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Synthesis, crystal structure and thermoelectric properties of the ternary skutterudite Fe2Pd2Sb12
Journal of Alloys and Compounds 493 (2010) 50–54
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Synthesis, crystal structure and thermoelectric properties of the ternary skutterudite Fe2 Pd2 Sb12 J. Navrátil a , F. Laufek b,∗ , T. Plecháˇcek a , J. Pláˇsil c ˇ and University of Pardubice (Faculty of Chemical Technology), Studentská 84, 532 10 Pardubice, Czech Republic Joint Laboratory of Solid State Chemistry of IMC AS CR Czech Geological Survey, Geologická 6, 152 00 Praha 5, Czech Republic c National Museum, Václavské námˇestí 84, 115 79 Praha 1, Czech Republic a
b
a r t i c l e
i n f o
Article history: Received 14 September 2009 Received in revised form 4 December 2009 Accepted 14 December 2009 Available online 23 December 2009 Keywords: Fe2 Pd2 Sb12 Crystal structure X-ray powder diffraction Transport properties
a b s t r a c t The Fe2 Pd2 Sb12 compound was synthesized and structurally characterized by powder X-ray diffraction. Fe2 Pd2 Sb12 has the skutterudite structure, Im3¯ symmetry, unit cell parameter a = 9.2048(2) Å, Z = 8. The transport properties of the title compound were investigated. From the temperature dependencies of electrical conductivity, the Hall coefficient and the Seebeck coefficient the existence of mixed conductivity mechanism by means of electrons and holes was proposed. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Compounds with the skutterudite structure have been recently identified as potential advanced thermoelectric materials [1]. The binary skutterudites with general formula MX3 (M = Co, Rh, Ir; X = P, As, Sb) display reasonably large Seebeck coefficient and good electrical conductivity, resulting in relatively large power factor values. Nevertheless, their thermoelectric figure-of-merit ZT is limited by their relatively large thermal conductivity [2]. Investigations [3,4] performed on skutterudite materials have showed, that it is possible to reduce the lattice thermal conductivity by forming solid solutions between isostructural compounds (e.g. CoSb3 –IrSb3 solid solution). Another approach is filling the voids located at the centre of [MX6 ]8 octahedral cluster in the skutterudite structure by other atoms (La–Yb [5,6]). These filling atoms scatter the phonons by “rattling” and consequently enhance thermoelectric properties [7,8]. The ideal skutterudite structure can be described as a collapsed perovskite structure ABX3 (tilt system a+ a+ a+ ) with four octahedral vertices to close enough to form four-member X4 rings [9]. A-sites, occupied in the perovskite structure, are vacant. In addition to binary skutterudites, ternary skutterudites also exist. Ternary skutterudites are materials isoelectronic to binary skutterudites, and can be prepared either by isoelectronic substitution at anionic site
X by a pair of elements from 14 and 16 groups (e.g. CoGe1.5 S1.5 [10], CoSn1.5 Se1.5 [11]), or by isoelectronic substitution at the cationic site M by a pair of elements from 8 and 10 groups (e.g. Fe0.5 Ni0.5 Sb3 [12], Ru0.5 Pd0.5 Sb3 [13]). In this work, we present a structural study of ternary skutterudite Fe2 Pd2 Sb12 using conventional powder X-ray diffraction. The thermoelectric properties are also reported. The existence of Fe2 Pd2 Sb12 phase was mentioned in a conference proceeding [14] as a part of review of skutterudite materials, however no detailed information concerning crystal structure and transport properties is available. 2. Experimental 2.1. Synthesis The Fe2 Pd2 Sb12 ternary compound was synthesized from individual elements by high-temperature solid-state reactions. Fe powder was first heated at 600 ◦ C for 2 h in H2 atmosphere to remove possible oxides. Stoichiometric amounts of Fe (99.9%), Pd (99.9%) and Sb (99.999%) were sealed into an evacuated silica glass tube and heated at 800 ◦ C for 48 h in a furnace. The material was then ground under acetone using agate mortar and pestle and heated at 550 ◦ C for 168 h. The resultant material was once again ground under acetone and heated again at 550 ◦ C for 240 h. After annealing, the furnace was turned off and allowed to cool slowly to room temperature. Finally, obtained powder samples were, after verification of the completion of the solid-state reaction with powder X-ray diffraction, hot-pressed at 500 ◦ C (HP-samples) and 50 MPa for 1 h. 2.2. Structure refinement
∗ Corresponding author. Fax: +420 251 818 748. E-mail address: [email protected] (F. Laufek). 0925-8388/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.12.085
The powder X-ray diffraction pattern of Fe2 Pd2 Sb12 was collected in Bragg–Brentano geometry on an X’Pert Pro PANalytical diffractometer equipped
J. Navrátil et al. / Journal of Alloys and Compounds 493 (2010) 50–54
51
Table 1 Data collection and Rietveld analysis. R agreement factors defined according to [27]. Data collection Radiation type, source Generator settings Data collection temperature Range in 2 (◦ ) Step size (◦ )
X-ray, CuK␣ 40 kV, 30 mA Room temperature 10–110 0.02
Crystal data Space group Unit cell content Unit cell parameters (Å)
Im3¯ (No. 204) Fe0.51 Pd0.49 Sb3 , Z = 8 a = 9.2048(2)
Rietveld analysis No. of reflections No. of structural parameters No. of profile parameters RBragg Rp Rwp Weighting scheme
102 3 4 0.059 0.052 0.067 1/yo Fig. 2. (a) Polyhedral representation and (b) ball-and-stick representation of the Fe2 Pd2 Sb12 structure showing the corner sharing arrangement of the [Fe(Pd)Sb6 ] octahedra and presence of four-member [Sb4 ] rings. (c) Detailed view of the [Sb4 ] ring.
