In crystalline electrical insulators, heat is carried by phonons, which are quantized vibrations of the crystal lattice. As these phonons travel through the material, they collide with each other, thereby limiting the material’s thermal conductivity (k). Predicting how frequent and strong these collisions are (“collision rates”) for each material under different experimental conditions is computationally expensive. This can slow down the discovery of new materials, with their k values and trends tailored to our needs.
New research led by Navaneetha Krishnan Ravichandran at the Department of Mechanical Engineering now provides a way to identify materials that show intriguing temperature- and pressure-dependencies of k, without performing these full, expensive computations.
In an earlier publication, Ravichandran and collaborator David Broido at Boston College, USA developed a set of guidelines to identify materials with unusually weak rates of three-phonon collisions, directly from the phonon dispersion relations, which describes the temporal frequencies and energy content in different collective vibration modes propagating through the crystal lattice of each material. These dispersion relations and the guidelines arising out of them are significantly less expensive to compute than the full three-phonon collision rates. The guidelines were derived from certain “selection rules” arising from the energy and momentum conservation restrictions on phonon collisions in quantum mechanics, which eventually control the relative strength of different three-phonon collision events.
In the new study, the researchers used these insights to predict an unusual pressure-dependence of the k of a material called boron phosphide (BP). They found that BP has a unique phonon dispersion relation: when pressure is applied, the resulting changes in the phonon dispersion relations cause a very strong interplay between different three-phonon collision processes, driven primarily by the aforementioned selection rules.
At the material level, this interplay results in an unusually sharp rise in its k with pressure, which the researchers predict to be the steepest in any material. It also results in a peak and subsequent drop in the k of BP with pressure, in stark contrast to the linearly increasing trend seen in most other materials. The current study is an exciting application of the selection rule framework to identify new materials with novel thermal transport phenomena.
Ravichandran, N.K., Broido, D. Exposing the hidden influence of selection rules on phonon–phonon scattering by pressure and temperature tuning. Nat Commun 12, 3473 (2021).