Materials discovery and properties prediction in thermal transport via

Subscriber access provided by UNIVERSITY OF TECHNOLOGY SYDNEY

Mini Review

Materials discovery and properties prediction in thermal transport via materials informatics: a mini-review Xiao Wan, Wentao Feng, Yunpeng Wang, Haidong Wang, Xing Zhang, Chengcheng Deng, and Nuo Yang Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b05196 • Publication Date (Web): 15 May 2019 Downloaded from http://pubs.acs.org on May 15, 2019

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

A graphic for the Table of Contents

ACS Paragon Plus Environment

Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Materials discovery and properties prediction in thermal transport via materials informatics: a mini-review Xiao Wan1,2#, Wentao Feng2#, Yunpeng Wang1,2, Haidong Wang3, Xing Zhang3, Chengcheng Deng2*, Nuo Yang1,2*

1. State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China. 2. School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, China. 3. Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China.

# X.W. and W.F. contributed equally to this work. * Corresponding email: [email protected] (C.D.); [email protected] (N.Y.)


Page 2 of 29

Page 3 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

ABSTRACT There has been increasing demand for materials with functional thermal properties, but traditional experiments and simulations are high-cost and time-consuming. The emerging discipline, materials informatics, is an effective approach that can accelerate materials development by combining material science and big data techniques. Recently, materials informatics has been successfully applied to designing thermal materials, such as thermal interface materials for heat-dissipation, thermoelectric materials for power generation, etc. This mini-review summarizes the research progress associated with studies regarding the prediction and discovery of materials with desirable thermal transport properties by using materials informatics. Based on the review of past research, perspectives are discussed and future directions for studying functional thermal materials by materials informatics are given.

KEYWORDS: Materials informatics, machine learning, material discovery, thermal conductivity, thermoelectric properties, interfacial thermal conductance


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1. Introduction Thermal properties, such as thermal conductivity, interfacial thermal conductance (ITC), etc., play a critical role in micro/nano-electronics, opto-electronics, thermoelectrics, and other thermal/phonon engineering areas.1,2 For example, there is increasing demand for materials with high thermal conductivities that can dissipate the massive heat in electronic devices.3-6 In addition, ITC dominates the thermal dissipation of composites with interfaces on the micro-/nano-scale.7,8 Therefore, the effective discovery of materials with high thermal conductivities or ITC is crucial for improving the performance and extending the lifetime of a wide variety of related devices. On the other hand, thermoelectric power generation is essential for utilizing low-grade wasted heat. Researchers have been seeking materials with high conversion efficiency for decades to improve their performance,9-14 for which materials with low thermal conductivity are essential. Due to the limitations of cost, time and hardware, the discovery of materials with desirable thermal properties remains challenging in both experiments and simulations.15 Materials informatics (Fig. 2) introduces a brand new way of accelerating the discovery of materials with special properties.16,17 Intrinsically, materials informatics is the process that allows one to survey complex, multiscale information in a high-throughput, statistically robust, and yet physically meaningful manner.17 Materials informatics is an emerging area of materials science16-18 based on simulations or experiments in materials science and machine learning algorithms.16 Materials informatics can effectively and accurately capture the relationship between structures and properties by data mining techniques for materials discovery and properties prediction. Seeking structure-property relationships is an accepted paradigm in materials science, yet these relationships are often nonlinear and complicated.17 There is rarely a well-accepted multiscale relationship that is accurately captured by traditional theory or experiments because there are different physical laws that act at the macro-/microscale. Hence, there are opportunities for using materials informatics,


Page 4 of 29

Page 5 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

which can build these relationships by data mining without concern for the principles. Data mining is a new field that merges ideas from statistics, machine learning, databases, and parallel and distributed computing.19 Data mining takes the form of building models from a given dataset, which can capture the nonlinear mapping relations between material structures and properties for materials discovery. In addition to pattern recognition, data mining in big data techniques has another primary function in understanding materials behavior: prediction. The predictive aspect of data mining, classification and regression analysis can help facilitate the understanding of multivariable correlations in the ‘processing-structure-properties’ paradigm that form the core of materials development.16 In light of this feature, materials informatics, seeking material structure-property relationships using the big data technique, can significantly advance all functional materials fields, such as optical/electronic/phononic materials, acoustics materials, magnetic materials, mechanical materials, nuclear materials, etc. The role of materials informatics is popular throughout all fields and applications in materials science and engineering.17 Recently, materials informatics has been successfully applied in the search for materials or structures with desirable thermal properties, such as thermal conductivity, ITC, and thermoelectric properties.20-23 Considering that there have already been studies in this emerging field, it is necessary to review their progress and provide an outlook on future work, which will be helpful for the development of materials informatics in the thermal field. In this paper, a mini-review is given of the recent research progress on the applications of materials informatics in studying thermal transport. First, we provide a brief introduction of materials informatics. Then, the related studies of using materials informatics in thermal properties, including thermal conductivity, interfacial thermal conductance and thermoelectric conversion efficiency, are summarized. Finally, some perspectives on the challenges, shortcomings and outlook are provided to aid future investigations related to this topic.


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

2. Materials informatics The framework of materials informatics mainly consists of three parts: 1) data procurement, or the acquisition of data generated by simulations or experiments in materials science; 2) data representation, or systematic storage of representative information about the structures and properties of these materials; and 3) data mining, or data analysis aimed at searching for relationships between structure information and desired properties.17 The procedure of materials informatics in the thermal field is shown in Fig. 1, and the specific contents of the three steps are described as follows.

