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Cite This: ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Machine-Learning-Assisted Development and Theoretical Consideration for the Al2Fe3Si3 Thermoelectric Material Zhufeng Hou,*,†,∥ Yoshiki Takagiwa,*,†,‡,∥ Yoshikazu Shinohara,†,‡ Yibin Xu,† and Koji Tsuda†,§ †
Research and Services Division of Materials Data and Integrated System and ‡Center for Green Research on Energy and Environmental Materials, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan § Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwa-no-ha, Kashiwa 277-8561, Japan
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S Supporting Information *
ABSTRACT: Chemical composition alteration is a general strategy to optimize the thermoelectric properties of a thermoelectric material to achieve high-efficiency conversion of waste heat into electricity. Recent studies show that the Al2Fe3Si3 intermetallic compound with a relatively high power factor of ∼700 μW m−1 K−2 at 400 K is promising for applications in low-cost and nontoxic thermoelectric devices. To accelerate the exploration of the thermoelectric properties of this material in a mid-temperature range and to enhance its power factor, a machine-learning method was employed herein to assist the synthesis of off-stoichiometric samples (namely, Al23.5+xFe36.5Si40−x) of the Al2Fe3Si3 compound by tuning the Al/Si ratio. The optimal Al/Si ratio for a high power factor in the mid-temperature range was found rapidly and efficiently, and the optimal ratio of the sample at x = 0.9 was found to increase the power factor at ∼510 K by about 40% with respect to that of the initial sample at x = 0.0. The possible mechanism for the enhanced power factor is discussed in terms of the precipitations of the metallic secondary phases in the Al23.5+xFe36.5Si40−x samples. Furthermore, the maximum achievable thermal conductivity of Al2Fe3Si3 estimated by the Slack model is ∼10 W m−1 K−1 at the Debye temperature. An avoided-crossing behavior of the acoustic and the low-lying optical modes along several crystallographic directions is found in the phonon dispersion of Al2Fe3Si3 calculated by ab initio density functional theory method. These preliminary results suggest that Al2Fe3Si3 can have a low thermal conductivity. The calculated formation energies of point defects suggest that the antisite defects between Al and Si are likely to cause the Al and Si off-stoichiometries in Al2Fe3Si3. The theoretically obtained insight provides additional information for the further understanding of Al2Fe3Si3. KEYWORDS: machine learning, thermoelectric materials, silicide, off-stoichiometric composition, narrow-gap semiconductor, thermoelectric power factor, density functional theory calculations
1. INTRODUCTION The thermoelectric (TE) effect enables a direct conversion between heat and electrical energy or vice versa, providing an alternative route for power generation and refrigeration.1−3 Furthermore, TE materials play a key role in the development of sustainable energy-efficient technologies.4 The TE conversion efficiency of TE materials depends on the dimensionless figure of merit ZT = S2σT/κ, where S, σ, κ, and T are the Seebeck coefficient, electrical conductivity, total thermal conductivity, and absolute temperature, respectively. The product S2σ is known as the power factor (PF), and the total thermal conductivity, κ = κe + κL, includes contributions from the electronic (κe) and lattice (κL) heat conduction.5 To achieve a high ZT value, TE materials should exhibit a high S to ensure a large potential/thermovoltage, a high σ to minimize the Joule heating effect, and a low κ to create a large temperature gradient.4,6,7 In the last 2 decades, many bulk TE materials have been explored and great achievements obtained for both n- and ptype materials, whose greatest ZT values are around or above 2.4,7 However, many of these materials are heavy-element© XXXX American Chemical Society
based materials and contain rare-earth, toxic (such as lead), and/or less abundant (such as tellurium) elements. From a practical and large-scale industrial application standpoint, where the cost and durability are important aspects, it is highly desirable to develop TE materials that are thermally stable at their intended operational temperature and are synthesized from low-cost, earth-abundant, and environmentally friendly chemical elements. Silicide-based TE materials consisting of earth-abundant and nontoxic elements have attracted sustained attention for their potential powergeneration applications in a temperature range of 500−800 K.6,8−11 It is known that silicon, aluminum, and iron are low-cost, earth-abundant, and environmentally friendly chemical elements.12 Extensive studies on β-FeSi2 have shown it to be a potential TE material in a high temperature range,13−16 where the PF of β-FeSi2 can be improved by chemical doping such as Received: February 6, 2019 Accepted: February 19, 2019
