Sage Journals: Discover world-class research

Abstract

Advancements in materials discovery tend to rely disproportionately on happenstance and luck rather than employing a systematic approach. Recently, advances in computational power have allowed researchers to build computer models to predict the material properties of any chemical formula. From energy minimization techniques to machine learning-based models, these algorithms have unique strengths and weaknesses. However, a computational model is only as good as its accuracy when compared to real-world measurements. In this work, we take two recommendations from a thermoelectric machine learning model, TaVO₅ and GdTaO₄, and measure their thermoelectric properties of Seebeck coefficient, thermal conductivity, and electrical conductivity. We see that the predictions are mixed; thermal conductivities are correctly predicted, while electrical conductivities and Seebeck coefficients are not. Furthermore, we explore TaVO₅’s unusually low thermal conductivity of 1.2 Wm⁻¹K⁻¹, and we discover a possible new avenue of research of a low thermal conductivity oxide family.

Keywords

Thermoelectrics oxides data-driven materials informatics thermal conductivity negative thermal expansion

Introduction

Accelerating worldwide energy demand and increasing interest in preventative measures regarding global climate change have led to the development of diverse methods of energy production. One such method is the use of thermoelectric generators to capture waste heat.¹ Thermoelectric generators rely on thermoelectric materials, which can generate an electric potential difference (i.e. a voltage) from a temperature gradient with no moving parts. This unique set of properties makes these materials promising for a wide variety of engineering applications. However, current thermoelectric devices suffer from low efficiency and often rely on rare and expensive elements, so they have thus far been relegated to use in mission-critical applications where no other options are available, such as space applications including rovers and probes.^2–5 Indeed, some of the highest-performing thermoelectric materials utilize toxic elements, such as PbTe, rendering them unsuitable for many applications. New high-efficiency and low-cost thermoelectric materials will need to be discovered to enable broader device applications.

Unfortunately, discovering new high-efficiency materials has proven challenging. Device efficiency scales with $z T$ , which can be calculated using the relation

z T = \frac{S^{2} σ}{κ} T

(1)

where

S

is the Seebeck coefficient,

σ

is the electrical conductivity,

κ

is thermal conductivity, and

T

is the temperature.¹ From this, it becomes evident that the ideal thermoelectric is electrically conductive but thermally resistive. The challenge is that these properties are interrelated, making the maximization of

z T

non-trivial. Many strategies have been developed for maximizing electrical transport while minimizing thermal transport, and previous work has shown that some chemical systems have reached the point of diminishing returns in enhancing

z T

through thermal conductivity reduction, while others have not.^1,6

The large potential compositional and structural space available for exploration makes this challenge perhaps well-suited for data-driven approaches. In recent years, materials informatics, or data science tools directed towards materials research, have proven valuable in the rapid discovery and development of a variety of different materials including photovoltaics, superhard materials, metal alloys, and more.^7–9 Pertinent to the field of thermoelectrics is the use of machine learning to predict thermal conductivity, which has become well-established in the last few years. Many have used machine learning to predict the lattice thermal conductivity of crystalline solids,^10,11 and a recent report used machine learning models to identify a new aperiodic structure transition metal oxide, Ba₁₀Y₆Ti₄O₂₇, with thermal conductivity among the lowest ever measured for an oxide.¹² Still, relatively few works have taken their predictions out of the computer and onto the bench to synthesize and characterize new materials with low thermal conductivity.¹³

In the field of thermoelectrics, materials informatics is finding increasing application.^14–19 A common refrain among articles concerning materials informatics is that these tools can help to explore chemical whitespace in an accelerated and structured manner, allowing for the discovery of remarkable compounds with desirable yet previously unknown properties.^{11,10,14–19,12,20,21} Many thermoelectric materials informatics articles present impressive performance metrics over existing data and compare their results to calculations, yet few, if any, present the recommendation, synthesis, and characterization of hitherto unexplored thermoelectric materials.¹⁸ We aim to address this gap in the literature by synthesizing and characterizing novel thermoelectric materials recommended by a previously published machine learning model.¹⁶ In this article, we evaluate two new oxides, TaVO₅ and GdTaO₄, as candidates for low thermal conductivity materials and measure their thermoelectric properties, relating the observed transport to their structures.

