Co3.7 Sb12 0.52 (773 K) Na0.48 Co4 Sb12 1.25 (800 K) Sr0.16 Tb0.03 Co4 Sb11.82 1.32 (850 K) Ba0.08 La0.05 Yb0.04 Co4 Sb12 1.7 (850 K) Yb0.2 Ba0.1 Al0.1 Ga0.1 In0.1 La0.05 Eu0.05 Co4 Sb12 1.2 (800 K) Ce0.12 Fe0.71 Co3.29 Sb12 0.8 (750 K) D. T. Morelli et al., Phys. Rev. B 51, 9622 (1995) Y. Lei et al., J. Mater. Sci. Mater. Electron. 30, 5929 (2019) Y. Z. Pei et al., Appl. Phys. Lett. 95, 042101 (2009) S. Q. Bai et al., Appl. Phys. A 100, 1109 (2010) X. Shi et al., J. Am. Chem. Soc. 133, 7837 (2011) S. Zhang et al., J. Alloys Compd. 814, 152272 (2020) X. F. Tang et al., J. Mater. Sci. 36, 5435 (2001) J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 5
4.0026 31 Ne 20.180 38 Ar 39.948 71 Kr 83.798 88 Xe 131.29 108 J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 6
B 91, 094306 (2015) 𝜿#$%% (𝑇) = 1 𝑁𝑉& 1 ' 𝐶'(𝑇)𝒗' ⊗ 𝒗'𝜏'(𝑇) The simplest model for 𝜅"#$$ is the relaxation time approximation (RTA) - a closed solution to the phonon Boltzmann transport equations Modal heat capacity Mode group velocity 𝜕𝜔& 𝜕𝐪 Sum over phonon modes 𝜆 Phonon MFP Mode lifetime 𝜏& = 1 2Γ& 𝚲' 𝑇 = 𝒗' 𝜏' 𝑇 J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 7
as a linewidth (inverse lifetime) of the form: 𝜏() = 4 * 𝑐* 𝜔+𝑇+ 𝜔* + − 𝜔+ + + 𝛾* 𝜔* +𝜔+ J. W. Schwartz and C. T. Walker, Phys. Rev. 155, 959 (1967) E. S. Toberer et al., J. Mater. Chem. 21, 15843 (2011) J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 11
lifetime (relaxation time) 𝜏-./0 defined as follows: 𝜿"#$$ ≈ 1 𝑁𝑉, 4 ' 𝐶' 𝒗' ⊗ 𝒗' × 𝜏-./0 J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 13 J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) 9-15 % reduction 5-13 % reduction 1-2 % change
M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 15 J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021) The rattling frequency is proportional to the force constant 𝚽 and inversely proportional to the atomic mass 𝑚1 : 𝑫 XX, 𝐪 = Γ = 1 𝑚1 4 2! 𝚽 X0, X𝑙3
- pristine CoSb3 has a poor 𝑍𝑇 of 0.05 at 773 K, but filling can increase 𝑍𝑇 by 20-40 × In pristine CoSb3 , 80 % of the 𝜿"#$$ is through the acoustic modes with 𝑓 < 2.5 THz, and the remaining 20 % through modes with 𝑓 ≈ 2.5-6 THz In noble gas-filled XCo8 Sb24 , the filler rattling frequency from He-Xe is determined by the competition between the force constants and the mass - I 𝑓1 ∝ 𝚽, I 𝑓1 ∝ ⁄ 1 𝑚1 For X = He-Xe, a maximum reduction of 15 % in the 𝜿"#$$ is obtained by suppressing transport through the optic modes through an avoided crossing-type mechanisms Artificially pushing the I 𝑓1 below ~1.5 THz leads to a larger reduction in transport through the acoustic modes through a mix of avoided crossing and resonant scattering-type mechanisms Preliminary calculations on molecule-filled MCo8 Sb24 models show that some small molecules have favourable binding energies and can reduce the 𝜿"#$$ J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 20