2.1 Data procurement Data procurement is acquiring the physical properties and structural information of given materials. Calculations (such as first-principles,21,24 molecular dynamics23,25,26 and lattice dynamics,27,28 etc.), experiments29 and online libraries30 have been used to collect these data. With these different techniques, database repositories containing effective training data can be constructed.

2.2 Data representation Data representation refers to the systematic storage of representative information about the structures and properties of materials. The key component of data representation is the selection of characteristics (e.g., formation energies, band structure, density of states, magnetic moments) to describe the materials, which are called ‘descriptors’. The descriptors represent different kinds of materials, and they are only one part of the input in data mining. One purpose of materials informatics is to establish mapping relations between the descriptors and target properties, which, herein, are thermal properties. Thus, good descriptors are the key to effective materials informatics. Once a series of good descriptors is identified, the search for optimum materials or properties prediction within the database can be performed intrinsically or extrinsically.31


Page 6 of 29

Page 7 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

2.3 Data mining Data mining aims at searching for novel materials or exploring new physical insights, in which machine learning is widely used.17 The main machine learning algorithms used in materials informatics include supervised learning, the task of which is finding a function that maps an input to an output based on samples.32 Through the training models built by machine learning algorithms, materials with novel properties can easily be selected or predicted. Currently, the most popular algorithms include Bayesian optimization, random-forest regression, and artificial neural networks. A brief introduction of these algorithms is provided below. Bayesian optimization is a well-established technique for the global optimization of black-box functions.33,34 Bayesian prediction models, most commonly based on the Gaussian process, are usually employed to predict the black-box function, where the uncertainty of the predicted function is also evaluated as predictive variance.35 The Bayesian optimization algorithm (BOA) typically works by assuming that the unknown predicted function is sampled from a Gaussian process and maintains a posterior distribution for this function as observations are made.34 The procedure for Bayesian optimization is as follows. First, a Gaussian process model is developed from two observations that are randomly selected from the database. The model is updated by (i) sampling the point at which the observation property is expected to be the best and (ii) updating the model by including the observation at the sampled point. These two steps are repeated until all data are sampled.31 Random forest36 is a prominent ensemble method adapted from bagging, which combines multiple decision trees into one predictive model to improve performance.20 Random forest is relatively robust to various problems, such as compound classification, and can handle outlier data or high-dimensional data well.36,37 A random forest model consists of K decision trees that are established in three steps. First, K sets of data are generated from the initial dataset by a bootstrap method. Second, a tree is grown with a particular random selection algorithm to obtain the predictions for each data point. Third, the final prediction is made by a weighted vote (in classification) or weighted


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

average (in regression) of all forest predictions.37 In addition to performing the prediction task, random forest also provides an intrinsic metric to evaluate the importance of each descriptor.20 The artificial neural network (ANN) and deep neural network are well-developed machine learning methods that mimic human brains to learn the relationships between certain inputs and outputs based on experience.38 The ANN has recently been successfully applied in the fields of modeling and prediction in many thermal engineering systems.39-41 The ANN has become increasingly attractive in the last decade. The assets of the ANN compared to classical methods are its high speed and simplicity, which decrease engineering efforts.29,42,43 The most basic and commonly used ANN consists of at least three or more layers, including an input layer, an output layer, and a number of hidden layers.29 The number of neurons in the input layer equals the number of parameters in the material selection process. The output layer represents the fitness of the candidate materials. In addition, the hidden layer represents the relationships between the input and output layers. Through training and testing stages, the ANN model is well-established. In the training stage, the network is trained to predict an output based on input data. The training stage is stopped when the testing error is within the tolerance limits. In the testing stage, the network is tested to stop or continue training according to measures of error.29,40-42 In addition to the three machine learning algorithms mentioned above, there are some other efficient algorithms in progress, such as autoencoder, convolutional neural networks and generative adversarial networks, which are more advanced and powerful. The autoencoder is a type of artificial neural network that is used to learn efficient data coding in an unsupervised manner. The convolutional neural network (CNN) is a class of deep neural networks that requires relatively little preprocessing compared to other image classification algorithms.44 The generative adversarial network (GAN) is a class of machine learning system in which two neural networks contest with each other in a zero-sum game framework.45 Recently, these three machine learning algorithms have become widely used for image recognition and data generation.


Page 8 of 29

Page 9 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

3. Thermal conductivity As a popular topic, thermal conductivity is one of the most important material properties. In some cases, materials with ultralow or superhigh thermal conductivities are essential for engineering applications.2,3,8,46-50 Many studies have focused on low thermal conductivity materials for thermoelectrics and thermal insulation materials.10,14 In search of compounds with ultralow thermal conductivity, several studies have been performed on predicting the lattice thermal conductivity by materials informatics. In addition, high thermal conductivity materials for improving the thermal management of electronic devices have also attracted wide attention, such as single-crystal boron arsenide with special band structure.46-50 However, no relevant reports on predicting high thermal conductivity materials by machine learning algorithms currently exist. In addition to the discovery of lattice thermal conductivity, there are also some studies of thermal conductivity prediction models for porous composites and liquids built by machine learning algorithms. In the study of lattice thermal conductivity (LTC, 𝜅𝜔), via random-forest regression among 79000 entries of the database (Fig. 3), Carrete et al. proposed three half-Heusler semiconductors with LTCs are below 5 𝑊𝑚 ―1𝐾 ―1 for further experimental study.20 These authors also found that materials with larger average atomic radii in positions A and B tend to have lower thermal conductivity. More importantly, efficient methods are introduced for reliably estimating the 𝜅𝜔 for a series of compounds, which are based on a combination of random-forest regression and first-principles calculations. That is, there is a very good prospect for machine learning methods for applications in accelerating material design. In this study, we note that the performance in predicting LTC using machine learning algorithms is largely affected by the selected descriptors. To find suitable descriptors, in 2017, Tanaka’s group proposed a procedure to generate a series of compound descriptors from simple atomic representations.31 When the procedure was applied to the LTC data set, these descriptors in terms of Bayesian optimization exhibited good predictive performance, which verified the accuracy of this


