# Fileset

[tstm_a_2545174_sm4025.pdf](https://mdr.nims.go.jp/filesets/492d6345-f460-45cc-a3c3-e25c440bee45/download)

## Creator

[Florent Pawula](https://orcid.org/0000-0002-2641-0521), Mathias Hamitouche, Linda Abbassi, Agathe Bajan, Cédric Bourgès, [Takao Mori](https://orcid.org/0000-0003-2682-1846), Jean-François Halet, David Berthebaud, [Guillaume Lambard](https://orcid.org/0000-0003-0275-4079)

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Enhancing thermoelectric efficiency of GeTe through process improvement via active learning assisted by Bayesian optimisation](https://mdr.nims.go.jp/datasets/1ab3ec9b-d053-4d99-801f-099313649483)

## Fulltext

Enhancing thermoelectric efficiency of GeTethrough process improvement assisted by activelearning and Bayesian optimizationFlorent Pawula,∗,†,‡,¶ Agathe Bajan,† Mathias Hamitouche,§,‡ Linda Abbassi,§,‡Cédric Bourgès,§ Takao Mori,§ Jean-François Halet,‡,∥ David Berthebaud,‡,¶ andGuillaume Lambard∗,†,‡†Data-driven materials design group, Center for Basic Research on Materials (CBRM),National Institute for Materials Science (NIMS), Namiki 1-1, Tsukuba, Ibaraki, 305-0044,Japan‡CNRS-Saint Gobain-NIMS, IRL 3629, Laboratory for Innovative Key Materials andStructures (LINK), National Institute for Materials Science (NIMS), Namiki 1-1, Tsukuba,Ibaraki, 305-0044, Japan¶Nantes Université, CNRS, Institut des Matériaux de Nantes Jean Rouxel, IMN, F-44000Nantes, France§Thermal Energy Group, WPI International Center for Materials Nanoarchitectonics(WPI-MANA), National Institute for Materials Science (NIMS), Tsukuba, Japan∥Univ Rennes, CNRS, Ecole Nationale Supérieure de Chimie de Rennes (ENSCR), Institutdes Sciences Chimiques de Rennes (ISCR), UMR 6226, F-35000, Rennes, FranceE-mail: florent.pawula@cnrs-imn.fr; LAMBARD.Guillaume@nims.go.jp1Supplementary informationTable S1: Process parameters of the samples.Sample# heating.rate T annealing t duration cooling.rate mass powder milling.time.1 heating.rate.1 T annealing.1 t duration.1 cooling.rate.1 Uniaxial pressure(K.h−1) (K) (h) (K.h−1) (g) (min) (K.min−1) (K) (min) (K.min−1) (MPa)0 25 1123 16 175 4.25 1 25 850 40 150 701 50 1323 16 75 5.75 1 100 800 20 175 402 50 1273 12 175 4.5 1 75 900 55 50 603 50 1073 12 50 5.25 1 50 750 30 75 504 115.625 1223 12 154.16667 6.7 15 75.33 750 5 75.33 605 25 1273 24 25 5.1982 10 50 900 30 25 406 25 1323 14 75 5.8184 6 150 750 15 75 507 75 1423 18 25 5.9029 9 50 938 0 140 408 50 1473 22 75 5.1522 6 200 850 35 200 509 75 1423 24 50 5.2986 4 175 850 25 25 5010 10.5 1348 24 75 4.52333 2 201 700 25 48 4011 30 1348 24 75 5.5103 8 138 850 25 139 4512 10.5 1448 0.1 75 4.52489 2 167 800 25 123 4013 30 1123 16 25 6.05351 4 151 750 25 47 5014 20 1348 24 50 5.75132 6 96 875 15 100 5515 52.4 1348 18 25 4.61276 9 27.2 900 25 105.4 6016 125 1373 6 100 4.10237 5 184 800 15 47.4 6017 113.9 1273 22 25 5.19576 15 138 800 10 106.8 5518 97.5 1223 6 77.3 3.74733 13 113 700 10 109 5019 32 1273 22 25 