A
DOI: 10.1021/acsami.9b02381 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
Research Article
ACS Applied Materials & Interfaces Al doping.17 Recently, binary iron aluminides such as Fe2Al5, Fe4Al13, and FeAl2 have been reported as potential TE materials owing to a lower phonon thermal conductivity.18,19 However, these iron aluminide materials with shallow pseudogaps have a low S of less than 30 μV K−1, which prevents their use in practical applications. In particular, the development of new TE materials applicable at low- and midtemperature ranges is vital for the autonomous power supply of Internet-of-Things devices. These studies have motivated the exploration of TE materials derived from Al−Fe−Si ternary compounds via both theoretical calculations and experiments.20,21 Among the 11 stable ternary phases (see the Supporting Information) found in the Al−Fe−Si system,22−28 the τ1-Al2Fe3Si3 phase has 14 valence electrons per Fe atom and has been shown to be a narrow-gap semiconductor,20 whose band-gap value was estimated to be 0.1 eV29 from Seebeck coefficient measurement or 0.2 eV20 from electrical conductivity measurement. Recently, Shiota et al.29 have reported the mechanical and p-type TE properties of the Al2Fe3Si3 compound. Previous experimental studies have reported that the Al2Fe3Si3 compound can exhibit a low lattice thermal conductivity value of about 4.5−5.5 W m−1 K−1 at 300 K20 and 4.0 W m−1 K−1 at 640 K.29 Furthermore, the measured maximum Seebeck coefficient |S| is about 130 μV K−1 at 423 K.21 However, the reported maximum PF is less than 1 mW m−1 K−2.20,21,29 Much effort has been made to improve the PF of Al2Fe3Si3 for practical applications, but the conversion efficiency of heat to electricity for a large number of potential applications requires enhancing the PF over a wide range of temperatures. Very recently, some studies have demonstrated that the conduction type of Al2Fe3Si3 could be controlled by changing the Al/Si ratio.20,21 The maximum PF of Al2Fe3Si3 was improved from 375 μW m−1 K−2 at 650 K (400 μW m−1 K−2 at 500−600 K) to 500 μW m−1 K−2 at 500 K (730 μW m−1 K−2 at 373 K) for p-type (n-type) by fine-tuning of the Al and Si contents in Al2Fe3Si3.20,21 However, these attempts were achieved by the traditional “trial-and-error” approach, which is generally costly in time and labor. Recently, the machinelearning (ML)-based tool has been shown as an alternative approach to accelerate the discovery and design of materials.30 For example, the Bayesian optimization (BO) algorithm has been employed to combine with atomistic simulation methods to search for the low-thermal-conductivity compounds31 and to design Si/Ge nanostructures for phonon transport.32 The BO shows great efficiency, although a high-dimensional search space was treated in these studies.31,32 In the search of a composition ratio in the off-stoichiometric compound of Al2Fe3Si3 that optimizes the PF, a low-dimensional search space needs to be managed. This work concentrates on searching for the Al/Si ratio; thus, the prediction of TE properties by machine learning is expected to facilitate the rational design and optimization of TE performance improvement of Al2Fe3Si3. As far as we know, the machine-learning algorithm has rarely been combined with the experimental synthesis of TE materials. In this work, the off-stoichiometric compound of Al2Fe3Si3 is taken as an example to demonstrate the application of the machine-learning algorithm for the determination of experimental specifications for high-performance TE material development. In this study, we proposed a framework for combining experiments and the machine-learning model to optimize the PF of Al2Fe3Si3. With the assistance of the machine-learning
prediction, an optimal Al/Si ratio in the Al2Fe3Si3-based offstoichiometric samples was identified (i.e., n-type Al23.5+xFe36.5Si40−x with x ≤ 2.2) for a higher PF in a midtemperature range. In the case of the optimal Al/Si ratio, namely, x = 0.9, we obtained a maximum PF of about 670 μW m−1 K−2 at a temperature of ∼510 K for the n-type Al23.5+xFe36.5Si40−x. Furthermore, we carried out density functional theory (DFT) calculations for a deeper understanding of the point defect stability and the thermal conductivity of Al2Fe3Si3, which is helpful for the further studies of Al2Fe3Si3 toward the practical module development and application.
