ARTICLE pubs.acs.org/cm
Multi-temperature Synchrotron Powder X-ray Diffraction Study and Hirshfeld Surface Analysis of Chemical Bonding in the Thermoelectric Zintl Phase Yb14MnSb11 Sofie Kastbjerg,† Catherine A. Uvarov,‡ Susan M. Kauzlarich,‡ Eiji Nishibori,§ Mark A. Spackman,|| and Bo Brummerstedt Iversen*,† †
Center for Materials Crystallography, Department of Chemistry and iNANO, Aarhus University, DK-8000 Aarhus C, Denmark Department of Chemistry, University of California, Davis, California 95616, United States § Department of Applied Physics, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan School of Biomedical, Biomolecular and Chemical Sciences, University of Western Australia, Crawley, Western Australia 6009, Australia
)
‡
bS Supporting Information ABSTRACT: High quality synchrotron powder X-ray diffraction (PXRD) data measured from 90 to 900 K were used to carry out crystal structure refinements of the thermoelectric Zintl phase, Yb14MnSb11, made up of Yb cations and polyanions along with Sb anions. The crystal structure exhibits near linear thermal expansion with high-temperature expansion coefficients of 2.20(3) 104 K1 and 3.67(3) 104 K1 for a and c of Yb14MnSb11. A subtle structural transition is observed between 500 and 600 K, which primarily involves the [MnSb49] tetrahedron where the MnSb bond length is increased by about 0.015 Å. The atomic displacement parameters (ADPs) of the Mn atom were found to be larger than the ADPs of the Sb and Yb atoms reflecting the lower mass of Mn. On the other hand the heavy Yb atoms were found to vibrate significantly more than the lighter Sb atoms, and this presumably reflects the stronger chemical bonding of the covalently bonded anions relative to the isolated Yb cations. Modeling of the ADPs gives a Debye temperature of 168(2) K. The chemical bonding in Yb14MnSb11 was analyzed using Atomic Hirshfeld Surfaces. Overall, the analysis supports the presence of the structural elements of Yb cations, [MnSb49] tetrahedra, linear [Sb37] trimers and isolated Sb3. There are, however, indications of a complex network of directional interactions between the Sb anions and the Yb cations. KEYWORDS: thermoelectrics, atomic Hirshfeld surfaces, synchrotron powder X-ray diffraction, Zintl phase
’ INTRODUCTION In the past decade, great focus has been put on solving the increasing energy problems of the world. Thermoelectric materials may contribute to future solutions by converting waste heat into electricity and improving active cooling systems. Thermoelectric materials possess the unique ability to interconvert heat and electricity, and by utilizing the Seebeck effect a temperature gradient can be converted into a potential difference. The thermoelectric efficiency of a material is described by the dimensionless figure of merit, zT = S2σT/k, where S is the Seebeck coefficient (ΔV/ΔT), T is the absolute temperature, and σ and k are the electrical and thermal conductivity, respectively. An ideal thermoelectric material fulfills the design concept of a “phonon glasselectron crystal” (PGEC), that is, it has a low thermal conductivity like a glass but a high electrical conductivity like a crystal.1 Some of the most promising candidates with these physical properties belong to the class of materials commonly referred to as Zintl phases, which are valence-precise semiconductors composed of electropositive cations and covalent r 2011 American Chemical Society
polyatomic anion units or networks. The Zintl compounds include clathrates, filled skutterudites, Zn4Sb3 as well as the complex 14-1-11 phases, such as Yb14MnSb11 explored in this work.210 Initially, the rare-earth Zintl phase Yb14MnSb11 was studied because of its exciting magnetic, optical, and transport properties,1118 and in 2006 exceptional high-temperature thermoelectric properties of the p-type material were reported by Brown et al.5 Around 1275 K Yb14MnSb11 has an extremely low lattice thermal conductivity (0.30.4 W/m K) and a maximum zT ≈ 0.8.19 These properties were attributed to the highly complex crystal structure. The family of Ca14AlSb11 compounds, including Yb14MnSb11, crystallizes in the tetragonal space group I41/acd, where the large complex unit cell contains 208 atoms as depicted in Figure 1.20 The primary guideline for understanding Received: May 10, 2011 Revised: July 6, 2011 Published: July 28, 2011 3723
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Figure 1. (a) View of the unit cell of the Yb14MnSb11 (14-1-11) structure along the c axis showing the distorted [MnSb4]9 tetrahedra (pink), the linear [Sb3]7 polyanion units (green trimers), the isolated Sb3 anions (green) and Yb2+ cations (purple). (b) Section of the unit cell showing the labeling of the atoms in the structure. The tetrahedron is composed of the manganese atom (Mn) and four Sb2 atoms. Sb4 is the central atom in the linear trimer, which also consists of two Sb1 atoms. The rest of the atoms (i.e., the ytterbium atoms and the Sb3 atoms) are isolated ions in the unit cell.
