Statistical and artificial intelligence approaches towards the optimization of thermoelectric materials synthesis: a review
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Abstract
Thermoelectric (TE) materials, capable of directly converting heat to electricity, offer a promising sustainable energy and waste heat recovery solution. Despite extensive research, a significant bottleneck remains: the synthesis of high-performance TE materials still relies heavily on trial-and-error approaches, which are time-consuming and resource-intensive. Moreover, while machine learning (ML) and design of experiments (DOE) have shown potential in optimizing synthesis processes across materials science, their systematic application to TE materials remains underexplored. In particular, very few reviews have addressed the integration of statistical and AI-guided methods for synthesizing and optimizing TE materials. This manuscript comprehensively reviews recent advances in statistical and artificial intelligence techniques for optimizing TE material synthesis. It first discusses the role of DOE in identifying critical synthesis parameters and explores various ML methods for predicting TE performance. This study then highlights case studies involving different TE material systems, synthesis strategies (e.g., ball milling, sputtering, electrodeposition), and ML-based performance prediction and optimization. This work fills a critical gap by linking data-driven optimization techniques with experimental synthesis in the TE field. It not only consolidates current knowledge but also sets the stage for future studies aiming to bridge material discovery and practical manufacturing. The insights presented are instrumental in accelerating the development of next-generation TE devices.
Keywords
INTRODUCTION
The ever-growing energy demand has become a global challenge due to the limited reserve of fossil fuels. There have been considerable efforts to develop alternatives to fossil fuels, such as solar, nuclear, and wind. Naturally, a lot of energy is wasted as heat in the modern world. Thermoelectric (TE) technologies, which utilize the phenomena of energy conversion between heat and electricity, have the potential to reuse waste heat for sustainable electrical energy generation[1]. Nevertheless, TE technologies are environmentally friendly renewable energy sources and have drawn tremendous attention over the last few decades[2].
Due to the ability to convert thermal to electrical energy and vice-versa, TE materials have potential in various applications, including refrigeration, power generation, and waste heat recovery[3]. Recently, there have been plenty of research activities in the area of the use of statistical methods such as design-of-experiment (DOE), machine learning (ML), and artificial intelligence (AI) in the area of TE technology with a focus on the design of TE materials and thermoelectric generators (TEGs).
DOE is a statistical way of optimizing the response of experiments. Constructing experiments with the minimum optimization parameter variations statistically to enhance the system's performance is crucial. AI is a technology operating to do the task, which is constructed through data collection, model training, optimization and deployment. It is used to find the new materials in the TE. ML belongs to AI, a statistical model for optimization and finding the relation between input and output parameters. ML is developed with mathematical models and algorithms for finding the pattern through statistical analysis of input data. Gorai et al. have reviewed optimizing materials properties and designing and discovering TE materials using ML[4]. Wang et al. have given an overview of the use of several ML methods, such as Bayesian optimization, regression, and neural network (NN) models in TE research[5]. Chen et al. have reviewed the use of ML in discovering and designing various materials for energy-related applications. This included ML in photovoltaics, batteries, catalysis, and thermoelectric[6]. Recatala-Gomez et al. reviewed the historical evolution of various inorganic TE materials. They postulated that combining data generation, ML, high-throughput synthesis and characterization, and high-performance computing can accelerate the discovery of novel TE materials[7]. Recently, Wang et al. have critically reviewed the progress on the application of ML in (i) predicting and optimizing the properties (electrical and thermal transport) of TE materials; and (ii) the designing and screening of TE materials[8]. Furthermore, the optimization of TEGs based on statistical approaches such as the Taguchi method, the response surface methodology (RSM), and the analysis of variance (ANOVA) has been reviewed by Chen et al.[9]. Kucova et al. reviewed waste heat harvesting from the Internet of Things (IoT) through ML[10]. The review concluded the suitability of TEG in low-grade waste heat harvesting through the results of various ML algorithms. Song et al. draw the roadmap from high throughput materials discovery to advanced device fabrication[11]. Also, this review discussed the discovery of new TE material through ML algorithms. Deng et al. discussed predictive ML algorithms based on the TE materials[12]. The previously reported reviews on TE mainly focused on new material discovery based on the ML algorithm. One important part that was not discussed is atomic characteristics relation with TE parameters and the parameter optimization in material synthesis through ML approach. However, these are important to understand the TE material tailored to find a suitable approach to tune the TE performance with minimal optimization parameters.
Regardless of the ability of ML and DOE to direct the discovery and optimization of TE materials and TEGs, the ultimate ability to control the synthesis in a rational and controllable way will determine the research and development of future TE technologies. However, the synthesis attempt of existing and unknown TE materials from existing literature based on knowledge of materials synthesis and the prediction and control of outcome is complicated. This is because the control over TE materials synthesis depends on carefully controlling many experimental parameters such as choice of precursors, synthetic methods, temperature, pressure, atmosphere, time, additives, etc.
