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Crystallographic study of ternary ordered skutterudite IrGe1.5Se1.5

Published online by Cambridge University Press:  29 February 2012

F. Laufek  and
J. Návrátil
F. Laufek*
Affiliation:
Czech Geological Survey, Geologická 6, 152 00 Praha 5, Czech Republic
J. Návrátil
Affiliation:
Joint Laboratory of Solid State Chemistry of IMC AS ČR, Studentská 84, 532 10 Pardubice, Czech Republic and University of Pardubice, Studentská 84, 532 10 Pardubice, Czech Republic
*
a)Author to whom correspondence should be addressed. Electronic mail: frantisek.laufek@geology.cz
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Abstract

The crystal structure of skutterudite-related phase IrGe1.5Se1.5 has been refined by the Rietveld method from laboratory X-ray powder diffraction data. Refined crystallographic data for IrGe1.5Se1.5 are a=12.0890(2) Å, c=14.8796(3) Å, V=1883.23(6) Å3, space group R3 (No. 148), Z=24, and Dc=8.87 g/cm3. Its crystal structure can be derived from the ideal skutterudite structure (CoAs3), where Se and Ge atoms are ordered in layers perpendicular to the [111] direction of the original skutterudite cell. Weak distortions of the anion and cation sublattices were also observed.

Keywords

IrGe1.5Se1.5X-ray powder diffraction dataRietveld refinementskutterudite
Type
Technical Articles
Information
Powder Diffraction , Volume 25 , Issue 3 , September 2010 , pp. 247 - 252
Copyright
Copyright © Cambridge University Press 2010

I. INTRODUCTION

Skutterudites (general formula MX 3, where M=Co, Rh, or Ir and X=P, As, or Sb) have, in the past two decades, attracted much interest because of their promising thermoelectric properties (Uher, Reference Uher, Kanatzidis, Mahanti and Hogan2003). The ideal skutterudite structure (space group Im 3) can be considered as a severe distortion of the ReO3 structure by tilting of the [MX 6] octahedra (tilt system a +a +a +) (Mitchell, Reference Mitchell2002). A consequence of such tilting is the proximity of four X anions forming rectangular rings [X 4] in which X-X bonds occur. In addition to the binary skutterudites, ternary skutterudites also exist. These compounds can be prepared by isoelectronic substitution at the cation site M by pair of elements from 8 and 10 groups, e.g., Fe0.5Ni0.5Sb3 (Kjekshus and Rakke, Reference Kjekshus and Rakke1974), or by isoelectronic substitution on the anion site X by a pair of elements from 14 and 16 groups, e.g., CoGe1.5Te1.5 (Vaqueiro et al., Reference Vaqueiro, Sobany, Powell and Knight2006). Lyons et al. Reference Lyons, Gruska, Case, Subbaro and Wold(1978) mentioned the synthesis of IrGe1.5Se1.5 and structural relation of this compound to the cubic skutterudite structure (space group Im 3). These authors also noticed the presence of weak superstructure diffractions violating the Im 3 symmetry in the powder diffraction pattern; however, no details were given. The crystal structure of the title phase is reported in the Linus Pauling File Reference Villars(2010) (collection code 461743) as being isostructural to the cubic skutterudite CoAs3, and its calculated powder diffraction data are included in ICDD Reference McClune(2005). IrGe1.5Se1.5 phase is also listed in the conference abstract of Fleurial et al. Reference Fleurial, Caillat and Borshchevsky(1997) as a part of review of skutterudite materials.

The aim of this work is to present a Rietveld structural study of IrGe1.5Se1.5 using conventional powder X-ray diffraction data and in particular shed the light on the ordering of Ge and Se atoms in its crystal structure.

