Correlations between Structural and Electronic Properties in the Filled

Feb 19, 2016 - INSTM—Interuniversitary Consortium of Science and Technology of Materials, Genova Research Unit, Via Dodecaneso 31, 16146 Genova, Ita...
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Correlations between Structural and Electronic Properties in the Filled Skutterudite Smy(FexNi1−x)4Sb12 Cristina Artini,*,†,‡ Gilda Zanicchi,†,§ Giorgio Andrea Costa,†,∥ Maria Maddalena Carnasciali,†,§ Carlo Fanciulli,⊥ and Riccardo Carlini†,§ †

Department of Chemistry and Industrial Chemistry, University of Genoa, Via Dodecaneso 31, 16146 Genova, Italy CNR-IENI, Via De Marini 6, 16149 Genova, Italy § INSTMInteruniversitary Consortium of Science and Technology of Materials, Genova Research Unit, Via Dodecaneso 31, 16146 Genova, Italy ∥ CNR-SPIN Genova, Corso Perrone 24, 16152 Genova, Italy ⊥ CNR-IENI, Corso Promessi Sposi 29, 23900 Lecco, Italy ‡

S Supporting Information *

ABSTRACT: A structural study of the filled skutterudite Smy(FexNi1−x)4Sb12 was performed by means of X-ray powder diffraction and μ-Raman spectroscopy with the aim to unveil the correlations between structural and electronic properties of this material and to favor the improvement of its thermoelectric performance. Samples were prepared by direct reaction of the elements at 1223 K, followed by quenching and subsequent sintering at 873 K; microstructure and composition of the obtained products were determined by SEM-EDS. The position of the boundary separating regions that obey hole- and electron-based conduction mechanisms was found by X-ray diffraction at x ≈ 0.63 and y ≈ 0.30, confirmed by measurements of room-temperature Seebeck coefficient, and discussed on the basis of crystallographic data. The presence of a discontinuity is observed in several structural and spectroscopic parameters at the p/n crossover; it is interpreted as associated with the change in the conduction mechanism. The role of the rare earth filling fraction in driving the structural response of the material is investigated too. The advantage of using X-ray diffraction and μ-Raman spectroscopy as aids in the study of electronic properties of this material is highlighted, as well as the complementarity of the two techniques.

1. INTRODUCTION Filled skutterudites form a fascinating class of intermetallic materials that has attracted the interest of the scientific community for several decades, thanks to their puzzling physical properties.1,2 They derive from the well-known family of skutterudites, the binary compounds with composition MX3 (M = Co, Rh, Ir and X = P, As, Sb), first studied and identified by Oftedal almost a century ago.3 The variety of the possible fillers, as well as the possibility of substitutions at the M and the X sites, allow to tune the electronic structure of these compounds, and so to obtain materials characterized by different and intriguing properties, such as superconductivity,4,5 mixed valence,6 heavy Fermion behavior7,8 and metal− insulator transitions.9 Indeed, the most striking property of many filled skutterudites and skutterudite-related compounds10,11 is their low thermal conductivity coupled to high electrical conductivity, which make them exceptional candidates for high-temperature thermoelectric applications.12 Skutterudites MX3 crystallize in a body-centered cubic cell (Pearson symbol cI32; isotypic crystal, CoAs3) belonging to the Im3̅ space group; it is characterized by two atomic positions, namely the 8c (1/4,1/4,1/4) and the 24g (0,y,z), occupied by © 2016 American Chemical Society

the M and X atom, respectively. In this atomic arrangement M is coordinated to 6 X atoms, forming slightly distorted and strongly tilted corner-sharing octahedra, while X atoms build nearly square rings; consequently, an X12 icosahedral cage is created in the 2a site located in (0,0,0) that, due to its size, can be filled by sufficiently big atoms, such as lanthanide elements. When all the available voids are filled, the composition of a filled skutterudite, REM4X12 (RE = rare earth), is obtained; the resulting crystal structure, depicted in Figure 1, has been originally studied by Jeitschko and Braun.13 The efficiency of a thermoelectric material is generally evaluated through the figure of merit ZT, defined as

ZT =

TσS2 λe + λph

(1)

where T is the temperature, σ is the electrical conductivity, S is the Seebeck coefficient, and λe and λph are the electronic and phononic contributions to thermal conductivity. The search for Received: December 18, 2015 Published: February 19, 2016 2574