the 14-1-11 phases has been the ZintlKlemm principle, which assumes that the valence electrons of the 14 electropositive Yb2+ cations are donated to be shared among isolated covalently bonded anions. As illustrated in Figure 1, the polyanions are a distorted [MnSb49] tetrahedron, a linear [Sb37] trimer, and four isolated Sb3 anions. Along the c-axis an alternating packing of tetrahedra and trimers is observed. In addition to this complex structure and the large unit cell, the many possibilities of tuning the thermoelectric properties through chemical doping or alloying make the 14-1-11 phases attractive for thermoelectric applications. The general formula of the family of Ca14AlSb11 compounds is A14MPn11, where A is an alkaline earth or divalent rare-earth element (Ca, Sr, Ba, Yb, Eu), M is a transition metal or a group 13 element (Mn, Zn, Al, Ga, In), and Pn is a group 15 element (P, As, Sb, Bi).1416,2027 While 14-1-11 phases containing a group 13 element (as Ca14AlSb11 with Al3+) are diamagnetic semiconductors, the Yb14MnSb11 structure containing Mn2+ is a ferromagnetic p-type metal. Substitutions of the three components affect the magnetic and transport properties by altering the number of charge carriers. The thermoelectric performance of Yb14MnSb11 is enhanced both by substitutions of La3+ for Yb2+ and of Al3+ for Mn2+.24,25 As mentioned above, the key model to discuss the 14-1-11 phases has been the ZintlKlemm concept.26,28 For intermetallic materials it is, however, often quite difficult to assign the structural units and provide a clear picture of the atomic interactions (chemical bonding). Recently, Skovsen et al. introduced the novel approach of atomic Hirshfeld surface analysis to discuss the structure and bonding in different polymorphs of CeMnNi4.29 In the present study we use the same approach to examine the 14-1-11 structure and bring the ZintlKlemm view of the structure on a more solid footing. We furthermore investigate the crystal structure up to high temperatures (900 K) using multi-temperature synchrotron powder X-ray diffraction (PXRD), since if the material is to be used for high temperature
Table 1. Crystallographic Details for the Multi-temperature Powder Diffraction Data of Yb14MnSb11 temperature 90 K
300 K
800 K
N(observations)
5734
5734
N(reflections)
10424
10513
10755
N(parameters)
109
109
109
a [Å]
16.5664(1)
16.6081(2)
16.7172(2)
c [Å] Uiso(Yb1) [Å2]
21.8907(2) 0.0022(2)
21.9883(2) 0.0092(3)
22.1732(2) 0.0223(4)
Uiso(Yb2) [Å2]
0.0040(3)
0.0133(3)
0.0356(5)
Uiso(Yb3) [Å2]
0.0025(3)
0.0094(4)
0.0224(6)
Uiso(Yb4) [Å2]
0.0041(3)
0.0135(4)
0.0356(6)
Uiso(Sb1) [Å2]
0.0016(5)
0.0051(6)
0.0178(8)
Uiso(Sb2) [Å2]
0.0034(4)
0.0089(5)
0.0256(6)
Uiso(Sb3) [Å2]
0.0026(4)
0.0099(5)
0.0224(7)
Uiso(Sb4) [Å2] Uiso(Mn) [Å2]
0.0015(7) 0.0012(14)
0.0053(9) 0.0160(22)
0.0163(13) 0.0523(35)
Rp/Rwp
4.74/6.96
6.08/7.7
7.82/8.31
RF/RI
1.18/2.27
2.31/2.7
10.5/3.96
χ2
6.02
5.94
4.63
5734
power generation, it is important to understand the structural behavior at working conditions.
’ EXPERIMENTAL SECTION Yb14MnSb11 was prepared from Sn flux as described by Cox et al.19 and investigated by multi-temperature, high-resolution synchrotron PXRD. The PXRD data were collected at beamline BL02B2, SPring8, Japan, using the large DebyeScherrer camera and a 0.2 mm quartz capillary.30 The synchrotron radiation wavelength was determined to be λ = 0.422731(2) Å using a CeO2 standard (a = 5.411102 Å). 3724
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Figure 3. Lattice parameters a (gray squares) and c (black circles) for the tetragonal Yb14MnSb11 as a function of temperature. Figure 2. Observed (red circles), calculated (black line) and difference (blue line) intensity for Rietveld refinement of powder diffraction data at 90 K. The green markers indicate positions of Bragg peaks for the Yb14MnSb11 structure. The insets show different parts of the data and good agreement is obtained between data and model both at low (top inset) and higher (bottom inset) angles. Temperature control during data collection was obtained using two different nitrogen flow systems for low (90300 K) and high (300 900 K) temperature, respectively. All data were Rietveld refined using the FullProf program package.31 The Yb14MnSb11 powder diffraction data were modeled in the tetragonal I41/acd space group with full site occupancy, a Lorentzian pseudo-Voigt peak shape, and an estimated absorption correction coefficient of μ*r = 1.55. The atomic displacements parameters (ADPs) were modeled isotropically, since anisotropic ADPs introduced 34 additional parameters with significant correlation. The data above 2θ = 60 were found to be very weak for all measurements and were consequently omitted in the final refinements. Selected details from the Rietveld refinements are listed in Table 1. Full details on the refinements can be found in the Supporting Information.