II. EXPERIMENTAL

The IrGe1.5Se1.5 ternary compound was synthesised from the elements by high-temperature solid-state reactions. Stoichiometric amounts of 3N5-Ir (Alfa Aesar), 5N-Ge (VÚK Panenské Břežany a.s.), and 5N-Se (Alfa Aesar) were weighed in a stoichiometric ratio into graphitized quartz ampoules and after evacuation (<10−2 Pa) the ampoules were sealed and ingoted at 1050 °C for 24 h. The ingot was consequently treated by the modified ceramic method and heated at 600 °C. Further details on this method are described in our previous paper (Navrátil et al., Reference Navrátil, Plecháček, Vlček, Beneš and Laufek2007).

The X-ray diffraction pattern was collected in the Bragg-Brentano geometry on an X'Pert Pro PANalytical diffractometer, equipped with an X'Celerator detector usingCu Kα radiation. To minimize the background, the specimen of IrGe1.5Se1.5 was placed on a flat low-background silicon wafer. Table I summarizes the experimental details for the recording of the powder diffraction pattern. The observed diffractogram of IrGe1.5Se1.5 phase is shown in Figure 1. A full width at half maximum of 0.067°2θ X-ray powder data was obtained at 14.595°2θ, demonstrating good crystallinity of the specimen under investigation.

TABLE I. Experimental conditions.

Figure 1. (Color online) Observed (circles), calculated (solid line), and difference Rietveld profiles for IrGe1.5Se1.5. The vertical bars indicate the positions of the Bragg reflections.

III. STRUCTURE REFINEMENT

The crystal structureIrGe1.5Se1.5 was refined by the Rietveld method for X-ray powder diffraction data using the FULLPROF program (Rodríguez-Carvajal, Reference Rodríguez-Carvajal1990). A preliminary Rietveld analysis of IrGe1.5Se1.5 using the cubic structure model for this compound included in the Linus Pauling File Reference Villars(2010) converged to rather high values of agreements factors (Rp=12.3%, Rwp=17.9%, and RB=8.68%). This structure model (space group Im 3 ) is isostructural to CoAs3 (Kjekshus and Rakke, Reference Kjekshus and Rakke1974), and the Ge and Se atoms randomly occupy the 24g position of the space group Im 3. Their occupancy factors were assigned according to the IrGe1.5Se1.5 composition.

However, apparent peak splitting and presence of weak superstructure reflections, which were not fitted by this cubic structural model, indicate an ordering of Ge and Se atoms. Analogous observation was made during the Rietveld refinement of IrSn1.5Te1.5 (Bos and Cava, Reference Bos and Cava2007) and CoSn1.5Te1.5 (Laufek et al., Reference Laufek, Navrátil and Goliáš2008). The structural studies of Vaqueiro et al. Reference Vaqueiro, Sobany, Powell and Knight(2006, Reference Vaqueiro, Sobany and Stindl2008) using high-resolution neutron powder diffraction on CoGe1.5Te1.5 and MGe1.5S1.5 (M=Co, Rh, Ir), respectively, showed that ordering among Ge and Te (S) atoms in the skutterudite structure leads to the lowering of the symmetry from cubic (space group Im 3) to trigonal (space group R 3). The Rietveld refinement of IrGe1.5Se1.5 based on the starting IrGe1.5S1.5 anion-ordered structure model in space group R 3 converged to the significantly better values of agreement factors (Rp=5.53%, Rwp=7.27%, and RB=5.98%) and accounted for all observed diffractions (see Fig. 2). The refined structural parameters of the structure IrGe1.5Se1.5 are given in Table II, and Figure 1 shows the final Rietveld plots.

TABLE II. Refined atomic coordinates for IrGe1.5Se1.5 [room temperature, space group R 3, a=12.0890(2) Å, c=14.8796(3) Å, V=1883.23(6) Å3, U iso=0.0078(3) Å2, Z=24, Dx=8.87 g/cm3, Rp=5.53%, Rwp=7.27%, and RB=5.98%].

