Thermoelectric Properties of Co-Substituted Al–Pd–Re Icosahedral Quasicrystals

The practical application of quasicrystals (QCs) as thermoelectric materials makes icosahedral (i-) Al–Pd–Re QC attractive because of its moderate electrical conductivity (~280 Ω−1 cm−1), relatively high Seebeck coefficient (~100 μV K−1), and low thermal conductivity (~1.3 W m−1 K−1) at room temperature. To develop a thermoelectric Π-shaped power generation module, we need both p- and n-type thermoelectric materials. In this work, we aimed to develop an n-type i-Al–Pd–Re-based QC and investigated the effect of Co substitution for Re on the thermoelectric properties, i.e., the electron-doping effect. We synthesized dense bulk samples with nominal compositions of Al71Pd20(Re1−xCox)9 (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5) via arc-melting, annealing, and sintering methods. We found that Co can produce n-type carriers in dilute substitution amounts of x = 0.1 and 0.2; however, the Seebeck coefficient at 300 K showed an n- to p-type transition with increasing x. This indicates that a simple rigid-band approximation is not applicable for i-Al–Pd–Re QC, which makes it difficult to synthesize an n-type i-Al–Pd–Re-based QC. Although the thermal conductivity was reduced from 1.28 (x = 0) to 1.08 W m−1 K−1 (x = 0.3) at 373 K by lowering of the electron thermal conductivity (electrical conductivity) and the alloying effect via Co substitution, the dimensionless figure of merit was not enhanced because of lowering of the power factor for all samples. The elastic moduli of i-Al–Pd–Re QC decreased by Co substitution, indicating that i-Al–Pd–Re-Co QC had a more ionic and brittle character.


Introduction
From the viewpoint of highly efficient energy use, the importance of thermoelectric conversion technology that directly converts thermal energy into electrical energy is increasing. There are many reports on research and development related to various high-performance thermoelectric materials [1] and modularization technology [2]. The dimensionless figure of merit (zT) is an evaluation index for a thermoelectric material, expressed as: where S, σ, κ total , and T are the Seebeck coefficient, electrical conductivity, total thermal conductivity, and temperature, respectively [3,4]. Here, κ total is the sum of two contributions: the electron contribution, κ electron , and the phonon contribution, κ phonon , i.e., κ total = κ electron + κ phonon (2) κ electron is proportional to σ through the Wiedemann-Franz law: where L 0 is the Lorenz number. Thus, both optimizing S and σ and lowering κ phonon are necessary to enhance the zT value. Relevant materials designs, such as band engineering and valleytronics [5], can improve the power factor (S 2 σ), and nano-structuring [6] and phonon engineering [2] can be employed to reduce κ phonon . In recent years, the application of thermoelectric materials as autonomous power supplies to drive Internet-of-Things (IoT) devices [7] has become possible [8,9]. The usable temperature range is below 200 • C, as derived from environmental heat sources and low-temperature waste heat, and it is crucial to ensure a temperature difference when using thermoelectric power generation modules. For this purpose, the κ total of a materialforming thermoelectric module should be low, i.e., less than a few W m −1 K −1 at operating temperature. In contrast, a high output voltage is required when driving IoT devices with a DC-DC converter; thus, a high S is required for the material.
To develop a robust thermoelectric Π-shaped power generation module, we need both p-and n-type thermoelectric materials with good mechanical properties. In this work, we aimed to develop an n-type i-Al-Pd-Re-based QC. We selected Co as an electron dopant because Co has a larger number of valence electrons than Re. Regarding the Al-Pd-Co ternary system, there is one report on the thermoelectric properties of 1/1cubic approximant crystal [21]. This paper reports the effect of Co substitution for Re in i-Al-Pd-Re QC on the thermoelectric and mechanical properties.