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

approach. In addition to the bulk lattice thermal conductivity, machine learning algorithms can also predict the thermal conductivities of composite materials. In August 2018, Wei et al. proposed models obtained from the support vector regression, including Gaussian process regression and convolution neural network.51 The prediction of effective thermal conductivity based on these models and effective medium theory is consistent with experimental data. Furthermore, Tanaka’s group combined the Bayesian optimization and firstprinciples anharmonic lattice-dynamics calculations to find materials with ultralow thermal conductivity.21 In 2015, these authors discovered 221 materials with very low thermal conductivity in a library containing 54,779 compounds. Two compounds even have an electronic band gap < 1 eV, which makes them promising for thermoelectric applications. Compared to other methods, this strategy does not have excessive computation costs due to the use of fewer initial data. However, Tanaka’s methods could just determine materials with low thermal conductivity instead of high thermoelectric figures of merit. In addition to the prediction and optimization of the thermal conductivity of solids, there some studies have focused on fluids. In early 2009, Kurt et al. reported an ANN model to predict the thermal conductivity of ethylene glycol-water solutions based on experimentally measured variables.29 The regression analysis between the prediction by the model and the experimental data proved the high accuracy of the ANN model. The superiority of this model compared to practical experiments lies in its lower time consumption and cost, which is the advantage of machine learning algorithms. In addition, a multilayer perceptron-artificial neural network (MLP-ANN) model was reported by Zendehboudi et al. to predict the effective thermal conductivity of nanofluids with desired accuracy.52 Overall, machine learning algorithms have been successfully applied to predict the thermal conductivity of crystals, composites and liquids. The predictions match well with ab initio calculations and experimental data. It is noted that different descriptors should be investigated and compared in order to decrease the deviation of the prediction. Although machine learning algorithms have been successfully applied in investigating


Page 10 of 29

Page 11 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

thermal conductivity, some issues remain. The accuracy of prediction via machine learning algorithms must be further improved. High-precision machine learning models usually need to be trained using massive numbers of data. However, the initial training data we obtain from experiments, simulations or online databases are often inadequate. More precise machine learning algorithms that do not depend on massive initial data must be applied in the research of thermal properties, such as autoencoder or generative adversarial network. In addition, well-accepted descriptors that represent the candidates must be established and verified. Further, the machine learning prediction model has a limited scope of application and is only valid to a certain or specific situation extent. For instance, the model that merges the effective medium theory and artificial neural network51 is suitable for dealing with macroscopic materials only. Prediction models aimed at the meso-/micro-/nanoscale or multiscale are necessary to develop in the future.

4. Interfacial thermal transport Interfacial thermal transport plays an important role in the thermal management of high power micro- and opto-electronic devices, in which a large number of interfaces exist.7,8,53 Prediction of the interfacial thermal transport property is important for guiding the discovery of interfaces with ultralow or superhigh interfacial thermal conductance, which can further adjust the thermal conductivity of the whole system. In 2017, three different machine learning algorithms were used by Zhan et al. to predict ITC, who compared their results with the commonly used acoustic mismatch model (AMM) and diffuse mismatch model (DMM) to verify the accuracy.54 The three different machine learning algorithms included generalized linear regression (GLR), Gaussian process regression (GPR) and support vector regression (SVR). The resulting correlation coefficient (R) (Fig. 4) showed the correlations between the experimental data and the prediction by different methods, demonstrating that these methods have better accuracy compared to traditional AMM and DMM.54 Then, via trained machine learning models, Yang et al. predicted the ITC between graphene and hexagonal boron-


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

nitride (h-BN) using only the known parameters of system temperature, coupling strength and tensile strains.23 The machine learning algorithms used in these predictions included linear regression, polynomial regression, decision trees, random forest and artificial neural network. In addition, the performances of these different methods were compared with molecular dynamics simulations. It was shown that the artificial neural network made the best predictions. These results illustrated the simplicity and accuracy of machine learning methods for the prediction of interfacial thermal transport properties. In addition to the prediction of the interfacial thermal transport property, the optimization of interfacial structures is also significant for the discovery of materials with special thermal transport properties. To minimize or maximize the value of ITC across Si-Si and Si-Ge interfaces (Fig. 5), Ju et al. proposed a method combining atomistic Green’s function (AGF) and Bayesian optimization in May 2017, which could obtain the optimal interfacial structures with a few calculations.22 Then, these authors applied this method to a Si/Ge superlattice and determined the interfaces with the highest and lowest ITC by calculating a few interface structures. These results deepen the understanding of the mechanisms in interfacial thermal transport. These results also indicate the effectiveness of materials informatics in designing nanostructures with desirable thermal properties. It has been reviewed that the interfacial thermal conductance was predicted via three different machine learning algorithms. The accuracy of machine learning results was confirmed by comparing the results to experimental measurements. Different machine learning methods had different accuracies. Some simple models, such as generalized linear regression and second order polynomial regression, were not accurate enough, whereas some complicated models, such as random forest and artificial neural network, were much more accurate. Moreover, accelerating methods were proposed for searching interfacial structures with the highest/lowest ITC. However, there are still many challenges that have not been overcome by existing studies. First, the studies have shown prediction accuracies using different algorithms and have determined the best algorithms, but they do not provide the physical explanations or mechanism for why


