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We present neutron and synchrotron powder-diffraction investigations as well as ab initio calculations to .... Even so, structural questions arise that cannot readily be solved by the ..... Ni-filled system from Co4Sb12 and Ni4Sb12 is endothermic or ..... reaction. The exothermic reaction is to be interpreted as the energy change.
JOURNAL OF APPLIED PHYSICS

VOLUME 96, NUMBER 6

15 SEPTEMBER 2004

Structural study of Fe doped and Ni substituted thermoelectric skutterudites by combined synchrotron and neutron powder diffraction and ab initio theory M. Christensen and B. B. Iversena) Department of Chemistry, University of Aarhus, Danmark-8000 Aarhus C, Denmark

L. Bertini and C. Gatti Istituto di Scienze e Tecnologie Molecolari, via Camillo Golgi 19, 20133 Milano, Italy

M. Toprak and M. Muhammed Materials Chemistry Division, Royal Institute of Technology, Sweden-10044 Stockholm, Sweden

E. Nishibori Department of Applied Physics, Nagoya University, Furo-Cho, Chikosa, Nagoya 464-8603, Japan

(Received 19 March 2004; accepted 14 June 2004) We present neutron and synchrotron powder-diffraction investigations as well as ab initio calculations to elucidate delicate structural features in doped skutterudites. Samples with assumed Fe doping were investigated (FeyCo4Sb12, y = 0.4, 0.8, 1.0, and 1.6), as well as samples with formal Ni substitution (Co4−xNixSb12, x = 0, 0.4, 0.8, and 1.2). The present study serves as a case story for the determination of fine structural details of thermoelectric skutterudites by diffraction methods in combination with ab initio calculations. We illustrate the problem of fluorescence in the conventional x-ray powder diffraction on the Fe-doped samples by a comparison with the neutron powder-diffraction data. On the series of the Ni-substituted samples, the neutron powder-diffraction data were collected to investigate the exact sitting of the Ni. The sample with the highest Ni substitution 共Co2.8Ni1.2Sb12兲 was also used for high resolution, high-energy synchrotron powder diffraction measurements. These revealed that the sample consists of two skutterudite phases. A complete description of the Ni-substituted samples was obtained in tandem with ab initio calculations, which show that the system contains a Ni-rich 共Co0.38Ni3.62Sb12兲 and a Ni-poor 共Co3.76Ni0.24Sb12兲) skutterudite phases. © 2004 American Institute of Physics. [DOI: 10.1063/1.1781762] I. INTRODUCTION

the transition metal framework, and the remaining voids potentially can be filled with interstitial dopant atoms 共R兲. Figure 1(b) gives a polyhedra representation of the structure with each transition metal placed at the center of the cornersharing octahedra formed by the group XV elements. The structures are equivalent, and the two representations serve to highlight the different aspects of the structure. The binary skutterudites 共y = 0兲 have moderate thermoelectric figures of merit Z due to a relatively high-lattice thermal conductivity ␬L compared with the filled skutterudites 共y ⬎ 0兲. The loosely bound interstitial atoms “rattle” in the oversized cages, which causes a scattering of the heatcarrying phonons.2 Another approach for lowering ␬L is to introduce the grain-boundary scattering through nanostructuring.3,4 However, the nanostructuring also affects the electrical conductivity, reducing the gain in Z obtained from the lower thermal conductivity.5 To control the electrical conductivity, Co or Sb can be substituted, e.g., by Ni or Te, respectively. Samples with small amounts of Ni dopant were recently investigated both experimentally and theoretically.6–8 A proper understanding of the doping mechanisms in the skutterudite system is crucial to suggest a strategy for improving the thermoelectric properties. Knowledge of the precise structure is therefore a prerequisite for any rational design of improved materials. The synthesis,

The recent interest in semiconducting skutterudite materials is due to their potential as effective thermoelectric materials.1 A prerequisite for an efficient energy conversion in thermoelectric devices is that the materials have highthermoelectric figures of merit, Z = S2␴ / ␬, where S is the Seebeck coefficient, ␴ the electric conductivity, and ␬ the thermal conductivity. The latter has an electronic 共␬e兲 and a lattice 共␬L兲 contribution. The performance of a thermoelectric material can be improved by tuning these parameters through doping. In general, the skutterudite formula unit can be written as Ry M 4X12, where M is a transition metal, mainly from group VIII of the periodic table, X is a group XV element, and R is a dopant (typically a rare earth atom), which is accommodated in the voids of the structure 共0 艋 y 艋 1兲, shown in Fig. 1. The skutterudite structure belongs to the cubic Im-3 space group and the unit cell contains eight formula units. The structure can be visualized in two different ways. Figure 1(a) shows the structure as a cubic framework formed by the transition metal 共M兲. The group XV elements 共X兲 form planar squares in six of the eight voids created by a)

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diffraction experiments are often low compared with the conventional x-ray experiments and certainly lower than that of the synchrotron experiments. However, a combination of neutron and x-ray diffraction can give complementary information, which cannot be obtained from a single technique alone. Even so, structural questions arise that cannot readily be solved by the neutron- and the x-ray diffraction experiments. In the present paper, we show that in such cases, the theoretical calculations are invaluable to add additional information. Our paper serves to illustrate how interaction between theory and experiment can solve complex structural questions of high technological importance. II. EXPERIMENT A. Synthesis