Methods and Materials
Mother ingots of nominal compositions of Al 71 Pd 20 (Re 1−x Co x ) 9 (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5) were synthesized by an arc-melting technique under a purified argon atmosphere (NEV-AD03TC; Nisshin Giken Co., Japan) using the starting materials Al (powder, 99.99%), Pd (powder, 99.9%), Re (powder, 99.9%), and Co (powder, >99%). The obtained bulk samples were annealed at 1223 K for 24 h under a purified argon atmosphere to prevent oxidization (MILA-5000; Advance Riko, Inc., Yokohama, Japan). The annealed samples were hand-milled in ethanol using an agate mortar and pestle. The hand-milled powder samples were sieved using a stainless-steel sieve of 45 µm mesh and then placed in a carbon die with an inner diameter of 10 mm for spark plasma sintering (SPS) (LABOX-110MC; SinterLand, Inc., Nagaoka, Japan) under a purified argon atmosphere. The applied pressure was set to 115 MPa during the sintering process to synthesize dense bulk samples. This value is twice as high as a condition that previously achieved a high relative density above 90% for i-Al-Pd-Re QC [22]. To obtain dense bulk samples, we performed 10 min at a sintering temperature (T S ) of 1223-1233 K, at which the degree of shrinkage was saturated. Table 1 lists T S and bulk densities (d bulk ) obtained from the Archimedes method for Al 71 Pd 20 (Re 1−x Co x ) 9 (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5). Here, the data for the sample with x = 0 are quoted from a reported paper [16].
Phase characterization of the samples was evaluated by X-ray diffraction (XRD) with Cu Kα radiation (Mini-Flex 600; Rigaku, Inc., Akishima, Japan) and a scanning thermal probe micro-imaging apparatus (STPM-1000; Advance-Riko, Inc., Yokohama, Japan). The σ and S values were measured between 300 and 873 K by the four-probe and steady-state temperature gradient methods, respectively (ZEM-3; Advance Riko, Inc., Yokohama, Japan). The κ total value was calculated from d bulk , the specific heat at constant pressure (C P ), and thermal diffusivity (λ) using the relationship κ total = d bulk ·C P ·λ. C P was measured using differential scanning calorimetry (DSC404-F3; NETZSCH Japan, Yokohama, Japan) and λ was measured by a light flash apparatus (LFA467-HT; NETZSCH Japan, Yokohama, Japan) from 373 to 873 K. The longitudinal (v long ) and transverse (v trans ) speeds of sound were measured by the ultrasonic pulse-echo method (Echometer 1062; Nihon Matech Corp., Tokyo, Japan). For rough estimations of the elastic moduli (Poisson's ratio (ν), Young's modulus (E), shear modulus (G), and bulk modulus (B)) for these QC samples, the following relations for isotropic materials were used for the calculations [23][24][25]:

Results and Discussion
The relative density of the sample with x = 0 was 95.7% [16], indicating that a dense bulk sample was fabricated by the SPS process. The ideal densities of the Co-substituted samples were calculated from d bulk (relative density:~100%, 6.30 g cm -3 ) of the sample with x = 0 [22] and the rate of change in average atomic weight ( Table 1). As a result, it was found that the dense bulk samples with relative densities of >95% were fabricated for Cosubstituted samples. The overall trend of d bulk decreased with increasing Co concentration x, which can be understood as decreasing the average mass by substitution of the lighter element Co for Re.
We confirmed that all synthesized bulk samples were identified as an F-type quasicrystalline phase [26], as shown in Figure 1A. In the Al-Pd-Re-Co system, the formation of 2/1-or 1/1-approximant crystal was not realized, unlike in Al-Pd-Re-Ru [27] and Al-Pd-Re-Fe [16] quaternary systems. We observed peak shifting to a higher degree with increasing x, indicating that the quasi-lattice constant (a R ) decreased by Co substitution for Re ( Figure 1B). This trend can be qualitatively explained by substitution of the smaller atomic radii of Co (0.125 nm) for Re (0.138 nm). However, we observed that the sample with x = 0.3 had a slight increase in a R , which may be brought about by a composition deviation, as discussed below.
The morphology of the dense bulk samples synthesized by the SPS process did not change with varying x. To assess the sample's quality, the mapping measurements of S at 300 K, which is sensitive to local composition, were performed ( Figure 2). As a result, homogeneous microstructures were obtained, except for the sample with x = 0.3, and there was no secondary precipitation. These results agree with the XRD measurements. The sample with x = 0.3 had a composite microstructure consisting of p-and n-type compositions with small absolute values of S. When x increased, the carrier type changed from p-to n-type, then turned to p-type again. However, its magnitude of S for an n-type material is relatively low (−10 µV K −1 ) for the sample with x = 0.2. with x = 0.3 had a slight increase in aR, which may be brought about by a composition deviation, as discussed below.