4.12751 3 27.4 850 25 159 6520 120 1098 22 75 5.252 3 125 750 5 175 4521 10 1448 2 100 4.505 12 150 850 10 100 5522 80 1398 22 100 5.752 3 125 900 0 50 5023 130 1023 6 100 5.25 11 175 900 5 125 40Figure S1: X-ray diffraction patterns associated with the Bragg peak positions of trigonalGeTe (R3m) and cubic Ge (Fd3̄m). The * denotes the presence of elemental Ge.Table S2: Le Bail refinement parameters extracted from XRD patterns.Sample a (Å) (a) (Å) c (Å) (c) (Å) ⟨d⟩ (Å) ⟨(d)⟩ (Å) Chi2 R Bragg R F0 8.32898 7E-5 10.67244 1.3E-4 755.81 0.87 2.45 1.8 3.311 8.3309 1.6E-4 10.6736 2.7E-4 637.31 0.05 3.47 2.38 3.732 8.33097 7E-5 10.66495 1.8E-4 750.39 0.05 2.83 4.65 10.523 8.32922 9E-5 10.6701 2.1E-4 550.67 0.57 3.18 2.73 5.24 8.33326 6E-5 10.6763 2E-4 305.8 0.25 3.69 2.03 5.685 8.32907 1.2E-4 10.67576 1.6E-4 488.49 0.33 2.36 5.52 10.026 8.33442 1.8E-4 10.67958 2.6E-4 412.33 0.28 1.69 1.66 2.437 8.33812 1.3E-4 10.69258 1.8E-4 471.05 0.68 2.03 2.32 6.28 8.32745 1E-4 10.67811 1.6E-4 524.09 0.53 2.59 1.51 2.719 8.33116 8E-5 10.67306 1.5E-4 569.24 0.59 2.23 1.15 2.4510 8.33295 9E-5 10.67242 2.2E-4 520.25 0.1 3.46 2.65 5.3511 8.32997 8E-5 10.67417 1.9E-4 692.56 0.92 4.32 1.68 4.6312 8.33044 9E-5 10.67576 2.1E-4 596.8 0.66 4.43 1.73 4.0613 8.33358 9E-5 10.67232 2.2E-4 538.64 0.25 3.94 1.96 3.3414 8.32923 1.1E-4 10.68117 2E-4 511.68 0.48 3.75 1.58 4.3115 8.33184 1.1E-4 10.68418 1.8E-4 431.48 0.12 2.54 1.45 4.5216 8.33128 1E-4 10.67865 1.6E-4 491.05 0.48 2.79 4.25 7.6117 8.3315 1.1E-4 10.6801 1.8E-4 474.62 0.18 2.98 1.87 4.3718 8.33429 1.4E-4 10.67578 2.4E-4 357.57 0.44 3.15 2.02 7.0719 8.33074 1.2E-4 10.68204 1.8E-4 474.67 0.43 2.66 1.34 2.4320 8.3337 1.3E-4 10.68167 1.9E-4 411.69 0.61 3.07 2.84 6.1821 8.32752 6E-5 10.67397 1.4E-4 898.95 0.56 3.02 1.65 2.7122 8.33156 9E-5 10.67583 1.6E-4 451.86 0.65 2.6 1.71 4.4823 8.32592 1.3E-4 10.67917 2E-4 413.46 0.56 3.16 2.58 5.79Figure S2: Thermoelectric properties of the samples as a function of temperature from cycle1 to cycle 5. Electrical conductivity (a), Seebeck coefficient (b), power factor (c), thermalconductivity (d), and figure of merit (e).Figure S3: Average of the thermoelectric properties at 700 K as a function of sample numberfrom cycle 1 to cycle 5. Electrical conductivity (a), Seebeck coefficient (b), power factor (c),thermal conductivity (d), and figure of merit (e).Figure S4: GP-fitted zT at 700 K as a function of measured zT at 700 K for all 25 GeTesamples. The perfect prediction line is shown in black. The error bars, large of 0.001 inaverage and therefore not visible, represent a single standard deviation of the GP-fitted zTat 700 K.Figure S5: Partial dependence plots of the GP-fitted zT at 700 K for the six most importantvariables, in descending order: melt-cooling rate, dwell time, annealing temperature, SPSuniaxial pressure P, milling-time.1 and heating-rate. A ridge of high zT appears at rapidmelt-quenching combined with short, slow-cooled SPS profiles.Figure