Materials and methods

Machine learning algorithm

The machine learning model used to make materials recommendations was described previously.¹⁶ Briefly, a random forest algorithm was trained on a combined dataset created using experimental data taken from literature values, the NIMS database, and the Materials Project. Rather than predicting materials properties via regression, the model instead treated predictions as classifications of whether or not they would have values above or below a given cut-off. For a given chemical formula, the model assigns a confidence value with a score $p$ , where $p \in (0, 1)$ , for four physical properties that correlate with desired thermoelectric behavior. The score represents the probability that the property meets the specified cutoffs defined for the absolute Seebeck coefficient (S > 100 $μ$ V $\cdot$ K⁻¹), electrical conductivity ( $σ < 10^{- 2} Ω \cdot$ cm), thermal conductivity ( $κ < 10$ W $\cdot$ $m^{- 1} \cdot$ K⁻¹), and band gap ( $E_{g} > 0$ eV).

Synthesis of TaVO₅

In accordance with Wang et al.,²² stoichiometric powders of Ta₂O₅ and V₂O₅ were mixed with ethanol and ball milled for 10 h with zirconia media. This mixture was then allowed to dry overnight. The dried powder mixture was then ground with an agate mortar and pestle and pressed into 13 mm diameter discs. These were buried in sacrificial powder and underwent reaction heating at 800 ^∘C for 24 h. Sacrificial powder was used to reduce vanadium loss during synthesis as vanadium would diffuse into the alumina crucible boats during reaction heating. The discs were then crushed into powder with an agate mortar and pestle, and the powder was spark plasma sintered at California Nanotechnologies Inc. under a load of 5.7 kN for 20 min at 1000 ^∘C to achieve maximum density for thermal and electrical measurements.

Synthesis of GdTaO₄

In accordance with Yang et al.,²³ GdTaO₄ was synthesized with starting materials Gd₂O₃ and Ta₂O₅, which were calcined at 800 ^∘C for 8 h. Stoichiometric powders of these calcined starting materials were mixed with ethanol and ball milled for 10 h with zirconia media. This mixture was allowed to dry overnight. The dried powder mixture was then ground with an agate mortar and pestle and pressed into 13 mm diameter discs. These discs underwent reaction heating at 1400 ^∘C for 12 h. The discs were then crushed into powder with an agate mortar and pestle, and the resulting powder was spark plasma sintered at California Nanotechnologies Inc. under a load of 5.7 kN for 29 min at 1500 ^∘C to achieve maximum density for thermal and electrical measurements.

Material characterization

Powder X-ray diffraction measurements were taken with a Bruker D2 Phaser diffractometer. Quantitative phase analysis was performed by the Rietveld refinement method using GSAS-II software.²⁴ Heat capacity measurements were taken in small portions of the synthesized powder using a Netzsch 3500 DSC differential scanning calorimeter.

The sintered discs were mounted in epoxy and cut with a diamond saw to a thickness of one to 2 mm for the measurement of the Seebeck coefficient, electrical conductivity, and thermal diffusivity. Prior to measurement, discs were sanded with a 1200 grit sandpaper on a Struers TegraPol-11. The electrical conductivity and Seebeck coefficient were measured using a Netzsch Nemesis 458 which has a 7% standard error for the Seebeck coefficient and a 5% standard error for electrical conductivity. The thermal diffusivity was measured via the laser flash technique on a Netzsch LFA 457, which has a standard error of 10%. The bulk density was measured with the Archimedes method in an immersion medium of deionized water. Thermal conductivity was calculated using the standard relationship:

κ = α C_{p} ρ

(2)

where

α

is the thermal diffusivity,

C_{p}

is the heat capacity, and

ρ

is the bulk density.

