By Josh Perry, Editor
[email protected]

Researchers have produced a study of phonon dispersion that gives a more detailed quantitative approach to understanding the thermal conductivity of lattice structures, which are the foundation for many of the recently-created, advanced materials.

Researchers have developed a new understanding of phonon dispersion.
(Wikimedia Commons)

The research was published by Science China Press and posted on Phys.org.

Scientists have been using a variation of a model for linear phonon dispersion that was originally proposed in 1912, but the researchers noticed significant deviations with high-frequency phonons that caused overestimations of lattice thermal conductivity.

“This work takes into account the BvK boundary condition,” the report explained, “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.”

By creating a more detailed understanding of phonon dispersion, the scientists are hoping to reduce the time and cost of predicting phonon transport and thermal conductivity in new materials.

“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, and therefore offers a more precise design of solids with expected lattice thermal conductivity,” the report concluded.

The research was recently published in the National Science Review. The abstract stated:

“Lattice thermal conductivity (κ_L) is one of the most fundamental properties of solids. The acoustic–elastic-wave assumption, proposed by Debye (Debye P. Ann Phys 1912; 344: 789–839), has led to linear phonon dispersion being the most common approximation for understanding phonon transport over the past century.

“Such an assumption does not take into account the effect of a periodic boundary condition on the phonon dispersion, originating from the nature of periodicity on atomic arrangements. Driven by modern demands on the thermal functionality of materials, with κ_L ranging from ultra-low to ultra-high, any deviation from the Debye approximation in real materials becomes more and more significant.

“This work takes into account the periodic boundary condition, and therefore rationalizes the phonon dispersion to be more realistic. This significantly improves the precision for quickly predicting κ_L without any fitting parameters, as demonstrated in hundreds of materials, and offers a theoretical basis rationalizing κ_L to be lower than the minimum currently accepted based on the Debye dispersion.

“This work paves the way for designing solids with expected κ_L and particularly inspires the advancement of low-κ_L materials for thermal energy applications.”