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Metallurgical and thermoelectric properties in Co1−xPdxSb3 and Co1−xNixSb3 revisited
Journal of Alloys and Compounds 572 (2013) 43–48
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Metallurgical and thermoelectric properties in Co1xPdxSb3 and Co1xNixSb3 revisited E. Alleno ⇑, E. Zehani 1, O. Rouleau ICMPE-CMTR, UMR7182 CNRS – UPEC, 2-8 rue Henri Dunant, 94320 Thiais, France
a r t i c l e
i n f o
Article history: Received 1 February 2013 Received in revised form 21 March 2013 Accepted 22 March 2013 Available online 29 March 2013 Keywords: Thermoelectricity Skutterudite Band gap Effective mass Power factor
a b s t r a c t Polycrystalline thermoelectric Co1xMxSb3 (M = Ni, Pd) skutterudites have been synthesized by melting, annealing, and spark plasma sintering. The solubility limit of Pd and Ni are determined to be respectively xmax = 0.03 and xmax = 0.09. The density of states effective masses range between 2.0m0 and 4m0 in Co1xPdxSb3 and Co1xNixSb3. These values are consistent with the effective band mass (0.3m0) and the degeneracy number Nv = 36 derived from band structure calculations. Power factor measurements and calculations in Co1xPdxSb3 show that at 300 K, the optimum electron concentration would be [n]opt = 1.4 1020 cm3, slightly beyond the electron concentration (1.1 1020 cm3) of the solubility limit composition Co0.97Pd0.03Sb3. The maximum power factor is effectively obtained for the composition Co0.97Pd0.03Sb3 and reaches 4.3 mW m1 K2 at 700 K. An activation energy, which can correspond to the intrinsic gap eG = 0.13 eV, is determined in Co0.98Ni0.02Sb3. Co1xNixSb3 displays smaller electronic mobilities than in Co1xPdxSb3 leading to smaller power factors. Best properties (3.4 mW m1 K2) are observed at 700 K in Co0.95Ni0.05Sb3–Co0.94Ni0.06Sb3. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Co1xMxSb3 (M = Ni, Pd) skutterudites are n-type thermoelectric materials [1–5]. In these solid solutions, Ni and Pd play the role of electron donors and their composition x controls the electrons concentration. They crystallize in the cubic CoAs3 structure type (Im3) with Sb octahedra surrounding the Co/M atoms forming a cubic network. They display thermoelectric power factors as high as a2/ q 3 mW m1 K2 at 300 K and figure of merit as high as ZT = a2T/ qk = 0.8 at 800 K [3] (a the Seebeck coefficient, q the resistivity and k the thermal conductivity). Despite these high values of ZT, their thermal conductivity is in the range 6–9 W m1 K1 at 300 K and it is dominated by the phonon contribution. The Co1xMxSb3 (M = Ni, Pd) do not display the best figure of merit among n-type skutterudites: partially filled skutterudites AyCo4Sb12 (A = alkaline, alkaline-earth, rare earth) display values of figure of merit at 800 K ranging from ZT = 0.4 in Nd0.1Co4Sb12 [6], ZT = 1.3 in Yb0.25Co4Sb12 [7] and up to ZT = 1.7 in multi-filled Ba0.08La0.05Yb0.04Co4Sb12 [8]. However, because of their apparent simplicity and reduced sensitivity to oxidation, the Co1xMxSb3 (M = Ni, Pd) have more often been considered as candidate for nanostructuring (reduced size grain and/or second phase nanoprecipitates) [5,9–12]. In all these
⇑ Corresponding author. Tel.: +33 1 49 78 12 37; fax: +33 1 49 78 12 03. E-mail address: [email protected] (E. Alleno). Present address: GEMaC, Université Versailles-Saint-Quentin, 45, avenue des Etats Unis – Bâtiment Fermat, 78035 Versailles, France. 1
0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.03.206
cases, the objective of nanostructuring was to reduce the lattice thermal conductivity and not to affect the power factor. This last quantity is determined by the electron concentrations which is controlled by the quantity of dopant (M = Ni, Pd). It is thus important to know in detail the Co1xMxSb3 (M = Ni, Pd) systems to chose the composition corresponding to the largest power factor, prior to any nanostructuring operation. If the Co1xNixSb3 system has been studied by several groups [3–5], the Co1xPdxSb3 system has been studied by only two groups [1–3] who reported a limited set of temperature data [1]. We thus re-examined the metallurgy and electronic transport properties of Co1xPdxSb3 and compared it to Co1xNixSb3. 2. Experiment The Co1xMxSb3 (M = Pd, Ni) polycrystalline samples (3.5 g) were prepared by melting the elements (Co 99.99%, Pd 99.9%, Ni 99.99%, Sb 99.999%) in stoichiometric quantity at 1100 °C during 24 h and annealing at 820 °C during 96 h in vitreous carbon crucibles sealed in a quartz tube. No mass loss larger than 1 mg could be detected. The buttons were finely crushed in an agate mortar and passed through a 36 lm sieve. The powders were then densified by SPS in graphite dies and punches for 10 min at 620 °C under 50 MPa in a SPS Syntex DR SINTER Lab 515S system. Disk- and bar-shaped samples were cut with a diamond saw for transport measurements. The density of the compacts was determined by measuring the geometrical volume of polished disk-shaped samples cut for transport measurements: its relative value was in every case larger than 98%. The samples were individually characterized by X-ray powder diffraction (XRD) using the Rietveld method. The main refined parameters were the Sb (0, y, z) coordinates and the lattice parameter a. A good accuracy, better than 4 104 Å, was achieved by making use of silicon NIST SRM 640 as an internal reference. Secondary phases percentages are X-ray lines
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intensity ratios: attempts to Rietveld – refine these phases did not improved the accuracy of these percentages, given their small amount. Hot temperature resistivity (van der Pauw, four-probe) and Seebeck coefficient measurements were carried out between 300 K and 800 K with a thermal gradient DT 2 K using a homemade apparatus. The estimated relative uncertainties on the measurement of a and q are respectively 5% and 5%, giving a relative uncertainty of 11% for the power factor (root of the sum of square of each independent uncertainty). The Hall effect measurements were carried out at 300 K in a PPMS (DC mode) in the van der Pauw geometry by varying the magnetic field between 5T and +5T. The Hall coefficient is then given by the relation RH = t DU/iDB with t the sample thickness, i the current and DU/DB the slope of the Hall voltage versus magnetic field. The electron concentration is then derived from the relation [n] = 1/e RH with e the electron charge, making the assumption that a single parabolic band describes well these systems. The Hall mobility (l) can be expressed as a function of RH and q: l = RH/q.