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and the compound is again a diamagnetic semiconductor.16 In filled skutterudites where Co is substituted by a mixture of two different transition metals (such as for example Fe/Ni or Fe/ Co), a linear correlation between the content of the filler atom and each one of the transition metals, is generally expected. Nevertheless, experiments show that it is in general not possible to fully compensate electron deficiency by filling, since the maximum amount of foreign atoms that can be inserted is often lower than necessary to equal the electronic count of the parent compound; this fact gives rise to the occurrence of the so-called p-type skutterudites, characterized by a slight metallic character. Under certain conditions it is also possible to provide a higher number of electrons than necessary, producing n-type skutterudites. The introduction of the filler atom affects not only thermal conductivity, but also electric conductivity, since from the electronic imbalance accounting for the existence of pand n-type skutterudites, it derives an enhancement of the carrier density and a slightly metallic character of the resulting phase; nevertheless, the net effect on thermoelectric performances is dominated by the strong decrease in the thermal conductivity. It is worth underlining that thermoelectric devices are built with a p- and an n-type leg, so that it is generally convenient to obtain both of them from the same matrix, mainly in order to reduce lattice thermal mismatch. As previously described, filled skutterudites fall within this case, since their electronic properties can be tuned by acting both on the filling fraction and on the substitution at the M site. Electronic properties of materials are generally quite difficult to study, since they need band structure calculations. In the case of filled skutterudites, a signature of the transition between different conduction mechanisms can be found in some structural parameters, which can indeed act as a bridge between crystallographic and electronic properties. Besides, the skutteruditic atomic arrangement shows a response to the introduction of filler atoms and to substitutions at the M site in terms, for example, of lattice parameters variation, shape of the Sb4 ring and atomic displacement parameters.17 The flexibility of the skutteruditic structure, which makes possible to tune the electronic, and hence the thermoelectric properties of the material, opened in the past 20 years an immense field to material scientists: even limiting the assessment to Sb-based filled skutterudites, Ni,18 Fe/Ni19,20 and Fe/Co21−23 compounds, filled with different lanthanide ions, can be found in the literature. Nevertheless, the great majority of papers regarding these compounds deals with the thermoelectric properties of the material rather than with their structure, and although Sm-filled Fe,24 Co,25 Fe/Co26 and Os27 antimonides are described in the literature, to the authors’ knowledge the Smy(FexNi1−x)4Sb12 system has been recently treated only by this research group with particular reference to its thermoelectric properties.28 In this work the structural response of Smy(FexNi1−x)4Sb12 to the combined effect of the variable Fe/Ni content and the Sm filling fraction is studied by X-ray powder diffraction and μRaman spectroscopy. A discontinuity in several structural parameters is observed at the boundary between compositions obeying to the hole- and electron-based conduction mechanism, so that the mark is believed to be related to the change in the electronic nature of the material. The position of the p/n crossover, derived from diffraction data, was confirmed through the information provided by room-temperature Seebeck measurements.

Figure 1. Crystal structure of a generic filled skutterudite REyM4X12. Tilted MSb6 octahedra and X4 rings are highlighted.

high ZT values is quite a complicated issue, as all the quantities appearing in eq 1 are strictly interconnected. In order to enhance ZT, high σ and low λ are required; since σ and λe are correlated, a reduction of the thermal conductivity that does not affect the σ value can be mostly obtained by reducing λph, i.e. by reducing the phonon mean free path. The decoupling of electrical and thermal conductivity is at the basis of the PGEC (phonon glass electron crystal) concept,14 stating that the ideal thermoelectric material should conduct heat like a glass and electricity like a crystal; in other words, phonons should be strongly scattered to ensure a low thermal conductivity, while electrons should maintain a high mean free path, in order to guarantee a high electric conductivity. Taking into account these requirements, the most efficient thermoelectric materials can be found among semiconductors for two main reasons: (1) Differently from metals, they show an increasing electric conductivity with increasing temperature, and σS2 (the power factor) has a maximum in the carrier density range proper of semiconductors. (2) In semiconductors λph prevails over λe so that it is possible to separately act on thermal and electric conductivity. In this respect, filled skutterudites represent an example of easily tunable thermoelectric materials. The electronic structure of the parent compound CoSb3 can be described according to the Zintl’s concept:15 Co (d7s2), being located at the center of the Sb6 octahedra, provides onehalf an electron to each Sb atom (s2p3), so acquiring a 3+ formal valence. Sb, in turn, receives two electrons from the two neighboring Sb atoms via σ bonds through the Sb4 ring, and one-half electron from two Co atoms, thus completing its outer electronic shell. By a simple electron count it can be concluded that Sb atoms contribute 9 electrons to each Co atom, so bringing the latter to its stable 18-electron configuration. Owing to the engagement of the three aforementioned electrons, Co is left with 6 nonbonding electrons, which occupy the three t2g low-energy orbitals resulting from the splitting of the five d orbitals due to the octahedral crystal field. This model is confirmed by the physical properties of CoSb3, which is a diamagnetic semiconductor. The insertion of a foreign atom in (0,0,0), necessary to lower λph through rattling around the equilibrium position, is however not possible in CoSb3 due to electronic reasons, since the filler atom would provide a certain amount of electrons in excess with respect to the stable configuration. Filling is, on the contrary, necessary to stabilize electron-deficient skutterudites, such as the ones where Co is partially or totally replaced by a lighter transition element. In P12CeFe4, for example, Ce provides the four missing electrons, 2575