Table 2 Refined parameters for the Fe2 Pd2 Sb12 . Atom
Site
x
y
z
Occ.
Biso [Å2 ]
Fe Pd Sb
8c 8c 24g
1/4 1/4 0
1/4 1/4 0.3374(2)
1/4 1/4 0.1549(2)
0.51(1) 0.49(1) 1
0.45(4) 0.45(4) 0.93(2)
breakpoints in the pattern. Refined structural parameters are given in Table 2, Fig. 1 shows final Rietveld plot. 2.3. Transport and thermoelectric properties
The displacement parameters of Pd and Fe were constrained to be equal.
with X’Celerator detector using CuK␣ radiation. To minimize background, the sample was placed on a flat-low background silicon wafer. The data were acquired in the angular range 10–110◦ 2. A full-width at half-maximum of 0.066◦ 2 was obtained at 13.340◦ 2 indicating good crystallinity of the sample studied. The details of data collection and basic crystallographic facts are given in Table 1. The crystal structure of Fe2 Pd2 Sb12 was refined by the Rietveld method for Xray powder diffraction data using the FullProf program [15]. With the exception of a small number of diffraction peaks attributable to Sb secondary phase (ca 2 wt%), all peaks can be indexed on a body-centred cubic lattice isotypic with CoSb3 [16]. Consequently, CoSb3 crystal structure was used as a starting structural model in Rietveld refinement. The refined parameters include those describing peak shape and width, peak asymmetry, unit cell parameters and fractional coordinates. Finally, 16 parameters were refined. The Pd and Fe atoms randomly occupy the 8c posi¯ their starting occupancy factors were assigned tion in the space group Im3; according to the Fe2 Pd2 Sb12 chemical composition. The subsequent refinement of individual occupancies of Pd and Fe atoms with the constraint that their sum corresponds to the 100% occupancy yielded the stoichiometry Fe2.03 Pd1.97 Sb12 . The pseudo-Voigt function was used to generate the line shape of the diffraction peaks. The background was determined by linear interpolation between consecutive
Electrical conductivity was measured with four-probe method using Lock-in Amplifier (EG&G model 5209) on the rectangular parallelepiped of dimensions about 10 mm × 3 mm × 1 mm. The measurements were performed on two different probes, one in the temperature region from about 100 to 350 K and the other from 300 to 800 K. The Hall constant RH was measured on the hot-pressed sample of dimensions 15 mm × 3 mm × 1 mm at 100–400 K temperature range. The measurement was realized using alternating current at a frequency of 1020 Hz, in magnetic field induction B = 0.7 T. The Seebeck coefficient was determined by means of static dc-method on rectangular shaped samples. The temperature gradient between two points was measured by two shielded K-type thermocouples that were pressed against the sample surface. A potential difference dU corresponding to the gradient dT was measured across the same legs of both attached thermocouples. The absolute Seebeck coefficient was determined from the slope of dU/dT dependence using 20 values of dT not exceeded 3 K. The thermal diffusivity was measured on round hot-pressed sample with help of LFA 457 (Netzsch). The thermal conductivity was then calculated using Pyroceram 9606 as a heat capacity standard.
3. Results and discussion 3.1. Crystal structure Fe2 Pd2 Sb12 adopts the skutterudite-type structure (CoAs3 ) and is depicted in Fig. 2. In this structure, each Pd/Fe atom is octahedraly coordinated by six Sb atoms with distance of 2.5915(8) Å. The [Fe(Pd)Sb6 ] octahedra share all six corners with adjacent octahedra forming a three-dimensional network. As is evident from Table 3, which shows comparison of selected bond distances and Table 3 Selected interatomic distances (Å) and bond angles (◦ ) for Fe2 Pd2 Sb12 and Fe2 Ni2 Sb12 [12] (M = Fe/Pd or Fe/Ni). Fe2 Pd2 Sb12 Distances M–Sb Sb–Sb
Fig. 1. Observed (circles), calculated (solid line) and difference Rietveld profiles for Fe2 Pd2 Sb12 . The upper reflection bars correspond to Fe2 Pd2 Sb12 and the lower bars to a 2 mass percent Sb impurity.
Angles Sb–M–Sb Sb–M–Sb M–Sb–M Sb–Sb–Sb
Fe2 Ni2 Sb12
6 × 2.590(2) 2.852(3) 2.993(3)
6 × 2.538(9) 2.89(1) 2.99(1)
6 × 85.374(1) 6 × 94.626(1) 125.3(1) 90.00
6 × 85.415(2) 6 × 94.458(3) 127.0(3) 90.00
52
J. Navrátil et al. / Journal of Alloys and Compounds 493 (2010) 50–54
Fig. 3. Positional parameters y and z for Sb-bearing skutterudites, Oftedal’s relation is shown for comparison. CoSb3 data from [16], RhSb3 , IrSb3 and Fe2 Ni2 Sb12 data from [12]. A linear fit for observed points is indicated by dashed line.
