The effect of extended strain fields on point defect scattering

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1 Engineering Conferences International ECI Digital Archives Nonstoichiometric Compounds VI Proceedings The effect of extended strain fields on point defect scattering Brenden R. Ortiz Colorado School of Mines, Haowei Peng National Renewable Energy Laboratory Philip Parilla National Renewable Energy Laboratory Stephan Lany National Renewable Energy Laboratory Armando Lopez Colorado School of Mines See next page for additional authors Follow this and additional works at: Recommended Citation Brenden R. Ortiz, Haowei Peng, Philip Parilla, Stephan Lany, Armando Lopez, and Eric S. Toberer, "The effect of extended strain fields on point defect scattering" in "Nonstoichiometric Compounds VI", ECI Symposium Series, (2016). nonstoichiometric_vi/37 This Abstract and Presentation is brought to you for free and open access by the Proceedings at ECI Digital Archives. It has been accepted for inclusion in Nonstoichiometric Compounds VI by an authorized administrator of ECI Digital Archives. For more information, please contact

2 Authors Brenden R. Ortiz, Haowei Peng, Philip Parilla, Stephan Lany, Armando Lopez, and Eric S. Toberer This abstract and presentation is available at ECI Digital Archives:

Extended Strain Fields and Point-Defect Phonon Scattering Brenden Ortiz, Haowei Peng, Armando Lopez, Phillip Parilla, Stephan Lany, Eric Toberer Colorado School of Mines, Golden, CO National

3 Extended Strain Fields and Point-Defect Phonon Scattering Brenden Ortiz, Haowei Peng, Armando Lopez, Phillip Parilla, Stephan Lany, Eric Toberer Colorado School of Mines, Golden, CO National Renewable Energy Laboratory, Golden, CO ECI Non-Stoichiometric Compounds (Santa Fe 2016) NREL is a national laboratory of the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

4 Thermoelectrics as an Optimization Problem 2 S zt σ κ Carrier Concentration + Each transport phenomenon also has T dependence

5 Thermoelectrics as an Optimization Problem 3 S zt σ κ The thermal conductivity, κ, is commonly targeted for optimization. Carrier Concentration + Each transport phenomenon also has T dependence

6 Thermoelectrics as an Optimization Problem 4

7 Thermoelectrics as an Optimization Problem 5

8 Thermoelectrics as an Optimization Problem 6 Alloys as a source of point defect scattering Mass contrast simple, but role of strain field not obvious in complex crystals

9 Thermoelectrics as an Optimization Problem 7 Chemical degrees of freedom can slow down experimental searches

10 Thermoelectrics as an Optimization Problem 8 Chemical degrees of freedom can slow down experimental searches

11 Mission Statement 9 Can we find a way to accelerate the discovery of effective alloys using simple, intuitive computational models?

12 Mission Statement 10 Can we find a way to accelerate the discovery of effective alloys using simple, intuitive computational models? Experiment / Modeling AbInitio Computation

13 Mission Statement 11 Can we find a way to accelerate the discovery of effective alloys using simple, intuitive computational models? Experiment / Modeling AbInitio Computation Model System Classical Alloy Models Experimental Results Toy Models for Strain Computational Methods Computational Results

14 Mission Statement 12 Can we find a way to accelerate the discovery of effective alloys using simple, intuitive computational models? Experiment / Modeling AbInitio Computation Model System Classical Alloy Models Experimental Results Toy Models for Strain Computational Methods Computational Results Effective Proxy?

15 Experiment Model System 13 SnSe (Pnma) + one of Sr, Ba, S, Se, Te (e.g. Sn 1-x Ba x Se) BaSe, SrSe, SnTe: Rock-salt SnS, GeSe: Layered Pnma (distorted-rs) Distorted-rock salt structure + Rock-salt and non rock-salt endpoints

16 Experiment Model System 14 SnSe (Pnma) + one of Sr, Ba, S, Se, Te (e.g. Sn 1-x Ba x Se) Synthesis (e.g SnSe + SnSe 2 + Ba) + Ball-milling and inductive hot-pressing

17 Experiment Model System 15 SnSe (Pnma) + one of Sr, Ba, S, Se, Te (e.g. Sn 1-x Ba x Se) X-ray Diffraction, Rietveld Refinement + Vegard s Law

