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Controlling the heat transport in thermoelectric materials

Controlling the heat transport in thermoelectric materials

Presented at the Royal Society of Chemistry (RSC) 16th International Conference on Materials Chemistry (MC16) on 6th July 2023.

Jonathan Skelton

July 06, 2023
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  1. Dr Jonathan Skelton
    Department of Chemistry, University of Manchester
    ([email protected])
    Controlling the heat transport
    in thermoelectric materials

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  2. Acknowledgements
    Dr Jonathan Skelton
    ... plus other students, mentors and
    collaborators too numerous to mention
    MC16, 6th July 2023 | Slide 2

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  3. The global energy challenge
    MC16, 6th July 2023 | Slide 3
    31 %
    23 %
    20 %
    19 %
    3 %
    1000 MW nuclear power plant:
    o 650 MW waste heat
    o 3 % ≈ 20 MW ≈ 50,000 homes
    300-500 W from exhaust gases:
    o 2 % lower fuel consumption
    o 2.4 Mt reduction in CO2
    Thermoelectric generators allow waste
    heat to be recovered as electricity
    TEGs with ~3 % energy recovery (𝑍𝑇 = 1) are
    considered industrially viable
    1. Provisional UK greenhouse gas emissions national statistics (published March 2022)
    2. EPSRC Thermoelectric Network Roadmap (2018)
    Dr Jonathan Skelton

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  4. Thermoelectric materials
    Dr Jonathan Skelton
    𝑍𝑇 =
    𝑆!𝜎
    𝜅"#" + 𝜅#$%
    𝑇
    𝑆 - Seebeck coefficient
    𝜎 - electrical conductivity
    𝜅!"!
    - electronic thermal conductivity
    𝜅"#$
    - lattice thermal conductivity
    G. Tan et al., Chem. Rev. 116 (19), 12123 (2016)
    MC16, 6th July 2023 | Slide 4

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  5. The IV-VI chalcogenides
    Dr Jonathan Skelton
    L.-D. Zhao et al., Nature 508, 373 (2014)
    MC16, 6th July 2023 | Slide 5

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  6. A comparative study
    Dr Jonathan Skelton
    GeSe GeTe SnSe SnTe
    𝑃𝑛𝑚𝑎 ü ü ü ü
    𝐶𝑚𝑐𝑚 ü
    𝑅3𝑚 ü ü ü
    𝐹𝑚0
    3𝑚 ü ü
    𝑃𝑛𝑚𝑎 𝐶𝑚𝑐𝑚
    𝑅3𝑚 𝐹𝑚*
    3𝑚
    MC16, 6th July 2023 | Slide 6

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  7. Modelling thermal conductivity
    A. Togo et al., Phys. Rev. B 91, 094306 (2015)
    Dr Jonathan Skelton
    The simplest model for 𝜅"#$$
    is the single-mode relaxation time approximation (SM-RTA) - a
    closed solution to the phonon Boltzmann transport equations
    𝜿!"##
    =
    1
    𝑁𝑉
    &
    $
    𝜿$
    =
    1
    𝑁𝑉
    &
    $
    𝐶$
    𝒗$
    ⊗ 𝒗$
    𝜏$
    𝐶%
    - phonon heat capacities
    𝒗%
    - phonon group velocities
    𝜏%
    - phonon lifetimes (inverse linewidths Γ%
    )
    𝑁 - number of 𝒒 in summation
    𝑉 - unit cell volume
    MC16, 6th July 2023 | Slide 7

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  8. A comparative study
    Dr Jonathan Skelton
    𝜅𝐥𝐚𝐭𝐭
    (𝑇 = 300 K)
    [W m-1 K-1]
    SnSe (𝐶𝑚𝑐𝑚) 0.96
    SnTe (𝑃𝑛𝑚𝑎) 1.09
    GeTe (𝑃𝑛𝑚𝑎) 1.32
    SnSe (𝑃𝑛𝑚𝑎) 1.36
    GeTe (𝐹𝑚+
    3𝑚) 1.57
    GeSe (𝐹𝑚+
    3𝑚) 1.67
    GeSe (𝑃𝑛𝑚𝑎) 2.36
    SnTe (𝑅3𝑚) 4.18
    GeTe (𝑅3𝑚) 4.36
    SnTe (𝐹𝑚+
    3𝑚) 5.01
    MC16, 6th July 2023 | Slide 8

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  9. Group velocities vs. lifetimes
    Dr Jonathan Skelton
    𝜿./00
    ≈ 𝜏1234×
    1
    𝑁𝑉
    2
    5
    𝜿5
    𝜏5
    =
    1
    𝑁𝑉
    2
    5
    𝐶5
    𝒗5
    ⊗ 𝒗5
    ×𝜏1234
    J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33, 164002 (2021)
    J. M. Skelton, J. Mater. Chem. C 9, 11772 (2021)
    MC16, 6th July 2023 | Slide 9