FIG. 1. Skutterudite structure (a) shows the cubic framework of Co with Sb forming the planar square ring and (b) shows the Sb atoms forming octahedrons around the Co. In both cases, the interstitial atoms are shown. The bottom of the figure is a neutron difference Fourier plot of the Co2.8Ni1.2Sb12 sample in the plane through the center of the cell.

thermoelectric characterization, and band structure calculations of the Ni-substituted samples 共Co4−xNixSb12兲 used in the present study were reported previously,9 whereas the thermoelectric characterization has been carried out for the iron-doped samples.10 In this study, we report detailed structural information on some of these samples based on the combined use of neutron and synchrotron powder diffraction and ab initio calculations. The key problem in the x-ray structural analysis of Co4Sb12 samples containing Ni and Fe is the very similar scattering power of the transition metals. This makes it difficult to locate the dopant atoms in the structure. In addition, Fe and Co-containing samples give rise to strong fluorescence when measured at conventional powder diffractometers equipped with Cu K␣ radiation sources. On top of this, Sb dominates the scattering relative to the transition metals and potential oxide impurities. The sum of these factors makes the detection of sample impurities complicated at the conventional x-ray sources. In the case of the neutron diffraction, there is a much larger contrast in the scattering lengths Co 共2.49 fm兲, Ni 共10.3 fm兲, and 共Fe 9.45 fm兲.11 The scattering from oxygen is also enhanced relative to the other atoms 共5.80 fm兲. The peak resolution in the neutron-

The Fe -doped samples were synthesized by a conventional powder metallurgical route. The pure elements of Fe, Co, and Sb were placed in a quartz tube, which was evacuated and heated. Four samples were prepared with the following formal stoichiometries: Fe0.4Co4Sb12, Fe0.8Co4Sb12, Fe1Co4Sb12, and Fe1.6Co4Sb12.10 The Ni-substituted samples were synthesized by a chemical alloying route, which uses optimized conditions for the coprecipitation of the desired precursor.9 The precipitates are calcined and reduced at low temperature to avoid grain growth.12 Four nanostructured samples with different Ni substitution (x = 0 , 0.4, 0.8, and 1.2) were prepared. For reference, a normal grain-size powder sample without substitution was prepared by a conventional solid-state reaction at an elevated temperature using stoichiometric amounts of the pure elements. To determine the total content of the different elements in the samples, atomic absorption measurements were carried out. The conventional x-ray powder-diffraction data were measured on all samples using a STOE powder diffractometer (Cu K␣1 from a curved graphite monochromator) at the Department of Chemistry, University of Aarhus, with a Ni filter mounted in front of the position sensitive detector. B. Neutron powder diffraction on FeyCo4Sb12

The Fe1.6Co4Sb12 sample has a higher concentration of iron than can be physically accommodated in the voids of the skutterudite structure. Nevertheless, the conventional x-ray powder-diffraction pattern of this sample indicated that it was phase pure (data not shown). Figure 2 illustrates the problem with high fluorescence data (exemplified by FeCo4Sb12), where impurities potentially can be hidden in the background. The neutron powder-diffraction data were therefore measured at the DMC instrument at the swiss spallation neutron source (SINQ), Paul Scherrer Institute (PSI), Switzerland. Initially, the FeCo4Sb12 sample was mounted in a low-background aluminum sample holder and was investigated with long wavelength neutrons 共␭ = 4.2 Å兲. Subsequently, data were measured on all samples with a wavelength of 2.56 Å for a better resolution in reciprocal space. The vanadium sample holders were used in order to avoid peak overlap between the aluminum diffraction peaks and the measured diffraction pattern. All data were measured at room temperature.

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in a 0.1 mm Lindeman glass capillary. The data was measured at room temperature with a “long” wavelength 共␭ = 0.8007 Å兲 in order to resolve closely spaced peaks. The incident x-ray wavelength was determined by a calibration with a standard CeO2 sample 共␣ = 5.4111 Å兲. E. Computational details

FIG. 2. Diffraction patterns of FeCo4Sb12 The top shows the ␭ = 4.2 Å neutron data, the middle shows the ␭ = 2.56 Å neutron data (Al sample holder), and the bottom shows the conventional Cu K␣1 x-ray data. The Bragg positions are also shown. All patterns have been normalized and are shown on a logarithmic scale.

C. Neutron powder diffraction on Co4-xNixSb12

The neutron powder-diffraction patterns of the nanostructured Ni-substituted samples were measured at the Studsvik neutron source in Sweden on the NPD instrument. The vanadium sample holders were used to obtain a uniform background. All data were measured at room temperature with a wavelength of ␭ = 1.47 Å. The measuring time for each pattern was adjusted to reach 4000 counts in the most intense peak (310), corresponding to approximately 24 h. D. Synchrotron powder diffraction

The high-resolution synchrotron powder-diffraction data was measured at beam line BL02B2, SPring8, Japan, using a large Debye-Scherrer image plate camera.13 The nanostructured sample with x = 1.2 nominal Ni substitution was sealed