The morphology of the dense bulk samples synthesized by the SPS process did not change with varying x. To assess the sample's quality, the mapping measurements of S at 300 K, which is sensitive to local composition, were performed ( Figure 2). As a result, homogeneous microstructures were obtained, except for the sample with x = 0.3, and there was no secondary precipitation. These results agree with the XRD measurements. The sample with x = 0.3 had a composite microstructure consisting of p-and n-type compositions with small absolute values of S. When x increased, the carrier type changed from pto n-type, then turned to p-type again. However, its magnitude of S for an n-type material is relatively low (−10 μV K −1 ) for the sample with x = 0.2.    [28] and i-Al-Pd-Re-Fe QC (0.14-0.17 eV) [16]. Since S at 300 K decreased owing to Co substitution for Re, the decrease in carrier concentration was not the cause of the decrease in σ, i.e., lowering of the relaxation time owing to chemical disordering of Co at Fe sites. The absolute value of S for p-type materials (except for samples with x = 0.2 and 0.3) decreased with the increasing temperature, which is attributed to an increase in minority carriers. This is consistent with the temperature dependence of σ. The S 2 σ value showed a similar temperature dependence, with a peak at mid-temperatures of 600-700 K for all samples, and exhibited a maximum value of~380 µW m −1 K −2 at 573 K for the unsubstituted sample, i.e., S 2 σ was not improved by Co substitution for Re because of the reduction of S and σ.   [28] and i-Al-Pd-Re-Fe QC (0. eV) [16]. Since S at 300 K decreased owing to Co substitution for Re, the decrease in concentration was not the cause of the decrease in σ, i.e., lowering of the relaxatio owing to chemical disordering of Co at Fe sites. The absolute value of S for p-typ rials (except for samples with x = 0.2 and 0.3) decreased with the increasing tempe which is attributed to an increase in minority carriers. This is consistent with the t ature dependence of σ. The S 2 σ value showed a similar temperature dependence The highest value of σ at 300 K was measured for the i-Al 71 Pd 20 Re 9 QC (~280 Ω −1 cm −1 ) [16]: σ decreased up to x = 0.4 and then increased for the sample with x = 0.5. This non-monotonic change in σ with varying x cannot be understood only in terms of the change in carrier concentration from the S measurement. Initially, we expected Co to be an n-type dopant and tried to replace it with Re. As expected, the S value of the sample with x = 0.2 showed n-type values (−10 µV K −1 at 300 K), but this changed to p-type with increasing x and its absolute value improved to 100 µV K −1 at 300 K for the sample with x = 0.5, which is close to that of the undoped sample (x = 0) [16]. These changes of σ and S suggest that a simple rigid-band approximation is not applicable to this system. As a result, we did not succeed in fabricating the desired n-type material with a high S.
The Co-substitution concentration dependence of σ and S is a rather complicated change and differs from those reported in previous studies on Ru [27] and Fe [28] substitu-tion. Mizutani et al. reported an electron per atom ratio (e/a) for elements in the Periodic Table [29]: e/a = 1.31 for Re and e/a = 1.11 for Co. Using these e/a values of the constituent elements, the e/a value of i-Al-Pd-Re-Co QCs decreases with increasing Co concentration and, thus, E F shifts to a lower energy, which seems to be an opposite way to obtain an n-type material. In contrast, in dilute substitution amounts of x = 0.1 and 0.2, Co appears to function as an n-type dopant. Hall coefficient measurements may clarify the underlying mechanism; however, the Hall voltage of i-Al-Pd-Re QC is too low to obtain reliable data at this stage. The Co-substitution concentration dependence of σ and S is a rather complicated change and differs from those reported in previous studies on Ru [27] and Fe [28] substitution. Mizutani et al. reported an electron per atom ratio (e/a) for elements in the Periodic Table [29]: e/a = 1.31 for Re and e/a = 1.11 for Co. Using these e/a values of the constituent elements, the e/a value of i-Al-Pd-Re-Co QCs decreases with increasing Co concentration and, thus, EF shifts to a lower energy, which seems to be an opposite way to obtain an ntype material. In contrast, in dilute substitution amounts of x = 0.1 and 0.2, Co appears to function as an n-type dopant. Hall coefficient measurements may clarify the underlying mechanism; however, the Hall voltage of i-Al-Pd-Re QC is too low to obtain reliable data at this stage.