There are a total of 38,413 published articles under the keyword 'thermoelectric materials' over the past ten years in the Science Direct database. Figure 1 shows how publication activity in TE materials has changed over the last ten years. The surge in TE materials research is apparent, and the number of publications has increased rapidly. Therefore, the research areas involving TE materials are popular among the scientific community. However, controllable synthesis of TE materials is a significant bottleneck for realizing practical thermoelectric devices such as TEGs. Notably, there is a knowledge gap between implementing statistical optimization methodologies, discovering new TE materials, and finding optimal synthesis and device fabrication conditions. This article covered the importance of ML in DOE for TE material synthesis, material chemistry parameters involving boosting TE performance, segregating materials based on performance, finding new material, and optimizing composition. In TE material creation such as a thin film, the ML approach in parameter optimization for coating and sintering is discussed.
Figure 1. (A) Showing histogram of several results as a function of publication years with keywords “thermoelectric materials” in the Science Direct database. (B) Map created by VOSViewer for “thermoelectric materials” from Web of Science.
PERFORMANCE ENHANCEMENT OF THERMOELECTRIC MATERIALS
The efficiency of TEGs depends on the performance of TE materials. In this direction, significant advancement has been achieved through research and development toward the optimal performance of TE materials[13-19].
The performance of TE materials is usually expressed as the “figure of merit” ZT = S2σT/ κe + κl, where the Seebeck coefficient is S, the electrical conductivity is σ, and electronic and lattice thermal conductivities are κe and κl espectively, at temperature T. Here (κe + κl) is known as the total thermal conductivity of TE materials. Thus, a high value of ZT implies high performance of TE materials. Moreover, TE materials with high ZT values can lead to efficient TE devices for commercial applications. The high value of ZT at a given temperature can be achieved with TE materials having high S, high σ, and low thermal conductivities κe and κl. However, σ decreases when S increases. On the other hand, total thermal conductivity (κe + κl) of TE materials is proportional to σ. Due to this complex interrelation between the TE parameters, it is pretty challenging to control independent parameters experimentally for the optimization of the performance of TE materials. Literature-reported methods for optimizing ZT focused on the methods for reducing thermal conductivity and enhancing S and σ, respectively[17,20]. Finally, when the thermal conductivity of materials is very low or unavailable, the performance of TE materials can be expressed as the power factor S2σ.
Thermoelectric materials development
The range of materials that exhibit TE properties encompasses wide varieties, including inorganic, organic, and inorganic-organic hybrid[21]. Naturally, each type of material has its advantages and disadvantages. There are vast numbers of inorganic materials that exhibit TE properties. Typical inorganic TE materials are based on chalcogenides (such as Bi2Te3, PbTe, SnSe, etc.), Si-Ge alloys, multicomponent oxides, skutterudite-type materials, half-Heusler alloys, and clathrates[14,19]. The variation of ZT with temperature of some typical inorganic TE materials is shown in Figure 2[22]. As a result of extensive research and development over the past few decades, Bi2Te3 and Si-Ge-based materials are used in commercial TE devices. The main advantage of inorganic TE materials is their high TE performance. Commercial TE devices use inorganic materials with ZT~1. Therefore, searching for new materials with high ZT values has been popular in TE material research[20,23]. The disadvantages of inorganic TE materials include poor abundance of elements, high cost, and toxicity[24]. On the other hand, the advantages of organic TE materials include earth-abundant elements, ease of manufacturing involving solution-based methods, the possibility of a cost-effective scale-up process, lightweight, mechanical flexibility, low toxicity, and low thermal conductivity[25,26]. However, due to poor Seebeck coefficient and electrical conductivity, organic materials have inferior ZT values[27]. Nevertheless, the development of organic materials for TE devices has been reviewed by several authors[25,27-29]. Interestingly, the inorganic-organic hybrid materials are emerging as novel TE materials. The hybrid TE materials could combine the high S and σ of inorganic materials and the low thermal conductivity of organic materials[21,30].
Figure 2. Variation of ZT with temperature of some common inorganic TE materials. Adapted from Jarman et al.[22]. (Licence CC By 4.0).
Design of experiment for TE materials synthesis
During the optimization of synthesis of TE materials, experiments are performed to measure the effects of experimental variables on responses. The optimization of preparation involves finding a combination of variables that gives the best response. Thus, there are many types of experiments. DOE is a statistical way of optimizing the response of experiments. An efficient DOE is a sequential approach wherein information gained in the initial stage can be used to decide which factors may be kept constant or varied in later stages. In this process, reducing the number of experimental variables to a more significant one is possible. Thus, statistical DOE through fractional factorial design can provide an opportunity to minimize the number of experiments by optimizing experimental conditions. The main advantages of DOE are efficiency, response analysis, and simple interpretation of statistical outcomes.
The DOE has existed for quite some time, but its use is very new in synthesizing TE materials.