Fully periodic ab initio calculations were performed using the CRYSTAL98 code.14 A generalized gradient approximation density functional theory approach was adopted using the B3PW91 (Refs. 15 and 16) functional and Hay-Wadt pseudo-potentials (PP).17,18 The small core PP for Co and Ni atoms (17 and 18 active electrons, respectively) and the large core PP for Sb atoms (5 active electrons) were selected. Starting from the double-␨ Gaussian basis sets relative to these PP,19 a new double-␨ Gaussian basis set was generated by cutting the most diffuse functions from the outer shells and by modifying the remaining functions and contraction coefficients so as to preserve the original atomic shell Mulliken populations, in the case of the isolated atoms. The s = p constraint was imposed on the most diffuse shell of the Sb atoms, in order to save computational time.20 All calculations were carried out in the asymmetric unit of the Im-3 space group (unit) cell, with 12 Sb atoms at the 24g special position. Four equivalent points of the 8c cubic framework special position were occupied by either Co or Ni, to yield Ni substituted for Co systems with progressively increased Ni content (Co4-xNixSb12, x = 0 – 4). For x = 0, the system with an interstitial Ni atom at the 2a special position, NiCo4Sb12, was also considered in order to include the case of a fully Ni-filled Co4Sb12. For each system, some of the structural parameters were optimized against the total energy using the LoptCG script21 and retaining the Im-3 space group special positions. The optimized parameters were the freefractional coordinates of the 24g position and the cell parameter. Results of the theoretical calculations are summarized in Table I. The Seebeck coefficient S was estimated through the semiclassical Boltzmann’s transport theory22 in its monoelectronic formulation and in the approximation of a constant

TABLE I. Theoretically optimized values for the cell parameter a 共Å兲, the fractional coordinates, y and z, of the Sb atoms at 24g special position, and the bond distances 共Å兲. Fermi level (FL) energies in hartree. Electron populations Pe (electrons/formula unit) computed from the total one-density matrix projected on the energy interval between the Fermi level and the top of the valence bands of the investigated system. a

y

z

aexp

RM-Sbc

RSb-Sb

Co4Sb12 Co3NiSb12 Co2Ni2Sb12 CoNi3Sb12 Ni4Sb12

9.1823 9.2101 9.2300 9.2443 9.2535

0.3308 0.3315 0.3316 0.3315 0.3338

0.1594 0.1592 0.1592 0.1590 0.1588

9.0353a

2.552 2.562 2.568 2.571 2.582 2.536d

2.927 2.933 2.939 2.943 2.939

NiCo4Sb12

9.1777

0.3243

0.1587

2.913

System

9.13b

FL

Pe

3.107 3.103 3.109 3.114 3.078

−0.1331 −0.1147 −0.1148 −0.1147 −0.1192

0 1.05 2.03 2.93 3.98

3.225

−0.1404

3.314e a

From a 300 K synchrotron experiment (Ref. 27). Reference 29. c M = Co or Ni. d Co-Sb bond distance. e Ni共i兲-Sb bond distance. b

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relaxation time.23 The Seebeck coefficient S is a second-rank tensor and the isotropic part 共S兲 is given as 1 / 3 of its trace. Integrals over the first Brillouin zone were evaluated numerically by sampling the band structure En共k兲 and using an equally spaced cubic grid with a total of 403k points for each n band.23 F. Structural refinements of FeyCo4Sb12

The main problem for the x-ray investigations of ironcontaining skutterudites performed with Cu K␣ radiation is the high fluorescence arising from Co and Fe. The crystal structures were refined using the full pattern Rietveld method with the program Fullprof.24 The skutterudite Co4Sb12 belongs to the cubic space group Im-3 and the undoped sample has been reported to have a lattice parameter of 9.035共6兲 Å.25 Analysis by conventional powder diffraction was first carried out using a powder diffractometer providing both the Cu K␣1 and the K␣2 radiations. The K␣2 radiation gives rise to shoulders to the right side of the Bragg peaks, which masks possible lattice changes for a secondary skutterudite phase with a smaller unit cell. The samples appeared to be phase pure based on these initial powder-diffraction investigations. However, the sample with formal stoichiometry, Fe1.6Co4Sb12, arose suspicion because the voids in the skutterudite structure can only accommodate one iron atom 共y = 1兲. The high background due to the fluorescence scattering from Fe and Co, therefore, must hide iron-containing impurities. The neutron powder-diffraction investigations were carried out in order to find the “missing” iron in the sample. The sample FeCo4Sb12 was measured with a long wavelength ␭ = 4.2 Å in order to have a high-peak resolution to resolve the closely spaced peaks. No peak splitting was observed, but the neutron powder-diffraction pattern clearly revealed impurity peaks belonging to Fe3O4. In Fig. 2, the neutron-diffraction patterns measured with ␭ = 4.2 Å and 2.56 Å, as well as the conventional x-ray pattern measured with ␭ = 1.54 Å, are shown for comparison. The Fe3O4 peaks are not observed with the conventional x-ray powder diffraction because the fluorescence scattering hides the weak scattering from the impurity. For neutrons, the scattering amplitudes of oxygen 共5.80 fm兲 and iron 共9.45 fm兲 are enhanced with respect to antimony 共5.57 fm兲, compared with the x-ray scattering, where Sb dominates the scattering. Since no additional skutterudite phases were observed, the wavelength was changed to 2.56 Å, to get a better resolution in reciprocal space. Unfortunately, the Al sample holder gives rise to additional diffraction peaks at the shorter wavelength. Alien peaks are observed at 2.69 Å−1 and the (240) skutterudite peak at 3.11 Å−1, which is much stronger than expected. These peaks can be explained by Al (a = 4.05 Å, fcc), and the 共111兲 and 共200兲 aluminum peaks are seen in Fig. 2. Unfortunately, Fe (a = 2.87 Å, bcc) has its 共110兲 reflection at the same position and it is not possible to distinguish between the 共240兲 skutterudite peak, the 共200兲 Al peak, and the (110) Fe peak. The Al sample holder was originally chosen in order to have a low background, emphasizing weak intensities from the small impurities. Indeed, the weak intensities do