Page 12 of 29

Page 13 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

those algorithms are best. The accuracy results of various algorithms cannot be simply referred to and used by other researchers in the selection of appropriate algorithms. That is, other researchers must test the accuracies of different algorithms themselves. Second, descriptors are selected as empirical parameters or by intuition, and correlations are ignored. In fact, data processing methods, such as principal component analysis and partial least squares regression, can discover the weight power of descriptors and provide the criteria for descriptor selection, further improving the accuracy of prediction. Third, the structures used in the prediction of ITC are quite simple and many practical factors are ignored, ultimately leading to poor applicability of predictions.

5. Thermoelectricity The performance of thermoelectric materials is characterized by the dimensionless thermoelectric figures of merit (ZT), which is defined as 𝑇𝜎𝑆2 𝜅, where 𝑇, 𝜎, 𝑆, and 𝜅

are temperature, electrical conductivity, Seebeck coefficient, and thermal

conductivity, respectively.55,56 A thermoelectric material with a high ZT is an “electroncrystal phonon-glass”, which has a low thermal conductivity, high electrical conductivity and high Seebeck coefficient. Recently, materials informatics has been used in the design and search for high-ZT thermoelectric materials, diminishing the need for exhaustive experiments and simulations. In 2014, Carrete et al. used the decision tree method to determine the rules that dictate the thermoelectric performance of a nanograined half-Heusler compound, good or bad.57 These authors found two key properties for high ZT, which are a large lattice parameter and either a wide gap (at high temperatures) or a large effective mass of holes (at room temperature). These results could stimulate experimental research for improving the thermoelectric performance of half-Heuslers semiconductors. In 2018, Yamawaki et al. realized the goal of searching structures with high ZT.58 These authors used Bayesian optimization to obtain an optimized graphene structure with a higher ZT. The procedure is similar to their group’s previous work.22 Bayesian optimization was superior for accelerating the searching procedure.


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

In addition to the prediction of figures of merit (ZT) directly, materials informatics were also used to predict the key factors that affect ZT. The Seebeck coefficient is an important factor related to ZT. To precisely predict the Seebeck coefficients of different crystalline materials, Furmanchuk et al. used the random forest algorithm and had great success.59 Some experimental results were used as inputs in their study to obtain an accurate prediction, indicating that it is unnecessary to synthesize or calculate materials to obtain their Seebeck coefficients. These authors also determined some important attributes of the Seebeck coefficient and explored the relationship between the Seebeck coefficient and ZT at different temperatures, the results of which will guide researchers to find materials with higher thermoelectric conversion efficiencies. It is also important to compare the feasibility and practicability of different methods. To guide the selection of materials for experimental researchers, a recommendation engine (http://thermoelectrics.citrination.com) based on machine learning was proposed by Gaultois et al. in 2016.30 To ensure accuracy, these authors tested an example set of compounds generated by the engine, RE12Co5Bi (RE = Gd, Er), which exhibited surprising thermoelectric performance (Fig. 6). Materials with low thermal conductivity and high electrical conductivity that were predicted by this engine were also confirmed experimentally. It is suggested that this paradigm could greatly promote the discovery of good thermoelectric materials. In summary, the studies mentioned above will accelerate advances in the procedures for finding materials with high ZT. This section shows that thermoelectric properties may be predicted by machine learning algorithms, such as the decision tree method. Specifically, some rules that determine the ZT of materials were revealed by the machine learning algorithm. In addition, an open-source machine learning-based recommendation engine was proposed to find new materials with high ZT. Although some studies of thermoelectric properties have been performed, a method to predict ZT is lacking. This lack is because the function of ZT has a complex correlation with the Seebeck coefficient, thermal conductivity, and electrical conductivity. In addition, the predictions, which use experiment results as inputs, ignore the sample differences in synthesis, experimental conditions, material microstructures and phase diagrams, and carrier concentrations,


Page 14 of 29

Page 15 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

etc., which could cause deviations in the predictions. With this in mind, a possible extension of the presented work lies in the exhaustive collection of such information for known thermoelectric materials.

