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Theory-led design of novel skutterudite thermoelectrics

Theory-led design of novel skutterudite thermoelectrics

Presented at the Royal Society of Chemistry 15th Annual Conference on Materials Chemistry (MC15).

Jonathan Skelton

July 11, 2021
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  1. J. M. Skelton, J. Tang and S. Guillemot
    Department of Chemistry, University of Manchester
    ([email protected])
    Theory-led design of
    novel skutterudite thermoelectrics

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  2. Thermoelectrics: motivation
    J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 2
    Provisional UK greenhouse gas emissions by sector (published June 2020)
    34 %
    19 %
    18 %
    26 %
    3 %

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  3. G. Tan et al., Chem. Rev. 116 (19), 12123 (2016)
    Thermoelectric performance
    J. M. Skelton, J. Tang and S. Guillemot
    𝑍𝑇 =
    𝑆!𝜎
    𝜅"#" + 𝜅#$%%
    𝑇
    𝑆 - Seebeck coefficient
    𝜎 - electrical conductivity
    𝜅!"!
    - electronic thermal conductivity
    𝜅"#$$
    - lattice thermal conductivity
    MC15 July 2021 | Slide 3
    e-
    ph
    HOT
    COLD

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  4. CoSb3
    : PGECs
    J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 4
    G. Tan et al., Chem. Rev. 116 (19), 12123 (2016)
    G. A. Slack in CRC Handbook of Thermoelectrics (1995)
    𝑍𝑇 =
    𝑆!𝜎
    𝜅"#" + 𝜅#$%%
    𝑇
    𝑆 - Seebeck coefficient
    𝜎 - electrical conductivity
    𝜅!"!
    - electronic thermal conductivity
    𝜅"#$$
    - lattice thermal conductivity
    Phonon scattering by
    “rattler” filler atoms
    Electron transport through
    crystalline host framework

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  5. CoSb3
    : fillers
    Composition 𝒁𝑻
    CoSb3
    0.05 (773 K)
    Ni0.3
    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

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  6. A “toy model” system
    Filler 𝒎𝐗
    [amu] 𝒓𝐗
    [pm]
    He 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

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  7. Microscopic model of 𝜿𝐥𝐚𝐭𝐭
    A. Togo et al., Phys. Rev. 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

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  8. Pristine CoSb3
    : 𝜿𝐥𝐚𝐭𝐭
    J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 8
    J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021)

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  9. Filled XCo8
    Sb24
    : 𝜿𝐥𝐚𝐭𝐭
    J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 9
    J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021)
    9-15 % reduction

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  10. Reduced 𝜿𝐥𝐚𝐭𝐭
    : avoided crossings
    J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 10
    E. S. Toberer et al., J. Mater. Chem. 21, 15843 (2011)

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  11. Reduced 𝜿𝐥𝐚𝐭𝐭
    : resonant scattering
    Resonant scattering is usually defined 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

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  12. Mechanism: the CRTA model
    Consider again the RTA model:
    𝜿"#$$
    =
    1
    𝑁𝑉,
    4
    '
    𝜿'
    =
    1
    𝑁𝑉,
    4
    '
    𝐶'
    𝒗'
    ⊗ 𝒗'
    𝜏'
    Replace the 𝜏'
    with a constant lifetime (relaxation time) 𝜏-./0 defined as follows:
    𝜿"#$$
    𝜏-./0
    =
    1
    𝑁𝑉,
    4
    '
    𝜿'
    𝜏'
    =
    1
    𝑁𝑉,
    4
    '
    𝐶'
    𝒗'
    ⊗ 𝒗'
    𝜿"#$$

    1
    𝑁𝑉,
    4
    '
    𝐶'
    𝒗'
    ⊗ 𝒗'
    ×𝜏-./0
    Avoided
    crossing
    Resonant
    scattering
    J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 12

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  13. Mechanism: the CRTA model
    Replace the 𝜏'
    with a constant 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

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  14. Why only a 15 % drop in 𝜿𝐥𝐚𝐭𝐭
    ?
    J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 14
    J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16), 164002 (2021)
    80 %
    20 %

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  15. Why only a 15 % drop in 𝜿𝐥𝐚𝐭𝐭
    ?
    J. 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

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  16. What about molecular fillers?
    J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 16
    L. D. Whalley et al., Phys. Rev. B 94, 220301(R) (2016)
    A. Gold-Parker et al., PNAS 115 (47), 11905 (2018)

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  17. What about molecular fillers?
    J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 17
    L. D. Whalley et al., Phys. Rev. B 94, 220301(R) (2016)
    A. Gold-Parker et al., PNAS 115 (47), 11905 (2018)

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  18. What about molecular fillers?
    J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 18

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  19. What about molecular fillers?
    J. M. Skelton, J. Tang and S. Guillemot MC15 July 2021 | Slide 19
    Filler
    𝒎𝐌
    [amu]
    𝑬𝐁
    [kJ mol-1]
    H2
    O 18.02 -31.9
    H2
    2.016 -19.5
    NH3
    17.03 -5.43
    BH3
    13.83 6.68
    N2
    28.01 38.4
    CH4
    16.04 72.6
    BF3
    67.80 830

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  20. Conclusions
    CoSb3
    is an archetypal “phonon glass electron crystal” material - 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

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  21. Acknowledgements
    MCCM Jan 2021 | Slide 21
    J. M. Skelton, J. Tang and S. Guillemot

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  22. Thankyou for listening!
    Speaker Deck:
    bit.ly/3AQmSZw
    iPoster (P213):
    bit.ly/3i0GXU7

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