FIG. 3. Part of the neutron-diffraction pattern measured on Fe1.6Co4Sb12 in the vanadium sample holder at ␭ = 2.56 Å. The plot shows the observed data (circles), the model for pure Co4Sb12 (solid line), and the difference (solid line below the data).

emerge at 1.10 and 1.55 Å−1, which are ␭ / 2 reflections from the monochromator. They arise because the Be-filter was removed in order to work below 4 Å. The problem with the aluminum sample holder was eliminated by changing it to a vanadium holder for the rest of the samples. The higher background from the vanadium sample holder hides the ␭ / 2 signal in the background. For the sample with x = 1.6, it is clearly seen that a bcc iron phase is present in the sample besides Fe3O4 (see Fig. 3). The iron content in the remaining samples is lower and it is difficult to quantify because the iron peak overlaps with the underlying (240) skutterudite peak. The samples with lower iron substitution have previously been studied by Yang et al.26 In that study, iron impurities were detected by susceptibility measurements, and it was observed that the unit cell expands upon iron substitution. The refined unit cells from the neutron data are found to be smaller than for the undoped Co4Sb12, but there is no clear trend in the values. The changes in the unit cells might indicate that some iron has entered the skutterudite structure, but the data resolutions do not allow quantification by refinement of site occupancies. It should also be noted that our unit cell estimates could be affected by uncertainties in the neutron wavelength. The refined compositions for the different iron-doped samples are summarized in Table II. The relatively high amount of impurity phases in the skutterudite samples make it difficult to interpret the macroscopic physical property data. G. Structural refinements of Co4−xNixSb12

Neighboring elements in the periodic table are another problem for the x-ray diffraction refinements, because the TABLE II. Unit cells and refined compositions of the FeyCo4Sb12 samples. Sample

Cell 共Å兲

Fe0.4Co4Sb12 Fe0.8Co4Sb12 Fe1.0Co4Sb12 Fe1.6Co4Sb12

9.023(1) 9.017(1) 9.021(1) 9.015(1)

CoSb3(mol%) 94(1) 98(1) 97(1) 94(1)

Fe3O4 (mol%)

Fe (mol %)

5.8(2) 2.1(1) 3.4(1) 3.6(1)

2.4(1)

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TABLE III. Refined Ni content 共x兲 in the different Co4−xNixSb12 samples obtained from the refinement of the neutron powder-diffraction data using a model without and with interstitial Ni. Results from the atomic absorption data are also listed (average of the sample including impurity phases). Sample

Without interstitial

With interstitial

Atomic absorption

Co2.8Ni1.2Sb12 Co3.2Ni0.8Sb12 Co3.6Ni0.4Sb12

0.64(4) 0.44(8) 0.16(8)

0.88(8) 0.60(12) 0.20(12)

1.20 0.76 0.32

atoms cannot easily be distinguished due to their similar scattering factors. This makes it difficult to refine site occupancies for Ni and Co from the x-ray data. In the case of neutrons, the difference in scattering length is much larger (a factor of four) and this facilitates reliable refinement of site occupancies. Nevertheless, the strong correlation between the site occupancy and the atomic displacement parameters (ADP) can be difficult to handle. To avoid this correlation, the isotropic ADPs for Ni and Co were fixed at the values found for Co in the undoped reference sample.27 In Table III, the formal stoichiometry, the refined stoichiometry based on the Rietveld refinements of the neutron-diffraction data, and the stoichiometry found by the atomic absorption, are listed. Clearly, there appears to be a Ni deficiency in the neutron model compared with the atomic absorption measurements. The latter is an average of the entire sample. A small impurity of NiSb2 can be detected (1%–2%), but it is too small to account for the large discrepancy. A difference Fourier map reveals a surplus of the scattering density at the centre of the cage (0,0,0), as shown in Fig. 1. In other words, some extra Ni appears to be located in the interstitial site, and this could explain the missing Ni. For comparison, the difference map of the reference sample is virtually flat.28 The addition of the interstitial Ni to the model brings the refined stoichiometry in reasonable agreement with the atomic absorption data as shown in Table III. In many ways, this refinement result is quite satisfactory and could have formed the basis for reporting. However, thorough investigation of the neutrondiffraction pattern reveals a small shoulder to the left side of the 240 and 422 peaks. The presence of peak shoulders is confirmed by the high-resolution synchrotron powderdiffraction data on the Co2.8Ni1.2Sb12 sample, where shoulders are observed to the left of all skutterudite peaks. This suggests that an additional skutterudite phase with a larger unit cell is present in the sample. The peak overlap with the second phase makes the integrated intensities used for the Fourier synthesis in error, and the observed interstitial nuclear density of Fig. 1 is an artifact of wrong modeling. This means that the Fourier mapping cannot be used to obtain further information about the multiphase sample. In Fig. 4, the neutron, the conventional x-ray, and the synchrotron x-ray diffraction patterns are shown for the Co2.8Ni1.2Sb12 sample. Note that the raw data only have been normalized. The figure therefore gives a qualitative idea of the background level in the different data sets and thus of the potential hiding of weak impurities. It is clear that impurities can be hidden in the high backgrounds of the neutron and the