angles for isostructural compounds Fe2 Pd2 Sb12 and Fe2 Ni2 Sb12 [12], the Fe/Pd–Sb distances are significantly larger than corresponding Fe/Ni–Sb distances in Fe2 Ni2 Sb12 . This can be explained by lower radius of the Ni atom (rNi = 1.25 Å [17]) compared to the radius of the Pd atom (rPd = 1.38 Å [17]). As was mentioned by Mitchell [9] and Vaqueiro et al. [10], the skutterudite structure can be considered as a derivative of the cubic perovskite structure ABX3 , characterized by vacant A-sites and tilting of octahedra (tilt system a+ a+ a+ ). The tilt angle (ϕ) for the ideal skutterudite structure can be calculated from unit cell dimension a and M–Sb distance (d) using a relationship [18] cos(ϕ) =
3a − 0.5 8d
Using this equation, we have calculated the values of tilt angles of 32.5◦ , 33.6◦ and 34.3◦ for Fe2 Ni2 Sb12 [12], Fe2 Pd2 Sb12 and IrSb3 [12], respectively. These values are in accordance with general trend observed in skutterudites; for a given “anion” the tilt angle (ϕ) increase with the increasing size of the cation [9,10]. The Sb atoms in the Fe2 Pd2 Sb12 structure form [Sb4 ] rings of rectangular shape with two very similar Sb–Sb distances (Fig. 2c). These rectangles are characteristic feature of the skutterudite structure. These distances become equal when the two fractional coordinates of the Sb atoms obey the so-called Oftedal’s relation y + z = ½ [19]. Fig. 3 shows y and z parameters for Sb-bearing skutterudites. As can be seen from this figure, Fe2 Pd2 Sb12 follows observed trend in unfilled Sb-bearing skutterudites; all compounds lie on one side of the Oftedal’s relation having two very similar (but not equal) Sb–Sb distances within the [Sb4 ] rings. Moreover, position of Fe2 Pd2 Sb12 point in Fig. 3 supports the observation of Kjekshus et al. [19] for binary skutterudites; all points are situated on a line approximately parallel to that given by Oftedal’s relation. It is also interesting to note, that a relatively large group of “anion-ordered” skutterudites has been prepared (e.g. CoGe1.5 Te1.5 [20] or CoSn1.5 Se1.5 [11]), cation-ordered analogues seems not to have been synthesized. In addition to the unfilled skutterudite structure, phases with the composition AB4 X12 , called filled skutterudites, can be created by the insertion of another atom (typically La–Yb [5,6]) in the
Fig. 4. Icosahedral voids (light grey) and [Fe(Pd)Sb6 ] octahedra (dark grey) in the crystal structure of Fe2 Pd2 Sb12 . Unit cell edges are highlighted.
icosahedral voids (Fig. 4) located at the centre of [MX6 ]8 octahedral cluster. The distance from hypothetical filling atom A to Sb atom in the Fe2 Pd2 Sb12 structure would have a value of 3.4 Å. This distance is in fact similar with that distance observed in filled skutterudite CeFe4 Sb12 [21]. As was mentioned by Makovicky [22] for the skutterudite structure, the icosahedral voids do not share any structural elements; they are connected by means of octahedra and Sb4 groups. 3.2. Transport and thermoelectric properties The ceramic method, widely used for solid-state synthesis of skutterudite compounds, suffers from several disadvantages. Mainly, it is very difficult, if not impossible, to achieve the full completion of reaction, and a lot of authors report (e.g. [23,24]) the existence of small quantity of other than desired reactants observed e.g. in powder X-ray diffraction patterns [25]. In case of skutterudites containing Sb on anion sites it is just unreacted antimony, which is detected in low, but detectable quantity in X-ray diffractograms. As it was mentioned above, this is also our case. One cannot also exclude that similar deficit, although undetectable, is also presented on cation sites. As a result, we obtained the compound, which contains quite large concentration of point defects, which behave both, as donors and acceptors and they are located in shallow levels inside of band gap. Such quite complicated point defects structure is, in our opinion, reflected in the temperature dependencies of the electrical conductivity , the Seebeck coefficient S (Fig. 5) and the Hall coefficient RH (Fig. 6) of the prepared compound. Just temperature dependence of RH product (Fig. 6) indicates the presence of the at least two types of carriers. The fact that it could be both electrons and holes is, in our opinion, suggested by the course of the temperature dependence of the Seebeck coefficient, which is at lowest measured temperatures negative and with the increasing temperature become positive. On the contrary, the values of RH stay in the whole measured temperature region (100–400 K) positive (Fig. 6). This contradiction could be explained e.g. by the higher mobility of holes compared to mobility of electrons, which was supposed to explain similar discrepancy in skutterudite semiconducting compounds [26]. Unfortunately, the lack of the low temperature data (below 90 K) excludes the closer elucidation of the observed problem.
J. Navrátil et al. / Journal of Alloys and Compounds 493 (2010) 50–54
53
Fig. 7. The log vs. 1000/T plot of the Fe2 Pd2 Sb12 compound. Dashed line represents fit of a form log = log 0 − Eg /(2kT) to the higher temperatures, indicating Eg ∼ 0.22 eV.
Fig. 5. The temperature dependencies of the Seebeck coefficient S and the electrical conductivity of the Fe2 Pd2 Sb12 compound.