2. EXPERIMENTAL AND THEORETICAL METHODS 2.1. Synthesis. As has been reported in ref 21, the τ1-Al2Fe3Si3 phase can be synthesized as the primary phase in the composition range of Fe-constant Al23.5+xFe36.5Si40−x (0 ≤ x ≤ 10). The Al-rich samples with x ≥ 3.0 exhibit p-type conduction, whereas the Si-rich samples with x ≤ 2.2 exhibit n-type conduction. In this work, we focused on n-type Al23.5+xFe36.5Si40−x (x ≤ 2.2) for optimizing the thermoelectric properties in the mid-temperature range. The synthesis procedure of the n-type Al23.5+xFe36.5Si40−x (x = 1.8, 2, and 2.2) samples has been described elsewhere.21 Mother ingots with nominal compositions of Al23.5+xFe36.5Si40−x (x = 0, 0.7, 0.9, and 1.5) were synthesized by arc melting under an argon atmosphere (NEV-AD03; Nissin Giken Co., Saitama, Japan). The high-purity elements of aluminum (powder, 99.99%), iron (grains, 99.9%), and silicon (chunk, 99.999%) were obtained from Kojundo Chemical Laboratory Co. Ltd., Tokyo, Japan. The ingots were flipped during arc melting to obtain homogeneous samples. The obtained bulk samples were crushed into a fine powder by wet hand milling using an agate mortar and ethanol. The ground powder samples were then classified using a stainless sieve using a 45 μm mesh and placed in a 10 mm diameter carbon die with carbon spacers for spark plasma sintering (LABOX-110MC, SinterLand, Inc., Niigata, Japan). The sintering temperatures and applied pressure were 1183−1213 K and 57.4 MPa, respectively. The relative densities of the obtained bulk samples were more than 95%, which is sufficiently high for thermoelectric property measurements. 2.2. Measurements and Phase Characterization. The phase characterization of the samples was performed by X-ray diffraction (XRD) measurements with Cu Kα radiation (MiniFlex 600, Rigaku, Tokyo, Japan). The σ and S values were measured in a helium atmosphere between 300 and 873 K by the four-probe method and the steady-state temperature gradient method, respectively (ZEM-3, Advance-Riko, Inc., Kanagawa, Japan). The PF was obtained at each temperature from the relation PF ≡ S2σ. The sound velocity was measured using the ultrasonic pulse-echo method (Echometer 1062, Nihon Matech Co., Tokyo, Japan). Figure 1a shows XRD patterns of the synthesized bulk Al23.5+xFe36.5Si40−x (x = 0, 0.7, 0.9, and 1.5) samples, together with those of reported samples with x = 1.8, 2.0, and 2.2.21 All synthesized samples primarily consisted of the τ1-Al2Fe3Si3 phase.33 However, the XRD patterns indicate that the samples with x = 0.0 and 0.7 contain small amounts of the secondary phase τ8-Al2Fe3Si4.33 This may be understood by a reported ternary phase diagram.28 At this stage, there has been no report on the physical properties for τ8-Al2Fe3Si4. A recent band structure calculation has indicated that the τ8-Al2Fe3Si4 phase does not form a narrow gap and/or pseudogap, implying that the τ8-Al2Fe3Si4 phase possesses metallic transport behavior.21 Such metallic precipitations can enhance σ but should lower |S|. To investigate the sample quality of the τ1-Al2Fe3Si3 phase, the variation of lattice parameters with Si concentration was examined using Rigaku-PDXL software, as shown in Figure 1b. The trend quantitatively agrees with data reported by Marker et al.;28 thus, we successfully synthesized the samples with 0 ≤ x ≤ 2.2 as an n-type material. B
DOI: 10.1021/acsami.9b02381 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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ACS Applied Materials & Interfaces
Figure 2. Framework for the design of Al23.5+xFe36.5Si40−x toward an optimized power factor (PF). The initial data set comprises PF measurements of several Al23.5+xFe36.5Si40−x compositions. After machine learning, the PFs of the unsynthesized compositions are predicted and one is chosen for synthesis according to a selection policy. Next, synthesis of the selected composition and measurements of its properties are performed. If the optimal target is not achieved, then the measured data is appended to the data set as feedback, and the next iteration is repeated. After several iterations, the optimized PF is successfully achieved. employed to adaptively optimize the sampling strategy in the X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism spectroscopy (XMCD).36,37 In those studies, the XAS and XMCD versus energy were interpolated by the GPR method so that the total number of data points in the experimental measurement can be reduced and the required accuracy provided meanwhile.36,37 Herein, the GPR method was used not only to interpolate the PFs versus temperature for the synthesized compositions but also to extrapolate the PFs versus temperature for the unsynthesized compositions. 2.4. Density Functional Theory Calculations. The τ1-Al2Fe3Si3 phase crystallizes in a triclinic structure with the space group P1̅,28 as depicted in Figure 3. The structural property of Al2Fe3Si3 was