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  10. Group velocities vs. lifetimes
    Dr Jonathan Skelton
    𝜅𝐥𝐚𝐭𝐭
    [W m-1 K-1]

    𝜅𝐥𝐚𝐭𝐭 𝝉𝐂𝐑𝐓𝐀
    [W m-1 K-1 ps-1]
    𝝉𝐂𝐑𝐓𝐀
    [ps]
    SnTe (𝑃𝑛𝑚𝑎) 1.09 0.27 3.98
    GeTe (𝑃𝑛𝑚𝑎) 1.32 0.34 3.91
    SnSe (𝑃𝑛𝑚𝑎) 1.36 0.35 3.89
    GeSe (𝑃𝑛𝑚𝑎) 2.36 0.39 6.03
    SnTe (𝑅3𝑚) 4.18 0.69 6.07
    GeTe (𝑅3𝑚) 4.36 0.87 5.01
    SnTe (𝐹𝑚+
    3𝑚) 5.01 1.07 4.67
    SnSe (𝐶𝑚𝑐𝑚) 0.96 1.09 0.88
    GeTe (𝐹𝑚+
    3𝑚) 1.67 2.99 0.56
    GeSe (𝐹𝑚+
    3𝑚) 1.57 3.29 0.48
    MC16, 6th July 2023 | Slide 10

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  11. Group velocities vs. lifetimes
    Dr Jonathan Skelton
    𝜅𝐥𝐚𝐭𝐭
    [W m-1 K-1]

    𝜅𝐥𝐚𝐭𝐭 𝝉𝐂𝐑𝐓𝐀
    [W m-1 K-1 ps-1]
    𝝉𝐂𝐑𝐓𝐀
    [ps]
    GeSe (𝐹𝑚+
    3𝑚) 1.57 3.29 0.48
    GeTe (𝐹𝑚+
    3𝑚) 1.67 2.99 0.56
    SnSe (𝐶𝑚𝑐𝑚) 0.96 1.09 0.88
    SnSe (𝑃𝑛𝑚𝑎) 1.36 0.35 3.89
    SnTe (𝑃𝑛𝑚𝑎) 1.32 0.34 3.91
    SnTe (𝑅3𝑚) 1.09 0.27 3.98
    SnTe (𝐹𝑚+
    3𝑚) 5.01 1.07 4.67
    GeTe (𝑅3𝑚) 4.36 0.87 5.01
    GeSe (𝑃𝑛𝑚𝑎) 2.36 0.39 6.03
    SnTe (𝑅3𝑚) 4.18 0.69 6.07
    MC16, 6th July 2023 | Slide 11

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  12. Anharmonicity vs. “selection rules”
    Γ5
    =
    36𝜋
    ℏ8
    2
    5&5&&
    Φ955&5&&
    8×{
    𝑛5& + 𝑛5&& + 1 𝛿 𝜔 − 𝜔5& − 𝜔5&&
    + 𝑛5& − 𝑛5&& 𝛿 𝜔 + 𝜔5& − 𝜔5&& − 𝛿 𝜔 − 𝜔5& + 𝜔5&&
    }
    Decay Collision
    Three-phonon interaction strength
    (includes conservation of momentum)
    Conservation of energy
    Dr Jonathan Skelton
    A. Togo et al., Phys. Rev. B 91, 094306 (2015)
    MC16, 6th July 2023 | Slide 12

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  13. Anharmonicity vs. “selection rules”
    Dr Jonathan Skelton
    𝜏:
    =
    1
    2𝜋Γ5
    Γ5

    36𝜋
    ℏ8
    𝑁8
    (𝒒5
    , 𝜔5
    )×𝑃5
    and
    A. Togo et al., Phys. Rev. B 91, 094306 (2015)
    B. Wei, J. Flitcroft and J. M. Skelton, Molecules 27 (19), 6431 (2022)
    MC16, 6th July 2023 | Slide 13

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  14. Anharmonicity vs. “selection rules”
    Dr Jonathan Skelton
    𝑃𝑛𝑚𝑎
    Other
    phases
    Other
    phases
    𝑃𝑛𝑚𝑎
    𝜏:
    =
    1
    2𝜋Γ5
    Γ5

    36𝜋
    ℏ8
    𝑁8
    (𝒒5
    , 𝜔5
    )×𝑃5
    and
    MC16, 6th July 2023 | Slide 14

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  15. Anharmonicity vs. “selection rules”
    Dr Jonathan Skelton
    𝝉𝐂𝐑𝐓𝐀
    [ps]
    ;
    𝑷× 𝟑𝒏𝒂
    𝟐
    [eV2]