Results

X-ray diffraction spectra for the TaVO₅ sample along with Rietveld refinement are shown in Figure 1. A good fit, $R_{w p} = 9.85$ %, was obtained by including two phases, TaVO₅ and Ta₂O₅, in the refinement. TaVO₅ was shown to be $\sim$ 98% pure with $\sim$ 2 wt% Ta₂O₅ impurities. Meanwhile, X-ray diffraction spectra for the GdTaO₄ sample along with Rietveld refinement are shown in Figure 2. A similarly good fit, $R_{w p} = 8.68$ %, was obtained by including two phases, GdTaO₄ and Gd₂O₃, in the refinement. GdTaO₄ was shown to be $\sim$ 95% pure with $\sim$ 5 wt% Gd₂O₃ impurities.

Figure 1.

Rietveld refinement of powder X-ray diffraction data from TaVO₅ samples showing a high purity sample with <2 wt% Ta₂O₅ impurity.

Figure 2.

Rietveld refinement of powder X-ray diffraction data from GdTaO₄ samples showing a high purity sample with $\sim$ 5 wt% Gd₂O₃ impurity.

Since this study was focused specifically on machine learning predictions of thermal conductivity, stoichiometric oxides of both TaVO₅ and GdTaO₄ were synthesized. By simple electron counting one would rightly predict both Ta[ $V$ ]V[ $V$ ]O₅ and Gd[ $I I I$ ]Ta[ $V$ ]O₄ to be insulators, and this was confirmed by electrical conductivity measurements which were all outside the bounds of the Nemesis 458, signifying a conductivity below the limitations of 0.05 S $\cdot$ cm⁻¹. Density functional theory (DFT) calculations from literature suggest TaVO₅ to have an indirect band gap of 2.11 eV,²⁵ and GdTaO₄ to have an indirect band gap of 4.86 eV.²⁶

Thermal conductivity measurements, shown in Figures 3 and 4, confirm the predictions that TaVO₅ is a very low thermal conductivity material, particularly among oxides, while GdTaO₄ is not. The thermal conductivity of TaVO₅ is both low and nearly independent of temperature. TaVO₅ reaches a maximum value of 1.34 W $\cdot$ $m^{- 1} \cdot$ K⁻¹ at 100 ^∘C and then drops consistently until reaching a minimum thermal conductivity of 1.2 W $\cdot$ $m^{- 1} \cdot$ K⁻¹, well below the machine learning threshold cutoff value of 10 W $\cdot$ $m^{- 1} \cdot$ K⁻¹. GdTaO₄, on the other hand, has a thermal conductivity of 4 W $\cdot$ $m^{- 1} \cdot$ K⁻¹ at room temperature and the typical 1/T temperature dependence as it approaches the value of 2.5 W $\cdot$ $m^{- 1} \cdot$ K⁻¹ at 500 ^∘C.

Figure 3.

Thermal conductivity of TaVO₅. Orange is thermal conductivity during heating while blue is during cooling.

Figure 4.

Thermal conductivity of GdTaO₄ during heating.

In TaVO₅, we observed during initial laser flash measurements that at higher temperatures, vanadium loss became apparent with TaVO₅ decomposing into Ta₉VO₂₅. Therefore, samples were only measured up to 500 ^∘C in order to maintain TaVO₅ phase stability. Samples measured at higher temperatures had large hysteresis between heating and cooling which we attribute to vanadium volatilization. New samples were synthesized, and laser flash measurements were taken up to 500 ^∘C to avoid volatilization and hysteresis.

TaVO₅ was measured to have a bulk density of 4.47 g $\cdot$ cm⁻³, and GdTaO₄ was measured to have a bulk density of 8.83 g $\cdot$ cm⁻³. Pearson’s Crystal Data lists TaVO₅’s theoretical density as 4.55 g $\cdot$ $m^{- 3}$ and GdTaO₄’s theoretical density as 8.85 g $\cdot$ $m^{- 3}$ , which gives relative densities of 98.2% and 99.7%, respectively.