The first example of the application of statistical DOE in TE materials synthesis is for the optimization of the sintering parameters of K2Bi8Se13-xSx (for x = 0, 4, 6, and 8)-based TE materials by Kyratsi et al.[34]. Sintering conditions must be optimized to obtain high-quality pellets of TE materials with the highest density. In this work statistical DOE through fractional factorial experiment and Taguchi table has been employed for identifying optimum parameters for sintering (duration, temperature, and pressure) for the fabrication of high-quality pellets. Based on the ANOVA, it has been postulated that the density of the pellet is more significantly affected by pressure than duration and temperature. The best condition for hot-press sintering of these TE materials has been 80 MPa pressure, 530 °C temperature, and 90 min duration, respectively, with a relative density of pellet approaching ~97%. These optimized sintering conditions have been used for sintering the pellets of the entire K2Bi8Se13-xSx compounds. Interestingly, the sample with x = 0 exhibited a ZT value of 0.58 at 673 K.
Bi2Te3 and its alloys, such as Bi2-xSbxTe3 and Bi2Te3- xSex, have been used in TE technologies for decades. However, Kanatzia et al. have employed factorial DOE via ANOVA for the ball-milling synthesis of Bi2Te3 for the first time[35]. The analysis of parameters for ball milling, such as duration, rotation speed, and ball-to-material ratio, respectively, suggests a strong influence of the duration and speed of ball milling on the TE properties of nanocrystalline Bi2Te3. The ZT value of optimized ball-milled nanocrystalline Bi2Te3 is 0.72 at 100 °C. It is expected that DOE can further improve the ZT value of Bi2Te3-based TE materials through efficient optimization of ball-milling parameters.
Nuthongkum et al. applied RSM and statistical central composite design (CCD) for modeling and optimizing thin film deposition parameters of thermoelectric Bi2Te3 material using the radiofrequency (RF) magnetron sputtering technique[36]. This study has statistically analyzed the formation of Bi-Te thin films considering several deposition factors, such as the flow rate of Ar gas and annealing temperature. The DOE using RSM to find the optimal conditions for the targeted response utilizes mathematical and statistical methods to develop models and evaluate factors. Thus, RSM plots suggest that the concentration of Te in Bi-Te thin film would decrease if the annealing temperature is increased at a lower Ar flow rate. Using this model, it has been determined that the optimized conditions for the deposition of good quality thin films
Carbon materials are widely studied in electronic devices due to their availability in different structures[38]. The high electrical conductivity is crucial for TE performance enhancement. Jagadish et al. developed a DOE study on the investigation of TE properties of thin films of Bi2Te3 on recycled carbon fiber by electrodeposition technique[39]. Herein, the DOE based on the D-optimal model under RSM has been adopted to optimize the combined effect of electrodeposition parameters, leading to the optimum Seebeck coefficient. The authors used a multivariate approach involving DOE based on 23 runs to optimize experimental parameters. The optimum electrodeposition parameters are potential -0.10 V, time 0.5 h, temperature 25 °C, and electrolyte compositions 0.240 Bi/(Bi + Te). Thus, using DOE, the optimized electrodeposition parameters yielded an experimental Seebeck coefficient of -13.42 μV/K, about 33% larger than samples prepared without DOE.
Lead chalcogenides (PbTe, PbSe, PbS) are excellent TE materials. In particular, Pb1-xSnxTe-based materials are promising for TE applications due to their high ZT values. Recently, Sam et al. have developed a DOE method for synthesizing Pb1-xSnxTe (x = 0.67) crystals by horizontal vapor phase growth method[40]. This study employs 2k full factorial design to correlate ZT with the effect of synthesis temperature and time. Based on the ANOVA of ZT, the synthesis temperature and time exhibit significant ZT response. Thus, the crystals prepared at 1,200 °C for 4 h have exhibited the highest ZT of approximately 0.084.
Due to high operating temperatures, SiGe alloy-based TE materials are widely used in radioisotope TEGs[41]. The n-type SiGe alloy may exhibit a very high ZT value of 1.84 at 1,073 K[42]. Ahmad et al. studied statistical DOE and RSM optimization of ball milling and hot press sintering parameters to prepare SiGe alloy[43]. In this study for TE properties of SiGe alloy, 13 experiments were incorporated in two-factor CCD for obtaining regression equations. For the maximum ZT, the hot press temperature is 1,504.5 K, and the time for ball milling is 53.6 h. Herein, the predicted and experimental optimum ZT values were 1.148 and 1.146, respectively.