6. Summary To date, there have been increasing investigations in the interdisciplinary field of materials informatics and thermal science. In this mini-review, we summarize recent representative research progress on thermal transport by materials informatics. The procedures for the practical implementation of materials informatics are presented, including the introduction of some important machine learning algorithms. A comprehensive framework and main conclusions are exhibited in discovering materials with

optimal

thermal

conductivity,

interfacial

thermal

conductance

and

thermoelectricity efficiency. Moreover, some critical factors that affect the discovery efficiency and predictive efficacy are discussed. The superiority of materials informatics in discovering novel materials with desirable thermal properties is also emphasized. For prediction accuracy via machine learning, present studies show reliable results. Most studies produced a high coefficient of determination (R2>0.88), showing that the computational accuracy is acceptable. The accuracy is largely influenced by the selection of models and descriptors. Generally, simple models, such as generalized linear regression and second order polynomial regression, show bad performance. Complicated models, such as random forest and artificial neural network, can be much more accurate. Moreover, a sophisticated selection of descriptors could also improve the accuracy; for example, it is observed that the coefficient of determination is improved from 0.92 to 0.96 in the prediction of ITC.54 Interestingly, the predicted value of the Seebeck coefficient is comparable to the measurement of recently manufactured materials, which is not included in the training database.59 However, machine learning methods can do little to predict abnormal properties. The machine learning model can predict a new sample within normal scope, but the amount


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 29

of abnormal data usually is not large enough to precisely predict outliers.60 For instance, in 2019, superhigh thermoelectric figures of merit (ZT > 400) were reported.61 However, this high ZT could only exist at the structure phase transition temperature; because there are insufficient similar data around that temperature, this abnormal value of ZT is difficult to predict using machine learning methods. Aside from the challenge of materials informatics in thermal field, there are some common issues that must be resolved. When performing materials informatics, it remains challenging to generate more multipurpose and time-saving machine learning algorithm codes, select fast and effective descriptors, and transfer data to practical knowledge or physical pictures. The main challenge lies in the physical interpretation of the process by machine learning. The underlying physical mechanism cannot be fully understood only by machine learning, which benefits from the use of other theoretical or

simulative

methods.

Advances

in

studying

heat

transfer

in

nanomaterials/nanostructures are needed by machine learning. Additionally, when preparing data, especially for complex structures, simulations or experiments require much time to obtain enough data for training. For example, the neural network usually requires a large amount of data. To avoid the difficulty in obtaining massive numbers of data, researchers may make full use of data reported in existing papers, instead of collecting all data themselves. Therefore, an online database containing comprehensive reported thermal properties of different materials is necessary and urgent.

7. Perspectives Looking beyond the success and shortage of materials informatics applications, there are some areas of progress that could be addressed in the near future. We conclude this paper by illustrating several important challenges that deserve further investigation. Recently, in the field of thermal transport, three main machine learning methods, including Bayesian optimization, random forest and artificial neural network, have been used in predicting the thermal transport properties of materials. With the development of machine learning methods, more efficient and powerful machine learning models,


Page 17 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

such as autoencoder, convolutional neural networks, generative adversarial network, etc., have been developed, which have been successfully used in other fields. Compared to the three machine learning algorithms that have already been used for investigating thermal properties, these newly developed algorithms are very suitable to model complex nonlinear relations, deal with small data sets and flexibly capture the relationships between different types of characteristic variables. These powerful methods are expected to be able to address the difficult problems associated with thermal transport (such as the size dependence function of thermal conductivity across multiscales) as mentioned above, or the direct prediction of ZT). Although materials informatics has been successfully applied in a few thermal problems, it is still controversial that materials informatics could make contributions in solving other, more difficult issues. For example, there is multiscale problem in nanostructured/composite materials. The multiscale prediction of thermal transport properties is still far from reality.62 The thermal conductivity is size-dependent at the micro-/nanoscale, and Fourier's law is no longer applicable when the materials’ sizes are comparable to the phonon mean free path.63-65 The gap between nano and macro is large; therefore, it remains to be seen if machine learning methods could make a difference in the multiscale prediction of thermal transport properties. Another important issue is the wave-particle duality of phonons, which are the main heat carriers in semiconductors. In past decades, most of the approaches to control phonon transport and tailor thermal properties have been based on particle66,67 or wave nature.68,69 As the phonon particle and wave transport are governed by different physical laws, the collective manipulations of two strategies can lead to ultralow thermal conductivity.70,71 However, the phonon particle and wave effects are intertwined, and their direct individual contributions to the modulation of thermal conductivity have not been well established. It is possible that machine learning methods would make a contribution and a convincing analysis in this field. As reviewed in this paper, previous materials informatics studies have mostly been based on the combination of simulations and machine learning algorithms. Therefore, how can we use these predictions to guide experiments? Moreover, how do we combine


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

experimental techniques and machine learning algorithms? In terms of machine learning models, the prediction of new materials with desirable thermal properties is obtained. Then, an experimental synthesis will be conducted according to the structure information (such as crystal configuration and element species) that corresponds to the desired properties. Further, to apply materials informatics in experiments, a clear iteration loop must be clarified, whose procedure is divided to three steps. First, a large amount of experimental data is needed. The combinatorial experiments are proposed to be controlled by work flows for meeting this requirement.72 Second, based on data mining, machine learning models could be built to search for or predict new materials with desired properties. The key metrics lie in the relationships learned by the machine learning models between the structure information and desirable thermal properties, which form the foundation of materials’ property prediction. Finally, if material properties meet the necessary requirements, the materials can be synthesized in terms of machine learning predictions. Otherwise, the predicted data will be added to the training database to improve the machine learning models. Hence, it may be possible to merge different machine learning models and a combinatorial experiments strategy to realize a loop process in materials informatics. The critical issues may include the management of work flows, the tracking of multivariable measurements and data storage. In addition, machine learning can be used to fit parameters in experiments. Recently, the regression algorithms in machine learning have become very popular in economics and statistics, and may also be widely applied to measuring the thermal properties of materials, especially at nanoscales. A proper regression algorithm can establish a specific mathematical model and obtain the quantitative relationship between the target properties and the experimental data, after which the unknown thermal properties can be calculated. The essence of the regression algorithm is to adjust a smooth and balanced model function f (x, y……), which aims to minimize the fitting error and avoid overfitting problems. In measurements of thermal properties, there are hard issues caused by fitting curves for which machine learning algorithms could make a difference. For instance, in the measurements of time-domain thermoreflectance (TDTR) or in the


