Four-Phonon Scattering

Four-phonon scattering is a higher-order phonon–phonon interaction in which four phonons participate in a scattering event, as opposed to the lower-order three-phonon process. The source archive boron arsenide dossier presents it as the key theoretical correction that reconciled first-principles predictions of BAs thermal conductivity with measurement.

The problem it addresses

For decades, the three-phonon scattering process was considered to govern thermal transport in solids, while the role of higher-order four-phonon scattering was "persistently unclear and so ignored." However, quantitative calculations of three-phonon scattering often significantly overestimated thermal conductivity compared with experimental values.

The Physical Review B Rapid Communication by Tianli Feng, Lucas Lindsay, and Xiulin Ruan ("Four-phonon scattering significantly reduces intrinsic thermal conductivity of solids") showed that four-phonon scattering is generally important and can remedy such discrepancies.

Reported effects

• Silicon and diamond: predicted thermal conductivity reduced by 30% at 1000 K after including four-phonon scattering, bringing predictions into excellent agreement with measurements.
• Zinc-blende BAs: four-phonon scattering is "strikingly strong" because three-phonon processes have an extremely limited phase space for scattering. It reduces the predicted room-temperature thermal conductivity from 2200 to 1400 W/(m·K), and the reduction at 1000 K is 60%.
• Optical phonons: scattering rates are largely affected, which the authors note is important in applications such as phonon bottlenecks in equilibrating electronic excitations.

Practical guidance

Because four-phonon scattering is expensive to calculate, the paper provides guidelines for quickly assessing its significance based on energy surface anharmonicity and the scattering phase space. The authors state the work "clears the decades-long fundamental question of the significance of higher-order scattering" and points to improvements in thermoelectrics, thermal barrier coatings, nuclear materials, and radiative heat transfer.

Relation to the BAs story

The four-phonon correction is one of two steps that brought BAs theory and measurement closer together; the other is the identification of antisite defects as the dominant extrinsic suppressor of conductivity. Both are discussed in Ultrahigh Thermal Conductivity in Boron Arsenide, and the material itself is described in Boron Arsenide (BAs). The antisite defect mechanism is treated separately in Antisite Defects in Boron Arsenide.

Related pages

• Ultrahigh Thermal Conductivity in Boron Arsenide
• Boron Arsenide (BAs)
• Antisite Defects in Boron Arsenide