FIG. 4. Part of the diffraction patterns of the Co2.8Ni1.2Sb12 sample. The data have only been normalized and the backgrounds therefore reflect the true counts.

conventional x-ray powder diffraction data. The figure also gives a nice impression of the peak resolution obtained with the different methods. The neutron powder-diffraction simulations show that a Ni-substituted skutterudite phase would give an increased intensity in the 200, 220, 240, and 422 reflections relative to an undoped-Co4Sb12 sample. It is indeed in these reflections that the largest deviations are observed between the measured data and the undoped model. Due to the severe peak overlap, the unit cell parameters of the second phase had to be fitted by visual inspection, and it was found to be 9.106 Å. Recently, the Ni4Sb12 phase was reported by the thin-film growth with a unit cell of 9.13 Å.29 This is larger than the unit cell found for the second phase of the present sample indicating less than the complete Ni substitution. The peaks of the second phase are very broad. This can be due to the nanostructuring (i.e., nanosized crystals) or possibly to the distribution of the secondary Co4-xNixSb3 phases. Additionally, the peak width could also be increased due to the stress/strain in the structure. In conclusion, the diffraction data suggest a two-phase system with a Ni-rich and a Ni-poor phase, which in the extreme would be Co4Sb12 and Ni4Sb12. To get further insight into the structure, theoretical investigations were performed. H. Theoretical modeling of Ni-substituted Co4Sb12

1. Band gap

All Ni-substituted systems with Ni in the cubic framework sites, including Ni4Sb12, turn out to be heavily n-doped semiconductors, whereas Co4Sb12 is a narrow band-gap semiconductor with an estimated band gap of 0.65 eV.30 This confirms that the substitution of Ni for Co has a beneficial effect on the electrical conductivity. On the other hand, Ni doping at the 2a special position to yield NiCo4Sb12 leads to a semiconductor with a very small band gap. 2. Cell parameters

The optimized cell parameters are listed in Table I and shown in Fig. 5 together with various experimental values. The theoretical Co4Sb12 and Ni4Sb12 cell parameters are overestimated with respect to the experimental values by 1.6% and 1.3%, respectively.29 The theoretical cell parameter for the Co4−xNixSb12 system 共x = 0 – 4兲 increases almost linearly with the average increase of about 0.018 Å for each Ni substituting for Co. A similar trend is found experimentally,

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FIG. 5. Theoretical and experimental unit cells for Co4−xNixSb12 and the fully filled NiCo4Sb12. The experimental value for the pure Co4Sb12 is taken from Ref. 27, and the value for Ni4Sb12 from Ref. 29.

although only values for x = 0 and x = 4 are available. When Ni is placed in the interstitial position, the cell parameter decreases by 0.005 Å compared with Co4Sb12. 3. Ni substitution and DOS changes

The density of states (DOS) for the investigated systems are shown in Fig. 6. In the Co4-xNixSb12 共x = 1 – 4兲 series, the band-gap zone becomes progressively filled, and complete filling is almost reached for x = 4 共Ni4Sb12兲. The electron population of the former band-gap zone in Co4Sb12 increases by about one electron for each Ni replacing a Co atom, and reaches a value of about four for Ni4Sb12 as shown in Table I. 4. Thermodynamic stabilities of Ni-substituted systems

Because the diffraction data suggest the presence of a two-phase system, we investigated (at T = 0 K) the thermodynamical stability of the Ni-substituted systems as a function of the Ni content and sitting, and relative to pure, unmixed Co4Sb12 and Ni4Sb12 phases. We consider the five hypothetical reactions summarized in Table IV. The stabilization of the systems with the Ni substitution in the cubic frame increases almost linearly with the Ni content, and reaches a maximum for CoNi3Sb12. The stabilization per Ni atom substituted for Co is approximately 170 kcal/ mol. The formation of the high Ni content substituted systems therefore seems favored with respect to the unmixed Co4Sb12 and Ni4Sb12 phases. On the other hand, the formation of a Ni-filled system from Co4Sb12 and Ni4Sb12 is endothermic or only slightly exothermic, depending on the formation reaction being considered (Table IV).31 The dissociation energies of Co4-xNixSb12 into Co4Sb12 + NiSb2 + Sb have also been calculated and are shown in Table V. Indeed, it is seen that the stability increases with the amount of Ni in the framework, although the pure Ni4Sb12 is highly unstable. Owing to this, the maximum stability is achieved for x = 3, which should represent the maximal Ni content into CoSb3 in the hypothesis of a unit cell structure containing just 12 Sb and 4 metal (Ni or Co) atoms. This confirms the DSC experiments by

FIG. 6. Total DOS for Co4−xNixSb12 共x = 0-4兲 and NiCo4Sb12. Vertical lines refer to the Fermi energy level.

