Thermoelectric properties of some skutterudite compounds with different grain size

Journal of Alloys and Compounds 375 (2004) 114–119

Thermoelectric properties of some skutterudite compounds with different grain size L. Yang∗ , J.S. Wu, L.T. Zhang Key Laboratory of the Ministry of Education for High Temperature Materials and Testing, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200030, PR China Received 8 September 2003; received in revised form 1 December 2003; accepted 8 December 2003

Abstract Some Fe-alloyed CoSb3 compounds (Lay Fe4−x Cox Sb12 , with x = 1–3 and y = 0–0.75) with/without rare-earth element filling with different average grain sizes (about 0.8, 3.9 and 6.7 ␮m) were prepared by hot pressing and their thermoelectric properties were measured from room temperature to 773 K. Grain size has an obvious effect on the electrical resistivity and Seebeck coefficient of the La-filled samples. The electrical resistivity decreases and the Seebeck coefficient increases with increasing grain size for the La-filled samples. However, the electrical resistivity and Seebeck coefficient of the unfilled samples are relatively independent of their grain sizes. Unlike binary CoSb3 , lattice thermal conductivity of the samples is found to be insensitive to the grain size within the investigated range. Theoretical analysis shows that the effect of boundary scattering on the lattice thermal conductivity in these Lay Fe4−x Cox Sb12 compounds is relatively weaker than that in CoSb3 . For the La-filled skutterudite compound, the figure of merit (ZT) increases with grain size, indicating that a relatively large grain size yields good thermoelectric properties for these compounds. © 2004 Elsevier B.V. All rights reserved. Keywords: Grain size; Skutterudite compound; Thermoelectric properties

1. Introduction Skutterudite compounds MX3 with a cubic structure (M = Co, Rh, Ir, Fe, Ru, X = P, As, Sb) are a class of prospective high performance thermoelectric material for power generation [1–4] and thus have attracted a great deal of interest in recent years. The performance of a thermoelectric material is characterized by a dimensionless parameter-figure of merit (ZT), defined as ZT = S 2 T/ρκ, where S is the Seebeck coefficient, ρ is the electrical resistivity, κ is the thermal conductivity and T is the temperature. Although binary skutterudite compounds possess good electrical transport properties, their overall ZT is not high due to the relatively high thermal conductivity. Alloying substitution [5,6] and doping [7–9] are very effective to improving the thermoelectric properties of this compound. It is found by Sales et al. [10,12] and Nolas et al. [11,13] that rare-earth atoms such as La, Ce, etc. may be inserted into the voids of the crystal structure where they “rattle” ∗ Corresponding author. Tel.: +86-21-62932440; fax: +86-21-62932587. E-mail address: [email protected] (L. Yang).

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around their equilibrium positions. This rattling motion can efficiently scatter the phonons and thus greatly reduce the lattice thermal conductivity without deteriorating the electrical transport properties. The ZT of the rare-earth filled skutterudite is more than 1 between 773 and 973 K [10]. Despite the effects from dopants and alloying elements, microstructure is believed to have an effect on both the electrical and thermal properties, especially for polycrystalline materials [14]. Finely grained materials are usually preferred for the state-of-the-art thermoelectric materials since grain boundary scattering is a way to lower thermal conductivity. However, electrical resistivity is also increased by increasing the number of grain boundaries. In order to enhance the thermoelectric performance, it is of importance to understand in detail the relationship between grain size and thermoelectric properties for the specific compound. Effects of grain size over a range of 0.9–300 ␮m on the thermoelectric properties of binary CoSb3 have been investigated by Anno et al. [14] and Nakagawa et al. [15]. Anno et al. [14] suggested that the grain size was one of the key factors determining the transport properties of CoSb3 , especially below room temperature. Nakagawa et al. [15] found that a relatively high ZT could be obtained in samples with an

L. Yang et al. / Journal of Alloys and Compounds 375 (2004) 114–119

average grain size between 1 and 10 ␮m. Rare-earth filled skutterudites with alloying elements addition are of practical interest for their desirably high ZT values. The properties of these compounds are quite different from those binary ones. Whether the grain size is important to the thermoelectric properties of polycrystalline rare-earth filled skutterudite compounds is not very clear at present. In order to clarify this, we have prepared some Fe-alloyed CoSb3 compounds (Lay Fe4−x Cox Sb12 ) with/without rare-earth element filling by hot pressing to investigate the effect of grain size on their properties in the present paper.

