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

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

Transcript

1. Dr Jonathan Skelton
   Department of Chemistry, University of Manchester
   (jonathan.skelton@manchester.ac.uk)
   Understanding the thermal transport in Sn(S,Se) alloys
   for thermoelectric applications
   

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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)
   

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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
   

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

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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
   

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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
   

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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
   

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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
   

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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
   

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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
    

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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)
    

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

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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
    

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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)
    

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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)
    

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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)
    

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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)
    

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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
    

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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
    

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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
    

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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
    

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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)
    

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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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