Discussion

Given the low electrical conductivity of both TaVO₅ and GdTaO₄, the electrical contributions to the overall thermal conductivities were calculated to be negligible. TaVO₅ ranks lower than many well-known low thermal conductivity oxides as outlined by Winter et al.²⁷ This is noteworthy considering that most low thermal conductivity oxides achieve low lattice thermal conductivities by relying on phonon scattering due to aliovalent doping producing vacancies on the cation or anion sublattices.^28,29

Why is the thermal conductivity of TaVO₅ so much lower than that of GdTaO₄? There are several possible factors that could be responsible. Let us first consider the Debye temperature, $θ_{D}$ . Previous work has shown that $θ_{D}$ , the temperature of a crystal’s highest normal mode of vibration, correlates with structural rigidity and thus has implications regarding a crystal’s thermal properties.³⁰ While the Debye temperature can difficult to measure in practice, it can be calculated using elastic constants with the following relation:

θ_{D} = \frac{h}{k_{B}} {[\frac{3 n}{4 π} (\frac{N_{A} ρ}{M})]}^{1 / 3} v_{m}

(3)

where

h

and

k_{B}

have their usual meanings,

n

is the number of atoms per formula unit,

N_{A}

is Avogadro’s number,

ρ

is the density of the crystal structure,

M

is the molar mass, and

v_{m}

is the mean sound speed.³¹ The mean sound speed for a polycrystalline material can be approximated with the relation:

v_{m} = {[\frac{1}{3} (\frac{2}{v_{T}^{3}} + \frac{1}{v_{L}^{3}})]}^{- 1 / 3}

(4)

where

v_{T}

is the transverse sound speed and

v_{L}

is the longitudinal sound speed. These can be obtained from the bulk and shear moduli³²:

v_{T} = {(\frac{G}{ρ})}^{1 / 2}

(5)

v_{L} = {(\frac{B + \frac{4 G}{3}}{ρ})}^{1 / 2}

(6)

Bulk and shear moduli values of 65 and 140 GPa, respectively, were previously calculated for GdTaO₄ via DFT.³³ Elastic constants for TaVO₅ were unavailable in the literature, so they were instead estimated using a machine learning model developed by our group and described in a previous publication.³⁴ The details including code and data are in Wang et al.’s original publication, but briefly, we summarize the method here. To estimate the bulk and shear moduli, Materials Project data was curated via the Materials Project Python API MPRester. Data for training the compositionally restricted attention-based network (CrabNet) model was extracted using three key fields; the chemical formula from the field ‘‘formula_pretty,” and the Voigt–Reuss–Hill average bulk and shear moduli from the fields ‘‘k_vrh’’ and ‘‘g_vrh.” The extraction of the data resulted in a DataFrame that contained 154,718 formulae. We then preprocessed the data, removing formulas for which ‘‘k_vrh’’ and ‘‘g_vrh’’ had not been calculated using DFT. The removal of cells containing NaN in either column (‘‘k_vrh’’ and ‘‘g_vrh’’) was done separately for each elastic constant to ensure the removal of cells that might have had only one value calculated. Next, we removed any formula that matched our target formula (TaVO₅) to ensure no data leakage when making a prediction using our models. The preprocessing steps resulted in 7107 training points for each model to train on. The CrabNet model internally scales and standardizes the input data, so this step was handled automatically. We then separately trained two models, one on ‘‘k_vrh’’ and another on ‘‘g_vrh.” Both models had a batch-size of 256 and were trained for 100 epochs. Each CrabNet model had 512 embedding dimensions and three layers, each with four parallel attention mechanisms. These predictions resulted in bulk and shear moduli of

49.7 \pm 11.0

and

156 \pm 15.1

GPa, respectively. Using these values, we report estimated Debye temperatures of 459 K for TaVO₅ and 406 K for GdTaO₄. It must be noted that higher accuracy estimates of the Debye temperature would come from calculations made with measured elastic constants or entirely DFT-calculated elastic constants.

While the two estimated Debye temperatures are quite close, the Debye temperature of TaVO₅ exceeds that of GdTaO₅. This is unexpected given that the thermal conductivity of TaVO₅ is considerably lower than that of GdTaO₄. However, the Debye temperature is not the only material property that influences thermal conductivity. Other metrics, such as mass contrast and polyhedral connectivity of the crystal structure itself, can also dictate thermal conductivity.

