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Understanding the thermal transport in Sn(S,Se) alloys for thermoelectric applications

Understanding the thermal transport in Sn(S,Se) alloys for thermoelectric applications

Presented as a keynote talk at the 2021 MISE Finale Workshop.

Jonathan Skelton

June 18, 2021
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  1. Dr Jonathan Skelton
    Department of Chemistry, University of Manchester
    ([email protected])
    Understanding the thermal transport in Sn(S,Se) alloys
    for thermoelectric applications

    View Slide

  2. Thermoelectrics: motivation
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 2
    34 %
    26 %
    19 %
    18 %
    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 June 2020)
    2. EPSRC Thermoelectric Network Roadmap (2018)

    View Slide

  3. Thermoelectrics: 𝒁𝑻
    𝑍𝑇 =
    𝑆2𝜎
    𝜅ele
    + 𝜅lat
    𝑇
    𝑆 - Seebeck coefficient
    𝜎 - electrical conductivity
    𝜅ele
    - electronic thermal conductivity
    𝜅lat
    - lattice thermal conductivity
    G. Tan et al., Chem. Rev. 116 (19), 12123 (2016)
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 3

    View Slide

  4. Thermoelectrics: SnSe
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 4
    L.-D. Zhao et al., Nature 508, 373 (2014)

    View Slide

  5. Sn(S1-x
    Sex
    ): thermal conductivity
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 5
    C.-C. Lin et al., Chem. Mater. 29 (12), 5344 (2017)
    SnSe
    15-20 % S

    View Slide

  6. Lattice thermal conductivity
    Phonons are generated at the hot side of the material and transport energy to the cold side
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 6

    View Slide

  7. Modelling 𝜿𝐥𝐚𝐭𝐭
    A. Togo et al., Phys. Rev. B 91, 094306 (2015)
    𝜿latt
    (𝑇) =
    1
    𝑁𝑉0

    𝜆
    𝐶𝜆
    (𝑇)𝒗𝜆
    ⊗ 𝒗𝜆
    𝜏𝜆
    (𝑇)
    The simplest model for 𝜅latt
    is the relaxation time approximation (RTA) - a closed solution to the
    phonon Boltzmann transport equations
    Modal heat capacity
    Mode group velocity
    𝜕𝜔λ
    𝜕𝐪
    Average over phonon
    modes λ
    Phonon MFP
    Mode lifetime
    𝜏λ
    =
    1
    2Γλ
    𝚲𝜆
    𝑇 = 𝒗𝜆
    𝜏𝜆
    𝑇
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 7

    View Slide

  8. Modelling 𝜿𝐥𝐚𝐭𝐭
    A. Togo et al., Phys. Rev. B 91, 094306 (2015)
    J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16) 164002 (2021)
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 8

    View Slide

  9. Interpreting 𝜿𝐥𝐚𝐭𝐭
    : the CRTA model
    Consider again the RTA model:
    𝜿latt
    =
    1
    𝑁𝑉0

    𝜆
    𝜿𝜆
    =
    1
    𝑁𝑉0

    𝜆
    𝐶𝜆
    𝒗𝜆
    ⊗ 𝒗𝜆
    𝜏𝜆
    Replace the 𝜏𝜆
    with a constant lifetime (relaxation time) 𝜏CRTA defined as follows:
    𝜿latt
    𝜏CRTA
    =
    1
    𝑁𝑉0

    𝜆
    𝜿𝜆
    𝜏𝜆
    =
    1
    𝑁𝑉0

    𝜆
    𝐶𝜆
    𝒗𝜆
    ⊗ 𝒗𝜆
    𝜿latt

    1
    𝑁𝑉0

    𝜆
    𝐶𝜆
    𝒗𝜆
    ⊗ 𝒗𝜆
    × 𝜏CRTA
    HA
    AH
    HA AH
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 9

    View Slide

  10. Interpreting 𝜿𝐥𝐚𝐭𝐭
    : the CRTA model
    SnS
    SnSe
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 10
    J. M. Skelton, J. Mater. Chem. C (2021), DOI: 10.1039/D1TC02026A

    View Slide

  11. Interpreting 𝜿𝐥𝐚𝐭𝐭
    : the CRTA model
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 11
    𝜅 [W m-1 K-1]
    Τ
    𝜅 𝝉𝐂𝐑𝐓𝐀
    [W m-1 K-1 ps-1] 𝝉𝐂𝐑𝐓𝐀 [ps]
    SnS 2.15 0.718 3.00
    SnSe 1.58 0.372 4.23
    CoSb3
    9.98 0.273 36.6
    Bi2
    S3
    (Pnma) 0.90 0.423 2.14
    Bi2
    Se3
    (R-3m) 1.82 0.293 6.20
    Bi2
    Te3
    (R-3m) 0.87 0.199 4.41
    J. M. Skelton, J. Mater. Chem. C (2021), DOI: 10.1039/D1TC02026A
    J. Tang and J. M. Skelton, J. Phys.: Condens. Matter 33 (16) 164002 (2021)

