[Paper Review] Crossover from Boltzmann to Wigner thermal transport in thermoelectric skutterudites

Enrico Di Lucente, Michele Simoncelli+1 more|arXiv (Cornell University)|Mar 13, 2023

Advanced Thermoelectric Materials and DevicesMaterials Science84 references3 citations

TL;DR

This paper introduces a Wigner formulation of thermal transport to explain the crossover from particlelike (Boltzmann) to wavelike (Wigner) heat conduction in thermoelectric skutterudites due to filler atoms. It identifies a Boltzmann deviation descriptor that quantifies the transition, showing wavelike tunneling becomes comparable to particlelike transport near peak thermoelectric efficiency, offering a design strategy for optimizing filler elements to minimize thermal conductivity.

ABSTRACT

Skutterudites are crystals with a cage-like structure that can be augmented with filler atoms ("rattlers"), usually leading to a reduction in thermal conductivity that can be exploited for thermoelectric applications. Here, we leverage the recently introduced Wigner formulation of thermal transport to elucidate the microscopic physics underlying heat conduction in skutterudites, showing that filler atoms can drive a crossover from the Boltzmann to the Wigner regimes of thermal transport, i.e., from particle-like conduction to wave-like tunnelling. At temperatures where the thermoelectric efficiency of skutterudites is largest, wave-like tunneling can become comparable to particle-like propagation. We define a Boltzmann deviation descriptor able to differentiate the two regimes and relate the competition between the two mechanisms to the materials' chemistry, providing a design strategy to select rattlers and identify optimal compositions for thermoelectric applications.

Motivation & Objective

• To understand the microscopic mechanisms behind reduced thermal conductivity in filled skutterudites, particularly the role of filler atoms.
• To bridge the gap in theoretical understanding of heat conduction in poor thermal conductors, especially in the regime of ultralow thermal conductivity.
• To develop a descriptor that differentiates between Boltzmann (particlelike) and Wigner (wavelike) thermal transport regimes in thermoelectric materials.
• To provide a predictive design strategy for selecting optimal filler atoms based on their impact on the transport regime crossover.

Proposed method

• Adopts the Wigner formulation of thermal transport, which unifies descriptions of harmonic, anharmonic, and glassy regimes in solids.
• Uses ab initio density functional theory (DFT) to compute phonon dispersions, linewidths, and intermode matrix elements.
• Applies the Wigner transport equation to calculate total thermal conductivity (κ_tot), separating contributions into particlelike (κ_P) and wavelike (κ_C) components.
• Introduces a Boltzmann deviation descriptor based on the ratio of phonon linewidths to interband spacings to quantify the crossover from Boltzmann to Wigner regimes.
• Performs systematic calculations on un-filled and filled skutterudites (e.g., FeSb3, CoSb3, IrSb3 with R = Ba, Ca, Nd, Yb, etc.) across 100–800 K.

Experimental results

Research questions

• RQ1 How do filler atoms in skutterudites influence the transition between particlelike and wavelike thermal transport?
• RQ2 To what extent does wavelike tunneling contribute to thermal transport in thermoelectric skutterudites at high-temperature operating conditions?
• RQ3 Can a quantitative descriptor be defined to distinguish between Boltzmann and Wigner regimes in thermal transport?
• RQ4 How does the chemical identity of the filler atom affect the crossover temperature and the relative contribution of wavelike vs. particlelike mechanisms?

Key findings

• Wavelike tunneling becomes comparable to particlelike propagation in filled skutterudites near their peak thermoelectric efficiency temperature (around 700 K), indicating a significant crossover from Boltzmann to Wigner transport.
• The Boltzmann deviation descriptor successfully identifies the crossover regime and correlates with the chemical nature of the filler, showing that heavier and more polarizable fillers (e.g., Yb, Nd) enhance the Wigner contribution.
• Thermal conductivity (κ_tot) in filled skutterudites shows a milder T⁻¹ decay than the particlelike component (κ_P), indicating a growing role of wavelike processes at higher temperatures.
• The Wigner formulation accurately captures the ultralow thermal conductivity observed experimentally in filled skutterudites, where the Peierls-Boltzmann equation fails due to strong anharmonicity and hybridization.
• The study reveals that the hybridization between filler vibrations and host phonon bands is not just a scattering mechanism but a key driver of wavelike heat transport, challenging the traditional 'rattling' picture.