Rationalizing phonon dispersion: an efficient and precise prediction of lattice thermal conductivity

October 26, 2018

Lattice thermal conductivity strongly affects the applications of materials related to thermal functionality, such as thermal management, thermal barrier coatings and thermoelectrics. In order to understand the lattice thermal conductivity more quantitatively and in a time- and cost-effective way, many researchers devoted their efforts and developed a few physical models using approximated phonon dispersions over the past century.

Most of these models use a linear phonon dispersion, proposed by Debye in 1912 based on an acoustic-elastic-wave assumption (Fig. 1a), while other models either involve fitting parameters on phonon dispersion or lack detailed equations for phonon transport properties. The linear phonon dispersion of Debye offers many simplifications on phonon transport properties, and was the most common approximation in the past century. The linear dispersion of Debye successfully predicts the T3 dependence of the heat capacity at very low temperatures and heat capacity approaches the Dulong-Petit limit at high temperatures. However, the nature of periodicity on atomic arrangements leads to a periodic boundary condition for lattice vibrations in solids (Fig. 1b), which actually creates lattice standing waves at Brillouin boundaries (Fig. 1c). This does not satisfy the acoustic-elastic-wave assumption of Debye, as proposed by Born and von Karman (BvK) in 1912--the same year that Debye proposed the linear dispersion.

This results in a significant deviation of Debye dispersion for periodic crystalline materials when phonons with wave vectors are close to the Brillouin boundaries (high frequency phonons). When these phonons are involved for phonon transport (i.e. at not extremely low temperatures), Debye dispersion leads to an overestimation of lattice thermal conductivity due to the overestimation of group velocity for these high-frequency phonons, as observed in materials with hundreds of known measured lattice thermal conductivity and necessary details for a time- and cost-effective model prediction to our best knowledge (Fig. 2g and h showing a mean absolute deviation of ~+40%). In addition, Debye dispersion overestimates the theoretically available lower bound of lattice thermal conductivity as well, leading the violations of the measured lattice thermal conductivity to be even lower than the current theoretical minimum predicted (based on the Debye-Cahill model) as observed in tens of materials.

This work takes into account the BvK boundary condition, and reveals that the product of acoustic and optical dispersions yields a sine function. In the case of which the mass (or the force constant) contrast between atoms is large, the acoustic dispersion tends to be a sine-function. This sine type dispersion indeed exists in both the simplest and the most complex materials. Approximating the acoustic dispersion to be sine, the BvK boundary condition subsequently reduces the remaining optical branches to be a series of localized modes with a series of constant frequencies. While first-principles calculations enable a more detailed phonon dispersion, a development of rationalized phonon dispersion for a time- and cost-effective prediction of phonon transport is significant due to the time-consuming and computationally expensive for first-principles calculations.

This work utilizes the above-mentioned rationalization of phonon dispersions, which enables both contributions to lattice thermal conductivity of acoustic and optical phonons to be included. This improvement in phonon dispersions significantly improves the accuracy of a time- and cost-effective prediction on lattice thermal conductivity of solids without any fitting parameters (Fig. 2c, showing a mean absolute deviation of only -2.5%), and therefore offers a more precise design of solids with expected lattice thermal conductivity. Furthermore, this work successfully removes the contradiction of the measured lattice thermal conductivity being even lower than the theoretical minimum predicted based on a linear dispersion of Debye (Fig. 3). This would provide the theoretical possibility of rationalizing lattice thermal conductivity to be lower than is currently thought, opening further opportunities for advancing thermally resistive materials for applications, including thermoelectrics.
See the article:

Zhiwei Chen, Xinyue Zhang, Siqi Lin, Lidong Chen, and Yanzhong Pei
Rationalizing phonon dispersion for lattice thermal conductivity of solids
Natl Sci Rev 2018; doi: 10.1093/nsr/nwy097


The National Science Review is the first comprehensive scholarly journal released in English in China that is aimed at linking the country's rapidly advancing community of scientists with the global frontiers of science and technology. The journal also aims to shine a worldwide spotlight on scientific research advances across China.

Science China Press

Related Phonons Articles from Brightsurf:

Clemson researchers decode thermal conductivity with light
Clemson researchers examine a highly efficient thermoelectric material in a new way - by using light.

Surface waves can help nanostructured devices keep their cool
A research team led by The Institute of Industrial Science, The University of Tokyo demonstrated that hybrid surface waves called surface phonon-polaritons provide enhanced thermal conductivity in nanoscale membranes.

Blocking vibrations that remove heat could boost efficiency of next-gen solar cells
Led by the Department of Energy's Oak Ridge National Laboratory and the University of Tennessee, Knoxville, a study of a solar-energy material with a bright future revealed a way to slow phonons, the waves that transport heat.

Rochester researchers document an optical fiber beyond compare
A new anti-resonant hollow core optical fiber produces a thousand times less ''noise'' interfering with signals it transmits compared to the single-mode fibers now widely used.

A phonon laser - coherent vibrations from a self-breathing resonator
Lasing - the emission of a collimated light beam of light with a well-defined wavelength (color) and phase - results from a self-organization process, in which a collection of emission centers synchronizes itself to produce identical light particles (photons).

New evidence for quantum fluctuations near a quantum critical point in a superconductor
A study has found evidence for quantum fluctuations near a quantum critical point in a superconductor.

New research advances Army's quest for quantum networking
Two U.S. Army research projects advance quantum networking, which will likely play a key role in future battlefield operations.

New techniques improve quantum communication, entangle phonons
PME scientists and engineers have demonstrated a new quantum communication technique, which bypasses traditional channels that can corrupt or lose information.

Cool down fast to advance quantum nanotechnology
An international team of scientists have found an easy way to trigger an unusual state of matter called a Bose-Einstein condensate.

Seeking sounds of superfluids
Sound waves reveal the unique properties of an ultracold quantum gas, a model system for describing certain superconductors and forms of nuclear matter.

Read More: Phonons News and Phonons Current Events
Brightsurf.com is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazon.com.