    ;
    𝑵𝟐 𝟑𝒏𝒂
    𝟐
    [THz-1]
    SnTe (𝑃𝑛𝑚𝑎) 3.98 9.07 × 10-9 1.70 × 10-2
    SnSe (𝑃𝑛𝑚𝑎) 3.89 1.20 × 10-8 1.31 × 10-2
    GeTe (𝑃𝑛𝑚𝑎) 3.91 1.35 × 10-8 1.15 × 10-2
    GeSe (𝑃𝑛𝑚𝑎) 6.03 1.36 × 10-8 7.44 × 10-3
    SnTe (𝑅3𝑚) 6.07 5.20 × 10-8 1.93 × 10-3
    GeTe (𝑅3𝑚) 5.01 8.97 × 10-8 1.36 × 10-3
    SnTe (𝐹𝑚+
    3𝑚) 4.67 1.09 × 10-7 1.20 × 10-3
    SnSe (𝐶𝑚𝑐𝑚) 0.88 1.46 × 10-7 4.74 × 10-3
    GeTe (𝐹𝑚+
    3𝑚) 0.56 1.31 × 10-6 8.35 × 10-4
    GeSe (𝐹𝑚+
    3𝑚) 0.48 2.24 × 10-6 5.69 × 10-4
    Calculate an averaged number of scattering pathways from 𝜏'()* and 7
    𝑃: 8
    𝑁+
    =
    ℏ!
    ,+-! .
    /0"#$%
    MC16, 6th July 2023 | Slide 15

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  16. Trends in structure type
    Dr Jonathan Skelton
    𝑃𝑛𝑚𝑎 𝐶𝑚𝑐𝑚 𝑅3𝑚 𝐹𝑚*
    3𝑚
    Lower 𝒗1
    : smaller ⁄
    𝜅"#$$
    𝜏'()*
    Stronger anharmonicity: larger 7
    𝑃 → shorter 𝜏'()*
    Larger scattering phase space: larger 8
    𝑁+
    → shorter 𝜏'()*
    MC16, 6th July 2023 | Slide 16

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  17. Interpretation: group velocities
    Dr Jonathan Skelton
    http://www-personal.umich.edu/~alberliu/writing/condensedmatter/1dlatticenormalmodes.pdf
    MC16, 6th July 2023 | Slide 17
    𝑣%
    ≈ 𝑎
    𝑘
    𝑚
    𝑣%
    ≈ 2𝑎
    𝑘×𝑔
    2𝑚(𝑘 + 𝑔)
    𝑘 𝑔
    𝑎
    2𝑎
    𝑘 Equiv. bonds (𝑔 = 𝑘)
    Broken chain (𝑔 = 0)
    𝑚 𝑚 𝑚 𝑚
    𝑚 𝑚 𝑚 𝑚

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  18. A. Walsh et al., Chem. Soc. Rev. 40, 4455 (2011)
    M. J. Smiles et al., J. Mater. Chem. A 9, 22440 (2021)
    Interpretation: anharmonicity
    Dr Jonathan Skelton MC16, 6th July 2023 | Slide 18

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  19. Trends in structure type
    Dr Jonathan Skelton
    𝐶𝑚𝑐𝑚 SnSe:
    ? Low symmetry
    ü Large(-ish) cell (𝑛2
    = 4)
    ü Sn constrained to a locally-symmetric
    environment
    𝜋-cubic SnSe:
    ? High symmetry
    ü (Very) large cell (𝑛2
    = 64)
    û Sn local geometry similar to 𝑃𝑛𝑚𝑎
    phase
    R. E. Abutbul et al., CrystEngComm 18, 1918 (2016)
    MC16, 6th July 2023 | Slide 19

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  20. Summary
    Dr Jonathan Skelton
    The SM-RTA model provides insight into the 𝜅"#$$
    at the level of individual phonon modes, which
    can be analysed to quantify the separate contributions of:
    o Group velocity vs. lifetimes - the CRTA model
    o Anharmonicity vs. selection rules - the constant interaction-strength model
    For a series of ten chalcogenides, we find that:
    o Low group velocities are favoured by complex structures with large unit cells
    o Strong phonon anharmonicity is favoured by structures where the tetrel atoms are
    constrained to locally-symmetric environments...
    o ... but less symmetric structures allow for a large scattering phase space
    These competing factors are optimally balanced in 𝐶𝑚𝑐𝑚 SnSe, which has:
    o a larger and lower-symmetry unit cell compared to 𝑅3𝑚/𝐹𝑚0
    3𝑚 phases...
    o ... but with the Sn atoms are constrained to a locally symmetric environment
    The trends in group velocity can be explained in terms of bonding inhomogeneity
    The trends in anharmonicity can be explained in terms of the revised lone pair model
    MC16, 6th July 2023 | Slide 20

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  21. bit.ly/3JFclWU
    These slides are available on Speaker Deck:

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