As follows from Fig. 5 with the increasing temperature the Seebeck coefficient peaks at about 500 K (∼60 V/K) and after quite steep fall changes again to negative value at about 780 K. The peak in the temperature dependence of S corresponds approximately with minimum in the same dependence of after that the electrical conductivity starts to increase. From the Arrhenius’ log vs. 1000/T plot (Fig. 7) it is evident that this increase is undoubtedly connected with excitation of electrons across band gap. Using a formula log = log 0 − Eg /(2kT) we were able to estimate value of the band gap of the studied compound Eg ∼ 0.22 eV. Similar band gap of Eg ∼ 0.16 eV was also reported for Fe2 Ni2 Sb12 [14]. The different sign of the Seebeck coefficient for Fe2 Ni2 Sb12 [14] (negative) and
Fig. 6. The temperature dependence of the Hall coefficient RH and the RH product (carriers mobility ) of the Fe2 Pd2 Sb12 compound at 100–400 K temperature range.
Fe2 Pd2 Sb12 (positive) in the temperature range from 300 to 800 K is just the matter of non-stoichiometry of these compounds and strongly depends on the Fe/Ni and Fe/Pd ratio. The temperature dependence of thermal conductivity total of the compound measured at temperature range 300–700 K is presented in Fig. 8. Its values are approximately two times lower than values for its binary analogues CoSb3 and RhSb3 [26], and approximately comparable with those found for Fe2 Ni2 Sb12 [14]. We suppose the degenerated case and the presence just two main contributions to thermal conductivity, i.e. its electronic part el and lattice part lat . Then it is possible to separate these parts using the formula el = L.T., where L = 2.443 × 10−8 V2 K−2 . The electronic part el presents about quarter of the total thermal conductivity. One can expect that filling the voids of the skutterudite structure with proper filler can lead even to lower values of the thermal conductivity. The thermoelectric figure-of-merit Z, defined as Z = S2 /total , was calculated. It reaches the maximum value of about 7 × 10−5 K−1
Fig. 8. The temperature dependence of the measured total thermal conductivity total of the Fe2 Pd2 Sb12 compound measured between 300 and 700 K. el and lat contributions were separated by calculation of el supposing the high degree of degeneration of the prepared semiconducting compound.
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J. Navrátil et al. / Journal of Alloys and Compounds 493 (2010) 50–54
at 500 K. This low value of parameter Z is caused by very low value of Seebeck coefficient ˛ due to the presence of two types of free current carriers. However, one can suppose that the suitable doping suppressing mainly the concentration of electrons could increase the value of Z. 4. Conclusion To conclude, Fe2 Pd2 Sb12 has cubic skutterudite structure with ¯ In the studied temperature range, the figurethe space group Im3. of-merit Z has maximum value of 7 × 10−5 K−1 at 500 K. This value is significantly lower compared with in the state-of-the-art thermoelectric materials, particularly because of the low value of Seebeck coefficient. Further optimisation of this parameter by proper doping can enhance the thermoelectric properties. Acknowledgements This research was supported by the Ministry of Education of the Czech Republic under the project MSM0021627501 and the project of Grant Agency CR No. 203/07/0267. References [1] C. Uher, in: M.G. Kanatzidis, S.D. Mahanti, T.P. Hogan (Eds.), Chemistry, Physics and Materials Science of Thermoelectric Materials: Beyond Bismuth Telluride, Kluwer Academics, Plenum Publishers, New York, 2003, p. 121. [2] Y. Nagamoto, K. Tanaka, T. Koyanagi, Proceedings of the 16th International Conference on Thermoelectrics, Dresden, Germany, 1997, pp. 330–333. [3] A. Borshchevsky, J.P. Fleurial, E. Allevato, T. Caillat, Proceedings of the 13th International Conference on Thermoelectric, Kansas City, USA, 1994, pp. 3–6.