Fig. 1 (top panel) shows the lattice parameters (a) of the Co1xPdxSb3 series of samples as a function of the nominal composition x. A linearly increases in Co1xPdxSb3 until the value x = 0.027 ± 0.006 is reached. For larger x, a still linearly increases with x but with a much smaller slope. Fig. 1 (bottom panel) shows the Hall electron concentration ([n]) as a function of x in Co1xPdxSb3. It also linearly increases as a function of x until x = 0.030 ± 0.003 is reached where it linearly decreases. Both these central values and confidence intervals derived from the a(x) and [n](x) data are consistent but because of its smaller uncertainty, we favour the Hall concentration result which indicate that the solubility limit of Pd in CoSb3 is xmax = 0.030. Tashiro et al. [2] and Anno et al. [3] respectively proposed 0.04 and 0.05 as the solubility limit of Pd in CoSb3. Our work shows that these former values are significantly overestimated. The effect of the solubility limit is also reflected in the content of the secondary phases. For x 6 0.03, 1–2% CoSb2 and 0.2% metastable cubic Sb [13] are typical impurity phases found in the corresponding X-ray pattern. For x P 0.04, in addition to the already mentioned secondary phases, increasing
quantities of rhombohedral Sb (3% for x = 0.07) and cubic PdSb2 (1.5% for x = 0.07) could be detected. It is currently difficult to interpret the linear decrease of [n] for x larger than the solubility limit because of the change in the nature of the secondary phases which can contribute to the Hall signal. Rhombohedral Sb is a semi-metal with equal numbers of electrons and holes if pure, but with anisotropic and unequal mobilities of the two types of charge carriers [14]. PdSb2 is reported as a metal with unknown type of dominant charge carriers [15]. Despite their small concentration, the two extra phases can significantly affect the apparent electron concentration since Sb displays large charge carrier mobilities (0.1–4 103 cm2 V1 s1) and PdSb2 should display a large charge carrier concentration. Nonetheless, indications on the intrinsic electron concentration beyond the solubility limit in Co1xPdxSb3 can be derived from the Seebeck coefficient displayed in Fig. 2. It clearly saturates for x > 0.03, which allows excluding significant electron concentration change arising from intrinsic changes in the chemical formula of Co1xPdxSb3 such as interstitials or vacancies in this Pd concentration range. It is thus difficult to provide a well defined reason for the small increase of a(x) for x > 0.03 if no drastic chemical changes occur. We can only speculate on micro-structural effect such as micro-stress arising from the secondary phases, which could indeed be at play in this case. The lattice parameter of Co1xNixSb3 shown in Fig. 1 (top panel) also linearly increases with the composition x until x = 0.091 ± 0.005 is reached. For larger Ni concentration, the lattice parameter saturates. A break point is also found at x = 0.092 ± 0.005 in the electron concentration versus x curve shown in Fig. 1 (bottom panel). The solubility limit is thus xmax = 0.091 ± 0.005. This time, our value is in line with previous values published in the literature: xmax = 0.1 was reported in Ref. [3] and in Ref. [5]. The nature of the secondary phases also changes at xmax. For x 6 0.09, 0–1% CoSb and 0.2% metastable cubic Sb [13] are typical secondary phases while for x P 0.12, from 1% to 2% rhombohedral Sb and from 1.5% to 5% NiSb2 are additional impurity phases. Contrary to Co1xPdxSb3, a(x) saturates in Co1xNixSb3
Fig. 1. Top panel: lattice parameter of the series Co1xPdxSb3 and Co1xNixSb3 as a function of the composition x. The solid lines are linear regression to the experimental data (see text). Bottom panel: Room temperature Hall electron concentration in Co1xPdxSb3 and Co1xNixSb3 as a function of the composition x. Please note the different vertical scales for Co1xPdxSb3 and Co1xNixSb3.
Fig. 2. Electronic transport properties as a function of temperature in Co1xPdxSb3. Top panel: Seebeck coefficient; middle panel: electrical resistivity; bottom panel: power factor. Please note the logarithmic scale for the resistivity.
3. Results and discussion 3.1. Lattice parameter and electron concentration
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beyond xmax(Ni), indicating that no strong changes in the chemical composition or the microstructure occur beyond the solubility limit. The apparent electron concentration does not saturate beyond xmax(Ni) and similarly to Co1xPdxSb3, this most likely arises from the change in the nature of the secondary phases such as semimetallic Sb and semiconducting NiSb2 [15] which can also contribute to the Hall signal. 3.2. Room temperature electronic transport properties Table 1 gathers electronic transport properties such as the Hall electron concentration, resistivity, Seebeck coefficient and mobility measured at 300 K in Co1xPdxSb3. For x 6 0.03, the electron concentration [n] increases proportionally with x. The proportionality factor corresponds to a fraction of 0.4 electrons per Pd atoms, which is exactly the value determined in Ref. [2]. The absolute value of the Seebeck coefficient (a) and the resistivity (q) decreases with x and [n] in accordance with Boltzman’s theory of transport. The most convenient comparison with literature is obtained by calculating the density of states effective mass m from the values of [n] and a. Assuming a single parabolic band and interaction with acoustic phonon as the dominant charge scattering mechanism [3], the Seebeck coefficient is related to the reduced Fermi energy h i (g) by the expression [16]: a ¼ keB 2 FF 12 ððggÞÞ g with kB, the Boltzman constant and Fn(g), Fermi integrals. The electron concentra 32 BT F 1 ðgÞ with T the tion can be expressed as: ½n ¼ 4p 2mk h2 2
temperature and h the Planck’s constant. The results of the density of states effective mass calculation are gathered in Table 1. Our values m = 2.5m0 (m0 is the free electron mass) for [n] = 6.4 1019 cm3 and m = 2.9m0 for [n] = 11 1019 cm3 compare very well with m = 2.3m0 for [n] = 6.2 1019 cm3 and m = 2.9m0 for [n] = 14 1019 cm3 as published by Anno et al. [3] and with m = 3m0 for [n] = 10 1019 cm3 as published by Caillat et al. [1]. This confirms the consistency of our Hall effect and Seebeck coefficient measurements. Table 1 also shows that the mobility decreases with increasing [n], as expected when the main scattering mechanism is acoustic phonon [1]. Our values of mobility are larger by at least 20% than the values reported in Ref. [3]: this most likely arises from a better shaping of our samples. For x > 0.03, the Seebeck coefficient saturates while the Hall concentration and the resistivity respectively decreases and increases. As previously discussed, the secondary phases Sb and PdSb2 can affect not only the apparent electron concentration but also the resistivity and it is difficult to draw a conclusion on the variations of these two transport coefficients. The electronic transport properties at 300 K of Co1xNixSb3 are reported in Table 2. For x 6 0.09, the electron concentration linearly increases with x with a slope of 0.6 electrons per Ni atoms, in fair agreement with the 0.5 electrons per Ni atom which can be extracted from the data of reference [3]. The increase of the electron concentration leads to the expected decrease of the resistivity and of the Hall mobility and to the expected decrease of the absolute value of the Seebeck coefficient. Again, assuming a single parabolic band, we derived the density of states effective mass. The obtained values m = 3.3m0 for [n] = 0.7 1020 cm3 and m = 3.8m0 for [n] = 3.4 1020 cm3 are consistent with the values m = 3.2m0 for [n] = 1.2 1020 cm3 and m = 3.7m0 for [n] = 2.8 1020 cm3 as published by Anno et al. [3]. According to band structure calculations by Sofo and Mahan [17], the bottom of the conduction band of CoSb3 is formed by a nonparabolic band of light electrons and a triply degenerate (orbital degeneracy) parabolic band of heavy electrons. The density of states effective masses derived from our measurements on Co1xPdxSb3 and Co1xNixSb3 are in the range 2.5–4m0 while the