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Figure 2. SEM photo taken by backscattered electrons of a hole just underneath the surface of Fe70. Crystals of the skutteruditic phase are clearly visible. a 50× magnification. The laser power was kept at 10% of the nominal value, i.e., at around 2 mW; the spectral resolution is 3 cm−1. 2.5. Room-Temperature Measurements of the Seebeck Coefficient. The room-temperature Seebeck coefficient of the samples was measured using two different systems: a homemade facility that measures the voltage produced by the sample under the application of a stable temperature difference, and a commercial instrument from MMR Technology that measures the Seebeck coefficient of the material by collecting the response of a thermocouple with a known constantan reference leg. The precision of the measurement performed by the homemade instrument was increased by applying temperature differences ranging between 2 and 8 K; in order to maintain the same mean temperature in each measurement, both cold and hot side temperatures were changed. Results obtained using both systems displayed a maximum discrepancy lower than 5%.

2. EXPERIMENTAL SECTION 2.1. Synthesis. Ten samples belonging to the Smy(FexNi1−x)4Sb12 system, with x = 1, 0.9, 0.8, 0.7, 0.63, 0.60, 0.58, 0.55, 0.5, and 0.4, were prepared. Synthesis was performed by direct reaction of pure elements Fe (Alfa-Aesar, 99.99 wt%), Ni, Sm (NewMet, 99.9 wt%), and Sb (Mateck, 99.99 wt%). The Sm amount to be added to the starting mixture was determined during a previous test by using an excess of Sm and evaluating for each composition the actual Sm content located in the voids. Sb was added in slight excess taking into account its high vapor pressure. The starting mixture was placed into an Ar-filled silica ampule and subsequently sealed under an Ar flow. The tube was heated up to 1223 K for 3 h and then quenched in an iced water bath; afterward, samples were annealed at 873 K for 4 days. Samples are hereafter named Fe100, Fe90, ..., according to the nominal % Fe content with respect to the total (Fe + Ni) amount. 2.2. Electronic Microscopy. With the aim to study microstructure and composition of the obtained compounds, micrographically polished surfaces of the samples were observed by scanning electron microscopy (SEM) equipped with energy-dispersive X-ray spectroscopy (EDS) (Zeiss EVO 40, with Oxford Instruments Pentafet Link; software package, Oxford-INCA v. 4.07; standard, Co; acceleration voltage, 20 kV; working distance, 12 mm; live time, 40 s). For each sample, photos were taken both by backscattered and secondary electrons, and EDS analyses were performed on at least five points or areas to identify the phases and determine the local composition. 2.3. X-ray Diffraction. Annealed samples were ground and sieved through a 44 μm sieve; precise lattice parameters were obtained from diffraction spectra collected by means of a Bragg−Brentano powder diffractometer (Philips PW1050/81, Fe-filtered Co Kα radiation) making use of a zero-background sample holder and Ge as an internal standard. Rietveld refinements were performed using the FullProf program29 on diffraction patterns collected by the same instrument in the range 15−120° (2θ step, 0.02°; counting time, 17 s). 2.4. μ-Raman Spectroscopy. μ-Raman spectra were acquired by a Renishaw System 2000 Raman imaging microscope; analyses were performed on powder samples at room temperature as a result of 16 accumulations, by using a 633 nm He−Ne laser in the range 1000−70 cm−1; they were recorded at least on three points for each sample, with