Figure 2. (Color online) Details of the two Rietveld fits for IrGe1.5Se1.5 showing the peak splitting. The left and right parts of Figure 2 show refinement based on disordered CoAs3 (space group Im 3) and on the anion-ordered CoGe1.5Te1.5 (space group R 3) structure models, respectively. The observed reflections are completely fitted in the anion-ordered IrGe1.5Se1.5 structure model.

Taking into account the similar X-ray scattering factors of Ge and Se atoms, the current Rietveld analysis does not provide any direct information regarding the ordering and assignment of Ge and Se atoms. The assignment of individual positions of Ge and Se atoms in the crystal structure of IrGe1.5Se1.5 was mainly based on different Ir-Se and Ir-Ge bonding distances. Despite the fact that the covalent radii of Ge and Se atoms are almost the same (r Ge=1.22 Å, r Se=1.19 Å) (Emsley, Reference Emsley1989), theoretical calculations of Partik and Lutz Reference Partik and Lutz(1999) on skutterudite-type compounds showed that the covalent bond between the metal and germanium is much stronger than that between the metal and the chalcogen atoms. Hence, two of the four available anion positions (all in general Wyckoff position 18f, space group R 3) in IrGe1.5Se1.5, which display shorter Ir-anion distances (from 2.40 to 2.42 Å), were assigned as Ge positions. Two residual anion positions showing slightly longer Ir-anion distances (from 2.47 to 2.51 Å) were assigned as Se positions. This distribution of Ge and Se atoms in the crystal structure of IrGe1.5Se1.5 is further supported by its comparison with its isostructural ternary skutterudite IrGe1.5S1.5 (Vaqueiro et al., Reference Vaqueiro, Sobany and Stindl2008). Table III presents a comparison of selected bond distances for IrGe1.5Se1.5 and IrGe1.5Se1.5 (Vaqueiro et al., Reference Vaqueiro, Sobany and Stindl2008). As is evident from Table III, the Ir-Ge distances are approximately the same in both compounds, while Ir-Se distances are significantly larger than corresponding Ir-S distances in IrGe1.5S1.5. This can be explained by the lower covalent radius of S (r S=1.04 Å) with respect to the covalent radius of Se (r Se=1.19 Å) (Emsley, Reference Emsley1989).

TABLE III. Selected interatomic distances (Å) for IrGe1.5Se1.5 and those for IrGe1.5S1.5 (Vaqueiro et al., Reference Vaqueiro, Sobany and Stindl2008; X=S or Se).

On other hand, the possibility that a certain degree of mixing of Ge and Se atoms occurs in the structure of IrGe1.5Se1.5 cannot be ruled out. Nevertheless, apparent peak splitting and presence of weak superstructure diffractions suggest that essential amounts of Ge and Se atoms are on different crystallographic positions.

Despite the other satisfactory agreement parameters, the overall goodness of fit (χ2) calculated by FULLPROF was 3.1, which is rather poor. According to Toby Reference Toby(2006), such high values of χ2 can occur when the diffraction data are collected with very high precision (i.e., with very good counting statistics) and the misfit between observed and calculated patterns becomes very large when compared with uncertainties in the measured intensities. In these cases, the more reasonable χ2 can be calculated using the Rwp value of a structureless Le Bail fit (Le Bail et al., Reference Le Bail, Duroy and Fourquet1988) to the same data, contrary to the conventional Rexp. In this case, the Rwp of the Le Bail fit was 5.9%, yielding a χ2 using Rexp=R wp(Le Bail) of 1.54. Similar observation was described by Whitfield et al. Reference Whitfield, LePage, Grice, Stanley, Jones, Rumsey, Blake, Robers, Stirling and Carpenter(2007) during the refinement of the mineral jadarite.