band effective mass calculated by Sofo and Mahan [17] for the heavy electron conduction band in CoSb3 is 0.35m0. The density of states effective mass (m) is related to the band effective mass (mb) by the number Nv of degeneracy of the band which includes orbital degeneracy and degeneracy imposed by the symmetry of the Brillouin zone: m = mb Nv2/3 [18,19]. Chaput et al. [20] indeed showed by using the same calculation technique as Sofo and Mahan (full potential augmented plane wave and generalized gradient approximation) that the heavy electron band can give rise to 12 electron pockets, situated along CN in the first Brillouin zone, when [n] 1020 cm3. Combining the orbital degeneracy and the degeneracy imposed by the Brillouin zone symmetry yields Nv = 3 12 = 36. From this, a range of experimental band effective masses mb 2.5m0–4m0/(36)2/3 0.23m0–0.37m0 can be obtained, in good agreement with the theory. This elementary calculation assumes that the contribution to the Seebeck coefficient of the light electron band can be neglected. Another comparison between experiment and theory can be obtained by using some of the results of Chaput et al. [20]. From their band structure calculation, they derived the Seebeck coefficient as a function of [n] and temperature with the assumption that the bands are rigid and the relaxation time of the electrons does not depend on energy (s = s0). Some of their calculations are reported in Tables 1 and 2. There is a good agreement between the theoretical and the experimental Seebeck values in the case of Co1xPdxSb3 (Table 1). On the other hand, the agreement between the theoretical and the experimental Seebeck values in the case of Co1xNixSb3 is only fair (Table 2) because the absolute experimental values are significantly larger. 3.3. Temperature dependent electronic transport properties Fig. 2 shows the Seebeck coefficient, the resistivity and power factor for Co1xPdxSb3 (0.01 < x < 0.07, nominal) as a function of temperature. At every temperature, the Seebeck coefficient of the Co1xPdxSb3 samples with x P 0.03 is identical within experimental uncertainty. As already discussed, this corresponds to the solubility limit xmax = 0.03. When x < 0.03, in the temperature range 300–700 K, the absolute value of the Seebeck coefficient decreases with increasing x and [n]. For all x, the values of the Seebeck coefficient decreases with temperature, as is expected in a degenerate semiconductor, until the minimum arising from the minority carriers conduction regime is reached. This minimum shifts to higher temperature (from 540 K to 630 K) in agreement with the increase of the electron concentration. The resistivity varies consistently with x, [n] and the Seebeck coefficient. Its thermal variations are also typical of a degenerate semiconductor with metallic behaviour at ‘‘low’’ temperature until the minority carrier conduction is activated at high temperature. An estimation of the activation energy is difficult because we did not measure at temperatures high enough. At every temperature, the power factor increases with x until
Table 1 Room temperature values of the palladium concentration, Hall electron concentration, Seebeck coefficient, effective mass, resistivity and Hall mobility in Co1xPdxSb3 as a function of the composition x. x 0.01 0.02 0.023 0.03 0.04 0.07 Ref. [20]
[n] (1019 cm3)
a (lV K1)
m
2.5 6.4 8.2 10.9 10.2 8.6 5.7
261 220 196 193 182 191 223
2.0 2.5 2.4 2.9 – – –
q
l
(105 X m)
(cm2 V1 s1)
2.971 1.583 1.187 1.057 1.080 1.216 –
83 62 64 55 57 59 –
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Table 2 Room temperature values of the nickel concentration, Hall electron concentration, Seebeck coefficient, effective mass, resistivity and Hall mobility in Co1xNixSb3 as a function of the composition x. x 0.02 0.03 0.045 0.06 0.075 0.09 0.12 0.15 Ref. [20]
[n] (1020 cm3)
a (lV K1)
m
0.7 1.5 2.5 3.4 4.4 5.5 12.0 20.9 1.5
243 207 144 133 113 101 88 74 187
3.3 3.8 3.5 3.8 3.9 4.4 – – –
q
l
(105 X m)
(cm2 V1 s1)
4.051 2.803 1.918 1.497 1.178 1.006 0.880 0.733 –
21 15 13 11 12 11 6 4 –
x = xmax is reached and then decreases for x > xmax. The maximum power factor at 700 K is indeed obtained for the composition Co0.97Pd0.03Sb3 and amounts to 4.3 mW m1 K2. A question arises from this result: is the maximum power factor yet reached or not when x = xmax? We calculated the power factor at 300 K as a function of [n] using the same formalism and assumption as the Seebeck coefficient: one parabolic band and charge scattering dominated by interactions with acoustic phonon. The electrical conductivity then given by the relation [16]: 3=2is 2 r ¼ 8pe3 s0 h22 ðm Þ1=2 kB TF 0 ðgÞ where s0 is the prefactor describing the energy dependence of the relaxation time s = s0e1/2. Notice that s0 is not a time since it is expressed in J1/2 s. Taking an average effective mass m = 2.7m0 over the electron concentration range 1018–1021 cm3, s0 was adjusted to two values: with the first one (s0 = 0.85 1023 J1/2 s), the calculated resistivity at 300 K matches our experimental value for x = 0.01 or [n] = 2.5 1019 cm3 while the second one (s0 = 0.62 1023 J1/2 s) allows matching the resistivity data of literature [1,3]. The two calculated curves are displayed in Fig. 3 and they compare very well with our experimental data and with literature respectively. Within this formalism, the optimum power factor should be reached for [n]opt = 1.4 1020 cm3 and amount to PFopt = 3.5 mW m1 K2. [n]opt corresponds to xopt = 0.037, which is close but significantly larger than xmax. Co0.97Pd0.03Sb3 can thus be considered as the accidental optimum composition of this system. In Ref. [3], maximum Z = 6 104 K1 at 300 K had been reported for Co0.95Pd0.05Sb3,
Fig. 3. Experimental (symbols) and calculated (lines) power factor in Co1xPdxSb3 and Co1xNixSb3 as a function of the electron concentration. Data from literature extracted from Refs. [1–4].
which we showed to be non-existant.The Seebeck coefficient is shown in Fig. 4 for Co1xNixSb3 (0.01 6 x 6 0.15 nominal). For all x, the absolute value of the Seebeck coefficient increases with temperature until the minority carriers conduction regime is reached, similarly to what is observed in Co1xPdxSb3. This leads to a minimum of the Seebeck value which shifts to higher temperature (from 500 K for x = 0.02 to 700 K for x = 0.09) when the electron concentration increases. At any temperature, the resistivity presented in Fig. 5 monotonously decreases with x in consistency with the variations of [n] and the Seebeck coefficient. However, the behaviour of the resistivity plotted in Fig. 5 as a function of temperature, changes with x. For x P 0.12, a metallic behaviour is observed. When x 6 0.06, the resistivity shows an activated behaviour in the temperature range [300–800 K]. For x = 0.075 and x = 0.09, the resistivity varies nonmonotonously and exhibits a maximum at 340 K and 410 K respectively. The shift with x of this maximum suggests that such a maximum also exists at temperatures lower than 300 K when x 6 0.06. Such maximum in q(T) points to the possible existence of a shallow donor level situated below the conduction band in Co1xNixSb3 and giving rise to minority carriers effect in the temperature range 200–400 K, depending on x. Low temperature measurements would be necessary to give more substance to this donor level. Fig. 6 shows a plot of Log(q) versus 1/T for x = 0.02. Only this sample displays a high temperature activation regime, which can be safely fitted: the activation energy which is derived is eAH = 0.066 eV. The value 2 eAH = 0.13 eV is close to the calculated value of the intrinsic gap eG = 0.14 eV reported in references [20,21] and can be ascribed to the gap. An estimate of the intrinsic gap can be obtained for Co1xPdxSb3 by scaling the gap of Co1xNixSb3 with the value of the maximum of the Seebeck coefficient arising from minority carriers’ effect and its temperature. Goldsmid and Sharp indeed showed [22] that the gap energy is close to 2eamaxTmax where amax is the value of the maximum of the Seebeck coefficient and Tmax its temperature. Co0.98Pd0.02Sb3 and Co0.98Ni0.02Sb3 roughly display
Fig. 4. Seebeck coefficient (top panel) and power factor (bottom panel) a function of temperature in Co1xNixSb3.