Effective heating and cooling on the surface of TEG increases the temperature difference across TEG, which directly relates to device efficiency and output power. However, the construction of the microstructure of TE materials is vital to withstand significant temperature differences for performance enhancement. The optimization of TE legs (such as the areas of hot and cold sides, pin configuration, contact angle, etc.) and the construction of the 3D architecture of TE legs tailors to avoid the brittleness of material and the heat stagnation in its legs[44]. Maduabuchi[45] studied thermomechanical optimization using a deep neural network (DNN). The data obtained from the finite element method was fed to the DNN to learn the pattern. The well-fitting of experimental and DNN results indicated the suitability of DNN, reducing the simulation time. The temperature difference between the hot and cold sides was crucial to maximize the output power. Besides, this report discussed the optimization of temperature effect on temperature on the hot side (Th) and temperature on the cold side (Tc) by the wind speed. This effective cooling was achieved by installing low thermal conductivity material on the cold side, and the cold side temperature was optimized with a cooling coefficient. Besides, the increment in Th increased the thermal stress on the legs, which accounted for performance reduction. Meanwhile, the optimized geometrical parameter of TEG minimized the thermal stress, avoiding the device's cracks and heat stagging. In the staggered and integrated device, mechanical stability was a crucial parameter. The same author reported the optimization focused on thermomechanical properties in the TEG and solar cell integrated device. The numerical method generated data was used to feed the DNN to predict the performance quickly and with more accuracy. After the optimization by focusing on the thermo-mechanical stability, the output power was increased, and the thermal stress was reduced[46].
Designing an ML model based on actual environmental conditions is crucial, which helps design the TEG for large-scale applications and suitable environmental conditions. However, the temperature of the TEG surface depends on the environmental conditions. Ameenuddin Irfan et al. designed the TEG based on the actual environment by analyzing the humidity variation and actual room temperature, predicting Th and
MACHINE LEARNING (ML) METHODS
In ML methods, problems are solved by developing mathematical models and algorithms by discovering patterns through statistical analysis of input data. The most common ML algorithms in chemistry are support vector machine (SVM), random forest (RF), k-nearest neighbors (kNN), ensemble, decision tree (DT), and NN methods, respectively.
Machine learning in materials chemistry
In materials chemistry, AI technologies, including ML methods, have been increasingly used to predict the crucial factors for the synthesis and select the optimal reaction conditions. Gulevich et al. have reviewed the application of ML methods to develop synthesis and choose the best synthesis conditions for colloidal nanomaterials[48]. As shown in Figure 3, AI technologies have several benefits for synthesizing colloidal nanomaterials[48]. Thus, optimization of synthesis parameters (time, temperature, concentration of precursors, and additives) necessary for the synthesis of nanocrystals of several chalcogenides (CdS, CdSe, PbS, and ZnSe) have been studied using ML[33]. The use of similar ML methods for synthesizing size and shape-controlled chalcogenides-based TE nanomaterials is yet to be known. This is one area that will expand in the coming future.
Figure 3. Showing the benefits of using AI for synthesizing colloidal nanomaterials[48]. (License Number 6015211273249).
The relation between the structural parameters in chemistry and the thermoelectric parameters is crucial to segregating the material from high performance to low performance. Compared with the conventional cascaded arrangement of TE devices, low-cost spin-driven thermoelectric (STE) consisting of simple layered structures gained much attention since it has been fabricated by sputtering, coating, and platting, which is a direct approach. However, STE consists of rare earth elements that are pretty costly. Applying ML to analyze suitable composition is more time-efficient and can reduce material waste.
Iwasaki et al. applied the ML approach to discover novel STE material through actual material synthesis[49]. The experimental data of series of rare earth substituted yttrium iron garnet Pt/R:YIG (R = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu, except Pm) fabricated on Gd3Ga5O12 (GGG) and
Further, analyzing new materials and their TE properties is crucial. Tewari et al. applied the ML approach to classify thermal conductivity among oxides and oxide alloys of transition metals, that is, elements of groups 3-11 and periods 4-6[50]. A two-step ML model was employed: one is classification, and another is regression. The complete set-off ML model is shown in Figure 4. Gradient boosted tree classifier was used to predict the key material properties influencing κl and to classify material with low, medium, and high κl. These key material properties were lattice energy per atom, atom density, band gap, mass density, and oxygen ratio by transition metal atoms. Above mentioned properties define the crystal structure, compound chemistry, and interatomic bonding of a compound. The regression model was employed to predict absolute κl with various models, including Cubist, GPR polykernel, kNN, GBM, XGBoost, RF, Kernel ridge, and deep neural nets. Among these, Cubist, GPR polykernel, GBM, and Kernel ridge models have better fit with actual value with the coefficient of determination (R2) > 0.9, which is mainly used on low κl materials. Another report by Juneja et al. detailed the segregation of low and high κl among 120 materials for TE and thermal barrier coatings, respectively[51]. These materials' maximum phonon frequency integrated Gruneisen parameter up to 3 THz, average atomic mass, and unit cell volume obtained from material project relay on κl. GPR was employed as an ML model to predict and segregate the materials based on κl. The data was collected from the material project, and the obtained log(κl) values between experimental and ML approaches were analyzed with fitting. In this study, 15 new materials were identified from primitive and face-centered crystal classes, with a very low κl range between 0.13 and 0.98 Wm-1K-1, considerable to TE performance. GPR model predicted the log-scaled κl through ARD Matern 5/2 covariance function, which gave the train/test RMSE of 0.20/0.21 and the R2 of 0.99/0.99. The same log-scaled κl predicted through the slacker model overestimated the values and showed poor variability with the slacker model.