S6: Partial dependence plots of the GP-fitted zT at 700 K for for the less influentialvariables, in descending order: annealing-temperature.1, heating-rate.1, dwell-time.1, mass-powder and cooling-rate.1. All show comparatively shallow trends, confirming their minorcontribution to the overall variance in zT at 700 K.References(1) Chattopadhyay, T.; Boucherle, J. X. Neutron diffraction study on the structuralphase transition in GeTe. 1987; J. Phys. C: Solid State Phys. 20(10), 1431–1440.DOI:10.1088/0022-3719/20/10/012.(2) Li, J.; Chen, Z.; Zhang, X.; Sun, Y.; Yang, J.; Pei, Y. Electronic Origin of the HighThermoelectric Performance of GeTe among the p-Type Group IVMonotellurides. NPGAsia Materials 2017, 9, e353.(3) Chen, H.; Song, Q.; Zhang, Z.; Luo, T.; Wei, Q.; Sun, L.; Li, Y. Anisotropic Thermo-electric Properties of GeTe Single Crystals. Journal of Materials Chemistry A 2024,12, 10974–10983.(4) Li, J.; Zhang, X.; Lin, S.; Chen, Z.; Li, W.; Pei, Y. Realizing the High ThermoelectricPerformance of GeTe by Sb-Doping and Se-Alloying. Chemistry of Materials 2017, 29,605–611.(5) Shuai, J.; Tan, X.; Guo, Q.; Zhang, Q.; Wang, H.; Pei, Y. Enhanced Thermoelec-tric Performance through Crystal Field Engineering in Transition-Metal-Doped GeTe.Materials Today Physics 9, 100094.(6) Ding, G.; Gao, G.; Yao, K. High-efficient thermoelectric materials: The case of or-thorhombic IV-VI compounds. 2015; Sci. Rep. 5:9567. DOI:10.1038/srep09567.(7) Allen, T.; Graser, J.; Issa, R.; Sparks, T. Machine learning predictions of lowthermal conductivity: comparing TaVO5 and GdTaO4. 2023; ChemRxiv preprint.DOI:10.26434/chemrxiv-2023-444s3.(8) Armida, S. A.; Ebrahimibagha, D.; Ray, M.; Arenas, E.; Schaadt, K.; Treece, R. As-sessing thermoelectric performance of quasi 0D carbon and polyaniline nanocompositesusing machine learning. 2023; Adv. Compos. Mater. 33(3), 388–410.(9) Packwood, D. Bayesian Optimization for Materials Science; Springer: Singapore, 2017.(10) Lambard, G.; Sasaki, T. T.; Sodeyama, K.; Ohkubo, T.; Hono, K. Optimiza-tion of direct extrusion process for Nd-Fe-B magnets using active learning as-sisted by machine learning and Bayesian optimization. 2022; Scr. Mater. 209:114341.DOI:10.1016/j.scriptamat.2021.114341.(11) Gelbstein, Y.; Dado, B.; Ben-Yehuda, O.; Sadia, Y.; Dashevsky, Z.; Dariel, M. P. HighlyEfficient Ge-Rich GexPb1−xTe Thermoelectric Alloys. Journal of Electronic Materials2010, 39, 2049–2052.(12) Kumar, A.; Bhumla, P.; Parashchuk, T.; Arora, K.; Yadava, N.; Sachdev, K.;Bathula, S.; Tyagi, H.; Sharma, Y. Engineering Electronic Structure and Lattice Dy-namics to Achieve Enhanced Thermoelectric Performance of Mn-Sb Co-Doped GeTe.Chemistry of Materials 2021, 33, 3611–3620.(13) Srinivasan, B.; Boussard-Plédel, C.; Bureau, B.; Le Gall, E.; Fan, X.; Halet, J.-F.;Halet, J.-F. Thermoelectric Performance of Codoped (Bi, In)-GeTe and (Ag, In, Sb)-SnTe Materials Processed by Spark Plasma Sintering. Materials Letters 2018, 230,191–194.