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to 773 K using the van der Pauw technique under an argon atmosphere. Carrier concentration n was determined from the measured Hall coefficient RH using n = 1/RH e relation, where e is the electron charge. Seebeck coefficient (S) was determined by applying a small temperature difference (3 K) to the two ends of a sample in a temperature range from RT to 773 K under an argon atmosphere. Thermal conductivity was calculated from the experimental values of thermal diffusivity, specific heat capacity and density. The thermal diffusivity was measured by an ac calorimetry method in a temperature range from RT to 473 K. The specific heat capacity was measured by a differential scanning calorimeter (DSC) in an Ar flow.

2. Experimental Three different compositions (Table 1) were synthesized from high purity La shot (99.9%), Sb shot (99.998%), Fe rod (99.9%), and Co shot (99.9%) following a melt-quench-annealing procedure [12]. Details of the procedure are available in our previous paper [16]. Grain size of the sample was controlled by adjusting the annealing temperature and ball-milling time. After melting in carbon-coated quartz tubes, the samples were quenched into water and then annealed at 700 ◦ C for 100 h to form the skutterudite phase. Some of the samples were annealed at 750 ◦ C to obtain large grain size. The reacted ingots were then crushed into powder and ball-milled in an agate vessel using a planetary attrition mill for 1–5 h to obtain different powder sizes. The milled powders were hot pressed under vacuum in a graphite die under a pressure of 60 MPa at 650 ◦ C for 2 h to form dense polycrystalline ingot with different grain sizes. Density of the hot-pressed ingots was identical to each other and was measured to be more than 90% of the theoretical value using the Archimedes method. Microstructure of the samples was characterized by powder X-ray diffraction (XRD, Cu K␣) and electron probe micro-analyzer (EPMA). Fractured surfaces were observed to determine the average grain size of each sample. The samples fractured in an inter-granular mode and the grains were clearly shown in the fractured surface. The conventional line-interception method was used to measure the average grain size. Electrical resistivity (ρ) and Hall coefficient RH were measured in a temperature range from room temperature (RT)

3. Results and discussion XRD profiles show that the skutterudite phase was formed in all the samples with three different compositions after hot pressing (Fig. 1). The lattice constants were determined to be 0.910, 0.907 and 0.906 nm for La0.75 Fe3 CoSb12 , La0.4 FeCo3 Sb12 and FeCo3 Sb12 , respectively. These values are larger than that of binary CoSb3 (0.9032 nm [13]) since the lattice is expanded by Fe substitution and La addition. For FeCo3 Sb12 , traces of impurity phases such as Sb and FeSb2 were identified from XRD and EPMA observations,

Fig. 1. XRD profiles of the hot-pressed samples: (a) FeCo3 Sb12 , (b) La0.4 FeCo3 Sb12 , and (c) La0.75 Fe3 CoSb12 .

Table 1 A list of the studied skutterudite compounds with different grain size and some of their room temperature transport properties No.