Let us first consider atomic mass. It is known that large atomic mass atoms, such as Ta, and compounds with large mass contrast between atoms result in lower thermal conductivity.^35,36,28 If we assume a Debye phonon spectrum, the thermal conductivity is dependent on the inverse square root of the defect phonon scattering coefficient at temperatures above the Debye temperature:

κ \propto Γ^{- 1 / 2}

(7)

where

Γ_{i} = x_{i} [{(\frac{M_{i} - \bar{M}}{\bar{M}})}^{2} + ϵ {(\frac{δ_{i} - \bar{δ}}{\bar{δ}})}^{2}]

(8)

for the

i

th defect, where

x_{i}

is the concentration of the defect,

M_{i}

is the mass of the defect,

δ_{i}

is the atomic size of the defect,

\bar{M}

is the average mass, and

\bar{δ}

is the average atomic size.²⁸ This implies that the scattering coefficient depends on the concentration of defects, their size contrast,

Δ δ^{2} = (δ_{i} - \bar{δ})^{2}

, and their mass contrast,

Δ M^{2} = (M_{i} - \bar{M})^{2}

. We don’t explicitly consider the size contrast as we lack sufficient information regarding the effective size of ions and vacancies to make any rigorous claims about the effect of size contrast on the scattering coefficient. Nevertheless, we can easily observe that the mass contrast of TaVO₅ is substantially higher than it is for GdTaO₄. This implies that TaVO₅ has a larger scattering coefficient and thus a lower thermal conductivity than does GdTaO₄, which our experiments confirm. However, this cannot alone explain the low thermal conductivity in TaVO₅. For example, consider Ta₂O₅ which exhibits both of these qualities (high atomic mass atoms and large mass contrast) but has a thermal conductivity over three times that of TaVO₅ in defect-free films.³⁷

The low thermal conductivity is likely intrinsically related to the crystal structure of TaVO₅ itself. As shown in Figure 5, the TaO₆ octahedra is only corner-shared with the VO₄ polyhedra. This flexible linkage implies that the structure is more likely to twist and change volume during acoustic phonon propagation, lowering its thermal conductivity.^27,28 Additionally, the large mass contrast between vanadium and tantalum within the lattice is likely to cause phonon dampening, limit the phonon’s degrees of freedom, and interrupt the possible phonon modes.²⁹ This determination is further supported by previous Raman scattering measurements showing limited vibrational nodes as well as distortion of octahedra and polyhedra at higher temperatures.⁶

Figure 5.

Extended crystal structure views of (a) TaVO₅ and (b) GdTaO₄ and local polyhedral connectivity diagrams (c) and atomic labels (d).

TaVO₅ and other comparable oxides in the same Pnma space group, such as NbVO₅ and TaPO₅, are negative thermal expansion (NTE) materials.^38–40 This is unsurprising as the same anharmonicity of low-frequency phonon modes that gives rise to NTE also results in the coupled phonons and shorter mean free path lengths that are typically associated with low thermal conductivity.⁴¹ The literature review shows a gap in thermal conductivity predictions and measurements for this family of oxides. These Pnma corner-shared oxides, such as NbVO₅ and TaPO₅, could represent a new avenue of low thermal conductivity materials that have yet to be fully explored.

Seebeck coefficient, as shown in Figure 6, was measured to be around $-$ 70 $\pm$ 10 $μ$ V $\cdot$ K⁻¹ within the range of 300 ^∘C to 600 ^∘C before vanadium loss became an issue. TaVO₅ lower Seebeck coefficient can be explained by using the DFT calculations of band structure which suggest that TaVO₅ has a broadband structure leading to a low effective mass of electrons in the conduction band.²² This makes TaVO₅ an improbable thermoelectric since improving the low electrical conductivity would require heavy doping which, following Mott’s formula and the Wiedemann-Franz law, would further decrease the Seebeck coefficient.^1,42

Figure 6.