The temperature dependences of CP, λ, and κtotal from 373 to 973 K for all samples are shown in Figure 4a Table 2 lists κtotal at 373 K (κtotal,373K) for all samples investigated. The κtotal,373K value decreased from 1.28 (x = 0) to 1.08 W m −1 K −1 (x = 0.3), probably due to the large decrease in σ, as shown in Figure 3a. Regarding the estimation of κelectron, the well-known Wiedemann-Franz law is not suited for QCs because it assumes that the spectral conductivity varies linearly with energy [30]. Maciá has discussed the validity of the Wiedemann-Franz law for QCs [31]. There is no empirical relationship to calculate κelectron for QCs; thus, we adopted the conventional relationship shown in Equation (8) Table 2 lists κ total at 373 K (κ total,373K ) for all samples investigated. The κ total,373K value decreased from 1.28 (x = 0) to 1.08 W m −1 K −1 (x = 0.3), probably due to the large decrease in σ, as shown in Figure 3a. Regarding the estimation of κ electron , the well-known Wiedemann-Franz law is not suited for QCs because it assumes that the spectral conductivity varies linearly with energy [30]. Maciá has discussed the validity of the Wiedemann-Franz law for QCs [31]. There is no empirical relationship to calculate κ electron for QCs; thus, we adopted the conventional relationship shown in Equation (8) and L 0 values using an empirical model (L 0 = 1.5 + exp[−|S|/116] × 10 −8 V 2 K −2 ) by Kim et al. [32] for a rough estimation of κ phonon: The calculated κ phonon as a function of temperature is shown in Figure 4d, and we list κ phonon at 373 K (κ phonon,373K ) for all samples in Table 2, together with the minimum thermal conductivity at 373 K (κ min,373K ) using the Cahill model [33,34], which provides the lower limit of κ phonon for amorphous solids and disordered crystals. The κ min value can be calculated as follows: Here, k B is the Boltzmann constant, n is the number density of atoms, and θ long,trans is the cutoff temperature, which is given by θ long,trans = v long,trans k B 6π 2 n 1 3 , whereh is Planck's constant. It should be noted that the apparent increase in κ phonon at high temperatures, including for the Co-substituted samples, originates from conduction carriers [30]. The κ phonon,373K was suppressed to 0.94 W m −1 K −1 by Co substitution, which is attributed to decreasing the phonon relaxation time (τ phonon ): where C v and v s are the specific heat at constant volume and the effective speed of sound, respectively. Here, the C V [35] and v s can be expressed as: where V and α are the atomic volume and the linear thermal expansion coefficient, respectively. Although we have no information on α for the present i-Al-Pd-Re-Co QCs, qualitative changes are discussed using C P . Table 2. Total thermal conductivity at 373 K (κ total,373K ), phonon thermal conductivity at 373 K (κ phonon,300K ), minimum thermal conductivity at 373 K (κ min,373K ), longitudinal (v long ) and transverse (v trans ) speeds of sound, effective speed of sound (v s ), rate of change in v s (∆v s /v s ), specific heat at constant pressure at 373 K (C P,373K ), and rate of change in C P,373K (∆C P,373K /C P,373K ) for Al 71 Pd 20 (Re 1−x Co x ) 9   The calculated κphonon as a function of temperature is shown in Figure 4d, and we list κphonon at 373 K (κphonon,373K) for all samples in Table 2, together with the minimum thermal conductivity at 373 K (κmin,373K) using the Cahill model [33,34], which provides the lower limit of κphonon for amorphous solids and disordered crystals. The κmin value can be calculated as follows: Here, kB is the Boltzmann constant, n is the number density of atoms, and θlong,trans is the cut-off temperature, which is given by Planck's constant. It should be noted that the apparent increase in κphonon at high temperatures, including for the Co-substituted samples, originates from conduction carriers [30]. The κphonon,373K was suppressed to 0.94 W m −1 K −1 by Co substitution, which is attributed to decreasing the phonon relaxation time (τphonon): where Cv and vs are the specific heat at constant volume and the effective speed of sound, respectively. Here, the CV [35] and vs can be expressed as: Co-substitution for Re could reduce κ phonon,373K from 1.05 (x = 0) to 0.94 (x = 0.3) W m −1 K −1 , i.e., up to a 10% reduction. The C P and v s values did not change significantly between samples with x = 0 and 0.3 (less than~2% for each) ( Table 2), so τ phonon is likely reduced because of the alloying effect. Here, we note that κ phonon,373K of the sample with x = 0 is the same as the κ min,373K value, and the observed κ min,373K > κ phonon,373K relationship is attributed to overestimation of L 0 [36]. This trend was also observed in the Al-Pd-Re-Fe quaternary system [16].