Figure 1. (a) X-ray diffraction patterns of synthesized bulk Al23.5+xFe36.5Si40−x (x = 0.0, 0.7, 0.9, 1.5, 1.8,21 2.0,21 and 2.221) samples, and calculated patterns for the τ1-Al2Fe3Si3 and τ8-Al2Fe3Si4 phases.33 (b) Lattice parameters as a function of Si content. 2.3. Machine-Learning Method. Herein, we employed an exploration strategy to accelerate the material design of thermoelectric materials toward a higher PF. Figure 2 shows the flowchart for the design of intermetallic Al23.5+xFe36.5Si40−x toward the targeted property of a high PF in a mid-temperature range. The initial data set consists of data from thermoelectric property measurement of several compositions. After constructing a machine-learning model and applying it to predict the PFs of unsynthesized compositions, we selected a candidate composition for synthesis that has the highest value of predicted maximum PF particularly in the temperature range of 450 K ≤ T ≤ 650 K. Then, the synthesis and property measurement were experimentally performed on the selected candidate composition, which produced new data that were added into the data set for further iterations. When the optimal thermoelectric properties were successfully obtained, further material characterizations and analyses were carried out. The algorithm used in the present machine-learning model is a Gaussian process regression (GPR) method,34 as implemented in a Python package called COMBO.35 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 herein. The hyperparameters in the SE covariance function were determined by maximizing the log marginal likelihood.34 We are aware that the GPR method has been recently
Figure 3. Crystal structure (ball-and-stick model) of Al2Fe3Si3, wherein Al (magenta), Fe (red), and Si (cyan) atoms have two, three, and three symmetry-inequivalent sites, respectively, as marked by the number.
calculated by the Vienna ab initio simulation package (VASP)38,39 based on density functional theory (DFT). The projector-augmented wave method40,41 and the generalized gradient approximation (GGA) with the Perdew−Burke−Ernzerhof (PBE) exchange−correlation functional42 were used. The plane wave cutoff energy was set at 550 eV. The Brillouin zone integration was approximated by the Monkhorst−Pack k-point sampling method43 with a Γ-centered 13 × 9 × 9 grid. The internal atomic positions and the lattice constants were allowed to relax until the maximal residual Hellmann−Feynman forces on the atoms and the stresses on the cell were less than 10−2 eV/Å and 0.1 GPa, respectively. The predicted lattice parameters of Al2Fe3Si3 by the GGA-PBE calculations are presented in Table 1 and are in good agreement with the experimental data available in literature28,33 and with this work. The optimized atomic positions in Al2Fe3Si3 are listed in Table S1 in the Supporting Information. C
DOI: 10.1021/acsami.9b02381 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX
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ACS Applied Materials & Interfaces Table 1. Calculated Lattice Parameters (a, b, and c in Å; α, β, and γ in Degree) of Al2Fe3Si3a
IFCs. For every displacement pattern, a displacement amplitude of 0.01 Å was considered, the corresponding supercell was constructed by the Phonopy54 code, and the Hellmann−Feynman forces on atoms in a supercell were calculated by the VASP code. In this DFT calculation, a tight convergence threshold for energy (i.e., 10−7 eV) was set and a Γ-centered 7 × 5 × 5 k-grid was used. The second-order IFCs in the harmonic approximation and the phonon dispersions of Al2Fe3Si3 were calculated by the Phonopy code. The point defects in Al2Fe3Si3 were studied using a 3 × 2 × 2 supercell (192 atoms), which was constructed from the optimized bulk structure of Al2Fe3Si3. Herein, we concentrated on the single Al vacancy (denoted VAl), Si vacancy (denoted VSi), antisite substitutional Al for Si (denoted AlSi), and antisite substitutional Si for Al (denoted SiAl), because they are correlated to Al and Si offstoichiometries in Al2Fe3Si3. As we noted high atomic coordination numbers in perfect Al2Fe3Si3, we did not study the interstitial defects herein. The VAl (VSi) was simulated by removing one Al (Si) atom from this 192-atom supercell and the AlSi (SiAl) by substituting one Al (Si) atom for a Si (Al) atom in the supercell, which correspond to Al 1 . 9 5 8 3 3 Fe 3 Si 3 (Al 2 Fe 3 Si 2 . 9 5 8 3 3 ) and Al 2 . 0 4 1 6 7 Fe 3 Si 2 . 9 5 8 3 3 (Al1.95833Fe3Si3.04167), respectively. All atom positions in the defective supercell were relaxed, whereas the lattice vectors of the supercell were fixed. A Γ-centered 3 × 5 × 5 k-grid was used in the calculations of the defective supercell. Generally, the formation energy of a studied point defect α in charge state q can be determined according to the following formula55
experimental parameters
GGA-PBE
this work
ref 28
ref 33
a b c α β γ
4.6032 6.3256 7.4594 101.90 106.79 100.59
4.5995 6.3352 7.521 101.827 106.427 100.729
4.684 6.325 7.498 100.99 105.6 101.62
4.6512 6.3261 7.499 101.375 105.923 101.237
a
The experimental results are listed for comparison, including those of Al23.5+xFe36.5Si40−x with x = 0.0 obtained in this work.