Figure 4. ML approach to predict low κl value among oxide-based alloys[50]. (License CC By 4.0).
TE parameters are related to one another, raising the importance of finding the physical descriptors that connect all the TE parameters. Juneja et al. applied ML to predict the relation between elemental descriptors and electronic transport properties (S and σ)[52]. Initially, 2838 compounds were screened based on the band gap (greater than zero) for nonmetallic compounds and the phonon frequency (greater than zero) for stability. After the screening process, 135 compounds remain and used for further process. GPR was developed as a predictor model by employing a 10-fold cross-validated least absolute shrinkage and selection operator (LASSO). Among 135 compounds, 34 compounds had a high-scaled power factor. In them, 6 has κl less than 2 Wm-1K-1. From these, a material PdBr2 was identified with a high power factor and low lattice thermal conductivity. LASSO helped to screen the descriptor in relation to electronic transport parameters. The higher accuracies were obtained through the elemental and bonding descriptors. The transport parameters σ and S revealed the dependency relation with coordination number, boiling point, the heat of formation, and molar-specific heat coming under the bonding descriptor. From this, σ and S commonly relate to the bond strength. Further, κl shows a close relation with the coordination number through anharmonicity. Volume is inversely correlated with the κl. Hence, electronegativity, bond strength, bond distance, volume, and coordination number have an excellent correlation with the electronic and thermal transport properties related to the chemical bonding descriptor. In conclusion, the chemical bonding-driven descriptor is a key point to connect the electronic and thermal transport properties. These reports find a common relation that could help to understand future experimental research in this domain. A total of 2,838 compounds were taken from different groups of materials: alkaline, transition, alkali, and lanthanide elements, and these were screened based on the band gap and phonon frequency; after that, 185 compounds were found to be nonmetallic and stable. Figure 5 illustrates the screening process, which includes the optimization, band gap, and phonon frequency. Also, another report has verified the relation between chemical bonding characteristics and κl. In this, the coordination number had a high value when the bond strength was weak and the bond distance was large[53].
Figure 5. Process of screening compounds under the optimization, band gap, and phonon frequency to get nonmetallic and stable compounds, to calculate electronic properties[53]. (Creative Commons Attribution 4.0 license).
Various atomic characteristics of materials that change the TE properties lead to identifying their relationship. Indeed, ML reduces the cost of material synthesis by predicting this relation. Li et al. applied the ML approach to analyze the TE performance of high entropy GeTe materials by correlating atomic features and the ZT[54]. Nine atomic features were selected for this analysis: atomic number, ionization energy, pseudopotential radius, atomic radius, electronegativity, electron affinity energy, molar volume, number of valence electrons, and atomic weight. Each element's atomic fraction is treated as a weighted score for its atomic properties. The following equation constructs the ML model in relation to atomic characteristics:
where the letters i and j represent certain elements, and Vi is the average atomic characteristic, which is defined before (V1 is the average atomic number, V2 is the average atomic radius, V3 is the average pseudopotential radius, V4 is the average molar volume, V5 is the average electronegativity, V6 is the average ionization energy, V7 is the average electron affinity energy, V8 is average ionization energy, V9 is the average atomic weight, V10 is the average number of valence electrons, T is measuring temperature), υi,jrepresents the atomic characteristic, and cj is the atomic fraction. Different ML models are tested in this, namely LightGBM, surface vector regression (SVR), Ridge E, XGBoost, RF, and linear regression. LightGBM exhibits the least error value among these, with an R2 of 0.954. Among the atomic characteristics, temperature has a greater impact on ZT, while V4 and V5 randomly decreased, and the optimum values of
The influence of input data size on training the ML model is vital to achieve accuracy. The sample data size defines the degree of freedom (DoF) on fitting. Zhang et al. studied the data size influence with descriptors to predict the band gap, κl, and elastic properties of zeolites[55]. Rather than directly influencing model precision, the size of the dataset exerts its effect indirectly through the model DoF. It was challenging to predict the results in unknown domains without affecting the precision. Integration of crude estimation features in ML model improved the predictive accuracy without using the high DoF. Experimental and density functional theory (DFT)-based datasets were used to train the model before and after integrating the crude estimation, respectively. Kerne ridge regression ML model was used to predict the κl, the error of 6.2% that occurred was reduced to 4.1% after the integration of the crude estimation feature. This study implies the improvement of accuracy with the integration of crude estimation, which needs less data to create an ML model.