(14) Srinivasan, B.; Gellé, A.; Halet, J.-F.; Fan, X.; Boussard-Plédel, C.; Bureau, B. Detri-mental Effects of Doping Al and Ba on the Thermoelectric Performance of GeTe. Ma-terials 2018, 11, 2237.(15) Srinivasan, B.; Gellé, A.; Gucci, F.; Fan, X.; Boussard-Plédel, C.; Bureau, B.; Halet, J.-F. Realizing a Stable High Thermoelectric zT ≈ 2 over a Broad Temperature Range inGe1−x−yGaxSbyTe via Band Engineering and Hybrid Flash-SPS Processing. InorganicChemistry Frontiers 2019, 6, 63–73.(16) Srinivasan, B.; Le Tonquesse, S.; Gellé, A.; Fan, X.; Boussard-Plédel, C.; Bureau, B.;Halet, J.-F. Screening of Various Elements as Potential Effective Dopants for Ther-moelectric GeTe - An Experimental and Theoretical Appraisal. Journal of MaterialsChemistry A 2020, 8, 19805–19821.(17) Perumal, S.; Samanta, M.; Ghosh, T.; Xie, L.; He, J.; Candidus, G.; Felser, C.;Biswas, K. Realization of High Thermoelectric Figure of Merit in GeTe by Comple-mentary Bi and In Co-doping. Joule 2019, 3, 2565–2580.(18) Hong, M.; Chen, Z.; Yang, L.; Qin, J.; Zhang, T.; Hu, H.; Yang, J.; Li, J.-F. RealizingzT of 2.3 in Ge 1-x-ySb xIn yTe via Reducing the Phase-Transition Temperature andIntroducing Resonant Energy Doping. Advanced Materials 2018, 30, 1705942.(19) Hong, M.; Wang, Y.; Feng, T.; Liu, W.; Zhang, T.; Qin, J.; Yang, L.; Li, J.-F. Strong Phonon-Phonon Interactions Securing Extraordinary Thermoelectric Ge 1-xSb xTe with Zn-alloying-induced Band Alignment. Journal of the American ChemicalSociety 2019, 141, 1742–1748.(20) Hong, M.; Lyv, W.; Li, M.; Qin, J.; Zhang, T.; Hu, H.; Yang, L.; Li, J.-F. Rashba EffectMaximizes Thermoelectric Performance of GeTe Derivatives. Joule 2020, 4, 2030–2043.(21) Shuai, J.; Sun, Y.; Tan, X.; Guo, Q.; Wang, H.; Xie, H.; Snyder, G. J.; Pei, Y. Ma-nipulating the Ge Vacancies and Ge Precipitates through Cr Doping for RealizingHigh-Performance GeTe Thermoelectric. Small 2020, 16, 1906921.(22) Liu, Z.; Gao, W.; Zhang, W.; Tan, X.; Wang, H.; Xie, H.; Zhang, Q.; Pei, Y. High PowerFactor and Enhanced Thermoelectric Performance in Sc and Bi Co-doped GeTe: HiddenRole of Rhombohedral Distortion. Advanced Energy Materials 2020, 10, 2002588.(23) Xing, T.; Zhu, C.; Song, Q.; Wang, S.; Zhao, L.-D.; He, J. Realizing High-EfficiencyThermoelectricity in GeTe through Synergetic Band Engineering and Nanostructuring.Advanced Materials 2021, 33, 2008773.(24) Gao, W.; Liu, Z.; Zhang, W.; Tan, X.; Wang, H.; Xie, H.; Pei, Y. Improved Ther-moelectric Performance of GeTe via Efficient Yttrium Doping. Applied Physics Letters2021, 118, 033901.(25) Bourgès, C. M. C.; Lambard, G.; Sato, N.; Tachibana, M.; Ishii, S.; Mori, T. Pro-cess optimization on kesterite-based ceramics for enhancing their thermoelectric per-formances assisted by active machine learning approach. 2024; Acta Mater. 281:120342.DOI:10.1016/j.actamat.2024.120342.(26) Roisnel, T.; Rodŕıguez-Carvajal, J. WinPLOTR: A Windows Tool for Pow-der Diffraction Pattern Analysis. 