E. Alleno et al. / Journal of Alloys and Compounds 572 (2013) 43–48
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Fig. 7. Power factor at 300 K, 700 K and averaged over [300–700 K] as a function of the composition x in Co1xNixSb3.
Fig. 5. Electrical resistivity a function of temperature in Co1xNixSb3.
Fig. 6. Logarithmic plot of the electrical resistivity as a function of the inverse temperature in Co0.98Ni0.02Sb3.
from the literature [3,4]. An average effective density of states mass m = 3.8 m0 was chosen and s0 was adjusted to s0 = 0.33 1023 J1/2 s in order to match the experimental data for [n] 1 1020 cm3. The agreement between this calculation and the experiments is not very good since it predicts a maximum power factor at T = 300 K for [n] 2.4 1020 cm3 while it is found experimentally for [n] 0.7 1020 cm3. We speculate that the possible shallow donor level combined with the nonparabolicity of the band, makes the transport properties deviate from the simple single band model in the temperature range 200–400 K. Fig. 3 also shows that the power factors in Co1xNixSb3 are smaller than in Co1xPdxSb3 in the temperature range 300–700 K. The main reason for these less favourable properties is the smaller values of the mobility in Co1xNixSb3 than in Co1xPdxSb3. On the other hand, Figs. 4 and 7 show that the power factor at 700 K is not maximum for x = 0.02 but rather when x = 0.06. A better estimation of the thermoelectric properties of Co1xNixSb3 as a material for electricity generation is the average power factor over a broad temperature range such as 300–700 K. This quantity is also plotted in Fig. 7. Within experimental uncertainty, the average power factor is independent of the nickel concentration for 0.02 < x < 0.09 or at worse, shows a very shallow maximum around x = 0.05. The composition range Co0.95Ni0.05Sb3–Co0.94Ni0.06Sb3 thus displays the largest average power factor (2.45 mW m1 K2) and the largest power factor (3.4 mW m1 K2) at 700 K. This is consistent with literature since maximum Z = 2 104 K1 at 300 K had been reported for Co0.95Ni0.05Sb3 [3] and maximum ZT = 0.5 at 700 K had been reported for Co0.94Ni0.06Sb3 [5]. 4. Summary
the same electron concentration [n] = 6–7 1019 cm3. The Seebeck coefficient reaches respectively 295 lV K1 and 305 lV K1 in these samples at 560 K and 520 K. The scaling relation eG ðPdÞ ¼ eG ðNiÞ 560 295 yields eG(Pd) = 0.14 eV. Both 520 305 Co0.98Pd0.02Sb3 and Co0.98Ni0.02Sb3 thus display close value of their intrinsic gap. The power factor as a function of temperature and as a function of the nickel concentration is shown for Co1xNixSb3 respectively in Figs. 4 and 7. At room temperature, the power factor monotonously decreases with x, indicating that the optimum value is obtained for nickel concentrations x < 0.02. These room temperature values of the power factor are plotted as a function of [n] in Fig. 3 and compared to the literature [3,4]. They indicate that the x = 0.02 sample is close to the optimum value for this temperature. Using the same formalism as for Co1xPdxSb3, a theoretical curve of the power factor was calculated for comparing to the present data and to those
The solubility limit of palladium and nickel in Co1xPdxSb3 and Co1xNixSb3 is respectively found at x = 0.03 and x = 0.09. The density of states effective masses derived from room temperature Hall effect and Seebeck measurements respectively range between 2.0m0 and 2.9m0 and 3.3m0 and 4.4m0 in Co1xPdxSb3 and Co1xNixSb3. These values are consistent with the effective band mass (0.3m0) and the degeneracy number Nv = 36 obtained by DFT calculations. Power factor measurements and calculations in Co1xPdxSb3 show that at 300 K, the optimum electron concentration is [n]opt = 1.4 1020 cm3 and that solubility limit composition Co0.97Pd0.03Sb3 reaches 1.09 1020 cm3, close to the optimum electron concentration. The maximum power factor at 700 K is also obtained for the composition Co0.97Pd0.03Sb3 and amounts to 4.3 mW m1 K2. Resistivity measurements in Co0.98Ni0.02Sb3 allow for the determination of an activation energy, which can
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correspond to the intrinsic gap eG = 0.13 eV. A smaller electronic mobility leads to smaller power factors in Co1xNixSb3 than in Co1xPdxSb3. Best properties (3.4 mW m1 K2) are observed at 700 K in Co0.95Ni0.05Sb3–Co0.94Ni0.06Sb3. Acknowledgement The authors thank B. Lenoir (Institute Jean Lamour, Nancy) for fruitful discussions. References [1] T. Caillat, A. Borshchevsky, J.P. Fleurial, J. Appl. Phys. 80 (1996) 4442. [2] H. Tashiro, Y. Notohara, T. Sakakibara, H. Anno, K. Matsubara, in: 16th International Conference on Thermoelectrics. 26–29 Auguest 1997 Dresden, Germany, 1997, p. 326. [3] H. Anno, K. Matsubara, Y. Notohara, T. Sakakibara, H. Tashiro, J. Appl. Phys. 86 (1999) 3780. [4] J.S. Dyck, W. Chen, J. Yang, G.P. Meisner, C. Uher, Phys. Rev. B 65 (2002) 115204. [5] S. Katsuyama, M. Watanabe, M. Kuroki, T. Maehala, M. Ito, J. Appl. Phys. 93 (2003) 2758. [6] V.L. Kuznetsov, L.A. Kuznetsova, D.M. Rowe, J. Phys.: Condens. Matter. 15 (2003) 5035. [7] Z. Xiong, X. Chen, X. Huang, S. Bai, L. Chen, Acta Mater. 58 (2010) 3995.