Both experimental measurement20,29 and theoretical prediction20 showed that Al2Fe3Si3 is a narrow-gap semiconductor. The GGA-PBE calculation in this work predicted that the band-gap (Eg) value of Al2Fe3Si3 is 0.248 eV, which is close to the experimental value (0.2 eV)20 and consistent with the previous calculation result.20 We have also employed the SCAN (strongly constrained and appropriately normed) meta-GGA functional,44 PBE0 hybrid functional,45,46 and HSE06 screened hybrid functional47 methods to check the electronic structures of Al2Fe3Si3. The detailed results of these advanced calculations will be given elsewhere. The Eg of Al2Fe3Si3 obtained by the SCAN meta-GGA method is 0.388 eV. It is known that hybrid functionals (either global or screened-exchange) have been characterized by a fixed and system-independent Fock exchange fraction α (for instance, 0.25 in PBE0 and HSE06 for a standard setup) and that the predicted properties including band gap can be significantly affected by the parameter α. It has been shown that both the PBE0 and HSE06 functionals might fail to describe systems with a large screening.48−50 The PBE0 and HSE06 hybrid functionals with the standard setup predicted the Eg of Al2Fe3Si3 to be 1.619 and 0.976 eV, respectively, which seem to be a significant overestimation of Eg as compared with the experiment. This is because Al2Fe3Si3 exhibits large values in its static dielectric constant tensor, whose average of the principal diagonal elements is about 22.2 based on the GGA-PBE calculation results. This large value of dielectric constant is caused by the localized Fe 3d states at the band edges. From the calculated electronic density of states (DOS) of Al2Fe3Si3, as shown in Figure S1a in the Supporting Information, it was noted that both the top valence bands and the bottom conduction bands are mainly dominated by the Fe 3d states. Recently, it has been argued from the screening behavior of nonmetallic systems that α can be related to the inverse of the static dielectric constant.51,52 However, the computation of α and the static dielectric constant in a self-consistent cycle requires additional computational effort, which is too heavy in the case of Al2Fe3Si3. Alternatively, we followed a non-self-consistent way,53 in which the inverse of the average of the principal diagonal elements in the static dielectric constant tensor of Al2Fe3Si3 obtained by the GGA-PBE calculation was used to determine the parameter α and then to modify the setup in the PBE0 and HSE06 hybrid functionals. In this way for Al2Fe3Si3, the exchange contribution is mainly dominated by the GGA-PBE exchange. The PBE0 and HSE06 hybrid functionals with this modified setup predicted the Eg of Al2Fe3Si3 to be 0.431 and 0.329 eV, respectively. These may serve as useful information to further assess the electronic properties of highquality and stoichiometric samples of Al2Fe3Si3. Regarding the computational efficiency in the GGA-PBE method and its reasonable prediction for the Eg of Al2Fe3Si3, we employed the GGA-PBE method mainly to carry out the following DFT calculations in this work. The second-order interatomic force constants (IFCs) in Al2Fe3Si3 were calculated by the finite-displacement method wherein a 2 × 2 × 2 supercell (128 atoms) was used. Because Al2Fe3Si3 has a lowsymmetry crystal structure with two, three, and three symmetryinequivalent Al, Fe, and Si sites (Figure 3), respectively, 48 displacement patterns are needed to compute the second-order
ΔEform = Et(α) − Et(0) −
∑ niμi + q(εF + εVBM) + Ecorr i
(1) where Et(α) and Et(0) are the total energies of supercells of the host material (herein, a 3 × 2 × 2 supercell of Al2Fe3Si3) with and without the defect α, respectively. The ni’s are the number of atoms added (ni > 0) to or subtracted (ni
