anisotropy-layered-materials

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1. Prashun Gorai, Robert McKinney High-Throughput Prediction of Anisotropic Transport Properties

   Colorado School of Mines National Renewable Energy Lab Golden, USA Eric Toberer, Vladan Stevanović

2. Anisotropic Transport in Thermoelectric Materials /10 2 ๏ Quasi-low dimensional

   structures are abundant among TE materials ๏ Transport can be anisotropic ๏ Lattice thermal conductivity in well- known TE materials is anisotropic ๏ Example: SnSe, BiCuOSe ๏ High-throughput searches require prediction of L A semi-empirical model to rapidly predict the anisotropic L CsBi4Te6 BiCuSeO InSe Sr3GaSb3 Bi2Te3 SnSe Sb2Te3 CaZn2Sb2 Ca3AlSb3 Quasi Low-dimensional Materials zT max 0 1 2 3 Lattice Therm. Conduc (Wm-1K-1) 1 10 1Gorai, Toberer, Stevanovic, J. Mater. Chem. A 4, 11110 (2016)

3. Isotropic Model for Predicting L /10 3 Miller, Gorai, Stevanovic,

   Toberer et al., Chem. Mater. 29, 2494 (2017) GaAs InI Cu3 TaTe4 SrTiO3 GaP Si SiC d-C PbTe factor of 2 Mg2 Si Modeled κL (Wm-1K-1) 0.1 1 10 100 1000 Experimental κL (Wm-1K-1) 0.1 1 10 100 1000 ๏ Isotropic speed of sound ๏ B: bulk modulus, d: density ๏ V: volume, n: number of atoms ๏ M: average atomic mass ๏ A1, A2, x, y, z: fitting parameters vs (B/d) <latexit sha1_base64="AVfgBYT3wOQkrLTvgUZJNrQLVwk=">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</latexit> <latexit sha1_base64="AVfgBYT3wOQkrLTvgUZJNrQLVwk=">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</latexit> <latexit sha1_base64="AVfgBYT3wOQkrLTvgUZJNrQLVwk=">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</latexit> <latexit sha1_base64="AVfgBYT3wOQkrLTvgUZJNrQLVwk=">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</latexit> Modeled L within average factor difference ~1.5 of experimental value L = A1 ¯ Mvy s nxVz 2T + A2 vs Vz 1 1 n2/3 <latexit sha1_base64="GDTL4DU9W0YmdP6vcLg1NT14KD8=">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</latexit>

4. Anisotropic Model for Predicting L /10 4 ๏ Direction-dependent speed

   of sound (vi) from elastic tensor and density using Christoffel equations ๏ L, T1, T2: longitudinal, transverse modes ๏ V: volume, n: number of atoms, M: average atomic mass ๏ A1, A2, x, y, z: fitting parameters Bi2Te3: speed of sound (km/s) 1.2 3.6 2.6 L T1 T2 Anisotropic model used to estimate L along principal axes L = A1 ¯ M nxVz 2T L,T1,T2 vy i + A2 1 Vz L,T1,T2 vi 1 1 n2/3 <latexit sha1_base64="pFDSYG62ReRhO6xVs4qmeYGWz8Y=">AAAC/3icbVLLbhMxFPUMr1JeKSy7sQiVUhHSmRQEG6TykMoiSEUkaaRMMrrjeBIrtmdke6oEaxZ8AZ/BDrHlU/gQ9jhpEE3aK1k6Ovece+17neScaRMEvz3/2vUbN29t3d6+c/fe/QeVnYddnRWK0A7JeKZ6CWjKmaQdwwynvVxREAmnp8n03SJ/ekaVZplsm3lOBwLGkqWMgHFUXPkWTSHPIW7h1/hNHOIoVUBslICyH8vSyuGsO/wSjUEIGDbbZaQLEdtWvR3W283SnsVsOC/xU2dtrqxhaZ3jCmEZcZqaGsYhfvZfK4e2eXBYljhSbDwx+3GlGjSCZeDLIFyBKlrFSbzj9aJRRgpBpSEctO6HQW4GFpRhhNNyOyo0zYFMYUz7DkoQVA/scnIl3nPMCKeZckcavGQvOiwIrecicUoBZqI3cwvyqly/MOmrgWUyLwyV5LxRWnBsMrxYAx4xRYnhcweAKObuiskE3FCMW9Zal2XtnJK1l9hZIRnJRnSD5WZmFDhSUyOAycWr7DHjHH8Gqf/xruAiUXvPxszoesv9BVk/VpRO9y+IsdtFuDn5y6DbbISHjRefnleP3q62soV20WNUQyF6iY7QB3SCOoigP96u98Tb87/63/0f/s9zqe+tPI/QWvi//gJdd/M9</latexit> L = A1 ¯ Mvy s nxVz 2T + A2 vs Vz 1 1 n2/3 <latexit sha1_base64="GDTL4DU9W0YmdP6vcLg1NT14KD8=">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</latexit>