[8] X. Shi, J. Yang, J.R. Salvador, M. Chi, J.Y. Cho, H. Wang, S. Bai, J. Yang, W. Zhang, L. Chen, J. Am. Chem. Soc. 133 (2011) 7837. [9] L. Bertini, C. Stiewe, M. Toprak, S. Williams, D. Platzek, A. Mrotzek, Y. Zhang, C. Gatti, E. Müller, M. Muhammed, D.M. Rowe, J. Appl. Phys. 93 (2003) 438. [10] L. Bertini, G. Borot, K. Billquist, M. Christensen, C. Gatti, L. Holmgren, B.B. Iversen, E. Mueller, M. Muhammed, G. Noriega, A.E.C. Palmqvist, D. Platzek, D.M. Rowe, A. Saramat, C. Stiewe, M. Toprak, S.G.K. Williams, Y. Zhang, in: 22nd International Conference on Thermoelectrics ICT2003, La Grand Motte, France, August, 2003, p. 117. [11] C. Stiewe, L. Bertini, M. Toprak, M. Christensen, D. Platek, S. Williams, C. Gatti, E. Müller, B.B. Iversen, M. Muhammed, D.M. Rowe, J. Appl. Phys. 97 (2005) 044317. [12] Q.Y. He, Q. Hao, X.W. Wang, J. Yang, Y.C. Lan, X. Yan, B. Yu, Y. Ma, B. Poudel, G. Joshi, D.Z. Wang, G. Chen, Z.F. Ren, J. Nanosci. Nanotechnol. 8 (2008) 4003. [13] P. Villars, K. Cenzual, Pearson’s Crystal Data: Crystal Structure Database for Inorganic Compounds, ASM International, Materials Park, Ohio, USA, 2009– 2010. [14] S.J. Freedman, H.J. Juretschke, Phys. Rev. 124 (1961) 1379. [15] F. Hulliger, Nature 200 (1963) 1064. [16] G.S. Nolas, J. Sharp, H.J. Goldsmid, Thermoelectrics: Basic principles and new materials developments, Springer, Berlin, Heidelberg, New-York, 2001. [17] J.O. Sofo, G.D. Mahan, Phys. Rev. B 58 (1998) 15620. [18] G.D. Mahan, Solid State Phys. 51 (1998) 81. [19] Y. Pei, X. Shi, A. LaLonde, H. Wang, L. Chen, G.J. Snyder, Nature 473 (2011) 66. [20] L. Chaput, P. Pécheur, J. Tobola, H. Scherrer, Phys. Rev. B 72 (2005) 085126. [21] E.Z. Kurmaev, A. Moewes, I.R. Shein, L.D. Finkels’tein, A.L. Ivanovskii, H. Anno, J. Phys., Condens. Matter. 16 (2004) 979. [22] H.J. Goldsmid, J.W. Sharp, J. Electron. Mater. 28 (1999) 869.
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Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jalcom
Metallurgical and thermoelectric properties in Co1xPdxSb3 and Co1xNixSb3 revisited E. Alleno ⇑, E. Zehani 1, O. Rouleau ICMPE-CMTR, UMR7182 CNRS – UPEC, 2-8 rue Henri Dunant, 94320 Thiais, France
a r t i c l e
i n f o
Article history: Received 1 February 2013 Received in revised form 21 March 2013 Accepted 22 March 2013 Available online 29 March 2013 Keywords: Thermoelectricity Skutterudite Band gap Effective mass Power factor
a b s t r a c t Polycrystalline thermoelectric Co1xMxSb3 (M = Ni, Pd) skutterudites have been synthesized by melting, annealing, and spark plasma sintering. The solubility limit of Pd and Ni are determined to be respectively xmax = 0.03 and xmax = 0.09. The density of states effective masses range between 2.0m0 and 4m0 in Co1xPdxSb3 and Co1xNixSb3. These values are consistent with the effective band mass (0.3m0) and the degeneracy number Nv = 36 derived from band structure calculations. Power factor measurements and calculations in Co1xPdxSb3 show that at 300 K, the optimum electron concentration would be [n]opt = 1.4 1020 cm3, slightly beyond the electron concentration (1.1 1020 cm3) of the solubility limit composition Co0.97Pd0.03Sb3. The maximum power factor is effectively obtained for the composition Co0.97Pd0.03Sb3 and reaches 4.3 mW m1 K2 at 700 K. An activation energy, which can correspond to the intrinsic gap eG = 0.13 eV, is determined in Co0.98Ni0.02Sb3. Co1xNixSb3 displays smaller electronic mobilities than in Co1xPdxSb3 leading to smaller power factors. Best properties (3.4 mW m1 K2) are observed at 700 K in Co0.95Ni0.05Sb3–Co0.94Ni0.06Sb3. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Co1xMxSb3 (M = Ni, Pd) skutterudites are n-type thermoelectric materials [1–5]. In these solid solutions, Ni and Pd play the role of electron donors and their composition x controls the electrons concentration. They crystallize in the cubic CoAs3 structure type (Im3) with Sb octahedra surrounding the Co/M atoms forming a cubic network. They display thermoelectric power factors as high as a2/ q 3 mW m1 K2 at 300 K and figure of merit as high as ZT = a2T/ qk = 0.8 at 800 K [3] (a the Seebeck coefficient, q the resistivity and k the thermal conductivity). Despite these high values of ZT, their thermal conductivity is in the range 6–9 W m1 K1 at 300 K and it is dominated by the phonon contribution. The Co1xMxSb3 (M = Ni, Pd) do not display the best figure of merit among n-type skutterudites: partially filled skutterudites AyCo4Sb12 (A = alkaline, alkaline-earth, rare earth) display values of figure of merit at 800 K ranging from ZT = 0.4 in Nd0.1Co4Sb12 [6], ZT = 1.3 in Yb0.25Co4Sb12 [7] and up to ZT = 1.7 in multi-filled Ba0.08La0.05Yb0.04Co4Sb12 [8]. However, because of their apparent simplicity and reduced sensitivity to oxidation, the Co1xMxSb3 (M = Ni, Pd) have more often been considered as candidate for nanostructuring (reduced size grain and/or second phase nanoprecipitates) [5,9–12]. In all these
⇑ Corresponding author. Tel.: +33 1 49 78 12 37; fax: +33 1 49 78 12 03. E-mail address: [email protected] (E. Alleno). Present address: GEMaC, Université Versailles-Saint-Quentin, 45, avenue des Etats Unis – Bâtiment Fermat, 78035 Versailles, France. 1
0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.03.206
cases, the objective of nanostructuring was to reduce the lattice thermal conductivity and not to affect the power factor. This last quantity is determined by the electron concentrations which is controlled by the quantity of dopant (M = Ni, Pd). It is thus important to know in detail the Co1xMxSb3 (M = Ni, Pd) systems to chose the composition corresponding to the largest power factor, prior to any nanostructuring operation. If the Co1xNixSb3 system has been studied by several groups [3–5], the Co1xPdxSb3 system has been studied by only two groups [1–3] who reported a limited set of temperature data [1]. We thus re-examined the metallurgy and electronic transport properties of Co1xPdxSb3 and compared it to Co1xNixSb3. 2. Experiment The Co1xMxSb3 (M = Pd, Ni) polycrystalline samples (3.5 g) were prepared by melting the elements (Co 99.99%, Pd 99.9%, Ni 99.99%, Sb 99.999%) in stoichiometric quantity at 1100 °C during 24 h and annealing at 820 °C during 96 h in vitreous carbon crucibles sealed in a quartz tube. No mass loss larger than 1 mg could be detected. The buttons were finely crushed in an agate mortar and passed through a 36 lm sieve. The powders were then densified by SPS in graphite dies and punches for 10 min at 620 °C under 50 MPa in a SPS Syntex DR SINTER Lab 515S system. Disk- and bar-shaped samples were cut with a diamond saw for transport measurements. The density of the compacts was determined by measuring the geometrical volume of polished disk-shaped samples cut for transport measurements: its relative value was in every case larger than 98%. The samples were individually characterized by X-ray powder diffraction (XRD) using the Rietveld method. The main refined parameters were the Sb (0, y, z) coordinates and the lattice parameter a. A good accuracy, better than 4 104 Å, was achieved by making use of silicon NIST SRM 640 as an internal reference. Secondary phases percentages are X-ray lines
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intensity ratios: attempts to Rietveld – refine these phases did not improved the accuracy of these percentages, given their small amount. Hot temperature resistivity (van der Pauw, four-probe) and Seebeck coefficient measurements were carried out between 300 K and 800 K with a thermal gradient DT 2 K using a homemade apparatus. The estimated relative uncertainties on the measurement of a and q are respectively 5% and 5%, giving a relative uncertainty of 11% for the power factor (root of the sum of square of each independent uncertainty). The Hall effect measurements were carried out at 300 K in a PPMS (DC mode) in the van der Pauw geometry by varying the magnetic field between 5T and +5T. The Hall coefficient is then given by the relation RH = t DU/iDB with t the sample thickness, i the current and DU/DB the slope of the Hall voltage versus magnetic field. The electron concentration is then derived from the relation [n] = 1/e RH with e the electron charge, making the assumption that a single parabolic band describes well these systems. The Hall mobility (l) can be expressed as a function of RH and q: l = RH/q.
