1. 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

2. 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

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

4. 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

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

6. Step 1: phonon band structure
Rather similar band structures.

7. The bulk materials have similar thermal conductivity

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

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

10. 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?

11. 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:

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

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

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

15. 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.

16. How to reduce further?
Derivative

17. Introduce grain boundary scattering
Grain size

18. Grain-boundaries scatter low-energetic acoustic phonons
Derivative

19. 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)