Page 18 of 29

Page 19 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

3ω method, thermal properties, such as thermal conductivity, electron-phonon coupling factor and interfacial thermal conductance, can be calculated by multivariable fitting the experimental data. Traditional successive iterations can produce a fitting curve with slight deviation, where the fitting result is sensitive to the setting of the initial values. Interestingly, in the machine learning algorithms, the kernel ridge regression can solve this multiple nonlinear model and avoid the sensitivity problem of initial values. On the other hand, many environmental parameters are involved in the fabrication of materials, such as temperature, time, humidity, intensity of illumination, and so on. These parameters may have a great influence on the thermal properties of nanomaterial samples. For instance, in the fabrication of metallic nanofilms by physical vapor deposition, parameters, such as the pressure and temperature of chamber, deposition rate and time, thickness of adhesion layer and annealing temperature, have significant effects on the final thermal properties of samples. Similarly, in Si nanowire synthesis by chemical vapor deposition, the ambient temperature and pause time in the ablation also have great influence on the final morphology of the Si nanowires.73 By principal component analysis or random forest algorithm, a relationship between the desired thermal properties and complicated environmental parameter setting can be obtained. Then, a sample with desired properties can be obtained by tuning the environmental parameters. Materials informatics has emerged as a powerful tool for many fields in materials science and engineering. It is highly desirable that materials informatics be applied in more fields to solve more difficult thermal issues.

Acknowledgements The work was sponsored by National Natural Science Foundation of China No. 51576076 (N.Y.), No. 51606072 (C.D.), No. 51711540031 (N.Y. and C.D.), the Natural Science Foundation of Hubei Province No. 2017CFA046 (N.Y.) and Fundamental Research Funds for the Central Universities No. 2019kfyRCPY045 (N.Y.). We are grateful to Xiaoxiang Yu, Dengke Ma and Han Meng for useful discussions. The


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

authors thank the National Supercomputing Center in Tianjin (NSCC-TJ) and the China Scientific Computing Grid (ScGrid) for providing assistance in computations.

References 1. Moore, A. L.; Shi, L. Materials Today 2014, 17, (4), 163-174. 2. Pop, E. Nano Research 2010, 3, (3), 147-169. 3. Xu, X.; Chen, J.; Zhou, J.; Li, B. Advanced Materials 2018, 30, (17), 1705544. 4. Hansson, J.; Nilsson, T. M. J.; Ye, L.; Liu, J. International Materials Reviews 2017, 63, (1), 22-45. 5. Razeeb, K. M.; Dalton, E.; Cross, G. L. W.; Robinson, A. J. International Materials Reviews 2018, 1, (63), 1-21. 6. Bar-Cohen, A.; Matin, K.; Narumanchi, S. Journal of Electronic Packaging 2015, 137, (4), 040803. 7. Norris, P. M.; Le, N. Q.; Baker, C. H. Journal of Heat Transfer 2013, 135, (6), 061604. 8. Volz, S.; Shiomi, J.; Nomura, M.; Miyazaki, K. Journal of Thermal Science and Technology 2016, 11, (1), JTST0001. 9. Yang, L.; Chen, Z.-G.; Dargusch, M. S.; Zou, J. Advanced Energy Materials 2018, 8, (6), 1701797. 10. Zhu, T.; Liu, Y.; Fu, C.; Heremans, J. P.; Snyder, J. G.; Zhao, X. Advanced Materials 2017, 29, (14), 1605884. 11. Tan, G.; Zhao, L. D.; Kanatzidis, M. G. Chemical Reviews 2016, 116, (19), 12123-12149. 12. Kroon, R.; Mengistie, D. A.; Kiefer, D.; Hynynen, J.; Ryan, J. D.; Yu, L.; Muller, C. Chemical Society Reviews 2016, 45, (22), 6147-6164. 13. Gorai, P.; Stevanović, V.; Toberer, E. S. Nature Reviews Materials 2017, 2, (9), 17053. 14. Russ, B.; Glaudell, A.; Urban, J. J.; Chabinyc, M. L.; Segalman, R. A. Nature Reviews Materials 2016, 1, (10), 16050. 15. Gomez-Bombarelli, R.; Aguilera-Iparraguirre, J.; Hirzel, T. D.; Duvenaud, D.; Maclaurin, D.; Blood-Forsythe, M. A.; Chae, H. S.; Einzinger, M.; Ha, D. G.; Wu, T.; Markopoulos, G.; Jeon, S.; Kang, H.; Miyazaki, H.; Numata, M.; Kim, S.; Huang, W.; Hong, S. I.; Baldo, M.; Adams, R. P.; Aspuru-Guzik, A. Nature Materials 2016, 15, (10), 1120-7. 16. Agrawal, A.; Choudhary, A. APL Materials 2016, 4, (5), 053208. 17. Rajan, K. Materials Today 2005, 8, (10), 38-45. 18. Rajan, K. Annual Review of Materials Research 2015, 45, (1), 153-169. 19. Wu, X.; Zhu, X.; Wu, G.; Ding, W. IEEE Transactions on Knowledge and Data Engineering 2014, 26, (1), 97-107. 20. Carrete, J.; Li, W.; Mingo, N.; Wang, S.; Curtarolo, S. Physical Review X 2014, 4, (1), 011019. 21. Seko, A.; Togo, A.; Hayashi, H.; Tsuda, K.; Chaput, L.; Tanaka, I. Physical Review Letters 2015, 115, (20), 205901. 22. Ju, S.; Shiga, T.; Feng, L.; Hou, Z.; Tsuda, K.; Shiomi, J. Physical Review X 2017, 7, (2), 021024.