Doping is crucial for TE material performance enhancement. However, more elements can be used for doping in a particular site due to the availability of more elements in a similar oxidation state. Determining the elements tailored to reduce material waste, cost, and time consumption is also crucial. He et al. reported the prediction of superior thermoelectric performance in unexplored doped-BiCuSeO via ML[56]. The experimental data of Bi1-xMxCuSeO (M represents Ca, Mg, Sr, Ba, Na, La, Sm, Er, Ho, Cd, Sb, Pb, Ag, Al, Fe, K, Rb, Co, Cs, Mn, Nd, Sn, Yb, Zn, and Ni) was collected from the literature. The descriptors, a set of input parameters such as temperature, the content of the doping element, the relative molecular mass of
Figure 6. (A) Workflow and (B) identified ZT of doped elements through the ML approach[56]. (License Number 6015491243882).
The ML model is accelerating to find a new TE material and highly efficient dopant. Parse et al. constructed an ML model to discover a new dopant to place in the Bi site in BiCuSeO[58]. The model design focused on the accuracy improvement by normalizing ZT of doped BiCuSeO with pristine BiCuSeO. The developed model produced the best fitting data with experimental. The R2 value of 0.93 from the developed extra tree regression model was much closer to 1, indicating more accuracy than the initial model. New dopants were discovered through this model without wasting the material, which satisfied the thermoelectric principle. Based on various descriptors, the selected Si as a dopant for the Bi site improves the ZT by increasing mobility. Table 1 lists the survey of this review and refers to the descriptors, targets, and findings of the study related to ML in material chemistry.
The survey of this review refers to the descriptors, targets, and findings of the study related to ML in material chemistry
| Publication | Sample source | Samples | Descriptors | Targets | Finding | Best ML algorithms |
| Juneja et al., 2019[51] | Material project | 2,162 binary, ternary, and quaternary compounds | Maximum phonon frequency, integrated Gruneisen parameter up to 3 THz, average atomic mass, and volume of the unit cell | Analyzed the κl for 120 materials in relation to the parameters | Low κl materials between 0.13 and 0.98 (CsK2Sb, TlI, Ba2BiAu, SrTePd, Ba2SbAu, TlBr, Cs2Se, PbI2, LiFeP, TlCl, Ba2AgSb, PbI2, LaCoTe) | GPR |
| Zhang et al., 2018[55] | Previous reports | 93 binary semiconductors | Electronegativity, atomic radius, effective nuclear charge, Vander Waals radius, covalent radius, row number in the periodic table, block number, enthalpy of formation of gaseous atoms, ionization energy, and valence number | Proposed a method to increase prediction accuracy by incorporating property estimation in the feature space to establish ML models | Increased accuracy about 2.1% than before. Used to more accurately predict the κl of materials having more than 0.1 Wm-1K-1 | Kernel ridge regression |
| Juneja et al., 2020[52] | DFT + Boltztrap code | 2,838 compounds | Boiling point, melting point, specific heat, molar specific heat, molar volume, heat of fusion, heat of vaporization, Pauling electronegativity, first ionization energy, group and period in the periodic table, elemental thermal conductivity, atomic number, atomic mass, covalent radius, van der Waals radius, density, the average bond distance, average bond strength, volume per atom, volume of cell, and coordination number | Found the common parameters influencing electrical and thermal transport properties. Tested with 135 compounds | Common parameters driving chemical bonding such as electronegativity, bond strength, bond distance, volume, and coordination number | GPR |
| Juneja et al., 2020[53] | DFT | 2,838 nonmetallic compounds after high throughput screening 185 compounds were analyzed | Boiling point, melting point, specific heat, molar specific heat, molar volume, heat of fusion, heat of vaporization, Pauling electronegativity, first ionization energy, group and period in the periodic table, elemental thermal conductivity, atomic number, atomic mass, covalent radius, van der Waals radius, density, the average bond distance, average bond strength, volume per atom, volume of cell, and coordination number | Found the correlation between the chemistry of bonding and κl | The bond strength obtained was weak for high coordination numbers, and the bonding distance was large | GPR |
| Tewari et al., 2020[50] | DFT | 315 compounds | lattice energy per atom, atom density, band gap, mass density, and oxygen ratio by transition metal atoms | Segregating and discovering material based on κl | Identified low κl among 315 transition metal oxides, values less than 5 Wm-1 K-1 | XGBoost classifier and regression (cubist, kernel ridge, and Gaussian process) |
Machine learning in TE materials synthesis
The efficient synthesis of TE materials requires understanding the connection between various parameters involving synthesis conditions. In this direction, ML has great potential to control the synthesis conditions of novel TE materials. By learning existing synthesis information, ML can recommend efficient synthesis conditions with few trials. Thus, the ML can be used to understand complex relationships and predict optimal synthesis conditions with a high probability of success by employing existing initial synthesis data of TE material. Tang et al. have explored the feasibility of ML for guiding the MoS2 synthesis by Chemical Vapor Deposition (CVD) and hydrothermal synthesis of carbon nanostructures for the first time[59]. Figure 7 shows the schematic of ML workflow for materials synthesis developed by Tang et al.[59]. This study has constructed an ML model for the general control of synthesis parameters for future experiments. The model could predict the probability of success and recommend the optimal synthesis conditions. Furthermore, a progressive adaptive model (PAM) to maximize the outcome of synthesis experiments through minimum trials has been introduced. This successful ML methodology for CVD of MoS2 has the potential to be expanded to efficient synthesis of chalcogenide-based TE materials using CVD techniques.