[4] A. Borshchevsky, T. Caillat, J.P. Fleurial, Proceedings of the 15th International Conference on Thermoelectric, Pasadena, USA, 1996, pp. 112–116. [5] W. Jeitschko, D. Braun, Acta Cryst. B 33 (1977) 3401–3406. [6] B.C. Chakoumakos, B.C. Sales, J. Alloys Compd. 407 (2006) 87–93. [7] D.T. Morelli, G.P. Meisner, J. Appl. Phys. 77 (1995) 3777–3781. [8] B.C. Sales, D. Mandrus, R.K. Williams, Science 272 (1996) 1325–1328. [9] R.H. Mitchell, Perovskites: Modern and Ancient, Almaz Press, Thunder Bay, Ontario, 2002. [10] P. Vaqueiro, G.G. Sobany, M. Stindl, J. Solid State Chem. 181 (2008) 768–776. ˇ Draˇsar, J. Alloys Compd. 479 (2009) [11] F. Laufek, J. Navrátil, J. Pláˇsil, T. Plecháˇcek, C. 102–106. [12] A. Kjekshus, T. Rakke, Acta Chem. Scand. A 28 (1974) 99–103. [13] T. Caillat, J. Kulleck, A. Borshchevsky, J.P. Fleurial, J. Appl. Phys. 79 (1996) 8419–8426. [14] J.P. Fleurial, T. Caillat, A. Borshchevsky, Proceedings of the 16th International Conference on Thermoelectrics, Dresden, Germany, 1997, pp. 1–11. [15] J. Rodríguez-Carvajal, FullProf.2k Rietveld Profile Matching & Integrated Intensities Refinement of X-ray and/or Neutron Data (powder and/or single-crystal). Laboratoire Léon Brillouin, Centre dˇıEtudes de Saclay, Gif-sur-Yvette Cedex, France. (2006). [16] M. Puyet, B. Lenoir, A. Dauscher, P. Weisbecker, S.J. Clarke, J. Solid State Chem. 177 (2004) 2138–2143. [17] J. Emsley, The Elements, Oxford University Press, New York, 1989. [18] M. O’Keefe, B.G. Hyde, Acta Cryst. B 33 (1977) 3802–3813. [19] A. Kjekshus, D.G. Nicholson, T. Rakke, Acta Chem. Scand. 27 (1973) 1307–1314. [20] P. Vaqueiro, G.G. Sobany, A.V. Powell, K.S. Knight, J. Solid State Chem. 179 (2006) 2047–2053. [21] J.W. Kaiser, W. Jeitschko, J. Alloys Compd. 291 (1999) 66–83. [22] E. Makovicky, In: G. Ferraris and S. Merlino (Eds). Micro- and Mesoporous Sulfide and Selenide Structures, Reviews in Mineralogy and Geochemistry, 57, Mineralogical Society of America, Virginia, USA, p. 403. [23] E. Bauer, A. Galatanu, H. Michor, G. Hilscher, P. Rogel, P. Boulet, H. Noel, Eur. Phys. J. B. 14 (2000) 483–493. [24] J. Peng, J. Yang, X. Song, Y. Chen, T. Zhang, J. Alloys Compd. 426 (2006) 7–11. [25] K.T. Wojciechowski, Mater. Res. Bull. 37 (2002) 2023–2033. [26] K.T. Wojciechowski, J. Alloys Compd. 439 (2007) 18–24. [27] L.B. McCusker, R.B. von Dreele, D.E. Cox, D. Louër, P. Scardi, J. Appl. Cryst. 32 (1999) 36.
Contents lists available at ScienceDirect
Journal of Alloys and Compounds journal homepage: www.elsevier.com/locate/jallcom
Synthesis, crystal structure and thermoelectric properties of the ternary skutterudite Fe2 Pd2 Sb12 J. Navrátil a , F. Laufek b,∗ , T. Plecháˇcek a , J. Pláˇsil c ˇ and University of Pardubice (Faculty of Chemical Technology), Studentská 84, 532 10 Pardubice, Czech Republic Joint Laboratory of Solid State Chemistry of IMC AS CR Czech Geological Survey, Geologická 6, 152 00 Praha 5, Czech Republic c National Museum, Václavské námˇestí 84, 115 79 Praha 1, Czech Republic a
b
a r t i c l e
i n f o
Article history: Received 14 September 2009 Received in revised form 4 December 2009 Accepted 14 December 2009 Available online 23 December 2009 Keywords: Fe2 Pd2 Sb12 Crystal structure X-ray powder diffraction Transport properties
a b s t r a c t The Fe2 Pd2 Sb12 compound was synthesized and structurally characterized by powder X-ray diffraction. Fe2 Pd2 Sb12 has the skutterudite structure, Im3¯ symmetry, unit cell parameter a = 9.2048(2) Å, Z = 8. The transport properties of the title compound were investigated. From the temperature dependencies of electrical conductivity, the Hall coefficient and the Seebeck coefficient the existence of mixed conductivity mechanism by means of electrons and holes was proposed. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Compounds with the skutterudite structure have been recently identified as potential advanced thermoelectric materials [1]. The binary skutterudites with general formula MX3 (M = Co, Rh, Ir; X = P, As, Sb) display reasonably large Seebeck coefficient and good electrical conductivity, resulting in relatively large power factor values. Nevertheless, their thermoelectric figure-of-merit ZT is limited by their relatively large thermal conductivity [2]. Investigations [3,4] performed on skutterudite materials have showed, that it is possible to reduce the lattice thermal conductivity by forming solid solutions between isostructural compounds (e.g. CoSb3 –IrSb3 solid solution). Another approach is filling the voids located at the centre of [MX6 ]8 octahedral cluster in the skutterudite structure by other atoms (La–Yb [5,6]). These filling atoms scatter the phonons by “rattling” and consequently enhance thermoelectric properties [7,8]. The ideal skutterudite structure can be described as a collapsed perovskite structure ABX3 (tilt system a+ a+ a+ ) with four octahedral vertices to close enough to form four-member X4 rings [9]. A-sites, occupied in the perovskite structure, are vacant. In addition to binary skutterudites, ternary skutterudites also exist. Ternary skutterudites are materials isoelectronic to binary skutterudites, and can be prepared either by isoelectronic substitution at anionic site