Page 20 of 29

Page 21 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

23. Yang, H.; Zhang, Z.; Zhang, J.; Zeng, X. C. Nanoscale 2018, 10, (40), 19092-19099. 24. Mi, X. Y.; Yu, X.; Yao, K. L.; Huang, X.; Yang, N.; Lu, J. T. Nano Letters 2015, 15, (8), 5229-34. 25. Song, Q.; An, M.; Chen, X.; Peng, Z.; Zang, J.; Yang, N. Nanoscale 2016, 8, (32), 14943-9. 26. Li, S.; Yu, X.; Bao, H.; Yang, N. The Journal of Physical Chemistry C 2018, 122, (24), 13140-13147. 27. Ma, D.; Ding, H.; Wang, X.; Yang, N.; Zhang, X. International Journal of Heat and Mass Transfer 2017, 108, 940-944. 28. Ma, D.; Ding, H.; Meng, H.; Feng, L.; Wu, Y.; Shiomi, J.; Yang, N. Physical Review B 2016, 94, (16), 165434. 29. Kurt, H.; Kayfeci, M. Applied Energy 2009, 86, (10), 2244-2248. 30. Gaultois, M. W.; Oliynyk, A. O.; Mar, A.; Sparks, T. D.; Mulholland, G. J.; Meredig, B. APL Materials 2016, 4, (5), 053213. 31. Seko, A.; Hayashi, H.; Nakayama, K.; Takahashi, A.; Tanaka, I. Physical Review B 2017, 95, (14), 144110. 32. Caruana, R.; Niculescu-Mizil, A., An Empirical Comparison of Supervised Learning Algorithms. In Proceedings of the 23rd international conference on Machine learning, 2006; pp 161-168. 33. Mockus, J., Bayesian Approach to Global Optimization. Kluwer Academic PUblishers: 1989; p 473-481. 34. Snoek, J.; Larochelle, H.; Adams, R. P. Advances in neural information processing systems 2012, 2951-2959. 35. E, R. C.; I, W. C. K., Gaussian processes for machine learning. The MIT Press, 2006. 36. Breiman, L., Random Forests. 2001; Vol. 45. 37. Svetnik, V.; Liaw, A.; Tong, C.; Culberson, J. C.; Sheridan, R. P.; Feuston, B. P. Journal of chemical information and computer sciences 2003, 43, (6), 1947-1958. 38. Hopfield, J. J. IEEE Circuits and Devices Magazine 1988, 4, (5), 3-10. 39. Aydinalp, M.; Ismet Ugursal, V.; Fung, A. S. Applied Energy 2002, 71, (2), 87-110. 40. Ertunc, H. M.; Hosoz, M. Applied Thermal Engineering 2006, 26, (5), 627-635. 41. Yang, I.-H.; Yeo, M.-S.; Kim, K.-W. Energy Conversion and Management 2003, 44, (17), 2791-2809. 42. Kurt, H.; Atik, K.; Ozkaymak, M.; Binark, A. K. Journal of the Energy Institute 2007, 80, (1), 46-51. 43. Kalogirou, S. A. Renewable and Sustainable Energy Reviews 2001, 5, (4), 373-401. 44. Zurada, J. M., Introduction to artificial neural systems. 1992. 45. Goodfellow, I. J.; Pouget-Abadie, J.; Mirza, M.; Bing, X.; Warde-Farley, D.; Ozair, S.; Courville, A.; Bengio, Y. In Generative Adversarial Nets, International Conference on Neural Information Processing Systems, 2014. 46. Lindsay, L.; Broido, D. A.; Reinecke, T. L. Physical Review Letters 2013, 111, (2), 025901-025901. 47. Kang, J. S.; Wu, H.; Hu, Y. Nano Letters 2017, 17, (12), 7507-7514. 48. Kang, J. S.; Li, M.; Wu, H.; Nguyen, H.; Hu, Y. Science 2018, 361, (6402), 575. 49. Li, S.; Zheng, Q.; Lv, Y.; Liu, X.; Wang, X.; Huang, P. Y.; Cahill, D. G.; Lv, B. Science 2018, 361, (6402), 579.