Fig. 1 (top panel) shows the lattice parameters (a) of the Co1xPdxSb3 series of samples as a function of the nominal composition x. A linearly increases in Co1xPdxSb3 until the value x = 0.027 ± 0.006 is reached. For larger x, a still linearly increases with x but with a much smaller slope. Fig. 1 (bottom panel) shows the Hall electron concentration ([n]) as a function of x in Co1xPdxSb3. It also linearly increases as a function of x until x = 0.030 ± 0.003 is reached where it linearly decreases. Both these central values and confidence intervals derived from the a(x) and [n](x) data are consistent but because of its smaller uncertainty, we favour the Hall concentration result which indicate that the solubility limit of Pd in CoSb3 is xmax = 0.030. Tashiro et al. [2] and Anno et al. [3] respectively proposed 0.04 and 0.05 as the solubility limit of Pd in CoSb3. Our work shows that these former values are significantly overestimated. The effect of the solubility limit is also reflected in the content of the secondary phases. For x 6 0.03, 1–2% CoSb2 and 0.2% metastable cubic Sb [13] are typical impurity phases found in the corresponding X-ray pattern. For x P 0.04, in addition to the already mentioned secondary phases, increasing
quantities of rhombohedral Sb (3% for x = 0.07) and cubic PdSb2 (1.5% for x = 0.07) could be detected. It is currently difficult to interpret the linear decrease of [n] for x larger than the solubility limit because of the change in the nature of the secondary phases which can contribute to the Hall signal. Rhombohedral Sb is a semi-metal with equal numbers of electrons and holes if pure, but with anisotropic and unequal mobilities of the two types of charge carriers [14]. PdSb2 is reported as a metal with unknown type of dominant charge carriers [15]. Despite their small concentration, the two extra phases can significantly affect the apparent electron concentration since Sb displays large charge carrier mobilities (0.1–4 103 cm2 V1 s1) and PdSb2 should display a large charge carrier concentration. Nonetheless, indications on the intrinsic electron concentration beyond the solubility limit in Co1xPdxSb3 can be derived from the Seebeck coefficient displayed in Fig. 2. It clearly saturates for x > 0.03, which allows excluding significant electron concentration change arising from intrinsic changes in the chemical formula of Co1xPdxSb3 such as interstitials or vacancies in this Pd concentration range. It is thus difficult to provide a well defined reason for the small increase of a(x) for x > 0.03 if no drastic chemical changes occur. We can only speculate on micro-structural effect such as micro-stress arising from the secondary phases, which could indeed be at play in this case. The lattice parameter of Co1xNixSb3 shown in Fig. 1 (top panel) also linearly increases with the composition x until x = 0.091 ± 0.005 is reached. For larger Ni concentration, the lattice parameter saturates. A break point is also found at x = 0.092 ± 0.005 in the electron concentration versus x curve shown in Fig. 1 (bottom panel). The solubility limit is thus xmax = 0.091 ± 0.005. This time, our value is in line with previous values published in the literature: xmax = 0.1 was reported in Ref. [3] and in Ref. [5]. The nature of the secondary phases also changes at xmax. For x 6 0.09, 0–1% CoSb and 0.2% metastable cubic Sb [13] are typical secondary phases while for x P 0.12, from 1% to 2% rhombohedral Sb and from 1.5% to 5% NiSb2 are additional impurity phases. Contrary to Co1xPdxSb3, a(x) saturates in Co1xNixSb3
Fig. 1. Top panel: lattice parameter of the series Co1xPdxSb3 and Co1xNixSb3 as a function of the composition x. The solid lines are linear regression to the experimental data (see text). Bottom panel: Room temperature Hall electron concentration in Co1xPdxSb3 and Co1xNixSb3 as a function of the composition x. Please note the different vertical scales for Co1xPdxSb3 and Co1xNixSb3.
Fig. 2. Electronic transport properties as a function of temperature in Co1xPdxSb3. Top panel: Seebeck coefficient; middle panel: electrical resistivity; bottom panel: power factor. Please note the logarithmic scale for the resistivity.
3. Results and discussion 3.1. Lattice parameter and electron concentration
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beyond xmax(Ni), indicating that no strong changes in the chemical composition or the microstructure occur beyond the solubility limit. The apparent electron concentration does not saturate beyond xmax(Ni) and similarly to Co1xPdxSb3, this most likely arises from the change in the nature of the secondary phases such as semimetallic Sb and semiconducting NiSb2 [15] which can also contribute to the Hall signal. 3.2. Room temperature electronic transport properties Table 1 gathers electronic transport properties such as the Hall electron concentration, resistivity, Seebeck coefficient and mobility measured at 300 K in Co1xPdxSb3. For x 6 0.03, the electron concentration [n] increases proportionally with x. The proportionality factor corresponds to a fraction of 0.4 electrons per Pd atoms, which is exactly the value determined in Ref. [2]. The absolute value of the Seebeck coefficient (a) and the resistivity (q) decreases with x and [n] in accordance with Boltzman’s theory of transport. The most convenient comparison with literature is obtained by calculating the density of states effective mass m from the values of [n] and a. Assuming a single parabolic band and interaction with acoustic phonon as the dominant charge scattering mechanism [3], the Seebeck coefficient is related to the reduced Fermi energy h i (g) by the expression [16]: a ¼ keB 2 FF 12 ððggÞÞ g with kB, the Boltzman constant and Fn(g), Fermi integrals. The electron concentra 32 BT F 1 ðgÞ with T the tion can be expressed as: ½n ¼ 4p 2mk h2 2
temperature and h the Planck’s constant. The results of the density of states effective mass calculation are gathered in Table 1. Our values m = 2.5m0 (m0 is the free electron mass) for [n] = 6.4 1019 cm3 and m = 2.9m0 for [n] = 11 1019 cm3 compare very well with m = 2.3m0 for [n] = 6.2 1019 cm3 and m = 2.9m0 for [n] = 14 1019 cm3 as published by Anno et al. [3] and with m = 3m0 for [n] = 10 1019 cm3 as published by Caillat et al. [1]. This confirms the consistency of our Hall effect and Seebeck coefficient measurements. Table 1 also shows that the mobility decreases with increasing [n], as expected when the main scattering mechanism is acoustic phonon [1]. Our values of mobility are larger by at least 20% than the values reported in Ref. [3]: this most likely arises from a better shaping of our samples. For x > 0.03, the Seebeck coefficient saturates while the Hall concentration and the resistivity respectively decreases and increases. As previously discussed, the secondary phases Sb and PdSb2 can affect not only the apparent electron concentration but also the resistivity and it is difficult to draw a conclusion on the variations of these two transport coefficients. The electronic transport properties