Figure 7. Schematics of ML-guided synthesis of materials by CVD and hydrothermal process. The three key steps of ML to material synthesis are model construction, optimization, and maximizing experimental outcomes. Adapted from Tang et al.[59]. (License Number 6015150101969).
Among chalcogenides, Bi2Te3-based materials show the best TE properties. Wang et al. have applied ML to optimize hot-extruded CuxBi2Te2.85+ySe0.15 TE materials for the first time[60]. Principal component analysis (PCA) has been employed to characterize multiple variables. It has been found that the extrusion temperature and Cu content are the most important parameters in the CuxBi2Te2.85+ySe0.15-based TE material processing design. This study developed artificial neural network (ANN), SVR, and RF regression models to analyze the relationships between processing conditions, microstructural information, and TE properties.
The ML approach was used to understand the practical conditions involving coating, printing, and synthesizing the TE materials, as a result of which the time required to carry out the experiment and recover the material costs was lowered. BiSbTe is a well-known composition in TE applications exhibiting ZT greater than 1. However, predicting the suitable printing parameter through ML is an effective way to optimize the ZT. Song et al. employed a GPR-based ML model to predict the thermoelectric properties as a function of ink formulation and printing parameters in 3D printing[61]. Initially, the data was collected through experiment results to make ML algorithm. Considering the TE particle loadings and X-gum concentrations for ink formulation, filament spacing, and stand-off distance for printing parameters, the ML approach optimizes the ZT of BiSbTe, as shown in Figure 8A. After round 4 optimization the predicted value through GPR was highly matched with the experimental value. Figure 8B shows the ML results. After applying the optimal condition, the material has a ZT of 1.3 at room temperature which was much higher than previous results.
Figure 8. (A) Workflow of the ML-assisted extrusion printing of thermoelectric inks, including the four input variables listed in box 1 and three out properties of interests in box 4, (B) ZT of BiSbTe using the optimum condition identified through this ML model and reported values. Reproduced from Ref.[61] with permission from the Royal Society of Chemistry. (License under Creative Commons Attribution 3.0 Unported License).
Bi2Te3 is a well-known inorganic commercialized TE material operating at mid-temperature. The dopants Cu, Se, and Pb have been studied for Bi2Te3. Analyzing dopant concentration through ML is an effective way to get peak ZT. Alrebdi et al. developed support vector regression (SVR) (using both radial basis function and polynomial kernels) and DTR ML models to solve some real-world problems, including the effect of
Sintering conditions influence the TE properties change while the optimum condition predicted through the ML approach reduces the number of iterations taken manually to increase the ZT. Also, more accurate knowledge about the sintering condition is not yet explored through experiments. Here, Headley et al. employed an ML approach to finding suitable sintering conditions for Ag1.96Se through an ultrafast flash sintering technique to achieve high performance[63]. The GPR model developed to identify optimum flash sintering variables includes voltage, pulse duration, pulse delay, number of pulses, and thickness related to power factor measured during the analysis based on Bayesian expected improvement. As the number of data increased, the GPR prediction uncertainty converged to the experimental measurement uncertainty. Finally, the optimum parameters were used to perform the experiment, and the maximum ZT was obtained within 1 s flash sintering time (optimized time). The sintering time was comparatively less than the previous sintering time.
Hou et al. applied ML to optimize the PF of Al2Fe3Si3 by varying the composition of Al/Si[64]. Experimentally obtained data was used to train the ML model to predict unknown power factors. The commonly used anisotropic squared-exponential (SE) covariance function in GPR was chosen to describe the covariance between the feature variables of composition and temperature. Finally, the optimal ratio of 0.9 shows the increase of PF up to 40% at 510 K compared with the original composition. Headley et al. applied the ML approach to make a n-type Bi2Te2.7Se0.3 under laser powder bed fusion (LPBF) processing[63]. The four steps are followed to predict the optimized LPBF-built complex geometries using an iterative augmented strategy, as shown in Figure 9. Initially, the new 13-line scan parameter (power and scan speed) combinations are predicted. Then, this parameter value was used as input for melt pool characterization. The width and depth of melt pool geometrical values were obtained, and these training datasets were used for ML. Again, 93-line scan parameter combinations were used to predict the melt pool geometry with uncertainties. Then, optimized parameter combinations were given to the LPBF-built to make Bi2Te2.7Se0.3 with three geometries: the rectangular prism, hollow rectangle, and trapezoid. Integrating ML techniques helps to visualize and quickly understand changing melt pool dimensions concerning varied laser parameters.