Sample (nominal)

Average grain size (␮m)

Conductivity type

Electrical resistivity ( cm)

Carrier concentration (cm−3 )

1 2 3 4 5 6 7

FeCo3 Sb12 FeCo3 Sb12 La0.4 FeCo3 Sb12 La0.4 FeCo3 Sb12 La0.4 FeCo3 Sb12 La0.75 Fe3 CoSb12 La0.75 Fe3 CoSb12

0.8 3.9 0.8 3.9 6.7 0.8 3.9

p p n n n p p

8 × 10−4 9 × 10−4 2.0 × 10−2 1.1 × 10−2 8.2 × 10−3 1.5 × 10−3 1.2 × 10−3

1.3 1.9 5.2 1.1 – 3.0 5.0

× × × ×

1020 1020 1019 1020

× 1020 × 1020

Mobility (cm2 V−1 s−1 ) 61 36 6.7 5.0 – 16 10

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which is consistent with previous reports [17,18]. The results of EPMA show that all the samples are homogeneous and their compositions are very close to the nominal ones. In addition, we noted a small number of silicon oxide and lanthanum oxide in some of the long time ball-milled samples. Average grain sizes of the samples are listed in Table 1. Typical fractured surfaces of La0.4 FeCo3 Sb12 having different grain size of about 0.8, 3.9 and 6.7 ␮m are shown in Fig. 2. Table 1 summarizes some electrical transport properties of the samples at RT. Measured electrical resistivity of FeCo3 Sb12 is quite comparable to the reported data [18].

Compared with binary CoSb3 (∼1018 cm−3 ), the carrier concentrations of the alloyed skutterudites are one to two orders of magnitude higher. La0.4 FeCo3 Sb12 shows n-type conductivity with a relatively low carrier concentration among the investigated three compositions. La0.75 Fe3 CoSb12 and FeCo3 Sb12 possess p-type conductivity and their carrier concentrations are higher than that of La0.4 FeCo3 Sb12 . This is in agreement with an analysis on the effect of Fe/Co ratio and rare-earth content on the conductivity type of CoSb3 [1,19]. Carrier mobility is high for the unfilled sample and low for the two La-filled samples as a general trend. For each composition, the carrier mobility is seen to be large for the sample having small grains, which is contradictory to the results on binary CoSb3 [15]. Fig. 3 shows the temperature dependence of electrical resistivity and Seebeck coefficient of the samples having different grain sizes. The electrical resistivity of the n-type La0.4 FeCo3 Sb12 is almost one order of magnitude higher than those of the other two compositions at RT and decreases with increasing temperature, showing a semiconductor behavior (Fig. 3(a)). The electrical resistivities of La0.75 Fe3 CoSb12 and FeCo3 Sb12 increase when temperature increases. Seebeck coefficient is positive for La0.75 Fe3 CoSb12 and FeCo3 Sb12 , and is negative for La0.4 FeCo3 Sb12 (Fig. 3(b)), which is in accordance with the results of Hall measurement. For the two La-filled

Fig. 2. Typical fractured surfaces of the hot-pressed La0.4 FeCo3 Sb12 , showing different grain size: (a) 0.8 ␮m, (b) 3.9 ␮m, and (c) 6.7 ␮m.

Fig. 3. Electrical resistivity and Seebeck coefficient as a function of temperature for the investigated samples with different grain size.

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skutterudites, samples having a larger grain size show lower electrical resistivity and higher Seebeck coefficient over the measured temperature range. However, due to enhanced thermal vibration at high temperature, this difference is quite noticeable at RT temperature and weakens at high temperatures for the electrical resistivity (Fig. 3(a)). Moreover, the grain size is seen to have a larger effect on the electrical resistivity and Seebeck coefficient in the two La-filled samples than in the unfilled sample. The electrical resistivity and Seebeck coefficient of the unfilled skutterudite FeCo3 Sb12 are almost independent of the grain size (Fig. 3). Dependence of power factor (S2 /ρ) on grain size at three representative temperatures is shown in Fig. 4. The power factors of the three compositions increase with temperature. The two p-type samples possess a higher power factor than the n-type samples do. Since the electrical resistivity

Fig. 5. (a) Thermal conductivity κ as a function of temperature and (b) room temperature lattice thermal conductivity κg as a function of grain size, showing weak dependence on grain size.