X by a pair of elements from 14 and 16 groups (e.g. CoGe1.5 S1.5 [10], CoSn1.5 Se1.5 [11]), or by isoelectronic substitution at the cationic site M by a pair of elements from 8 and 10 groups (e.g. Fe0.5 Ni0.5 Sb3 [12], Ru0.5 Pd0.5 Sb3 [13]). In this work, we present a structural study of ternary skutterudite Fe2 Pd2 Sb12 using conventional powder X-ray diffraction. The thermoelectric properties are also reported. The existence of Fe2 Pd2 Sb12 phase was mentioned in a conference proceeding [14] as a part of review of skutterudite materials, however no detailed information concerning crystal structure and transport properties is available. 2. Experimental 2.1. Synthesis The Fe2 Pd2 Sb12 ternary compound was synthesized from individual elements by high-temperature solid-state reactions. Fe powder was first heated at 600 ◦ C for 2 h in H2 atmosphere to remove possible oxides. Stoichiometric amounts of Fe (99.9%), Pd (99.9%) and Sb (99.999%) were sealed into an evacuated silica glass tube and heated at 800 ◦ C for 48 h in a furnace. The material was then ground under acetone using agate mortar and pestle and heated at 550 ◦ C for 168 h. The resultant material was once again ground under acetone and heated again at 550 ◦ C for 240 h. After annealing, the furnace was turned off and allowed to cool slowly to room temperature. Finally, obtained powder samples were, after verification of the completion of the solid-state reaction with powder X-ray diffraction, hot-pressed at 500 ◦ C (HP-samples) and 50 MPa for 1 h. 2.2. Structure refinement
∗ Corresponding author. Fax: +420 251 818 748. E-mail address: [email protected] (F. Laufek). 0925-8388/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.12.085
The powder X-ray diffraction pattern of Fe2 Pd2 Sb12 was collected in Bragg–Brentano geometry on an X’Pert Pro PANalytical diffractometer equipped
J. Navrátil et al. / Journal of Alloys and Compounds 493 (2010) 50–54
51
Table 1 Data collection and Rietveld analysis. R agreement factors defined according to [27]. Data collection Radiation type, source Generator settings Data collection temperature Range in 2 (◦ ) Step size (◦ )
X-ray, CuK␣ 40 kV, 30 mA Room temperature 10–110 0.02
Crystal data Space group Unit cell content Unit cell parameters (Å)
Im3¯ (No. 204) Fe0.51 Pd0.49 Sb3 , Z = 8 a = 9.2048(2)
Rietveld analysis No. of reflections No. of structural parameters No. of profile parameters RBragg Rp Rwp Weighting scheme
102 3 4 0.059 0.052 0.067 1/yo Fig. 2. (a) Polyhedral representation and (b) ball-and-stick representation of the Fe2 Pd2 Sb12 structure showing the corner sharing arrangement of the [Fe(Pd)Sb6 ] octahedra and presence of four-member [Sb4 ] rings. (c) Detailed view of the [Sb4 ] ring.
Table 2 Refined parameters for the Fe2 Pd2 Sb12 . Atom
Site
x
y
z
Occ.
Biso [Å2 ]
Fe Pd Sb
8c 8c 24g
1/4 1/4 0
1/4 1/4 0.3374(2)
1/4 1/4 0.1549(2)
0.51(1) 0.49(1) 1
0.45(4) 0.45(4) 0.93(2)
breakpoints in the pattern. Refined structural parameters are given in Table 2, Fig. 1 shows final Rietveld plot. 2.3. Transport and thermoelectric properties
The displacement parameters of Pd and Fe were constrained to be equal.
with X’Celerator detector using CuK␣ radiation. To minimize background, the sample was placed on a flat-low background silicon wafer. The data were acquired in the angular range 10–110◦ 2. A full-width at half-maximum of 0.066◦ 2 was obtained at 13.340◦ 2 indicating good crystallinity of the sample studied. The details of data collection and basic crystallographic facts are given in Table 1. The crystal structure of Fe2 Pd2 Sb12 was refined by the Rietveld method for Xray powder diffraction data using the FullProf program [15]. With the exception of a small number of diffraction peaks attributable to Sb secondary phase (ca 2 wt%), all peaks can be indexed on a body-centred cubic lattice isotypic with CoSb3 [16]. Consequently, CoSb3 crystal structure was used as a starting structural model in Rietveld refinement. The refined parameters include those describing peak shape and width, peak asymmetry, unit cell parameters and fractional coordinates. Finally, 16 parameters were refined. The Pd and Fe atoms randomly occupy the 8c posi¯ their starting occupancy factors were assigned tion in the space group Im3; according to the Fe2 Pd2 Sb12 chemical composition. The subsequent refinement of individual occupancies of Pd and Fe atoms with the constraint that their sum corresponds to the 100% occupancy yielded the stoichiometry Fe2.03 Pd1.97 Sb12 . The pseudo-Voigt function was used to generate the line shape of the diffraction peaks. The background was determined by linear interpolation between consecutive
Electrical conductivity was measured with four-probe method using Lock-in Amplifier (EG&G model 5209) on the rectangular parallelepiped of dimensions about 10 mm × 3 mm × 1 mm. The measurements were performed on two different probes, one in the temperature region from about 100 to 350 K and the other from 300 to 800 K. The Hall constant RH was measured on the hot-pressed sample of dimensions 15 mm × 3 mm × 1 mm at 100–400 K temperature range. The measurement was realized using alternating current at a frequency of 1020 Hz, in magnetic field induction B = 0.7 T. The Seebeck coefficient was determined by means of static dc-method on rectangular shaped samples. The temperature gradient between two points was measured by two shielded K-type thermocouples that were pressed against the sample surface. A potential difference dU corresponding to the gradient dT was measured across the same legs of both attached thermocouples. The absolute Seebeck coefficient was determined from the slope of dU/dT dependence using 20 values of dT not exceeded 3 K. The thermal diffusivity was measured on round hot-pressed sample with help of LFA 457 (Netzsch). The thermal conductivity was then calculated using Pyroceram 9606 as a heat capacity standard.