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

50. Tian, F.; Song, B.; Chen, X.; Ravichandran, N. K.; Lv, Y.; Chen, K.; Sullivan, S.; Kim, J.; Zhou, Y.; Liu, T.-H.; Goni, M.; Ding, Z.; Sun, J.; Udalamatta Gamage, G. A. G.; Sun, H.; Ziyaee, H.; Huyan, S.; Deng, L.; Zhou, J.; Schmidt, A. J.; Chen, S.; Chu, C.-W.; Huang, P. Y.; Broido, D.; Shi, L.; Chen, G.; Ren, Z. Science 2018, 361, (6402), 582. 51. Wei, H.; Zhao, S.; Rong, Q.; Bao, H. International Journal of Heat and Mass Transfer 2018, 127, 908-916. 52. Zendehboudi, A.; Saidur, R. Heat and Mass Transfer 2018, 1-15. 53. Prasher, R. Proceedings of the IEEE 2006, 94, (8), 1571-1586. 54. Zhan, T.; Fang, L.; Xu, Y. Scientific Reports 2017, 7, (1), 7109. 55. Dresselhaus, M. S.; Chen, G.; Tang, M. Y.; Yang, R. G.; Lee, H.; Wang, D. Z.; Ren, Z. F.; Fleurial, J. P.; Gogna, P. Advanced Materials 2007, 19, (8), 1043-1053. 56. Majumdar, A. Science 2004, 303, (5659), 777. 57. Carrete, J.; Mingo, N.; Wang, S.; Curtarolo, S. Advanced Functional Materials 2014, 24, (47), 7427-7432. 58. Yamawaki, M.; Ohnishi, M.; Ju, S.; Shiomi, J. Science Advances 2018, 4, (6), eaar4192. 59. Furmanchuk, A.; Saal, J. E.; Doak, J. W.; Olson, G. B.; Choudhary, A.; Agrawal, A. Journal of Computational Chemistry 2018, 39, (4), 191-202. 60. Witten, I. H.; Frank, E.; Hall, M. A., Chapter 6 - Implementations: Real Machine Learning Schemes. In Data Mining: Practical Machine Learning Tools and Techniques (Third Edition), Witten, I. H.; Frank, E.; Hall, M. A., Eds. Morgan Kaufmann: Boston, 2011; pp 191-304. 61. Byeon, D.; Sobota, R.; Delime-Codrin, K.; Choi, S.; Hirata, K.; Adachi, M.; Kiyama, M.; Matsuura, T.; Yamamoto, Y.; Matsunami, M.; Takeuchi, T. Nature Communications 2019, 10, (1), 72. 62. Chen, G. Annual Review of Heat Transfer 2014, 17, 1-8. 63. An, M.; Song, Q.; Yu, X.; Meng, H.; Ma, D.; Li, R.; Jin, Z.; Huang, B.; Yang, N. Nano Letters 2017, 17, (9), 5805-5810. 64. Xu, X.; Pereira, L. F. C.; Wang, Y.; Wu, J.; Zhang, K.; Zhao, X.; Bae, S.; Tinh Bui, C.; Xie, R.; Thong, J. T. L.; Hong, B. H.; Loh, K. P.; Donadio, D.; Li, B.; Özyilmaz, B. Nature Communications 2014, 5, 3689. 65. Yang, N.; Zhang, G.; Li, B. Nano Today 2010, 5, (2), 85-90. 66. Chen, S.; Wu, Q.; Mishra, C.; Kang, J.; Zhang, H.; Cho, K.; Cai, W.; Balandin, A. A.; Ruoff, R. S. Nature Materials 2012, 11, 203. 67. Lim, J.; Hippalgaonkar, K.; Andrews, S. C.; Majumdar, A.; Yang, P. Nano Letters 2012, 12, (5), 2475-82. 68. Davis, B. L.; Hussein, M. I. Physical Review Letters 2014, 112, (5), 055505. 69. Yu, J.-K.; Mitrovic, S.; Tham, D.; Varghese, J.; Heath, J. R. Nature Nanotechnology 2010, 5, 718. 70. Ma, D.; Arora, A.; Deng, S.; Xie, G.; Shiomi, J.; Yang, N. Materials Today Physics 2019, 8, 56-61. 71. Qian, F.; Lan, P. C.; Freyman, M. C.; Chen, W.; Kou, T.; Olson, T. Y.; Zhu, C.; Worsley, M. A.; Duoss, E. B.; Spadaccini, C. M.; Baumann, T.; Han, T. Y.-J. Nano Letters 2017, 17, (12), 7171-7176. 72. Rajan, K. Annual Review of Materials Research 2008, 38, (1), 299-322. 73. Gudiksen, M. S.; Lauhon, L. J.; Wang, J.; Smith, D. C.; Lieber, C. M. Nature 2002, 415,


Page 22 of 29

Page 23 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

(6872), 617-620.


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figures

Fig. 1. Schematics of applying the materials informatics method to studying thermal transport issues.


Page 24 of 29

Page 25 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Fig. 2. The processing-structure-property-performance relationships of materials science and engineering, and how materials informatics approaches can help decipher these relationships via forward and inverse models.16


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 3. (a) Prototype Half-Heusler structure with primitive vectors and a conventional cell. (b) Elements considered in this study.20


Page 26 of 29

Page 27 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Fig. 4. Correlation between the experimental values and the values of interfacial thermal resistance predicted by the AMM, DMM, GLR, GPR, and SVR using the same descriptors.54


Nano Letters 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 5. Interfacial Si/Ge alloy structure optimization. (a)-(d) Optimal structures with the maximum and minimum interfacial thermal conductance for Si-Si and Si-Ge interface. (e), (f) The 10 optimization runs with different initial choices of candidates, where the insets show the probability distributions of ITC obtained from calculations of all candidates.22


Page 28 of 29

Page 29 of 29 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Nano Letters

Fig. 6. Thermoelectric characterization of RE12Co5Bi (RE = Gd, Er). (a) Electrical resistivity, (b) Seebeck coefficient, (c) thermal conductivity, and (d) thermoelectric figure of merit zT as a function of temperature.30


Materials discovery and properties prediction in thermal transport via

Recommend Documents