Fig. 4. Dependence of power factors of the samples as a function of grain size at (a) RT, (b) 473 K, and (c) 773 K.

decreases and Seebeck coefficient increases with an increase in grain size for the La-filled samples, the power factor increases as a function of increasing grain size over the measured temperature range. However, the power factor is almost independent of grain size for the unfilled sample, which even decreases slightly when the grain size changes from 0.8 to 3.9 ␮m. This will be discussed later. Fig. 5(a) shows the temperature dependence of thermal conductivity of all the investigated samples, compared with that of binary CoSb3 [20]. The effect of Fe substitution and La doping on lowering the thermal conductivity is clear from the plot. The La-filled samples show a further decrease in thermal conductivity in addition to the effect from Fe substitution compared with the unfilled ones. Fig. 5(b) compares lattice thermal conductivity of all the samples at RT. Lattice thermal conductivity κg is estimated by subtracting the electronic contribution part κe from the overall measured thermal conductivity κ = κe + κg , according to the Wiedemann–Franz law κe = LσT , where L is the Lorenz number (2.0 × 10−8 V2 K−2 [13]). As shown in Fig. 5(b), there is very weak dependence of lattice thermal conductivity on grain size for the investigated samples within the

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range of grain size considered in this study. This is quite different from the situation in binary CoSb3 . After Fe substitution and La doping in CoSb3 , carrier concentration of the skutterudite compound is increased [12], which is also shown in the present investigation. Anno et al. [9] point out that the lattice thermal conductivity of doped CoSb3 decreases when the carrier concentration increases. Following a theory of relaxation times on phonon based on the Debye model, it is found that the coupling of point-defect scattering introduced by doping with the electron–phonon scattering is the major contribution to the reduced lattice thermal conductivity [14]. For the La-filled skutterudite compounds, the rattling of rare-earth atoms around their equilibrium positions is another major contribution to the reduced lattice thermal conductivity. This is estimated to account for perhaps 70% of the thermal resistivity [21]. According to the theory, each scattering process can be characterized by the respective relaxation time [22–24]. While it is difficult to estimate the relaxation time of the resonant scattering by the rare-earth atoms, the relaxation time of electron–phonon scattering τ EP can be estimated as [23] (for T = θ): −1 = τEP

n2c e2 ν2 ρ NkB θα

(1)

where nc is the carrier concentration, e is the electronic charge, ν is the phonon velocity (4.59 × 105 cm s−1 [9]), ρ is the electrical resistivity, N is the number density of atoms, θ is the Debye temperature (θ = 307 K for skutterudite compound [23]), kB is the Boltzmamm constant, α = 16/(31/2 π)(νm∗ δ/¯h)2/3 , m∗ is the carrier effective mass, h ¯ = h/2π, h is the Planck’s constant and δ is the atomic size determined by the cube root of the atomic volume. Taking the experimental values in the present investigation and the data in literature for the binary CoSb3 [15], the electron–phonon relaxation rates are calculated, as shown in Table 2. For grain boundary scattering, the relaxation time τ B can be estimated as [24] ν (2) τB−1 = l where l is the average grain size. Assuming l is in the range of 1–10 ␮m and taking ν from the literature [9], thus τ B is on the order of 108 to 109 s−1 , which is two orders of magnitude lower than that of electron–phonon scattering listed in Table 2 Calculated electron–phonon scattering relaxation time of the investigated samples Sample

Average grain size (␮m)

1/τ EP (1011 s−1 )

FeCo3 Sb12 FeCo3 Sb12 La0.4 FeCo3 Sb12 La0.4 FeCo3 Sb12 La0.75 Fe3 CoSb12 La0.75 Fe3 CoSb12 CoSb3 [15]

0.8 3.9 0.8 3.9 0.8 3.9 0.9–7.9

2.34 4.21 1.43 0.85 5.98 5.03 0.02

Fig. 6. Dependence of calculated ZT on grain size for the three samples at RT and 473 K.

