researchers from purdue university (west lafayette, ind.) and the oak ridge national laboratory (oak ridge, tenn.) have demonstrated a method for accurately modeling the interactions of four phonons and the impact they have on thermal conductivity in solid materials.

these diagrams describe the interactions of four phonons, quantum-mechanical phenomena related to the effects of heat conduction in solid materials.
(purdue university image/tianli feng, xiulin ruan)

according to an article on the purdue website, previous research had only been able to model the interactions of three phonons and the scattering behavior that is “fundamental” to how a material conducts heat. the new research ends a decades-long challenge to physicists.

“the discovery could aid efforts to improve a host of technologies including thermoelectric devices, which turn heat into electricity; thermal-barrier coatings such as those used to protect turbine-engine blades from extreme heating; heat sinks for electronics cooling; nuclear fuels; and research into solid-state heat transfer in general,” the article noted.

to model four-phonon scattering required 10,000 times as much computing power as three-phonon scattering, which made the effort previously unfeasible. the team from purdue created a new physical picture of four-phonon scattering to assist in creating theoretical computations and optimizing simulations, which greatly decreased the necessary computing power.

“the new findings demonstrate that only using three-phonon scattering in calculations produces results that overestimate the performance of some materials while underestimating the performance of others,” the article explained.

this new model will assist in the creation of new materials that can be used for heat sinks or for thermoelectric applications.

“the research, which has been entirely theoretical, can explain the previous discrepancy between predicted and experimental thermal conductivities of silicon at high temperature,” the article continued. “it will expand to include more laboratory experiments.”

the full paper was published online by physical review b and was highlighted as a “rapid communications” paper because of its relevance. the abstract stated:

“for decades, the three-phonon scattering process has been considered to govern thermal transport in solids, while the role of higher-order four-phonon scattering has been persistently unclear and so ignored. however, recent quantitative calculations of three-phonon scattering have often shown a significant overestimation of thermal conductivity as compared to experimental values.

“in this rapid communication we show that four-phonon scattering is generally important in solids and can remedy such discrepancies. for silicon and diamond, the predicted thermal conductivity is reduced by 30% at 1000 k after including four-phonon scattering, bringing predictions in excellent agreement with measurements.

“for the projected ultrahigh-thermal conductivity material, zinc-blende bas, a competitor of diamond as a heat sink material, four-phonon scattering is found to be strikingly strong as three-phonon processes have an extremely limited phase space for scattering. the four-phonon scattering reduces the predicted thermal conductivity from 2200 to 1400 w/m k at room temperature. the reduction at 1000 k is 60%.

“we also find that optical phonon scattering rates are largely affected, being important in applications such as phonon bottlenecks in equilibrating electronic excitations. recognizing that four-phonon scattering is expensive to calculate, in the end we provide some guidelines on how to quickly assess the significance of four-phonon scattering, based on energy surface anharmonicity and the scattering phase space.

“our work clears the decades-long fundamental question of the significance of higher-order scattering, and points out ways to improve thermoelectrics, thermal barrier coatings, nuclear materials, and radiative heat transfer.”