18 Experiment Model System Note large spread in the thermal conductivity w/alloying species. Depressions range from slight (e.g. Sulfur) to severe (e.g. Ba) Need to model to understand role of chemistry on scattering. Abeles Model for Alloy Scattering. 1 [1] B. Abeles, Phys. Rev., 1963, 131,

19 Experiment Transport and Modeling 17 Abeles model for composition dependent thermal conductivity Thermal Conductivity of Alloy (κ alloy )

20 Experiment Transport and Modeling 18 Abeles model for composition dependent thermal conductivity Thermal Conductivity of Alloy (κ alloy ) Disorder Scaling Parameter (u)

21 Experiment Transport and Modeling 19 Abeles model for composition dependent thermal conductivity Thermal Conductivity of Alloy (κ alloy ) Disorder Scaling Parameter (u) Net Scattering Factor (Γ tot )

22 Experiment Transport and Modeling 20

23 Experiment Transport and Modeling 21 Mass Contrast

24 Experiment Transport and Modeling 22 Mass Contrast Radii Contrast

25 Experiment Transport and Modeling 23 Mass Contrast Free parameter Radii Contrast

26 Experiment Transport and Modeling 24 Mass Contrast Free parameter Radii Contrast

27 Experimental Summary 25 Increasing Strain Contribution + Decreasing Thermal Conductivity

28 Computational Toy Models 26

29 Computational Methods 27 Approach 1: Pair-Distribution Function (Supercell) 32-atom special quasi-random structures (SQS) to mimic 25% alloy PDF s

30 Computational Methods 28 Approach 1: Pair-Distribution Function (Supercell) 32-atom special quasi-random structures (SQS) to mimic 25% alloy PDF s r + dr

31 Computational Methods 29 Approach 1: Pair-Distribution Function (Supercell) 32-atom special quasi-random structures (SQS) to mimic 25% alloy PDF s r + dr

32 Computational Methods Pair Distribution Fn 30 Approach 1: Pair-Distribution Function (Supercell)

33 Computational Methods Pair Distribution Fn 31 Approach 1: Pair-Distribution Function (Supercell)

34 Computational Methods Pair Distribution Fn 32 Approach 1: Pair-Distribution Function (Supercell)

35 Computational Methods Pair Distribution Fn 33 Approach 1: Pair-Distribution Function (Supercell)

36 Computational Methods 34 Approach 2: Single Atom Distortion (Supercell) 256-atom supercell with singular atom replaced by alloying species

37 Computational Methods 35 Approach 2: Single Atom Distortion (Supercell) 256-atom supercell with singular atom replaced by alloying species

38 Computational Methods 36 Approach 2: Single Atom Distortion (Supercell) 256-atom supercell with singular atom replaced by alloying species

39 Computational Methods 37 Approach 2: Single Atom Distortion (Supercell) 256-atom supercell with singular atom replaced by alloying species

alloying species Change in local coordination around species How far

40 Computational Methods 38 Approach 2: Single Atom Distortion (Supercell) 256-atom supercell with singular atom replaced by alloying species Change in local coordination around species How far from source atom does it extend? How large of a distortion? Relation with chemistry?

41 Computational Methods Single Atom Distortion 39

42 Computational Methods Single Atom Distortion 40

43 Computational Methods Single Atom Distortion 41 r SnSe,i

44 Computational Methods Single Atom Distortion 42 r SnSe,i r Alloy,i

45 Computational Methods Single Atom Distortion 43 Δ SAD,i r SnSe,i r Alloy,i

46 Computational Methods Single Atom Distortion 44 Δ SAD,i r SnSe,i r Alloy,i

47 Computational Summary 45 Approach 3: Bulk Modulus (Supercell) Standard calculation of total energy in DFT (LDA) as a function of cell volume Fitting of the Murnaghan equation of state to E(Ω)

48 Hybridization of Experimental and Computation 46 Do experiment and computation agree?

49 Hybridization of Experimental and Computation 47 Do experiment and computation agree?

50 Hybridization of Experimental and Computation 48 Do experiment and computation agree?

51 Only determined by experiment Hybridization of Experimental and Computation 49 Do experiment and computation agree? Only determined by computation

52 Only determined by experiment Hybridization of Experimental and Computation 50 Do experiment and computation agree? Only determined by computation Yes! Computation successfully ranks relative changes in strain and transport by proxy.

53 Conclusion 51 Presented inexpensive, conceptually transparent methods to visualize alloying in SnSe. Strain effects can be observed far from host lattice site. Computational ranking successful as proxy for experiment. Possible down-selection of effective alloying agents.

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