5. Prediction of Anisotropic L /10 5 McKinney, Gorai, Toberer, Stevanovic,

   Chem. Mater. 6, 2048 (2019) ZnO SnO2 WS2 Si3 N4 MoS2 graphite-C GaS Bi2 Te3 InSe ZnSb GaSe AlN TlSe diam-C modeled κL (W/mK) 1 101 102 103 104 experimental κL (W/mK) 1 101 102 103 104 ๏ Symmetry-appropriate L tensors created from principal values ๏ Fitting parameters (A1, x, y, z) - same as isotropic model (no refit) ๏ Model predictions compared with experimental anisotropic L Modeled L within average factor difference ~1.5 of experimental values!

6. Anisotropic L of Thermoelectric Materials /10 6 L,min L,max [L,min,

   L,max] (W/mK) PbTe [4.7, 4.7] Bi2Te3 [1.5, 2.8] SnSe [2.0, 5.3] Mg3Sb2 [2.3, 2.4]

7. Application of the Model to Layered Materials /10 7 1Gorai,

   Toberer, Stevanovic, J. Mater. Chem. A 4, 11110 (2016) ๏ Automated identification of layered materials in ICSD with a surface- cutting approach1 ๏ Considered van der Waals (vdW) and ionic layered materials 354 binary vdW, 413 ternary vdW, 1852 ternary ionic layered materials SnSe CuGeO3 RbAg3Te2

8. κL,max (W/mK) 1 101 102 103 κL,min (W/mK) 1 101

   102 binary vdw ternary vdw ionic max/min ≤ 2 Anisotropic L of 2500+ Layered Materials /10 8 κL,max (W/mK) 1 101 102 103 κL,min (W/mK) 1 101 102 ionic McKinney et al., Chem. Mater. 6, 2048 (2019) “Layered” materials can also exhibit nearly isotropic L

9. Examples: Highly Anisotropic to Nearly Isotropic /10 9 L,min L,max

   MoS2 [2.6, 43.4] CuGeO3 [0.6, 0.7] TaOI2 [0.5, 150.3] RbAg3Te2 “Layered” materials exhibit all sorts of L anisotropies [L,min, L,max] (W/mK) [3.1, 82.5]

10. 1-2-2 Phases: Are They Really “Layered”? /11 10 Mg3Sb2 [2.3,

    2.4] L,min L,max [L,min, L,max] (W/mK) *Zhang, Iversen et al., Nature Comm. 9 (2018) ๏ Mg3Sb2: consider Zintl phase due to its “layered” structure ๏ Recent experiments shows it cannot be considered layered* ๏ We find nearly isotropic L CaZn2Sb2 [2.2, 3.3] ๏ CaZn2Sb2: more anisotropic than Mg3Sb2 ๏ Can be considered “layered” and therefore, Zintl phase

11. Conclusion and Future Directions National Science Foundation - DMREF Program

    NREL High Performance Computing (HPC) pgorai@mines.edu ๏ Developed a computationally-tractable model to predict anisotropic L ๏ Unexpected anisotropy in the transport properties of layered materials ๏ Ongoing work to predict direction-dependent carrier mobility, TE performance