2001; Mater. Sci. Forum 378-381, 118–123.DOI:10.4028/www.scientific.net/MSF.378-381.118.(27) Jones, D. R.; Schonlau, M. Efficient Global Optimization of Expensive Black-Box Func-tions. 1998; J. Global Optim. 13(4), 455–492. DOI:10.1023/A:1008306431147.(28) The GPyOpt authors GPyOpt: A Bayesian Optimization framework in Python. 2016;Available at http://github.com/SheffieldML/GPyOpt.(29) Pedregosa, F. et al. Scikit-learn: Machine Learning in Python. 2011; Journal of MachineLearning Research 12, 2825–2830.(30) Cheng, H.; Zhang, J.; Lin, C. Persistence of the R3m Phase in Powder GeTe atHigh Pressure and High Temperature. 2018; J. Phys. Chem. C 122(50), 28460–28465.DOI:10.1021/acs.jpcc.8b06511.(31) Edwards, A. H.; Pineda, A. C.; Schultz, P. A. Theory of persistent, p-type, metal-lic conduction in c-GeTe. 2005; J. Phys. Condens. Matter 17(32), L329–L335.DOI:10.1088/0953-8984/17/32/L01.(32) Alleno, E. et al. A round robin test of the uncertainty on the measurement of the ther-moelectric dimensionless figure of merit of Co0.97Ni0.03Sb3. 2015; Rev. Sci. Instrum.86(1):011301. DOI:10.1063/1.4905250.(33) Nugraha, A. S.; Lambard, G.; Na, J.; Hossain, M. S. A.; Asahi, T.; Chaikit-tisilp, W.; Yamauchi, Y. Mesoporous trimetallic PtPdAu alloy films toward enhancedelectrocatalytic activity in methanol oxidation: unexpected chemical compositionsdiscovered by Bayesian optimization. 2020; J. Mater. Chem. A 8(27), 13532–13540.DOI:10.1039/d0ta04096g.(34) Matsuda, S.; Lambard, G.; Sodeyama, K. Data-driven automated robotic experimentsaccelerate discovery of multi-component electrolyte for rechargeable Li-O2 batteries.2022; Cell Rep. Phys. Sci. 3(4):100832. DOI:10.1016/j.xcrp.2022.100832.(35) Gandhi, J. R.; Nehru, R.; Chen, S.-M.; Sankar, R.; Bayikadi, K. S.; Sureshkumar, P.;Chen, K.-H.; Chen, L.-C. Influence of GeP precipitates on the thermoelectric propertiesof P-type GeTe and Ge0.9−xPxSb0.1Te compounds. CrystEngComm 2018, 20, 6449–6457.(36) Xing, T.; Song, Q.; Qiu, P.; Zhang, Q.; Gu, M.; Xia, X.; Liao, J.; Shi, X.; Chen, L.High efficiency GeTe-based materials and modules for thermoelectric power generation.Energy & Environmental Science 2021, 14, 995–1003.(37) Tang, S.; Dresselhaus, M. S. Building the Principle of Thermoelectric ZT Enhancement.arXiv:1406.1842, 2014.(38) Lookman, T.; Balachandran, P. V.; Xue, D.; Yuan, R. Active learning in materialsscience with emphasis on adaptive sampling using uncertainties for targeted design. npjComputational Materials 2019, 5, 21.(39) Zhang, H.; Xie, H. Spark-plasma sintering of thermoelectric materials: A review. Small2021, 17, 2006921.(40) Bochmann, S.; Schilm, J.; Gas, P.; et al. Round robin test of Seebeck and electricalresistivity measurements on CoSb3. Journal of Electronic Materials 2018, 47, 2534–2543.(41) Mockus, J.; Tiesis, V.; Zilinskas, A. In Towards Global Optimisation 2 ; Dixon, L. C. W.,Szegö, G. P., Eds.; North-Holland: Amsterdam, 1978; pp 117–129.