Identifying Materials with Low Lattice Thermal Conductivity Using Machine Learning and Computational Modeling

Abstract

Lattice thermal conductivity is a key materials property in applications related to thermal functionality, such as thermal barrier coatings, thermal conductors in microelectronics, and solid-state waste-heat recovery devices. The lattice thermal conductivity governs the rate of heat energy transfer in thermoelectric materials, which are materials that can directly convert heat to electricity and vice versa. These materials become interesting in applications that require electricity generation or local cooling. Thermoelectric materials depend on a low lattice thermal conductivity to attain high heat-to-electricity conversion efficiency. The materials used in present thermoelectric generators are often based on toxic or scarce elements. New high-efficiency thermoelectric materials are therefore desired for sustainable and environmentally friendly energy harvesting. Two main research challenges are investigated in this thesis: 1) reducing the lattice thermal conductivity to enhance thermoelectric performance, and 2) identifying new compounds with low lattice thermal conductivity. Addressing these challenges experimentally is a daunting task -- especially for 100s or 1000s of compounds -- as experiments are costly, time-consuming, and require expert domain knowledge. This thesis, therefore, relies on lattice thermal conductivity from theoretical calculations based on quantum mechanical simulations.

Addressing challenge 1), the lattice thermal conductivity of 122 half-Heusler compounds is calculated using density functional theory and the temperature-dependent effective potential method. Phonon scattering from partial sublattice substitutions and grain boundaries are included in calculations, in an attempt to reduce the lattice thermal conductivity. We find that isovalent substitutions on the site hosting the heaviest atom should be performed to optimally reduce the lattice thermal conductivity in most half-Heuslers. Compounds with large atomic mass differences can have a large drop in lattice thermal conductivity with substitutions. Examples of such compounds are AlSiLi and TiNiPb, which achieve a $\sim 70$~\% reduction of their lattice thermal conductivity when substituting Si by Ge and Pb by Sn at 10~\% concentration. The reduction from additional scattering mechanisms enables a handful half-Heuslers to attain a lattice thermal conductivity close to $2$~W/Km at 300~K. Calculations for full-Heusler $\rm{AlVFe}_2$ reveal that the introduction of 15~\% Ru substitutions on the Fe-site and 100~nm grain boundaries can reduce the lattice thermal conductivity from 46~W/Km to 7~W/Km.

Tackling challenge 2) is done by computational screening for low lattice thermal conductivity compounds. Coupling calculations with machine learning accelerates the screening. When training the machine learning model on calculated lattice thermal conductivities, it learns to recognize descriptor patterns for compounds with low lattice thermal conductivity. The size of the training set is limited by the large computational cost of calculating lattice thermal conductivity. It is therefore challenging to obtain a diverse set of training compounds, especially so because low lattice thermal conductivity compounds tend to be rare. We find that including certain compounds in the training can be crucial for identifying low lattice thermal conductivity compounds. Active sampling enables scouting of the compound space for compounds that should enter the training set. Principal component analysis and Gaussian process regression are used in the active sampling schemes. With Gaussian process regression we screen 1573 cubic compounds, where 34 have predicted lattice thermal conductivity $\leq 1.3$~W/Km at 300 K -- as well as electronic band gaps -- indicating that they could be potential thermoelectric compounds.

The findings in this thesis show that certain compounds could have a drastic reduction in the lattice thermal conductivity with sublattice substitutions. Thermoelectric compounds with favorable electronic properties -- but high lattice thermal conductivity -- can be investigated in future studies if there is a potential for a large drop in the lattice thermal conductivity with sublattice substitutions. The machine learning and active sampling schemes are scalable, and future works could expand upon this thesis by including different compound classes in training and screening. This would enlarge the search space for promising thermoelectric compounds, increasing the likelihood of encountering high-efficiency candidates. It is also possible to combine the two challenges faced in this thesis. A machine learning model can be trained to predict the lattice thermal conductivity of compounds with sublattice substitutions. This would further increase the pool of possible compounds where promising thermoelectric compounds could reside.

Termisk gitterledningsevne er en viktig materialegenskap i tekniske instrumenter som anvender varmeledningsteknologi, slik som termiske barriere-belegg, termiske ledere i mikroelektronikk, og varmegjenvinningsenheter. Denne egenskapen styrer raten av varmeenergi-overføring i termoelektriske materialer. Disse materialene kan omgjøre varmeenergi til elektrisk energi og motsatt, og er derfor lovende i produkter som avhenger av elektrisitetsgenerering eller utnytter lokal kjøling. Termoelektriske materialer må ha lav termisk gitterledningsevne for å opprettholde høy effektivitet. Dagens termoelektriske materialer er ofte basert på giftige eller sjeldne materialer, slik som bly eller tellur. Det er derfor nyttig å finne nye materialer med høy effektivitet for å videre anvende termoelektrisk energi-høsting på en bærekraftig måte. To hovedutfordringer er undersøkt i denne avhandlinga: 1) reduksjon av termisk gitterledningsevne for å øke termoelektrisk effekt, og 2) identifikasjon av nye materialer med lav gitterledningsevne. Å løse disse utfordringene eksperimentelt er krevende siden eksperimenter er dyre, tar mye tid, og krever ekspert-kunnskap. I denne avhandlinga brukes derfor teoretiske beregninger basert på kvantemekaniske simuleringer for å estimere termisk gitterledningsevne. I arbeidet med utfordring 1) beregnes termisk gitterledningsevne til 122 half-Heusler-materialer basert på temperaturavhengige materialsimuleringer. For å redusere termisk gitterledningsevne inkluderes ekstra fonon-spredningsmekanismer: sub-gitter-substitusjoner (legeringer) og korngrenser. Vi finner at isovalente substitusjoner på gitter-plassen som innehar det tyngste atomet gir den største reduksjonen i termisk gitterledningsevne for de fleste materialene. Materialer med stor atommasse-forskjell kan ha en stor reduksjon i termisk gitterledningsevne med substitusjoner. AlSiLi og TiNiPb er eksempler på slike materialer, og oppnår en ∼ 70 % reduksjon i termisk gitterledningsevne når Si er substituert med Ge og Pb er substituert med Sn med 10 % konsentrasjon. Reduksjonen fra ekstra spredningsmekanismer gjør at en håndfull half-Heuslere oppnår termisk gitterledningsevne nærme 2 W/Km. Beregninger for fullHeusleren AlVFe2 viser at introduksjonen av 15 % Ru-substitusjon på Fegitterplassen og 100 nm korngrenser kan redusere termisk gitterledningsevne fra 46 W/Km til 7 W/Km.