Williams and Johnson showing that NiSb3 disproportionates at 250° C.28 The calculated thermodynamic stabilities corroborate the experimental finding of a secondary skutterudite phase with high Ni content. TABLE IV. Formation energies 共kJ mol−1兲 of the Ni-doped and Ni-filled systems from the Co4Sb12 and the Ni4Sb12 pure phases. In the case of the filled NiCo4Sb12 system, the formation energy from Co4Sb12 and the filled system with Co atoms removed from the cubic framework, is also reported. Reaction Ni substitution for Co 0.75 Co4Sb12 + 0.25 Ni4Sb12 → Co3NiSb12 0.50 Co4Sb12 + 0.50 Ni4Sb12 → Co2Ni2Sb12 0.25 Co4Sb12 + 0.75 Ni4Sb12 → CoNi3Sb12 Ni-filled system Co4Sb12 + 0.25 Ni4Sb12 → NiCo4Sb12 + 0.25 Sb12 Co4Sb12 + Ni共i兲Sb12 → NiCo4Sb12 + Sb12 a

⌬E共kJ/ mol兲a

−152.3 −329.3 −510.9 262.0 −82.8

⌬E values refer to the formation of one mole of the skutterudite product.

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TABLE V. The dissociation energies with respect to the reaction Co4−xNixSb12 → 关共4 − x兲 / 4兴Co4Sb12 + xNiSb2 + xSb. Reaction

⌬E 共kJ/ mol兲

Ni4Sb12 → 4NiSb2 + 4Sb Co3NiSb12 → 0.75 Co4Sb12 + NiSb2 + Sb Co2Ni2Sb12 → 0.5 Co4Sb12 + 2NiSb2 + 2Sb CoNi3Sb12 → 0.25 Co4Sb12 + 3NiSb2 + 3Sb

−543.1 +17.2 +53.1 +71.2

5. Seebeck coefficients and Ni-substituted skutterudites phases

For the Co4Sb12, the Seebeck coefficient is found to be positive at all temperatures with values ranging from 140 to 66 ␮V / K as shown in Fig. 7. In strong contrast, the Seebeck coefficient is negative for all Ni-substituted systems (Co4−xNixSb12, x = 1 – 4) at all temperatures considered. The magnitude of S increases linearly with temperature for x = 2 and 3 and almost quadratically for x = 1 and 4. This trend is in agreement with the experimental results,9 although theory underestimates the values of 兩S兩 in particular at low temperatures. The S values for the filled NiCo4Sb12 system are also found to be negative, with similar temperature dependence as for the Ni-substituted systems but always smaller in magnitude. The diffraction data suggest a two-phase model for the Co2.8Ni1.2Sb12 sample. The hypothesis of a material consisting of pure Co4Sb12 and Ni4Sb12 phases is to be discarded also on the basis of the Seebeck coefficient S. CoSb3 has a positive S but the scanning Seebeck micro-thermoprobe measurements, which yield a spatially resolved S, found negative values everywhere in the −50– 30 ␮V / K range.9 Therefore, the system should be considered as composed of Co-rich, Co4−xNixSb12, and a Ni-rich CoyNi4−ySb12 phases. The Seebeck coefficient for the two-phases mixture Smix has been shown to be approximated by32 Smix共T兲 = 共1 / ␴mix共T兲兲关S1共T兲␴1共T兲 + S2共T兲␴2共T兲兴, where Si and ␴i (i

FIG. 7. Calculated Seebeck coefficients for the single-phase Co4−xNixSb12 for the different doping levels (x = 0, 1, 2, 3, and 4). Additionally, the Seebeck coefficient for the interstitial model NiCo4Sb12 is shown.

= 1 and 2) are the values of the Seebeck and the electrical conductivity of the i-phase, respectively, and ␴mix is the electrical conductivity of the mixture. Unfortunately, this formula does not enable us to determine the composition of the two phases because we can calculate ␴ and S only for x = 1 and y = 1 compositions. Moreover, owing to the indeterminacy of the relaxation time, the computed ␴i values are not necessarily compatible with the single available experimental value for ␴mix. However, it is worth noting that the scatter of the S values determined with the spatially resolved Seebeck measures, nicely fits with the differences of the theoretical S values calculated for the x = y = 1 composition of the biphasic system (−25 and −10 ␮V / K for Co3NiSb12 and CoNi3Sb12 at 300 K, respectively, as shown in Fig. 7). This corroborates the other evidence for the existence of a two-phase system, which, on the basis of the joined experimental and theoretical S results, seems characterized by two phases with quite dissimilar Ni and Co contents. III. DISCUSSION