The refined parameters include those describing peak shape and width, peak asymmetry, unit-cell parameters, and fractional coordinates. Finally, 25 parameters were refined. Isotropic displacement parameters were constrained to be the equal for all atoms. The pseudo-Voigt function was used to generate the line shape of the diffraction peaks. The background was determined by linear interpolation between consecutive breakpoints in the pattern. The convergence criterion, ε, forcing the termination of the refinement when parameter shifts <ε×σ was set to 0.1. The refined 2θ zero error of 0.030(1)° matches very well the zero shift of about 0.038°2θ which was determined from a linear interpolation function deduced from the LaB6 external standard.

IV. RESULTS AND DISCUSSION

The powder diffraction data are listed in Table IV. The observed values of diffraction positions, d spacing, and intensities were extracted by the program XFIT (Coelho and Cheary, Reference Coelho and Cheary1997), employing the split Pearson VII profile function. The 2θobs and d obs were corrected for the zero-point shift of 0.030°2θ. The powder data presented here for IrGe1.5Se1.5 differ from ICDD Reference McClune(2005) in presence of weak superstructure reflections, indicating ordering of Ge and Se atoms (see structure refinement). The most obvious superstructure reflections are (hkl, °2θ, I calc) 208 (52.145, 22), 428, 6 to 28 (69.273, 15), and 006 (36.189, 9).

The crystal structure of the title phase is isostructural with IrSn1.5Te1.5 (Bos and Cava, Reference Bos and Cava2007), CoGe1.5Te1.5 (Vaqueiro et al., Reference Vaqueiro, Sobany, Powell and Knight2006), CoSn1.5Se1.5 (Laufek et al., Reference Laufek, Navrátil, Plášil, Plecháček and Drašar2009), and IrGe1.5S1.5 (Vaqueiro et al., Reference Vaqueiro, Sobany and Stindl2008). As was proposed by Vaqueiro et al. Reference Vaqueiro, Sobany, Powell and Knight(2006) and Partik et al. Reference Partik, Kringe and Lutz(1996), crystal structures of these phases can be derived from the cubic skutterudite structure MX 3 (M=Co, Rh, or Ir; X=P, As, or Sb), where Ge (Sn) and Te (Se) atoms show long-range ordering in planes perpendicular to the [111] direction of the original cubic cell. As a consequence of ordering, the symmetry is lowered from cubic to trigonal. However, the a +a +a + tilt system of octahedra of parent skutterudite structure is preserved. In the crystal structure of IrGe1.5Se1.5, each Ir atom is octahedrally coordinated by three Ge and three Se atoms. The Ge and Se atoms are arranged in a facial configuration. The [IrGe3Se3] octahedra share all six corners with adjacent octahedra, forming perovskitelike three-dimensional network [Figure 3(a)]. The cubic structure model of IrGe1.5Se1.5 included in Linus Pauling File Reference Villars(2010) has the same crystallographic data as the CoAs3 skutterudite structure (Kjekshus and Rakke, Reference Kjekshus and Rakke1974). This cubic model apparently represents an average crystal structure of IrGe1.5Se1.5 prepared by the method described in this paper and does not take into account the ordering of Ge and Se atoms (see above).

As was mentioned by Mitchell Reference Mitchell(2002) and Vaqueiro et al. Reference Vaqueiro, Sobany and Stindl(2008), the skutterudite structure can be derived from the perovskite structure ABX 3 by omission of A atoms and tilting of the octahedra (tilt system a +a +a +). According to O'Keeffe and Hyde Reference O’Keeffe and Hyde(1977), the tilt angle (φ) can be calculated from M-X-M angle using a relationship

Using this equation and the average Ir-X-Ir angle for IrGe1.5S1.5 (Vaqueiro et al., Reference Vaqueiro, Sobany and Stindl2008), IrGe1.5Se1.5 (this work), and IrSn1.5Te1.5 (Bos and Cava, Reference Bos and Cava2007), we have estimated the tilt angles for above mentioned phases to be 37.0°, 35.6°, and 33.4°. These values of tilt angles are in accordance with general trend observed in skutterudites; for a given cation (i.e., Ir), the tilt angle (φ) decreases with increasing size of the anions (Mitchell, Reference Mitchell2002). The empty A site, which is located at the centre of the octahedral cluster [IrGe3Se3]8, has approximately icosahedral coordination. However, contrary to the binary skutterudites, the icosahedral coordination is slightly distorted. The distances from hypothetical filler atom A to the Ge and Se atoms would have values of 3.10 and 3.26 Å, respectively.