at 300 K of Co1xNixSb3 are reported in Table 2. For x 6 0.09, the electron concentration linearly increases with x with a slope of 0.6 electrons per Ni atoms, in fair agreement with the 0.5 electrons per Ni atom which can be extracted from the data of reference [3]. The increase of the electron concentration leads to the expected decrease of the resistivity and of the Hall mobility and to the expected decrease of the absolute value of the Seebeck coefficient. Again, assuming a single parabolic band, we derived the density of states effective mass. The obtained values m = 3.3m0 for [n] = 0.7 1020 cm3 and m = 3.8m0 for [n] = 3.4 1020 cm3 are consistent with the values m = 3.2m0 for [n] = 1.2 1020 cm3 and m = 3.7m0 for [n] = 2.8 1020 cm3 as published by Anno et al. [3]. According to band structure calculations by Sofo and Mahan [17], the bottom of the conduction band of CoSb3 is formed by a nonparabolic band of light electrons and a triply degenerate (orbital degeneracy) parabolic band of heavy electrons. The density of states effective masses derived from our measurements on Co1xPdxSb3 and Co1xNixSb3 are in the range 2.5–4m0 while the
band effective mass calculated by Sofo and Mahan [17] for the heavy electron conduction band in CoSb3 is 0.35m0. The density of states effective mass (m) is related to the band effective mass (mb) by the number Nv of degeneracy of the band which includes orbital degeneracy and degeneracy imposed by the symmetry of the Brillouin zone: m = mb Nv2/3 [18,19]. Chaput et al. [20] indeed showed by using the same calculation technique as Sofo and Mahan (full potential augmented plane wave and generalized gradient approximation) that the heavy electron band can give rise to 12 electron pockets, situated along CN in the first Brillouin zone, when [n] 1020 cm3. Combining the orbital degeneracy and the degeneracy imposed by the Brillouin zone symmetry yields Nv = 3 12 = 36. From this, a range of experimental band effective masses mb 2.5m0–4m0/(36)2/3 0.23m0–0.37m0 can be obtained, in good agreement with the theory. This elementary calculation assumes that the contribution to the Seebeck coefficient of the light electron band can be neglected. Another comparison between experiment and theory can be obtained by using some of the results of Chaput et al. [20]. From their band structure calculation, they derived the Seebeck coefficient as a function of [n] and temperature with the assumption that the bands are rigid and the relaxation time of the electrons does not depend on energy (s = s0). Some of their calculations are reported in Tables 1 and 2. There is a good agreement between the theoretical and the experimental Seebeck values in the case of Co1xPdxSb3 (Table 1). On the other hand, the agreement between the theoretical and the experimental Seebeck values in the case of Co1xNixSb3 is only fair (Table 2) because the absolute experimental values are significantly larger. 3.3. Temperature dependent electronic transport properties Fig. 2 shows the Seebeck coefficient, the resistivity and power factor for Co1xPdxSb3 (0.01 < x < 0.07, nominal) as a function of temperature. At every temperature, the Seebeck coefficient of the Co1xPdxSb3 samples with x P 0.03 is identical within experimental uncertainty. As already discussed, this corresponds to the solubility limit xmax = 0.03. When x < 0.03, in the temperature range 300–700 K, the absolute value of the Seebeck coefficient decreases with increasing x and [n]. For all x, the values of the Seebeck coefficient decreases with temperature, as is expected in a degenerate semiconductor, until the minimum arising from the minority carriers conduction regime is reached. This minimum shifts to higher temperature (from 540 K to 630 K) in agreement with the increase of the electron concentration. The resistivity varies consistently with x, [n] and the Seebeck coefficient. Its thermal variations are also typical of a degenerate semiconductor with metallic behaviour at ‘‘low’’ temperature until the minority carrier conduction is activated at high temperature. An estimation of the activation energy is difficult because we did not measure at temperatures high enough. At every temperature, the power factor increases with x until
Table 1 Room temperature values of the palladium concentration, Hall electron concentration, Seebeck coefficient, effective mass, resistivity and Hall mobility in Co1xPdxSb3 as a function of the composition x. x 0.01 0.02 0.023 0.03 0.04 0.07 Ref. [20]
[n] (1019 cm3)
a (lV K1)
m
2.5 6.4 8.2 10.9 10.2 8.6 5.7
261 220 196 193 182 191 223
2.0 2.5 2.4 2.9 – – –
q
l
(105 X m)
(cm2 V1 s1)
2.971 1.583 1.187 1.057 1.080 1.216 –
83 62 64 55 57 59 –
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Table 2 Room temperature values of the nickel concentration, Hall electron concentration, Seebeck coefficient, effective mass, resistivity and Hall mobility in Co1xNixSb3 as a function of the composition x. x 0.02 0.03 0.045 0.06 0.075 0.09 0.12 0.15 Ref. [20]
[n] (1020 cm3)
a (lV K1)
m
0.7 1.5 2.5 3.4 4.4 5.5 12.0 20.9 1.5
243 207 144 133 113 101 88 74 187
3.3 3.8 3.5 3.8 3.9 4.4 – – –
q
l
(105 X m)
(cm2 V1 s1)
4.051 2.803 1.918 1.497 1.178 1.006 0.880 0.733 –
21 15 13 11 12 11 6 4 –
x = xmax is reached and then decreases for x > xmax. The maximum power factor at 700 K is indeed obtained for the composition Co0.97Pd0.03Sb3 and amounts to 4.3 mW m1 K2. A question arises from this result: is the maximum power factor yet reached or not when x = xmax? We calculated the power factor at 300 K as a function of [n] using the same formalism and assumption as the Seebeck coefficient: one parabolic band and charge scattering dominated by interactions with acoustic phonon. The electrical conductivity then given by the relation [16]: 3=2is 2 r ¼ 8pe3 s0 h22 ðm Þ1=2 kB TF 0 ðgÞ where s0 is the prefactor describing the energy dependence of the relaxation time s = s0e1/2. Notice that s0 is not a time since it is expressed in J1/2 s. Taking an average effective mass m = 2.7m0 over the electron concentration range 1018–1021 cm3, s0 was adjusted to two values: with the first one (s0 = 0.85 1023 J1/2 s), the calculated resistivity at 300 K matches our experimental value for x = 0.01 or [n] = 2.5 1019 cm3 while the second one (s0 = 0.62 1023 J1/2 s) allows matching the resistivity data of literature [1,3]. The two calculated curves are displayed in Fig. 3 and they compare very well with our experimental data and with literature respectively. Within this formalism, the optimum power factor should be reached for [n]opt = 1.4 1020 cm3 and amount to PFopt = 3.5 mW m1 K2. [n]opt corresponds to xopt = 0.037, which is close but significantly larger than xmax. Co0.97Pd0.03Sb3 can thus be considered as the accidental optimum composition of this system. In Ref. [3], maximum Z = 6 104 K1 at 300 K had been reported for Co0.95Pd0.05Sb3,
Fig. 3. Experimental (symbols) and calculated (lines) power factor in Co1xPdxSb3 and Co1xNixSb3 as a function of the electron concentration. Data from literature extracted from Refs. [1–4].