Seebeck coefficient of TaVO₅.

The electrical conductivity of GdTaO₄ was unmeasurable on the Nemesis 458, suggesting its conductivity to be somewhere below the limitations of 0.05 S $\cdot$ cm⁻¹. Further measurements done at room temperature with a Keithley 2000 multimeter showed the resistance above the limitations of the machine at 120 M $Ω$ . This is likely due to the oxide following the completed shell of 18 electron rule, as well as having a large band gap, requiring a noticeable energy to excite electrons into the valence band.

Thermal conductivity, as shown in Figure 4, was shown to start at 4 W $\cdot$ $m^{- 1} \cdot$ K⁻¹ and steadily decrease to 2.5 W $\cdot$ $m^{- 1} \cdot$ K⁻¹ at the 500 ^∘C upper bound of our differential scanning calorimeter. This is on par with literature from single crystal and polycrystal measurements.^23,43–45

The higher than expected thermal conductivity of GdTaO₄ can be explained by having a more interconnected crystal structure, as well as the similar atomic weights of gadolinium and tantalum. This allows a greater number of phonon modes to exist within the structure. Single crystal studies support this theory, showing similar sloping decreases in thermal conductivity as well as low thermal anisotropy.²³ Despite the fact that the GdTaO₄ exhibits thermal conductivity well below the cutoff value of 10 W $\cdot$ $m^{- 1} \cdot$ K⁻¹ given by the machine learning algorithm, GdTaO₄ seems questionable as a thermoelectric material without a noticeable decrease in the higher temperature ranges when compared to known thermoelectric systems of interest, which reside below 1 W $\cdot$ $m^{- 1} \cdot$ K⁻¹ before doping.^6,42

The Seebeck coefficient measurements of GdTaO₄ showed large variation and lack of continuity and are thus not reported. The large amount of noise and lack of linearity in the measurement suggests that the Seebeck coefficient is far below the limitations of the Nemesis 458 of 10 $μ$ V $\cdot$ K⁻¹. GdTaO₄ shows a shallow band structure as given by Ding et al.,²⁶ Materials Project,⁴⁶ and Topological Materials Database^43–45 which suggest low effective masses for both carriers.

It should be noted that these sources have similar shallow band structures but show contradictions for band gap. The Topological Materials Database^43–45 lists GdTaO₄ as a semimetal while others such as the Materials Project⁴⁶ and Ding et al.²⁶ suggest a large band gap ranging from 3.26 to 4.86 eV, respectively. Our electrical conductivity measurements support the notion that this material is a wide-gap semiconductor and is not a semimetal. The curvature of the band structure indicates similar effective masses for both carriers which, in conjunction with a large band gap, means the bipolar effect further constrains the magnitude of the Seebeck coefficient.²³

Conclusion

By using predictions to excite and motivate scientists, machine learning gives us a promising direction to explore chemical whitespace. However, these tools are very dependent on training data and the choice of algorithm, and as such require scrutiny and verification. In the case of the Citrination engine model, we chose two of the recommended oxide compounds to test as thermoelectric materials: TaVO₅ and GdTaO₄. We have shown that for predicting thermal conductivity, the model performed as expected, with both compounds being well below the cutoff of 10 W $\cdot$ $m^{- 1} \cdot$ K⁻¹. However, other predictions, such as electrical conductivity and Seebeck coefficient, were incorrect, making the model an imperfect tool. Nevertheless, the pursuit of data-driven research has pointed us to the possibility of a new family of low thermal conductivity oxides which require further study. These physical measurements will also contribute to the refinement and growth of thermoelectric-based machine learning algorithms, paving the way for even more robust recommendations in the future.

Footnotes

Acknowledgements

The authors gratefully acknowledge funding and support from the National Science Foundation through Award NSF DMR 1651668. Special thanks to Clayton Cozzan and Dr Ram Seshadri for preliminary assistance in sintering trial runs prior to final synthesis. We would like to thank Eric Eyerman at California Nanotechnologies Inc. for his assistance.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship and/or publication of this article.