TABLE IV. Powder data for IrGe1.5Se1.5. Reflections with I calc and I obs < 1% are not shown in I calc, which are obtained by using the structural parameters from the Rietveld refinement.

Analogically to the binary skutterudites, the Ge and Se atoms form two crystallographically distinct four-membered rings [Ge2Se2], in which the Se and Ge atoms are in transpositions to each other. The Ge-Se distances within the rings [Figures 3(b) and 3(c)] are more or less comparable with those observed in binary germanium selenides, e.g., GeSe (from 2.51 to 2.59 Å) (Dutta and Jeffrey, Reference Dutta and Jeffrey1965) or Ge4Se9 (from 2.32 to 2.48 Å) (Fjellvag et al., Reference Fjellvag, Kongshaug and Stolen2001). Contrary to the rectangular shape of [As4] rings found in the structure of CoAs3 (Kjekshus and Rakke, Reference Kjekshus and Rakke1974), the [Ge2Se2] rings in the IrGe1.5Se1.5 structure are more distorted [Figure 3(c)]. The ratio of X-X distances is 1.03 for the CoAs3 structure, while for IrGe1.5Se1.5 this ratio ranges from 1.07 to 1.08, indicating the weak distortion of the anion lattice.

ACKNOWLEDGMENTS

This study was supported by internal project of Czech Geological Survey (Project No. 332300) and P108/10/1315. The kind help of Vojtěch Vlček (University of Bayreuth) with X-ray diffraction measurement is highly acknowledged.

Figure 3. (a) Polyhedral and (b) ball-and-stick representation of the IrGe1.5Se1.5 structure emphasising the corner sharing arrangement of the IrGe1.5Se1.5 octahedra (rhombohedral setting). (c) Comparison of four-membered [As4] and [Ge2Se2] rings found in the CoAs3 (Kjekshus and Rakke, Reference Kjekshus and Rakke1974) and IrGe1.5Se1.5 structures, respectively.

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Figure 0

TABLE I. Experimental conditions.

Figure 1

Figure 1. (Color online) Observed (circles), calculated (solid line), and difference Rietveld profiles for IrGe1.5Se1.5. The vertical bars indicate the positions of the Bragg reflections.

Figure 2

TABLE II. Refined atomic coordinates for IrGe1.5Se1.5 [room temperature, space group R3, a=12.0890(2) Å, c=14.8796(3) Å, V=1883.23(6) Å3, Uiso=0.0078(3) Å2, Z=24, Dx=8.87 g/cm3, Rp=5.53%, Rwp=7.27%, and RB=5.98%].

Figure 3

Figure 2. (Color online) Details of the two Rietveld fits for IrGe1.5Se1.5 showing the peak splitting. The left and right parts of Figure 2 show refinement based on disordered CoAs3 (space group Im3) and on the anion-ordered CoGe1.5Te1.5 (space group R3) structure models, respectively. The observed reflections are completely fitted in the anion-ordered IrGe1.5Se1.5 structure model.

Figure 4

TABLE III. Selected interatomic distances (Å) for IrGe1.5Se1.5 and those for IrGe1.5S1.5 (Vaqueiro et al., 2008; X=S or Se).

Figure 5

TABLE IV. Powder data for IrGe1.5Se1.5. Reflections with Icalc and Iobs < 1% are not shown in Icalc, which are obtained by using the structural parameters from the Rietveld refinement.