3. RESULTS The high melting temperature of the M atom, together with the high vapor pressures of the pnictide atom, generally make the synthsis of skutterudites difficult. Several methods for the preparation of bulk samples are reported in the literature, including high-pressure, high-temperature synthesis,30 arcmelting,23 high-frequency induction melting,31 and various two-step processes.32,33 In this work samples were prepared by an effective method derived from a modification of the synthetic path proposed by Sales et al.,12 similarly to the technique described in ref 19, the procedure resulted to be energy- and time-saving, due to the lower temperature and the shorter duration of thermal treatments with respect to what suggested in the cited papers. 3.1. SEM-EDS Characterization. SEM images and EDS analyses, as well as X-ray diffraction patterns, show that for each composition the main phase is the filled skutterudite; the average size of skutterudite crystals ranges between 30 and 80 μm, as observable in Figure 2, where crystals of the Fe70 sample can be seen. In all the samples, the evaluated Fe/Ni ratio is very close to the nominal value; however, small amounts of different additional phases can be observed. In particular, the 2576

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parameters, and the background points, were allowed to vary simultaneously. Individual isotropic displacement parameters Biso were refined for each atom. Occupational ratios of Fe and Ni were fixed to the value resulting from the EDS analysis and not refined, due to the similarity of their scattering factors; the Sb occupancy factor, on the contrary, was refined. In Figure 4 the Rietveld refinement plot of Fe60 is reported as a representative example, while agreement factors are listed in Table 1. The filler atom content is a key parameter when discussing the electronic properties of filled skutterudites and the correlations with the structural features of the phase; therefore, the Sm occupancy factor of the 2a position as resulting from Rietveld refinements, is shown in Figure 5a as a function of the Fe amount. As expected, a decreasing linear behavior is observed with increasing the Fe substitution by Ni, due to the increasing negative charge provided by the latter. The thick black line represents the Sm amount theoretically necessary to exactly reproduce the electronic count of the parent compound CoSb3, while the thin one is the regression line interpolating experimental data; the crossing point of the two lines, located at x ≈ 0.63 and y ≈ 0.30, represents the boundary composition between p- and n-type skutterudites, according to the structural investigation. This conclusion is fully compatible with the measurements of the room-temperature Seebeck coefficient, as discussed later. A further indication regarding the filler content derives from the (3 1 0)/(2 1 1) X-ray intensity ratio: a relationship is in fact claimed to exist between the cited parameter and the filling fraction,17,31 so that the former is often used as an indirect way to measure the latter. The (3 1 0)/(2 1 1) ratio obtained from observed and calculated integrated intensities is plotted in Figure 5b as a function of the Sm amount: a regularly decreasing trend can be observed with increasing the Sm content, similarly to what observed in the Cey(FexCo1−x)4Sb12.31 Interestingly, close to the boundary composition the presence of a discontinuity is observed in several structural parameters. The trend of the lattice parameter as a function of the Fe amount (shown in Figure 5c), for example, reveals a decrease with the progressive substitution of Fe by Ni, reflecting the diminution in the mean atomic size at the Fe/ Ni site; the presence of the aforementioned slope change can be noticed in correspondence of the p/n boundary. Similarly, a discontinuity can be observed in the trend of the Fe/Ni−Sb interatomic distance within the Sb6 octahedra, as observable in the inset of Figure 5c. The coincidence between the position of the discontinuity and the p/n boundary suggests a possible correlation between structural and electronic properties. 3.3. Spectroscopic Characterization. μ-Raman spectra were collected on powders of all samples; significant signals were found only in the 200−70 cm−1 region. In Figure 6 spectra collected on samples Fe40, Fe50, and Fe90 are shown; the presence of three vibrational modes (at ∼170, ∼140, and ∼120 cm−1) can be noticed, as well as their shift as a function of composition; peaks of single Raman signals were fitted by interpolating the experimental points with a pseudo-Voigt function. It is worth underlining that signals generated by the Raman-active modes of skutterudites are generally quite weak; moreover, Raman bands deriving from the presence of Sb (i.e., of the main additional phase) occur essentially in the same region. Therefore, in order to unequivocally distinguish between signals deriving from both phases, a μ-Raman

presence of few Sb is recognizable both by SEM-EDS and X-ray diffraction, as well as a minimum amount of the pseudobinary phase (Fe,Ni)Sb2. Moreover, many of the samples display also traces of a Sm-based phase (mainly SmSb2 and (Fe,Ni)SmSb3 in high- and low-Fe content samples, respectively), suggesting that the observed Sm content is an intrinsic property of the filled skutterudite, not depending on the Sm availability. It is noteworthy that only the Sb amount could be evaluated by Rietveld refinement, since (Fe,Ni)Sb2 is present only in traces, and the content of Sm-based additional phases lies below the detection limit of the technique. In Figure 3, a SEM microphotograph of Fe60 is reported; in Table 1, the refined compositions and a list of additional phases are reported for each sample.