The high-resolution synchrotron-diffraction pattern clearly shows that the Co2.8Ni1.2Sb12 sample is a two-phase system. This was not obvious from the neutron data alone. The following models were suggested to account for the observations: i) a sample with a phase having Ni filling in addition to a pure Co4Sb12 phase, ii) a sample with a Co4Sb12 phase and a Ni4Sb12 phase, and iii) a sample with a Ni-rich phase 共x ⬎ 2兲 and a Ni-poor phase 共x ⬍ 2兲. Considering the interstitial model (i), the theoretical calculations predict that the unit cell is smaller than that of Co4Sb12. Because both of the observed phases have larger unit cells than the pure phase, the interstitial Ni-skutterudite structure can be ruled out. The interstitial Ni would also significantly change the diffraction pattern if it is found in large amounts in the voids, and this is not observed. Finally, the thermodynamic stability calculations are also against the interstitial model. The model with a Co4Sb12 phase and a Ni4Sb12 phase (ii) is also not favored by the thermodynamic calculations. Ni4Sb12 is metastable and it disproportionates into NiSb2 and Sb upon annealing at 250° C.29 The present samples were prepared at 723 K and also pressed at elevated temperatures, and yet the secondary phase is still present. Furthermore, the unit cell does not match the values of the pure phases found in other experiments. The phase with the large unit cell has a smaller cell than the one reported for Ni4Sb12 and the unit cell of the main phase is larger than that of Co4Sb12 as shown in Fig. 5. All this speaks against a sample with two-pure phases. However, the strongest evidence against the model with the pure Co4Sb12 and Ni4Sb12 phases probably is that such a sample would likely have islands of positive 共Co4Sb12兲 and negative 共Ni4Sb12兲 Seebeck coefficients. Instead, the spatially resolved measurements of the Seebeck coefficient found only negative S regions with values between −30 and −50 ␮V / K.9 The computed S values for Co3NiSb12 and CoNi3Sb12 are both negative and their difference agrees with the spread found in the spatially resolved S measurements. All evidence therefore points to the sample

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TABLE VI. Results from the simultaneous refinements of the three data sets (Studvik, SPring8, and conventional x-ray) using three different models for the Co2.8Ni1.2Sb12 sample. The data resolutions are 共sin ␪ / ␭兲max = 0.64, 0.77, and 0.43 Å−1 (Nobs = 1700, 7550, and 7076) for the Studsvik, SPring8, and conventional x-ray data, respectively. The numbers of Bragg reflections are 175, 285, and 54 for the small unit cell phase, and 177, 311, and 58 for the large unit cell phase (Studvik, SPring8, and conventional x-ray). The agreement factors are defined as R p = ⌺ 兩 y o,i-y c,i 兩 / ⌺ 兩 y o,i, Rwp = 关⌺wi 兩 y o,i-y c,i兩2 / ⌺wi 兩 y o,i兩2兴1/2, ␹2 = ⌺wi 兩 y o,i-y c,i兩2 / ␴i2, RI = ⌺ 兩 Io-Ic 兩 / ⌺ 兩 Io兩, and RF = ⌺ 兩 Fo-Fc 兩 / ⌺ 兩 Fo兩. The occupancy is given as the site multiplicity restricted by symmetry divided by the general site multiplicity of the space group. Studsvik Model Npar R p (%) Rwp (%) ␹2 Small cell a Sb共y兲 Sb共z兲 Occ Ni RI RF Large Cell a Sb共y兲 Sb共z兲 Occ Ni RI RF Mol frac Small cell Large cell NiSb2 Sb CoSb Elements Ni Co Sb

Spring8 Co4Sb12 Ni4Sb12

Conv. x-ray

Studsvik

3.44 4.58 2.54

3.74 4.71 1.60

93 7.46 10.1 2.77

8.16 5.05

9.04892(3) 0.33517(9) 0.15771(9) 0.024共−兲 2.76 1.27 9.106共−兲 0.33757(28) 0.15760(29) 0.124共−兲 4.61 2.25 72.7(3) 16.4(1) 5.8(1) 4.84(6) 0.29(0)

3.74 4.75 1.63

93 7.46 10.1 2.76

8.16 5.24

9.04892(3) 0.33516(9) 0.15772(9) 0共−兲 2.72 1.27

14.6 8.44

9.106共−兲 0.33759(28) 0.15758(29) 0.16667共−兲 4.60 2.26

7.85 9.31

16.1 8.89

72.7(3) 16.4(1) 5.8(1) 4.84(6) 0.29(0)

75.1(9) 13.6(4) 7.4(6) 1.5(2) 2.5(3)

81.9(3.7) 12.8(1.7) 3.3(8) 2.1(1.0)

82.5(3.2) 11.1(1.1) 4.3(8) 2.1(1.0)

3.68 4.09

1.004(9) 2.910(12) 12.000(41)

having a Ni-rich phase and a Ni-poor phase. The theoretical unit cell is almost linear as a function of the Ni substitution. If the linearity is assumed for the experimental data, the Ni content of the two phases can be established as shown in Fig. 5. This results in a sample containing two phases with the Co3.42Ni0.58Sb12 and the Co0.92Ni3.08Sb12 stoichiometries, respectively. This result is of course subject to the uncertainties related to the unit cell determination. In light of the previous discussion, the following three models were considered in the final Rietveld co-refinements on the three different data sets on the Co2.8Ni1.2Sb12 sample: a) Co4Sb12 + Ni4Sb12, b) Co3.42Ni0.58Sb12 + Co0.92Ni3.08Sb12, and c) Co4-xNixSb12 + CoyNi4-ySb12. In model c, the Ni/ Co contents of the two phases were refined independently with no chemical constraints imposed. The starting point for the Ni and Co occupancies was model b. The a and b models have been included in order to test whether it is possible to differentiate between the suggested models on the basis of the diffraction patterns alone. All three diffraction patterns were refined simultaneously against the three different models. The refinement results are listed in Table VI. The profile agreement factors, R p and Rwp, are equal for the three models