References

Snyder

Toberer

. Complex thermoelectric materials. Nat Mater 2008; 7: 105–114.

Jones

Moreno

Zimmerman

. The f1 multi-mission radioisotope thermoelectric generator (MMRTG): a power subsystem enabler for the Mars Science Laboratory (MSL) mission, 2013.

Gaultois

Sparks

Borg

, et al. Data-driven review of thermoelectric materials: performance and resource considerations. Chem Mater 2013; 25: 2911–2920.

Haxel

. Rare earth elements: critical resources for high technology. US Department of the Interior, US Geological Survey, 2002, vol. 87, no. 2.

DoE

. Critical materials strategy 2011. Washington, DC: United States Department of Energy, 2011.

Gaultois

Sparks

. How much improvement in thermoelectric performance can come from reducing thermal conductivity?. Appl Phys Lett 2014; 104: 113906.

Cao

Adutwum

Oliynyk

, et al. How to optimize materials and devices via design of experiments and machine learning: demonstration using organic photovoltaics. ACS Nano 2018; 12: 7434–7444.

Mansouri Tehrani

Oliynyk

Parry

, et al. Machine learning directed search for ultraincompressible, superhard materials. J Am Chem Soc 2018; 140: 9844–9853.

Martin

Yahata

Hundley

, et al. 3d printing of high-strength aluminium alloys. Nature 2017; 549: 365–369.

10.

Miyazaki

Tamura

Mikami

, et al. Machine learning based prediction of lattice thermal conductivity for half-Heusler compounds using atomic information. Sci Rep 2021; 11: 13410.

11.

Jaafreh

Kang

Hamad

. Lattice thermal conductivity: an accelerated discovery guided by machine learning. ACS Appl Mater Interfaces 2021; 13: 57 204.

12.

Collins

Daniels

Gibson

, et al. Discovery of a low thermal conductivity oxide guided by probe structure prediction and machine learning. Angew Chem Int Edit 2021; 60: 16 457.

13.

Luo

Yuan

, et al. Predicting lattice thermal conductivity via machine learning: a mini review. NPJ Comput Mater 2023; 9: 4.

14.

Carrete

Mingo

, et al. Finding unprecedentedly low-thermal-conductivity half-Heusler semiconductors via high-throughput materials modeling. Phys Rev X 2014; 4: 011019.

15.

Sparks

Gaultois

Oliynyk

, et al. Data mining our way to the next generation of thermoelectrics. Scr Mater 2016; 111: 10–15.

16.

Gaultois

Oliynyk

Mar

, et al. Perspective: web-based machine learning models for real-time screening of thermoelectric materials properties. APL Mater 2016; 4: 053213.

17.

Zhang

, et al. Large data set-driven machine learning models for accurate prediction of the thermoelectric figure of merit. ACS Appl Mater Interfaces 2022; 14: 55 517.

18.

Antunes, Vikram

Plata

, et al. Machine learning approaches for accelerating the discovery of thermoelectric materials. In Machine Learning in Materials Informatics: Methods and Applications. ACS Publications, 2022, pp. 1–32.

19.

Gan

Wang

Zhou

, et al. Prediction of thermoelectric performance for layered iv–v–vi semiconductors by high-throughput ab initio calculations and machine learning. NPJ Comput Mater 2021; 7: 176.

20.

Chowdhury

Reynolds

Garrett

, et al. Machine learning maximized anderson localization of phonons in aperiodic superlattices. Nano Energy 2020; 69: 104428.

21.

Wang

Z-L

Adachi

Chen

Z-C

. Processing optimization and property predictions of hot-extruded bi–te–se thermoelectric materials via machine learning. Adv Theory Simul 2020; 3: 1900197.

22.

Wang

Huang

Deng

, et al. Phase transformation and negative thermal expansion in tavo5. Inorg Chem 2011; 50: 2685–2690.

23.

Yang

Peng

Zhang

et al. A promising high-density scintillator of gdtao4 single crystal. CrystEngComm 2014; 16: 2480–2485.

