusion coefficients.Less

TRANSPORT PHENOMENA

R. E. Peierls

in Quantum Theory of Solids

An electron in the field of force of a perfect lattice has stationary states in which the mean velocity and hence the mean transport of charge and of energy do not vanish. This means that an electric ... More

An electron in the field of force of a perfect lattice has stationary states in which the mean velocity and hence the mean transport of charge and of energy do not vanish. This means that an electric current and energy flux can be set up without an electric field or a temperature gradient to maintain them. In other words, the electric and thermal resistivities are zero in a perfect lattice. The actual resistivities therefore depend on disturbances, which, for the equilibrium problems of Chapter IV, are usually negligible. The problem of treating these disturbances is similar to problem of the calculation of transport phenomena in the kinetic theory of gases, but the nature of interactions and importance of quantum effects brings in a number of new points. Collision time, thermal conductivity, static obstacles, effects of lattice vibrations, collisions between electrons, collisions at high temperatures, low temperatures, and validity of assumptions are discussed.Less

CRYSTAL LATTICES. APPLICATIONS

R. E. Peierls

in Quantum Theory of Solids

This chapter discusses applications of crystal lattices. Topics covered include specific heat, thermal expansion, linear term in specific heat, thermal conductivity, the Boltzmann equation, high ... More

This chapter discusses applications of crystal lattices. Topics covered include specific heat, thermal expansion, linear term in specific heat, thermal conductivity, the Boltzmann equation, high temperature, and impurities and size effect.Less

DYNAMICS OF IMPERFECT LATTICES

A.M. Stoneham

in Theory of Defects in Solids: Electronic Structure of Defects in Insulators and Semiconductors

Defects and impurities affect the vibrations of a solid, and hence properties such as infra-red spectra and thermal conductivity. There can be new, high-frequency, local modes; there can be new, ... More

Defects and impurities affect the vibrations of a solid, and hence properties such as infra-red spectra and thermal conductivity. There can be new, high-frequency, local modes; there can be new, low-frequency, resonances. This chapter analyses key results systematically, including some convenient simple limits. It also goes into detail concerning classical Green's functions, thermodynamic Green's functions, response functions, isotopic impurity, and asymptotic expansions. Local and resonance modes, Rayleigh scattering, and the peak theorem are also considered.Less

Elastic, thermal, and lattice dynamical properties

Victor F. Petrenko and Robert W. Whitworth

in Physics of Ice

This chapter focuses on those effects that depend on small displacements of atoms from their equilibrium sites. It starts with the theory of anisotropic elasticity as applied to a crystalline ... More

This chapter focuses on those effects that depend on small displacements of atoms from their equilibrium sites. It starts with the theory of anisotropic elasticity as applied to a crystalline material with the symmetry of ice Ih, and then gives the experimental parameters for mono-crystalline and polycrystalline ice. The basic thermal properties that arise from lattice vibrations are heat capacity, thermal expansion, and thermal conductivity. A major topic is then the spectroscopy of lattice vibrations as determined by infrared absorption, Raman scattering, and inelastic neutron scattering. These results are then interpreted in terms of the dispersion curves of the lattice, which are modelled by the translational, librational, and molecular modes of the structure.Less

Kinetic Coefficients and Velocity Distribution for Gases of Elastic Particles

Nikolai V. Brilliantov and Thorsten Pöschel

in Kinetic Theory of Granular Gases

This chapter applies the Chapman–Enskog approach to an inhomogeneous gas of elastic particles. It derives the coefficients of viscosity, thermal conductivity, and velocity distribution function.

EFFECT OF FLUCTUATIONS ON THERMOELECTRICITY AND HEAT TRANSPORT

Anatoly Larkin and Andrei Varlamov

in Theory of Fluctuations in Superconductors

This chapter introduces a phenomenological definition of the heat current. An explicit expression for the heat current operator in interacting electron system is derived in the framework of ... More

This chapter introduces a phenomenological definition of the heat current. An explicit expression for the heat current operator in interacting electron system is derived in the framework of microscopic theory, and is used to study the behaviour of fluctuation thermoelectric power and thermal conductivity above the superconducting transition. The final section of this chapter discusses the manifestation of fluctuations in the Nernst effect, which is of current interest in relation to the giant effect observed in high-temperature superconductors.Less

Thermal Expansion, Phonon–Phonon Interactions, and Heat Transport

J. B. Ketterson

in The Physics of Solids

The discussion of Chapter 16, although presenting a general strategy for treating lattice dynamics, was limited in its application to the harmonic approximation. This chapter treats a number of ... More