3. Results and discussion 3.1. Crystal structure Fe2 Pd2 Sb12 adopts the skutterudite-type structure (CoAs3 ) and is depicted in Fig. 2. In this structure, each Pd/Fe atom is octahedraly coordinated by six Sb atoms with distance of 2.5915(8) Å. The [Fe(Pd)Sb6 ] octahedra share all six corners with adjacent octahedra forming a three-dimensional network. As is evident from Table 3, which shows comparison of selected bond distances and Table 3 Selected interatomic distances (Å) and bond angles (◦ ) for Fe2 Pd2 Sb12 and Fe2 Ni2 Sb12 [12] (M = Fe/Pd or Fe/Ni). Fe2 Pd2 Sb12 Distances M–Sb Sb–Sb
Fig. 1. Observed (circles), calculated (solid line) and difference Rietveld profiles for Fe2 Pd2 Sb12 . The upper reflection bars correspond to Fe2 Pd2 Sb12 and the lower bars to a 2 mass percent Sb impurity.
Angles Sb–M–Sb Sb–M–Sb M–Sb–M Sb–Sb–Sb
Fe2 Ni2 Sb12
6 × 2.590(2) 2.852(3) 2.993(3)
6 × 2.538(9) 2.89(1) 2.99(1)
6 × 85.374(1) 6 × 94.626(1) 125.3(1) 90.00
6 × 85.415(2) 6 × 94.458(3) 127.0(3) 90.00
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Fig. 3. Positional parameters y and z for Sb-bearing skutterudites, Oftedal’s relation is shown for comparison. CoSb3 data from [16], RhSb3 , IrSb3 and Fe2 Ni2 Sb12 data from [12]. A linear fit for observed points is indicated by dashed line.
angles for isostructural compounds Fe2 Pd2 Sb12 and Fe2 Ni2 Sb12 [12], the Fe/Pd–Sb distances are significantly larger than corresponding Fe/Ni–Sb distances in Fe2 Ni2 Sb12 . This can be explained by lower radius of the Ni atom (rNi = 1.25 Å [17]) compared to the radius of the Pd atom (rPd = 1.38 Å [17]). As was mentioned by Mitchell [9] and Vaqueiro et al. [10], the skutterudite structure can be considered as a derivative of the cubic perovskite structure ABX3 , characterized by vacant A-sites and tilting of octahedra (tilt system a+ a+ a+ ). The tilt angle (ϕ) for the ideal skutterudite structure can be calculated from unit cell dimension a and M–Sb distance (d) using a relationship [18] cos(ϕ) =
3a − 0.5 8d
Using this equation, we have calculated the values of tilt angles of 32.5◦ , 33.6◦ and 34.3◦ for Fe2 Ni2 Sb12 [12], Fe2 Pd2 Sb12 and IrSb3 [12], respectively. These values are in accordance with general trend observed in skutterudites; for a given “anion” the tilt angle (ϕ) increase with the increasing size of the cation [9,10]. The Sb atoms in the Fe2 Pd2 Sb12 structure form [Sb4 ] rings of rectangular shape with two very similar Sb–Sb distances (Fig. 2c). These rectangles are characteristic feature of the skutterudite structure. These distances become equal when the two fractional coordinates of the Sb atoms obey the so-called Oftedal’s relation y + z = ½ [19]. Fig. 3 shows y and z parameters for Sb-bearing skutterudites. As can be seen from this figure, Fe2 Pd2 Sb12 follows observed trend in unfilled Sb-bearing skutterudites; all compounds lie on one side of the Oftedal’s relation having two very similar (but not equal) Sb–Sb distances within the [Sb4 ] rings. Moreover, position of Fe2 Pd2 Sb12 point in Fig. 3 supports the observation of Kjekshus et al. [19] for binary skutterudites; all points are situated on a line approximately parallel to that given by Oftedal’s relation. It is also interesting to note, that a relatively large group of “anion-ordered” skutterudites has been prepared (e.g. CoGe1.5 Te1.5 [20] or CoSn1.5 Se1.5 [11]), cation-ordered analogues seems not to have been synthesized. In addition to the unfilled skutterudite structure, phases with the composition AB4 X12 , called filled skutterudites, can be created by the insertion of another atom (typically La–Yb [5,6]) in the
Fig. 4. Icosahedral voids (light grey) and [Fe(Pd)Sb6 ] octahedra (dark grey) in the crystal structure of Fe2 Pd2 Sb12 . Unit cell edges are highlighted.