24.

Toby

Von Dreele

. Gsas-ii: the genesis of a modern open-source all purpose crystallography software package. J Appl Crystallogr 2013; 46: 544–549.

25.

Kontic

. New pathways to oxide materials for photocatalytic applications. PhD dissertation, University of Zurich, 2014.

26.

Ding

Kinross

Wang

, et al. Experiment and density functional theory analyses of gdtao4 single crystal. Solid State Commun 2018; 273: 5–10.

27.

Winter

Clarke

. Oxide materials with low thermal conductivity. J Am Ceram Soc 2007; 90: 533–540.

28.

Sparks

Pan

, et al. Thermal conductivity of the gadolinium calcium silicate apatites: effect of different point defect types. Acta Mater 2011; 59: 3841–3850.

29.

Pan

Phillpot

Wan

, et al. Low thermal conductivity oxides. Mrs Bulletin 2012; 37: 917–922.

30.

Brgoch

DenBaars

Seshadri

. Proxies from ab initio calculations for screening efficient Ce3+ phosphor hosts. J Phys Chem C 2013; 117: 17 955.

31.

Anderson

. A simplified method for calculating the Debye temperature from elastic constants. J Phys Chem Solids 1963; 24: 909–917.

32.

Zhuo

Mansouri Tehrani

Oliynyk

, et al. Identifying an efficient, thermally robust inorganic phosphor host via machine learning. Nat Commun 2018; 9: 1–10.

33.

De Jong

Chen

Angsten

, et al. Charting the complete elastic properties of inorganic crystalline compounds. Sci Data 2015; 2: 1–13.

34.

Wang

AY-T

Kauwe

Murdock

, et al. Compositionally restricted attention-based network for materials property predictions. NPJ Comput Mater 2021; 7: 1–10.

35.

DiSalvo

. Thermoelectric cooling and power generation. Science 1999; 285: 703–706.

36.

Toberer

Baranowski

Dames

. Advances in thermal conductivity. Annu Rev Mater Res 2012; 42: 179–209.

37.

Landon

Wilke

Brumbach

, et al. Thermal transport in tantalum oxide films for memristive applications. Appl Phys Lett 2015; 107: 023108.

38.

Wang

Deng

, et al. Coprecipitation synthesis and negative thermal expansion of nbvo5. Dalton Trans 2011; 40: 3394–3397.

39.

Amos

. Negative thermal expansion in AOMO (4) compounds. Ann Arbor, Ml: Oregon State University, 2000.

40.

Shi

Song

Xing

, et al. Negative thermal expansion in framework structure materials. Coord Chem Rev 2021; 449: 214204.

41.

Kennedy

White

. Unusual thermal conductivity of the negative thermal expansion material, zrw2o8. Solid State Commun 2005; 134: 271–276.

42.

Zevalkink

Smiadak

Blackburn

, et al. A practical field guide to thermoelectrics: fundamentals, synthesis, and characterization. Appl Phys Rev 2018; 5: 021303.

43.

Bradlyn

Elcoro

Cano

, et al. Topological quantum chemistry. Nature 2017; 547: 298–305.

44.

Vergniory

Elcoro

Felser

, et al. A complete catalogue of high-quality topological materials. Nature 2019; 566: 480–485.

45.

Vergniory

Wieder

Elcoro

, et al. All topological bands of all nonmagnetic stoichiometric materials. Science 2022; 376: eabg9094.

46.

Jain

Ong

Hautier

, et al. Commentary: the materials project: a materials genome approach to accelerating materials innovation. APL Mater 2013; 1: 011002.

Thermoelectric properties of TaVO 5 and GdTaO 4 : An experimental verification of machine learning prediction

Abstract

Keywords

Introduction

Materials and methods

Machine learning algorithm

Synthesis of TaVO5

Synthesis of GdTaO4

Material characterization

Results

Discussion

Conclusion

Footnotes

Acknowledgements

Declaration of conflicting interests

Funding

References

Synthesis of TaVO₅

Synthesis of GdTaO₄