The discussion of Chapter 16, although presenting a general strategy for treating lattice dynamics, was limited in its application to the harmonic approximation. This chapter treats a number of applications where the effects of anharmonicity enter. In the same way that collisions among molecules are essential for establishing thermal equilibrium in a gas, so interactions among lattice vibrations are required to equilibrate the mechanical excitations in solids; these interactions arise from the anharmonic terms in the expansion of the lattice potential. In addition to driving the system toward equilibrium, anharmonicity also results in thermal expansion, a linear term in the high-temperature specific heat, and finite thermal conductivity. It is shown here that both the cubic and quartic terms must be included in discussing some of these phenomena. The treatment here is limited to insulators.Less

Transport properties

E. R. DOBBS

in Helium Three

This chapter first outlines Fermi liquid theory for the transport coefficients of viscosity, η, thermal conductivity λ, and spin diffusion D. It then shows how far various approximations in the ... More

This chapter first outlines Fermi liquid theory for the transport coefficients of viscosity, η, thermal conductivity λ, and spin diffusion D. It then shows how far various approximations in the theory can lead to reasonable predictions of experimental results. The Leggett–Rice effect and studies of the spin-lattice relaxation time T1 are also considered.Less

Thermodynamics and general properties

A.V. Narlikar

in Superconductors

This chapter discusses the essential thermodynamic aspects of superconductors (with details left to an appendix for the interested reader). Four prominent thermal properties described are heat ... More

This chapter discusses the essential thermodynamic aspects of superconductors (with details left to an appendix for the interested reader). Four prominent thermal properties described are heat capacity, thermal conductivity, thermoelectric power, and thermal expansion, all of which are relevant to engineering applications. They are also fundamentally important in materials characterisation because they yield valuable microscopic parameters of superconductors (e.g. the nature of the charge carriers, the electronic density of states, the Debye temperature, and the energy gap). The first indication of the energy gap in superconductors came through heat capacity and thermal conductivity studies, which paved the way to a successful formulation of the microscopic theory of superconductivity. Ultrasonic, optical, and AC properties of superconductors are also briefly presented. Different features of tunnelling phenomena, including Giaever tunnelling and the Josephson effect, are described. All these experiments put the BCS theory on a firm footing.Less

First-principles approaches

Veljko Zlatić and René Monnier

in Modern Theory of Thermoelectricity

This chapter presents a compact introduction to density functional theory (DFT) and the standard approximations used in practical applications (local density and generalized gradient approximations, ... More

This chapter presents a compact introduction to density functional theory (DFT) and the standard approximations used in practical applications (local density and generalized gradient approximations, LDA and GGA). Improved treatments of the electronic excitations in weakly correlated semiconductors (GW method) and strongly correlated systems (LDA + dynamical mean field theory) are briefly described. The bulk transport coefficients are derived in terms of quantities obtained from self-consistent calculations at the different levels of approximation. Results for the thermopower thus obtained are shown for a number of compounds. A major limiting factor for the efficiency of thermoelectric materials is the lattice thermal conductivity. First-principles-based methods for the calculation of this quantity are presented, with illustrative examples from the literature. Finally, the ab initio treatment of the thermopower of nanostructured materials is illustrated by the example of a molecular junction between two metallic electrodes.Less

Physical interpretation

Veljko Zlatić and René Monnier

in Modern Theory of Thermoelectricity

This chapter describes how, by expressing the elements of the transport matrix obtained for the charge current density–heat current density pair in terms of the electrical conductivity σ, the thermal ... More

This chapter describes how, by expressing the elements of the transport matrix obtained for the charge current density–heat current density pair in terms of the electrical conductivity σ, the thermal conductivity κ, and the Seebeck coefficient α, the standard form of the transport equations is obtained. Imposing the requirement that, in a stationary state, the total energy current density has to be divergence-free leads to the Domenicali equation, the key differential equation for determining the temperature profile in a thermoelectric sample. By looking at particular cases, the defining equations for the Joule heat, the heat current in an open circuit, and the Peltier, Seebeck, and Thomson effects are derived.Less

Thermal Properties of the Ocean

Gino Segrè and John Stack

in Unearthing Fermi's Geophysics

This chapter deals with the thermal properties of ocean water, beginning with some of the basics of heat transmission. Starting with the assumption that heat flow is generated by a temperature ... More

This chapter deals with the thermal properties of ocean water, beginning with some of the basics of heat transmission. Starting with the assumption that heat flow is generated by a temperature gradient, the heat equation is derived. It is a second order differential equation that relates temperature variations in time to ones with position. Since water has such a small thermal conductivity, currents and convection are the main causes of heat transfer in ocean water, leading to the introduction of an effective thermal conductivity. The heat equation is solved to study diurnal and annual variations in the temperature of seawater near the surface. Ocean temperature at greater depths, ocean circulation and the effect of salinity are also discussed.Less