Figure 3. SEM microphotograph taken by backscattered electrons on Fe60.

Table 1. Refined Compositions, List of Additional Phases, and Agreement Factors of Rietveld Refinements sample

refined composition

Fe100

Sm0.75Fe3.7Sb12

Fe90

Sm0.65Fe3.3Ni0.4Sb11.7

Fe80 Fe70 Fe63 Fe60 Fe58

Sm0.58Fe2.9Ni0.6Sb11.6 Sm0.45Fe2.5Ni0.9Sb11.6 Sm0.31Fe2.5Ni1.5Sb11.6 Sm0.23Fe2.2Ni1.6Sb11.4 Sm0.22Fe2.1Ni1.7Sb12

Fe55 Fe50

Sm0.27Fe2.1Ni1.7Sb12 Sm0.18Fe1.8Ni1.8Sb12

Fe40

Sm0.06Fe1.5Ni1.9Sb11.1

a

additional phases

χ2

RBa

Sb, FeSb2, SmSb2 (traces) Sb, (Fe,Ni)Sb2 (traces), SmSb2 (traces) Sb, (Fe,Ni)Sb2 (traces) Sb (Ni,Fe,Sm)Sb2 (traces) (Fe,Ni)Sb2 (traces) Sb, SmSb2, (Fe,Ni)Sb2 (traces) Sb Sb, (Ni,Fe)Sb2 (traces), (Fe,Ni)SmSb3 (traces) Sb, (Fe,Ni)Sb2 (traces), (Fe,Ni)SmSb3 (traces)

5.52

5.74

5.47

4.07

3.09 4.69 2.15 4.83 4.31

9.14 5.04 4.80 3.03 4.28

2.92 8.77

4.87 4.90

9.27

5.15

RB is referred to the skutterudite.

3.2. Structural Characterization. X-ray powder patterns were refined according to the cubic cell crystallizing in the Im3̅ space group, as previously described. For all the diffractograms, the background was fitted by linear interpolation of a set of ∼70 points taken from the collected spectrum, while peak profiles were modeled using the pseudo-Voigt function. In the last refinement cycles, the structural parameters (x and y atomic coordinates of Sm, and the Sm and Sb occupation in the 2a and 24g positions, respectively), as well as the scale factor, nine peak 2577

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Figure 4. Plot of Rietveld refinement of Fe60. The red and black lines are the experimental and the calculated diffractogram, respectively. The lower line is the difference curve. Vertical bars indicate the calculated positions of Bragg peaks of the filled skutterudite.

Fe content up to a maximum located at x ≈ 0.58; with further decreasing the Fe amount, it abruptly decreases until it becomes negative close to x = 0.55. This trend has already been observed for other similar systems, such as Mmy(FexCo1−x)4Sb12, Mmy(FexNi1−x)4Sb12,42 Cey(FexCo1−x)4Sb12, Yby(FexCo1−x)4Sb12, Cey(FexNi1−x)4Sb12, Yb y (Fe x Ni 1 − x ) 4 Sb 1 2 , Ce y / 2 Yb y / 2 (Fe x Ni 1 − x ) 4 Sb 1 2 and Cey/2Yby/2(FexCo1−x)4Sb12;23 in all the cited systems the p/n crossover has been observed close to the x value corresponding to the electronic count of an intrinsic semiconductor. The close resemblance among the behaviors of different systems allows to conclude that the room-temperature thermopower is driven by the amount of charge carriers irrespective of the identity of the filler atom. Conventionally, the p/n crossover takes place at the composition where the Seebeck coefficient changes its sign; nevertheless, the physical meaning of the thermopower behavior is much more complicated, since in the transition region the multiband electronic structure of the material gives rise to the existence of two contributions to the Seebeck coefficient that can be described by the following expression:

