Related Experiment Video
Updated: Aug 10, 2026
05:20
Characterization of Thermal Transport in One-dimensional Solid Materials
Published on: January 26, 2014
Heat conduction in one-dimensional lattices with on-site potential
1Institute of Chemical Physics, RAS, Kosygin Street 4, Moscow, Russia. asavin@center.chph.ras.ru
Summary
Anharmonicity alone does not guarantee normal heat conduction in 1D lattices. Nonlinear excitations, like solitons and breathers, dictate energy scattering and thus heat transport properties, depending on the lattice model and temperature.
Area of Science:
- Condensed matter physics
- Statistical mechanics
- Nonlinear dynamics
Background:
- Heat conduction in low-dimensional systems is complex.
- The role of anharmonicity in lattice thermal conductivity is debated.
- One-dimensional lattices offer a simplified yet rich model for studying transport phenomena.
Purpose of the Study:
- To investigate the conditions for normal heat conduction in 1D lattices with on-site potentials.
- To determine if sole anharmonicity of the on-site potential is sufficient for normal heat conductivity.
- To elucidate the influence of nonlinear excitations on heat transport.
Main Methods:
- Numerical simulations of heat conduction.
- Utilized discrete Frenkel-Kontorova, phi(4), and sinh-Gordon models.
- Analysis of nonlinear excitation spectra and their interactions.
Main Results:
- The sole anharmonicity of the on-site potential is insufficient for normal heat conductivity.
- Heat conduction character depends on the spectrum of nonlinear excitations.
- Phonons scatter at topological solitons (sine-Gordon, phi(4)) or localized breathers (sinh-Gordon, phi(4)).
- The scattering mechanism can switch with increasing temperature (phi(4)).
Conclusions:
- Nonlinear excitations, not just anharmonicity, govern heat transport in these 1D lattices.
- The specific potential shape and temperature determine the dominant energy scattering mechanisms.
- Understanding nonlinear excitation dynamics is crucial for predicting thermal conductivity in such systems.
Related Concept Videos
02:54Trends in Lattice Energy: Ion Size and Charge
An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
02:33Lattice Centering and Coordination Number
The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
Types of Unit Cells
Imagine taking a large number of identical...
01:21Current Density
The total amount of current flowing through one unit value of a cross-sectional area is referred to as current density. If the current flow is uniform, the amount of current flowing through a conductor is the same at all points along the conductor, even if the conductor area varies. The current density consists of the local magnitude and direction of the charge flow, which varies from point to point. Current density is measured in amperes per meter square, and direction is defined as the net...
01:17Theory of Metallic Conduction
The conduction of free electrons inside a conductor is best described by quantum mechanics. However, a classical model makes predictions close to the results of quantum mechanics. It is called the theory of metallic conduction.
In this theory, Newton's second law of motion is used to determine the acceleration of an electron in the presence of an applied electric field. Then, its velocity is expressed via this acceleration.
An electron moves through the crystal, containing positive ions,...
In this theory, Newton's second law of motion is used to determine the acceleration of an electron in the presence of an applied electric field. Then, its velocity is expressed via this acceleration.
An electron moves through the crystal, containing positive ions,...
01:30The Electrical Double Layer
In the region where two bulk phases meet, an intricate electric charge distribution arises due to charge transfer, ion adsorption, molecular orientation, and charge distortion. This complex distribution is commonly referred to as the electrical double layer.When a solid electrode interfaces with ions in an electrolyte solution, the speed of electron transfer dictates the rates of oxidation and reduction. The electrode acquires a charge through the escape of atoms into the solution as cations or...
01:27Lattice Energies of Ionic Crystals
Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...