Kristian Berland, Simen N. H. Eliassen,

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Lattice Dynamics related to movement of atoms

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Presentation transcript:

Kristian Berland, Simen N. H. Eliassen, How to bring down the thermal conductivity of MNiSn Half-Heuslers - a theoretical analysis Kristian Berland, Simen N. H. Eliassen, A. Katre, G.K.H. Madsen, Clas Persson, O.M. Løvvik

THELMA thermoelectric project - Half-Heusler branch Experimental: Synthesis Microstructure analysis (TEM etc) Electronic and thermal transport Theory Electrons Phonons: engineer materials to get low thermal conductivity

Aside: Corrected based interpolation scheme arxiv.org/abs/1607.01429 Electronic transport demands dense sampling of the Brillouin zone. Hybrid calculations too costly New interpolation scheme combined with BoltzTraP. Resolve band crossings

Boltztmann transport to calculate lattice thermal conductivity of alloys Lattice thermal transport calculated using Density functional theory Phono3py (finite differences) Boltzmann-transport equation Relaxation-time approximation Alloys using virtual crystal approximation Linear averaging of masses Linear averaging of forces

Anharmonic three-phonon scattering Scattering mechanism Anharmonic three-phonon scattering Mass-disorder scattering Boundary scattering

Step 1: phonon band structure Rather similar band structures.

The bulk materials have similar thermal conductivity

The bulk materials have similar thermal conductivity Derivative Derivative Energetic acoustic phonons carry the most heat

Theory captures trend for binary alloying Ni interstitials could be cause of overestimation for bulk.

How does alloying affect lattice thermal conductivity? Zr-Ti, highest thermal conductivity Ti-Hf mixing gives lowest thermal conductivity Why does it look like this?

Mass-disorder parameter only part of the story Ti 48u Zr: 91 u Hf: 178 u Can not explain minimum close to Ti0.5Hf0.5. Can not explain difference between Ti-Zr and Zr-Hf. Only mass variance:

Three-phonon scattering does not at all explain trend in thermal conductivity Why is 40% Hf, 60% Zr a maximum?

Phonon-mode nature plays a key role in trends Acoustic phonon changes nature as we go from ZrNiSn to HfNiSn.

Mass-disorder scattering enhanced due to phonon modes Mode nature explains why (Hf- Zr)NiSn has lower thermal conductivity than (Ti-Zr)NiSn.

Alloying on Ti site less effective for TiNiSn Mass-variance perspective: Alloying Ti with Hf is very effective Mode perspective: Alloying Ti site is not that effective.

How to reduce further? Derivative

Introduce grain boundary scattering Grain size

Grain-boundaries scatter low-energetic acoustic phonons Derivative

Conclusion: Mode-engineering to lower thermal conductivity To bring down thermal conductivity, Optimal alloying element can be selected based on the nature of the phonon modes. For ultra-low thermal conductivity, mechanism is also needed to scatter low-energetic phonon modes (nanostructuring)