spectrum was collected also on Sb and reported in Figure 6 too: the two signals present at 152 and 114 cm−1 are attributed to an A1g and an Eg mode of Sb, respectively.34,35 The presence of a weak signal in Raman spectra of Fe40 and Fe50 in correspondence of the strongest Sb band confirms the results obtained from X-ray diffraction and SEM-EDS. The Raman response of skutterudites has been quite widely studied from both theoretical36 and experimental points of view.37−40 Eight Raman-active modes are predicted, namely 2Ag + 2Eg + 4Tg (with Ag, Eg, and Tg being the irreducible representations), and all of them are due to the vibration of the Sb atoms. The two main signals are observed for example in Co-based filled skutterudites at ∼180 and ∼150 cm−1,38 with the former remarkably stronger than the latter; they are generally attributed to the stretching of the shorter and the longer Sb−Sb bond in the Sb ring, respectively. In addition to the described signals, bands located at lower Raman shift (for Os-based filled skutterudites at ∼100 cm−1)40 are observed, and attributed to second-order phonons due to the vibration of the rare earth. Based on the described literature data, both signals collected on our samples at higher Raman shift are ascribed to the Sb−Sb vibration, while the one at the lowest Raman shift is attributed to the rare earth-related second order phonons. A general intensity decrease and broadening of the skutterudites’ Raman signals is observed with increasing filling fraction, so that at high Sm content the band at ∼150 cm−1 can hardly be detected; this behavior is commonly observed, and it is attributed to the presence of the filler atom, which through its rattling motion gives rise to fluctuating bonds with Sb atoms, so contributing to distortions that cause the broadening and the height reduction of the peak. Figure 7a shows the trend vs Sm amount of the peak frequencies related to the vibration of the shorter Sb−Sb distance: it can be observed that with increasing Sm content a redshift takes place, as can be expected from the behavior of the cited interatomic distance as a function of the Sm amount (see inset). Similarly, the lowest-frequency signal moves toward lower Raman shift values with increasing Sm content, as observable in Figure 7b. A slope change can be noticed close to the p/n boundary in both plots, analogously to what observed in the trend of the lattice parameter. 3.4. Room-Temperature Seebeck Coefficient. The behavior of the room-temperature thermopower as a function of Fe amount is shown in Figure 8. It can be observed that the value of the Seebeck coefficient increases with decreasing the

S=

∑i σiSi ∑i σi

=

neμe Se + nhμ h S h neμe + nhμ h

(2)

where S, Se, and Sh are the overall, electron, and hole Seebeck coefficient, respectively, σ is the electrical conductivity, ne and nh are the negative and positive charge carriers, respectively, and μe and μh are the mobility of electrons and holes, respectively. Therefore, as the mobilities are involved too, the sign change does not necessarily represent the crossover in terms of amount of charge carrier. Since the Seebeck coefficient is inversely proportional to the charge carriers density, the p/n crossover can be more conveniently located close to the composition where it assumes the maximum value; thus, Seebeck measurements indicate that the p/n crossover is in the close vicinity of the boundary composition obtained from the analysis of structural data.

4. DISCUSSION The effort to reduce thermal conductivity, based on filling the cavity located in (0,0,0), has led material scientists to the use of lanthanide ions as the most common filler atoms. Their size allows them in fact to be bound weakly enough to properly 2578

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Figure 6. Raman spectra of Sb and samples Fe40, Fe50, and Fe90.

Figure 5. (a) Sm content (y) in Sm y(FexNi1−x) 4Sb12 filled skutterudites as a function of x. The thick line represents the theoretical Sm amount necessary to reproduce the electronic count of the compensated semiconductor CoSb3; the thin one is the regression line interpolating experimental points; the red dashed line highlights the position of the p/n crossover. Error bars are hidden by data markers. (b) Ratio of the (3 1 0)/(2 1 1) observed and calculated integrated intensities as a function of the Sm amount. Calculated values were obtained by Rietveld refinements. (c) Trend of the cell parameter of Smy(FexNi1−x)4Sb12 filled skutterudites as a function of x. Blue dashed lines are the regression lines interpolating experimental data; in the inset the trend of the Fe/Ni−Sb distance within the Sb6 octahedra as a function of x. Error bars are hidden by data markers.