Spring8 Co3.42Ni0.58Sb12 Co1.02Ni2.98Sb12

1.301(8) 2.758(10) 12.000(41)

Conv. x-ray

Studsvik

3.43 4.58 2.54

3.66 4.63 1.54

95 7.46 10.1 2.77

3.43 4.58 2.54

7.46 4.76

9.04892(3) 0.33517(9) 0.15771(9) 0.010(3) 2.73 1.26

3.86 4.10

7.83 9.3

15.1 8.53

9.106共−兲 0.33758(28) 0.15759(29) 0.151(22) 4.61 2.26

7.84 9.31

75.1(9) 13.6(4) 7.4(6) 1.5(2) 2.5(3)

82.4(4.3) 11.7(2.5) 3.9(8) 2.1(1.0)

72.7(3) 16.4(1) 5.8(1) 4.84(6) 0.29(0)

75.1(9) 13.6(4) 7.4(6) 1.5(2) 2.5(3)

3.86 4.10

Spring8 Co4-xNixSb12 CoyNi4-ySb12

Conv. x-ray

1.16(11) 2.91(11) 12.00(4)

in the case of the x-ray data, but for the neutrons data a slight decrease is seen for model c compared to model a. The crystallographic agreement factors RF and RI are also unchanged between models for the x-ray data. This illustrates that in the present case, neighboring elements cannot be distinguished using only the x-ray data, unless perhaps an anomalous scattering experiment33 or a maximum entropy method analysis34 is carried out. For the neutron data, the small unit cell phase has a smaller RF and RI for model c than for models a and b. The same trend is not observed for the large unit cell phase, where model a is slightly favored. In all cases, it is questionable whether the differences in the agreement factors are significant. The refined stoichiometries of the two phases in model c are Co3.76Ni0.24Sb12 and Co0.38Ni3.62Sb12, in reasonable agreement with the estimates obtained from the unit cell dimensions 共Co3.42Ni0.58Sb12 + Co0.92Ni3.08Sb12兲.35 From the synchrotron radiation data, it is also possible to do quantitative-phase analysis and estimate the fraction of different impurity phases and thereby the relative amounts of the different elements. The total stoichiometry, which is listed at the bottom of Table VI, is obtained by summing the Ni, Co, and Sb contents in all the skutterudite and impurity

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phases, and normalizing by setting the amount of Sb equal to 12. The stoichiometry found by the atomic absorption measurements was Co2.8Ni1.2Sb12. Model a has somewhat less Ni than expected, whereas model b has a slight surplus of Ni. In model c, the composition agrees within one standard deviation of the expected stoichiometry. The three refinements emphasize that a discrimination between the models cannot be based on the diffraction data alone. The composition of the sample cannot be determined with better accuracy using the present data, and further experimental progress probably would require high-peak resolution neutron powderdiffraction experiments or anomalous x-ray diffraction experiments at the edges of Ni and Co.

IV. CONCLUSION

Comparison of the conventional CuK␣ xray and the neutron powder-diffraction data on iron-doped skutterudite samples have illustrated the problem of fluorescence in the CuK␣ x-ray diffraction data, where impurities of about 3 mol% can be hidden in the background. The conventional CuK␣ x-ray powder-diffraction data therefore cannot be used to determine the phase purity, when samples with small amounts of doping are investigated. The nickel-doped skutterudite samples surprisingly were two-phase systems, which were revealed by high-resolution synchrotron data. The joint analysis of the synchrotron and the neutron powderdiffraction data, as well as the theoretical calculations, made it possible to estimate the content of the two phases to be Co3.4Ni0.6Sb12 and Co0.9Ni3.1Sb12 based on the unit cell dimensions. The refinement of the site occupancies gives a slightly different composition of the two phases, Co3.8Ni0.2Sb12 and Co0.4Ni3.6Sb12. The total molar fraction of elements is Co2.9共1兲Ni1.2共1兲Sb12.00共4兲, when including impurities of NiSb2, Sb and CoSb. This is in excellent agreement with the atomic absorption data and the known synthesis conditions. It is well known that even small dopant or impurity concentrations can have large effects on the transport properties of the semiconducting skutterudites. The present study shows that it is necessary to carry out very detailed crystallographic analysis on such samples. Substantial progress in the optimization of the properties of many complex thermoelectric materials probably can be obtained only if the commonly reported very elaborate physical property investigations are coupled with equally elaborate structural investigations.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the beam time obtained at Studsvik in Sweden, PSI in Switzerland, and SPring8 in Japan. The authors would like to thank Håkan Rundlöf for the assistance during the Neutron experiment at Studsvik, Lukas Keller for the assistance at PSI, and Kenichi Kato for the assistance at SPring8. This work is supported by the European Community under Contract No. G5RDCT2000-00292 (NanoThermel project). They would also like to thank all NanoThermel partners for the useful discus-

sions. The neutron measurements were supported by DANSCATT and the synchrotron measurements by DANSYNC. 1

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proach, we found S values equal to −49.6 and −5.4 ␮V / K at 300 K, for Co3.5Ni0.5Sb12 and Co0.5Ni3.5Sb12, respectively. The most probable experimental S value from the scanning microprobe measurements was −40␮V / K, and this is obtained for Co3.65Ni0.35Sb12.

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