The estimated elastic parameters of ν, E, G, and B for Al 71 Pd 20 (Re 1−x Co x ) 9 (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5) are listed in Table 3. The general mechanical properties of QCs are hard and brittle, so the estimated elastic moduli are consistent with the general trend. There is no literature on the mechanical properties of i-Al-Pd-Re QC. In general, an arc-melted and annealed i-Al-Pd-Re sample has a porous microstructure of a relative density of <70% because i-Al-Pd-Re QC forms from the peritectic reaction of Al 3 Pd 2 and Al 11 Re 4 , and thus is very fragile [22]. We speculate that such a porous sample makes it difficult to measure intrinsic mechanical properties. The sintered bulk samples of i-Al-Pd-Re(-Co) QCs were dense enough to measure their intrinsic mechanical properties. Indeed, we obtained a higher B value of over 150 GPa for the sample with x = 0, which is close to Fe-based thermoelectric materials of Fe 3 Al 2 Si 3 , β-FeSi 2 , and FeAl 2 [37]. It was found that Co substitution for Re slightly reduced the elastic moduli of ν, E, G, and B. The ν value is related to the volume change in the uniaxial deformation. Classical elastic theory predicts ν to be −1 to 0.5. A larger ν value means that a material possesses better plasticity. The estimated ν values of 0.260-0.303 for i-Al-Pd-Re-Co QCs are between those of ionic materials, such as NaCl (ν = 0.253) and CsCl (ν = 0.266) [38], and metallic materials, such as Aluminum 6061-T6 (ν = 0.33) and Cu (ν = 0.355) [38]. This may indicate that Co substitution for Re gives i-Al-Pd-Re QC a more ionic and brittle character. Compared with other i-QCs, such as i-Al-Pd-Mn QC [39,40] and i-Al-Cu-Fe QC [39], i-Al-Pd-Re-Co QCs had higher ν and B values, but the G value was almost identical. Decreasing ν will be associated with increasing covalency between atoms because covalent materials such as diamond and cubic boron nitride have low ν values of 0.069 and 0.14-0.18, respectively [38]. Finally, we briefly mention zT as a function of temperature, as shown in Figure 5. The maximum zT value (zT max ) was 0.12 at 573 K for the sample with x = 0. Although κ total was reduced by the alloying effect via Co substitution for Re, zT max was not enhanced because of the lowering of S 2 σ for all measured temperature ranges. as i-Al-Pd-Mn QC [39,40] and i-Al-Cu-Fe QC [39], i-Al-Pd-Re-Co QCs had higher ν and B values, but the G value was almost identical. Decreasing ν will be associated with increasing covalency between atoms because covalent materials such as diamond and cubic boron nitride have low ν values of 0.069 and 0.14-0.18, respectively [38]. Finally, we briefly mention zT as a function of temperature, as shown in Figure 5. The maximum zT value (zTmax) was 0.12 at 573 K for the sample with x = 0. Although κtotal was reduced by the alloying effect via Co substitution for Re, zTmax was not enhanced because of the lowering of S 2 σ for all measured temperature ranges.

Conclusions
In this study, we systematically investigated the effect of Co substitution for Re for i-Al-Pd-Re QC on thermoelectric and mechanical properties. We found that the icosahedral quasi-crystalline phase can be synthesized by 50% replacement of Co for Re. Although κtotal was reduced by the alloying effect via Co substitution for Re, zTmax was not enhanced because of the lowering of S 2 σ for all measured temperature ranges. Co could produce n-type carriers in dilute substitution amounts of x = 0.1 and 0.2; however, S at 300 K showed an n-to p-type transition with increasing x. The observed effects of Co concentration on σ and S showed a complicated change, suggesting that a simple rigid-band approximation is not applicable to i-Al-Pd-Re QC. To develop a robust thermoelectric power generation module using Al-based QCs, we need to synthesize a high-performance n-type QC. This is a future challenge for the practical application of QCs.

Conclusions
In this study, we systematically investigated the effect of Co substitution for Re for i-Al-Pd-Re QC on thermoelectric and mechanical properties. We found that the icosahedral quasi-crystalline phase can be synthesized by 50% replacement of Co for Re. Although κ total was reduced by the alloying effect via Co substitution for Re, zT max was not enhanced because of the lowering of S 2 σ for all measured temperature ranges. Co could produce n-type carriers in dilute substitution amounts of x = 0.1 and 0.2; however, S at 300 K showed an n-to p-type transition with increasing x. The observed effects of Co concentration on σ and S showed a complicated change, suggesting that a simple rigid-band approximation is not applicable to i-Al-Pd-Re QC. To develop a robust thermoelectric power generation module using Al-based QCs, we need to synthesize a high-performance n-type QC. This is a future challenge for the practical application of QCs.

Data Availability Statement:
The data presented in this study are available upon reasonable request from the corresponding author.