    View Slide

  12. Modelling alloys
    Build supercell
    Enumerate
    structures
    Optimise
    structures
    Thermodynamics
    + Properties
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 12

    View Slide

  13. Modelling alloys
    Build supercell
    Enumerate
    structures
    Optimise
    structures
    Thermodynamics
    + Properties
    1 10 100 1,000 10,000
    1.000
    0.875
    0.750
    0.625
    0.500
    0.375
    0.250
    0.125
    0.000
    Number of Structures
    Se Fraction
    Total Unique
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 13

    View Slide

  14. The Snm
    (S1-x
    Sex
    )m
    system
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 14
    D. S. D. Gunn et al., Chem. Mater. 31 (10), 3672 (2019)

    View Slide

  15. The Snm
    (S1-x
    Sex
    )m
    system
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 15
    D. S. D. Gunn et al., Chem. Mater. 31 (10), 3672 (2019)

    View Slide

  16. The Snm
    (S1-x
    Sex
    )m
    system
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 16
    D. S. D. Gunn et al., Chem. Mater. 31 (10), 3672 (2019)

    View Slide

  17. The Snm
    (S1-x
    Sex
    )m
    system
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 17
    D. S. D. Gunn et al., Chem. Mater. 31 (10), 3672 (2019)

    View Slide

  18. Pnma Sn(S1-x
    Sex
    ): 𝜿𝐥𝐚𝐭𝐭
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 18
    C.-C. Lin et al., Chem. Mater. 29 (12), 5344 (2017)
    SnSe
    15-20 % S

    View Slide

  19. Pnma Sn(S0.1875
    Se0.8125
    ): phonons
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 19
    J. M. Skelton, J. Mater. Chem. C (2021), DOI: 10.1039/D1TC02026A
    SnS
    SnSe

    View Slide

  20. Pnma Sn(S0.1875
    Se0.8125
    ): phonons
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 20
    J. M. Skelton, J. Mater. Chem. C (2021), DOI: 10.1039/D1TC02026A

    View Slide

  21. Pnma Sn(S0.1875
    Se0.8125
    ): 𝜿𝐥𝐚𝐭𝐭
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 21
    J. M. Skelton, J. Mater. Chem. C (2021), DOI: 10.1039/D1TC02026A
    54.2 % ↓
    Sn(S0.1875
    Se0.8125
    )
    SnSe

    View Slide

  22. Pnma Sn(S0.1875
    Se0.8125
    ): 𝜿𝐥𝐚𝐭𝐭
    “Model 1”: 39.2 % ↓
    “Model 2”: 54.9 % ↓
    “Model 3”: 59.4 % ↓
    Expt: ~60-70 % ↓
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 22
    J. M. Skelton, J. Mater. Chem. C (2021), DOI: 10.1039/D1TC02026A
    C.-C. Lin et al., Chem. Mater. 29 (12), 5344 (2017)

    View Slide

  23. Summary
    First-principles modelling of the lattice thermal conductivity can provide accurate predictions
    and useful insight into how the 𝜅latt
    of thermoelectric materials “works”
    The CRTA model separates the 𝜅latt
    of a material into harmonic (heat capacity/group
    velocity) and anharmonic (lifetime) components, and may be a useful metric for comparing
    different TE materials
    The 𝜅latt
    of SnS and SnSe are a balance of smaller group velocities and longer lifetimes in the
    selenide
    A theoretical model for the Snm
    (S1-x
    Sex
    )n
    system suggests:
    o close to ideal mixing behaviour;
    o volume variation in accordance with Vegard’s law; and
    o a predictable variation in the bandgap of Sn(S1-x
    Sex
    )2
    with composition, covering the
    Shockley–Queisser limit
    Calculations predict a 40-60 % reduction in the 𝜅latt
    of the Sn(S0.1875
    Se0.8125
    ) compared to SnSe,
    which can be ascribed mainly to a “smearing” of the phonon dispersion and a consequent
    reduction in the mode group velocities
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 23

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  24. Acknowledgements
    Dr Jonathan Skelton MISE Finale Workshop June 2021 | Slide 24

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  25. These slides are available on Speaker Deck:
    https://bit.ly/3q4MT24

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