Figure 7. Peak frequencies as a function of Sm amount of the Raman mode at (a) ∼170 cm−1 (inset: trend of the Sm−Sm interatomic distance vs the Sm amount) and (b) ∼120 cm−1 (inset: trend of the Sb−Sb interatomic distance vs the Sm amount). Blue dashed lines are the regression lines interpolating experimental data.

compared to data referred to Sm. It can be noticed that, considering filler atoms in the same oxidation state and having ionic radius within the range of rare earths sizes, filling fractions at a given Fe/Ni content are comparable, thus indicating a strong dependence on the electronic contribution of the filler atom, rather than on its size. A higher filler content is observed only for the Ba2+-based compound, due to the lower oxidation state, which induces a higher filling fraction in the 2a site. Making use of the results of Rietveld refinements, the space available for each Sm atom can be evaluated by considering the 12 equal Sm−Sb interatomic distances within the cage centered

rattle, but strongly enough to be retained within the cage. Thus, the maximum amount of lanthanide ions acceptable by the structure is found to be a fundamental parameter. In Table 2 a collection of values of rare earth filling fractions in Fe/Ni filled skutterudites taken from the literature is reported and 2579

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example, from the Sb−H distance in SbH3),47 after subtracting it from the Sm−Sb distance, the space available for the Sm atom would range between 1.6 and 1.7 Å. Since the covalent radius of Sm3+ [C.N. 12] is 1.24 Å,41 it can be concluded that Sm can rattle around its atomic position. Nevertheless, although the void is oversized with respect to the filler atom dimension, the trend appearing in Figure 9 indicates that the cage size is sensitive to the Sm occupancy factor, since a larger size is observed with increasing the Sm amount. This evidence implies that even the Sm content contributes to the value of the lattice parameter, as will be discussed later. The atomic displacement parameter B, as obtained from Rietveld refinements, is the sum of the contributions due to thermal vibrations and positional disorder. The analysis of this parameter in our samples reveals remarkably higher values for Sm than for all the other elements, as can be inferred from the comparison between Figure 10, where the trend of the BSm is

Figure 8. Room-temperature Seebeck coefficient as a function of Fe amount.

Table 2. Values of the Filler Atom Content (y) at a Given x in Smy(FexNi1−x)4Sb12 for Different Filler Atoms filler ion

x

y

ionic radiusa (Å)

2+

0.75 0.625 0.63 0.625 0.642 0.70 0.70 0.74 0.875 0.90

0.96 0.33 0.31 0.4 0.38 0.40 0.45 0.61 0.71 0.64

1.61 (C.N. 12) 1.34 (C.N. 12) 1.24 (C.N. 12) 1.042 (C.N. 9) 1.31 1.26 (C.N. 12) 1.24 (C.N. 12) 1.27 (C.N. 12) 1.179 (C.N. 9) 1.24 (C.N. 12)

Ba Ce3+ Sm3+ Yb3+ Mm3+ DD3+ Sm3+ Nd3+ Pr3+ Sm3+

reference 44 18

this work 23 42 45

this work 44 46

this work

a

Ionic radii are taken from ref 41. Approximated values for the average ionic size of DD (didymium) and Mm (mischmetal) were calculated by considering the composition of Mm and DD as indicated in refs 42 and 43, respectively.

Figure 10. Atomic displacement parameter of Sm and, in the inset, of Fe/Ni, as a function of x in Smy(FexNi1−x)4Sb12. Error bars are hidden by data markers.

in (0,0,0); their trend is reported as a function of the Sm amount in Figure 9. It can be observed that the values of the cited distance increase with increasing Sm amount (and thus with increasing Fe amount), as expected due to the bigger size of Fe with respect to Ni, and range between 3.3402(4) Å (Fe40) and 3.3910(5) Å (Fe100). If a value of ∼1.7 Å is considered suitable for the Sb3− covalent radius (derived, for

reported as a function of the Fe amount, and the inset, showing the same for BFe/Ni. This evidence, commonly observed in filled skutterudites, is due to the vibration of the filler atom around its equilibrium position, responsible for the low values of thermal conductivity. The increasing trend of the Sm B parameter with decreasing Fe amount (and thus with decreasing Sm amount), on the contrary, is related to the predominance of the temperature-independent contribution over the thermal one: with decreasing the Sm amount, the Sm positional disorder increases. This conclusion is corroborated by the fact that the effectiveness of filled skutterudites at scattering heat-carrying phonons, which determines the thermal contribution to B, is larger at higher filling fractions.17 Values of the Sb displacement parameter are quite scattered and low (