which we showed to be non-existant.The Seebeck coefficient is shown in Fig. 4 for Co1xNixSb3 (0.01 6 x 6 0.15 nominal). For all x, the absolute value of the Seebeck coefficient increases with temperature until the minority carriers conduction regime is reached, similarly to what is observed in Co1xPdxSb3. This leads to a minimum of the Seebeck value which shifts to higher temperature (from 500 K for x = 0.02 to 700 K for x = 0.09) when the electron concentration increases. At any temperature, the resistivity presented in Fig. 5 monotonously decreases with x in consistency with the variations of [n] and the Seebeck coefficient. However, the behaviour of the resistivity plotted in Fig. 5 as a function of temperature, changes with x. For x P 0.12, a metallic behaviour is observed. When x 6 0.06, the resistivity shows an activated behaviour in the temperature range [300–800 K]. For x = 0.075 and x = 0.09, the resistivity varies nonmonotonously and exhibits a maximum at 340 K and 410 K respectively. The shift with x of this maximum suggests that such a maximum also exists at temperatures lower than 300 K when x 6 0.06. Such maximum in q(T) points to the possible existence of a shallow donor level situated below the conduction band in Co1xNixSb3 and giving rise to minority carriers effect in the temperature range 200–400 K, depending on x. Low temperature measurements would be necessary to give more substance to this donor level. Fig. 6 shows a plot of Log(q) versus 1/T for x = 0.02. Only this sample displays a high temperature activation regime, which can be safely fitted: the activation energy which is derived is eAH = 0.066 eV. The value 2 eAH = 0.13 eV is close to the calculated value of the intrinsic gap eG = 0.14 eV reported in references [20,21] and can be ascribed to the gap. An estimate of the intrinsic gap can be obtained for Co1xPdxSb3 by scaling the gap of Co1xNixSb3 with the value of the maximum of the Seebeck coefficient arising from minority carriers’ effect and its temperature. Goldsmid and Sharp indeed showed [22] that the gap energy is close to 2eamaxTmax where amax is the value of the maximum of the Seebeck coefficient and Tmax its temperature. Co0.98Pd0.02Sb3 and Co0.98Ni0.02Sb3 roughly display
Fig. 4. Seebeck coefficient (top panel) and power factor (bottom panel) a function of temperature in Co1xNixSb3.
E. Alleno et al. / Journal of Alloys and Compounds 572 (2013) 43–48
47
Fig. 7. Power factor at 300 K, 700 K and averaged over [300–700 K] as a function of the composition x in Co1xNixSb3.
Fig. 5. Electrical resistivity a function of temperature in Co1xNixSb3.
Fig. 6. Logarithmic plot of the electrical resistivity as a function of the inverse temperature in Co0.98Ni0.02Sb3.
from the literature [3,4]. An average effective density of states mass m = 3.8 m0 was chosen and s0 was adjusted to s0 = 0.33 1023 J1/2 s in order to match the experimental data for [n] 1 1020 cm3. The agreement between this calculation and the experiments is not very good since it predicts a maximum power factor at T = 300 K for [n] 2.4 1020 cm3 while it is found experimentally for [n] 0.7 1020 cm3. We speculate that the possible shallow donor level combined with the nonparabolicity of the band, makes the transport properties deviate from the simple single band model in the temperature range 200–400 K. Fig. 3 also shows that the power factors in Co1xNixSb3 are smaller than in Co1xPdxSb3 in the temperature range 300–700 K. The main reason for these less favourable properties is the smaller values of the mobility in Co1xNixSb3 than in Co1xPdxSb3. On the other hand, Figs. 4 and 7 show that the power factor at 700 K is not maximum for x = 0.02 but rather when x = 0.06. A better estimation of the thermoelectric properties of Co1xNixSb3 as a material for electricity generation is the average power factor over a broad temperature range such as 300–700 K. This quantity is also plotted in Fig. 7. Within experimental uncertainty, the average power factor is independent of the nickel concentration for 0.02 < x < 0.09 or at worse, shows a very shallow maximum around x = 0.05. The composition range Co0.95Ni0.05Sb3–Co0.94Ni0.06Sb3 thus displays the largest average power factor (2.45 mW m1 K2) and the largest power factor (3.4 mW m1 K2) at 700 K. This is consistent with literature since maximum Z = 2 104 K1 at 300 K had been reported for Co0.95Ni0.05Sb3 [3] and maximum ZT = 0.5 at 700 K had been reported for Co0.94Ni0.06Sb3 [5]. 4. Summary
the same electron concentration [n] = 6–7 1019 cm3. The Seebeck coefficient reaches respectively 295 lV K1 and 305 lV K1 in these samples at 560 K and 520 K. The scaling relation eG ðPdÞ ¼ eG ðNiÞ 560 295 yields eG(Pd) = 0.14 eV. Both 520 305 Co0.98Pd0.02Sb3 and Co0.98Ni0.02Sb3 thus display close value of their intrinsic gap. The power factor as a function of temperature and as a function of the nickel concentration is shown for Co1xNixSb3 respectively in Figs. 4 and 7. At room temperature, the power factor monotonously decreases with x, indicating that the optimum value is obtained for nickel concentrations x < 0.02. These room temperature values of the power factor are plotted as a function of [n] in Fig. 3 and compared to the literature [3,4]. They indicate that the x = 0.02 sample is close to the optimum value for this temperature. Using the same formalism as for Co1xPdxSb3, a theoretical curve of the power factor was calculated for comparing to the present data and to those
The solubility limit of palladium and nickel in Co1xPdxSb3 and Co1xNixSb3 is respectively found at x = 0.03 and x = 0.09. The density of states effective masses derived from room temperature Hall effect and Seebeck measurements respectively range between 2.0m0 and 2.9m0 and 3.3m0 and 4.4m0 in Co1xPdxSb3 and Co1xNixSb3. These values are consistent with the effective band mass (0.3m0) and the degeneracy number Nv = 36 obtained by DFT calculations. Power factor measurements and calculations in Co1xPdxSb3 show that at 300 K, the optimum electron concentration is [n]opt = 1.4 1020 cm3 and that solubility limit composition Co0.97Pd0.03Sb3 reaches 1.09 1020 cm3, close to the optimum electron concentration. The maximum power factor at 700 K is also obtained for the composition Co0.97Pd0.03Sb3 and amounts to 4.3 mW m1 K2. Resistivity measurements in Co0.98Ni0.02Sb3 allow for the determination of an activation energy, which can
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correspond to the intrinsic gap eG = 0.13 eV. A smaller electronic mobility leads to smaller power factors in Co1xNixSb3 than in Co1xPdxSb3. Best properties (3.4 mW m1 K2) are observed at 700 K in Co0.95Ni0.05Sb3–Co0.94Ni0.06Sb3. Acknowledgement The authors thank B. Lenoir (Institute Jean Lamour, Nancy) for fruitful discussions. References [1] T. Caillat, A. Borshchevsky, J.P. Fleurial, J. Appl. Phys. 80 (1996) 4442. [2] H. Tashiro, Y. Notohara, T. Sakakibara, H. Anno, K. Matsubara, in: 16th International Conference on Thermoelectrics. 26–29 Auguest 1997 Dresden, Germany, 1997, p. 326. [3] H. Anno, K. Matsubara, Y. Notohara, T. Sakakibara, H. Tashiro, J. Appl. Phys. 86 (1999) 3780. [4] J.S. Dyck, W. Chen, J. Yang, G.P. Meisner, C. Uher, Phys. Rev. B 65 (2002) 115204. [5] S. Katsuyama, M. Watanabe, M. Kuroki, T. Maehala, M. Ito, J. Appl. Phys. 93 (2003) 2758. [6] V.L. Kuznetsov, L.A. Kuznetsova, D.M. Rowe, J. Phys.: Condens. Matter. 15 (2003) 5035. [7] Z. Xiong, X. Chen, X. Huang, S. Bai, L. Chen, Acta Mater. 58 (2010) 3995.
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