Figure 9. Showing the iterative augmented strategy to understand the melt pool geometrical (width and depth) using LPBF processing of n-type Bi2Te2.7Se0.3 thermoelectric. A total of six iterations were performed with feedback[63]. (License number 6015220339088).
AI for TE materials synthesis
The first and only report during the writing of this article on the application of AI for TE materials synthesis is by Na et al.[65]. This study converts chemical reaction formulas into a machine-readable format using a "synthesis graph". The synthesis graph describes the chemical formula in terms of the elements present in the starting and final materials, as shown in Figure 10. To predict the synthesis recipe of TE materials, a DNN-based architecture called the synthesis process encoder-decoder (SPENDE) has been developed [Figure 11]. Herein, based on the benchmark of synthesis dataset of 771 unique TE materials; first, a synthesis graph has been generated followed by calculation of graph embedding vector using a graph NN graph-based reaction encoder (GRE). Then, the NN operation sequence decoder (OSD) has achieved the prediction of each step's operation level. Finally, the preparation conditions are predicted by engineering conditions networks (ECNs) predicts. Thus, this architecture has successfully predicted the synthesis parameters involving grinding, heating, cooling, and sintering for synthesizing TE materials.
Figure 10. Example of a synthesis-graph for the conversion of a chemical reaction into a machine readable format developed by
Figure 11. SPENDE architecture and its forward process for the prediction of synthesis sequence of a chemical reaction. Adapted from
CHALLENGES AND PERSPECTIVES
The rapid development of statistical methods has significantly influenced the discovery and design of TE material. This critically means that exciting new materials are being discovered; however, these materials are yet to be produced. ML and AI have the potential to learn patterns of synthesis design from a given data set of experimental synthesis procedures and then predict the outcome. Nevertheless, the design of synthesis parameters for TE materials is challenging because the sequence of reactions during the synthesis depends on many factors including choice of synthesis procedure and precursors. Therefore, the unavailability of an organized and comprehensive database of synthesis procedures of TE materials is a big challenge that needs to be overcome. For training the algorithm, converting available synthesis condition data and processing it into a suitable format for the algorithm is another obstacle. Finally, the synthesis parameters predicted by statistical optimization can be confirmed by experiments and further improved and developed.
Atomic properties are building blocks to construct the crystal system. Also, these parameters are related to the TE performance. Experimentally, finding this relation consumes more time and material cost. However, ML easily and quickly interprets this relation through the available data from materials projects or research articles. Interpretation of atomic properties with TE parameters tends to material classification which could help to identify new materials or compositions without any cost. Besides, the ML approach quickly identifies the exact atomic properties among many other atomic properties, helping to understand the material chemistry of the system. Further, it would help to develop the appropriate synthesis by controlling the identified atomic properties for high-performance TE material. Besides, controlling this parameter through experiments needs to be explored through the ML.
CONCLUSIONS
In conclusion, statistical and data-driven methods such as DOE, ML, and AI have been reviewed to optimize and guide the synthesis of TE materials. Advanced statistical methods can simplify the complex TE materials synthesis process. In the traditional synthesis of TE materials, experiments are performed to measure the effects of experimental variables on responses. The optimization of the preparation of TE materials involves finding a combination of variables that gives the best results. Recent advances can guide the multi-variable synthesis of new TE material, improve the outcome of experiments, and save time. It has been demonstrated that the proposed methodologies may be extended to synthesize various categories of TE materials. Various atomic properties are involved in material chemistry. Also, finding atomic properties related to TE parameters extends to the material classification based on the performance. Materials classification based on the performance can be easily achieved through ML concerning atomic properties. Identifying suitable atomic properties helps develop a new composition or class of materials for TE without experimental cost.
DECLARATIONS
Acknowledgments
The authors gratefully acknowledge the financial support from the National Science and Technology Council, Taiwan, R.O.C, under the contract NSTC 113-2221-E-006-195-MY3 for this study. This research is also supported in part by Higher Education Sprout Project, Ministry of Education to the Headquarters of University Advancement at National Cheng Kung University (NCKU).
Authors’ contributions
Conceptualization, formal analysis, funding acquisition, investigation, project administration, resources, software, supervision, writing - review & editing: Chen, W. H.
Data collection, formal analysis, investigation, writing - original draft: Aishwarya, K.; Sardar, K.
Availability of data and materials
The data used for this study are confidential.
Financial support and sponsorship
This work was financially supported by the National Science and Technology Council, Taiwan, R.O.C, under the contract NSTC 113-2221-E-006-195-MY3 for this study. This research is also supported in part by Higher Education Sprout Project, Ministry of Education to the Headquarters of University Advancement at National Cheng Kung University (NCKU).
Conflicts of interest
All authors declared that there are no conflicts of interest.
Ethical approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Copyright
© The Author(s) 2025.
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