icosahedral voids (Fig. 4) located at the centre of [MX6 ]8 octahedral cluster. The distance from hypothetical filling atom A to Sb atom in the Fe2 Pd2 Sb12 structure would have a value of 3.4 Å. This distance is in fact similar with that distance observed in filled skutterudite CeFe4 Sb12 [21]. As was mentioned by Makovicky [22] for the skutterudite structure, the icosahedral voids do not share any structural elements; they are connected by means of octahedra and Sb4 groups. 3.2. Transport and thermoelectric properties The ceramic method, widely used for solid-state synthesis of skutterudite compounds, suffers from several disadvantages. Mainly, it is very difficult, if not impossible, to achieve the full completion of reaction, and a lot of authors report (e.g. [23,24]) the existence of small quantity of other than desired reactants observed e.g. in powder X-ray diffraction patterns [25]. In case of skutterudites containing Sb on anion sites it is just unreacted antimony, which is detected in low, but detectable quantity in X-ray diffractograms. As it was mentioned above, this is also our case. One cannot also exclude that similar deficit, although undetectable, is also presented on cation sites. As a result, we obtained the compound, which contains quite large concentration of point defects, which behave both, as donors and acceptors and they are located in shallow levels inside of band gap. Such quite complicated point defects structure is, in our opinion, reflected in the temperature dependencies of the electrical conductivity , the Seebeck coefficient S (Fig. 5) and the Hall coefficient RH (Fig. 6) of the prepared compound. Just temperature dependence of RH product (Fig. 6) indicates the presence of the at least two types of carriers. The fact that it could be both electrons and holes is, in our opinion, suggested by the course of the temperature dependence of the Seebeck coefficient, which is at lowest measured temperatures negative and with the increasing temperature become positive. On the contrary, the values of RH stay in the whole measured temperature region (100–400 K) positive (Fig. 6). This contradiction could be explained e.g. by the higher mobility of holes compared to mobility of electrons, which was supposed to explain similar discrepancy in skutterudite semiconducting compounds [26]. Unfortunately, the lack of the low temperature data (below 90 K) excludes the closer elucidation of the observed problem.
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Fig. 7. The log vs. 1000/T plot of the Fe2 Pd2 Sb12 compound. Dashed line represents fit of a form log = log 0 − Eg /(2kT) to the higher temperatures, indicating Eg ∼ 0.22 eV.
Fig. 5. The temperature dependencies of the Seebeck coefficient S and the electrical conductivity of the Fe2 Pd2 Sb12 compound.
As follows from Fig. 5 with the increasing temperature the Seebeck coefficient peaks at about 500 K (∼60 V/K) and after quite steep fall changes again to negative value at about 780 K. The peak in the temperature dependence of S corresponds approximately with minimum in the same dependence of after that the electrical conductivity starts to increase. From the Arrhenius’ log vs. 1000/T plot (Fig. 7) it is evident that this increase is undoubtedly connected with excitation of electrons across band gap. Using a formula log = log 0 − Eg /(2kT) we were able to estimate value of the band gap of the studied compound Eg ∼ 0.22 eV. Similar band gap of Eg ∼ 0.16 eV was also reported for Fe2 Ni2 Sb12 [14]. The different sign of the Seebeck coefficient for Fe2 Ni2 Sb12 [14] (negative) and
Fig. 6. The temperature dependence of the Hall coefficient RH and the RH product (carriers mobility ) of the Fe2 Pd2 Sb12 compound at 100–400 K temperature range.
Fe2 Pd2 Sb12 (positive) in the temperature range from 300 to 800 K is just the matter of non-stoichiometry of these compounds and strongly depends on the Fe/Ni and Fe/Pd ratio. The temperature dependence of thermal conductivity total of the compound measured at temperature range 300–700 K is presented in Fig. 8. Its values are approximately two times lower than values for its binary analogues CoSb3 and RhSb3 [26], and approximately comparable with those found for Fe2 Ni2 Sb12 [14]. We suppose the degenerated case and the presence just two main contributions to thermal conductivity, i.e. its electronic part el and lattice part lat . Then it is possible to separate these parts using the formula el = L.T., where L = 2.443 × 10−8 V2 K−2 . The electronic part el presents about quarter of the total thermal conductivity. One can expect that filling the voids of the skutterudite structure with proper filler can lead even to lower values of the thermal conductivity. The thermoelectric figure-of-merit Z, defined as Z = S2 /total , was calculated. It reaches the maximum value of about 7 × 10−5 K−1
Fig. 8. The temperature dependence of the measured total thermal conductivity total of the Fe2 Pd2 Sb12 compound measured between 300 and 700 K. el and lat contributions were separated by calculation of el supposing the high degree of degeneration of the prepared semiconducting compound.
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at 500 K. This low value of parameter Z is caused by very low value of Seebeck coefficient ˛ due to the presence of two types of free current carriers. However, one can suppose that the suitable doping suppressing mainly the concentration of electrons could increase the value of Z. 4. Conclusion To conclude, Fe2 Pd2 Sb12 has cubic skutterudite structure with ¯ In the studied temperature range, the figurethe space group Im3. of-merit Z has maximum value of 7 × 10−5 K−1 at 500 K. This value is significantly lower compared with in the state-of-the-art thermoelectric materials, particularly because of the low value of Seebeck coefficient. Further optimisation of this parameter by proper doping can enhance the thermoelectric properties. Acknowledgements This research was supported by the Ministry of Education of the Czech Republic under the project MSM0021627501 and the project of Grant Agency CR No. 203/07/0267. References [1] C. Uher, in: M.G. Kanatzidis, S.D. Mahanti, T.P. Hogan (Eds.), Chemistry, Physics and Materials Science of Thermoelectric Materials: Beyond Bismuth Telluride, Kluwer Academics, Plenum Publishers, New York, 2003, p. 121. [2] Y. Nagamoto, K. Tanaka, T. Koyanagi, Proceedings of the 16th International Conference on Thermoelectrics, Dresden, Germany, 1997, pp. 330–333. [3] A. Borshchevsky, J.P. Fleurial, E. Allevato, T. Caillat, Proceedings of the 13th International Conference on Thermoelectric, Kansas City, USA, 1994, pp. 3–6.
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