Table 2, indicating additional scattering from grain boundary is almost negligible in the present case. However, this τ B is comparable to the electron–phonon scattering rate for the binary CoSb3 . This explains why grain size has a larger effect on the binary CoSb3 than on the presently investigated skutterudite compounds. Calculated ZT values are shown in Fig. 6. Similar to the results of power factor, the ZT values increase with grain size for the La-filled samples and those of the unfilled samples are almost independent of the grain size. La0.75 Fe3 CoSb12 displays the highest ZT among the investigated samples. Since the thermal conductivity is almost independent of the grain size for these doped skutterudite compounds, the effect of grain size on the thermoelectric performance is mainly dependent on the electrical transport properties. When grain size increases, the electrical resistivity decreases because scattering electrons from grain boundary is reduced. This effect is clearly seen at low temperature and in the samples having a low carrier concentration. The increase in the absolute value of Seebeck coefficient with increasing grain size may be attributed to impurities. As mentioned in the above analysis, point defect scattering becomes dominant in the alloyed skutterudite compounds. In general, the Seebeck coefficient of a homogeneous materials is given by [25] S∝±

kB [r − ln(nH )] e

(3)

where kB is the Boltzmann’s constant, e is the elementary charge, r is the scattering parameter and nH is the carrier concentration. This equation indicates that the Seebeck coefficient fundamentally depends on the carrier concentration and the scattering parameter r (for acoustic phonon scattering, r = −1/2; for neutral impurity scattering, r = 0; for optical phonon scattering, r = 1/2 and for ionized impurity scattering, r = 3/2). Hall mobility measurement shows that the carrier mobility decreases with increasing grain size (Table 1), implying an enhanced scattering due to decreased number of grain boundaries. According to Eq. (3), Seebeck coefficient may be increased with the increasing scattering

L. Yang et al. / Journal of Alloys and Compounds 375 (2004) 114–119

parameter r due to intensified impurities scattering. As grain boundary is the trapping site for the impurities and point defects, the number of impurities and point defects inside the grain tends to increase with decreasing grain boundaries. This may result in an increased Seebeck coefficient. Furthermore, the power factor is the integrated response for the electrical resistivity and the Seebeck coefficient, both of which increase with the grain size. Therefore, a relatively large grain size yields good thermoelectric properties for the La-filled skutterudite compounds. For the unfilled skutterudite compounds, as pointed out by Katsuyama et al. [18], the electrical transport properties are mainly affect by the inclusion of a second phase (e.g. FeSb2 ). This may explain the observation in the present investigation.

4. Conclusion One n-type (La0.4 FeCo3 Sb12 ) and two p-type (La0.75 Fe3 CoSb12 and FeCo3 Sb12 ) skutterudite compounds with different grain sizes (about 0.8, 3.9 and 6.7 ␮m) were prepared by hot pressing and their thermoelectric properties were studied. The results show: 1. Compared with the two p-type compounds, the electrical resistivity of the n-type compound is almost one order of magnitude higher at RT. For the two La-filled compounds, the electrical resistivity decreases and the absolute value of Seebeck coefficient increase when the average grain size of the sample increases. However, the electrical resistivity and Seebeck coefficient of the unfilled compound is almost independent of grain size. 2. Thermal conductivities of the samples are much lower than that of binary CoSb3 . The two La-filled samples show the lowest thermal conductivity among the investigated samples. Lattice thermal conductivity of the samples is found to be insensitive to the grain size. 3. For the La-filled skutterudite compounds, calculated ZT values increase with grain size indicating a relatively large grain size yields good thermoelectric properties.

Acknowledgements This work was supported by the National Natural Science Foundation of China (grant no. 59902003). Parts of

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the measurements were carried out at Kyoto University, Japan.

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