’ RESULTS AND DISCUSSION Multi-temperature Crystal Structure of Yb14MnSb11. In Figure 2 the 90 K synchrotron PXRD data for Yb14MnSb11 are displayed, and the diffractogram contains more than 10,000 Bragg reflections up to 2θ = 60. In addition to the main phase of Yb14MnSb11, some small unidentified impurity phases are observed. The lattice parameters, a and c, of the tetragonal unit cell are shown as functions of temperature in Figure 3. The experimentally observed room temperature values (a = 16.6081(2) Å and c = 21.9883(2) Å) are within 0.01 Å of previous reported values of a = 16.617(1) Å and c = 21.999(1) Å.32 At 300 K a systematic error between the low- and hightemperature data series is observed, which presumably is due to changes in the temperature control setup, and hence the sample environment.33 The unit cell axes show near linear thermal expansion with low-temperature expansion coefficients of 2.71(3) 104 K1 and 4.50(7) 104 K1 for a and c, respectively, and hightemperature expansion coefficients of 2.20(3) 104 K1 and 3.67(3) 104 K1 for a and c, respectively. The atomic displacement parameters (ADPs) extracted from the multi-temperature refinements are plotted in Figure 4.
The Mn atom has the largest ADP consistent with the fact that it is much lighter than the other atoms. The ADPs of Sb1 and Sb4 atoms are relatively small, which is in good agreement with the expected strong covalent bonding between these atoms in the linear polyanion unit. In general, the heavy Yb atoms have larger ADPs than the lighter Sb atoms. This counterintuitive result indicates that the Yb atoms are more loosely bound in the structure leading to larger vibration than the more tightly bound lighter Sb atoms. In some thermoelectric materials, the thermal conductivity can be lowered by rattling atoms as seen in clathrates and skutterudites.2,10,34,35 A rattling atom is a loosely bound guest atom in a framework host structure, and it is expected to vibrate independently of the framework atoms resulting in remarkably higher ADPs. Since the Uiso values in Figure 4 are roughly the same (despite the light manganese atom), there are no indications of rattling atoms or Zintl anion units in the 14-1-11 structure. The structural dynamics of the 14-1-11 phase can be probed by modeling the ADPs using the Debye expression.36 This has previously been done extensively for thermoelectric clathrate and skutterudite materials,7,37 although it must be remembered that the validity of the single atom Debye model may be somewhat limited for a material with hundreds of atoms in the unit cell. In the Debye model the mean square displacement is given as Æu2 æ ¼ Uiso ðTÞ 3T T ¼ 2 mkB θD θD
Z 0
θD =T
x θD dx þ expðxÞ 1 4T
! þ d2
where Uiso(T) is a weighted isotropic ADP for all the atoms, θD is the Debye temperature, m is the weighted mass of the Debye oscillators, and d2 denotes a temperature-independent disorder parameter. The disorder term, d2, refines to values close to zero, and this indicates that unlike clathrates the 14-1-11 structure is well ordered. However, the exact value of this disorder parameter cannot be fully trusted since it is affected by systematic errors in the Rietveld refinements. A low Debye temperature signifies a low velocity of sound in the lattice, and this leads to a low phonon mean free path and a corresponding low lattice thermal conductivity.38 The fit to the ADPs (illustrated by the dashed line in Figure 4) gives a Debye temperature for Yb14MnSb11 of 168 (2) K, in good agreement with the previously reported 3725
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Figure 4. Atomic displacement parameters of Yb14MnSb11 as a function of temperature. The dashed line illustrates the extrapolation of Uiso from the fitted Debye model.
Figure 5. Bond distances in the Yb14MnSb11 unit cell as function of temperature. Top left: The bond distances Yb2Sb2 (open squares), Yb3Sb3 (gray solid circles) and in the linear Sb37 trimer, Sb1Sb4 (black up-pointing triangles). Top right: Distances between antimony atoms Sb2Sb2 (black down-pointing triangles) and Sb3Sb3 (open circles). Bottom left and right: Bond distance between Sb and Mn and SbMnSb angles in the [MnSb4]9 tetrahedron.
Debye temperature of 160 (10) K by Fisher et al.12 According to the Debye expression at temperatures above the Debye temperature (T > θD), the ADPs should depend linearly on the temperature, which is also observed by looking closer at the Uiso(T) plots above 168 K. By using measured values of heat capacity (Cp = 750(J/mol 3 K)) and lattice thermal conductivity (kl = 0.4(W/ m 3 k)) around 1000 K from Cox et al.19 an approximate phonon mean free path of 34 Å is found. This is equal to about 11/2 -2 unit cell lengths, which is quite long in such a complex structure. A selection of some of the shortest interatomic distances as a function of temperature is shown in Figure 5. The bond distances increase as expected when the unit cell expands at elevated
temperatures. However, peculiar anomalies are observed in some of the bond distances around 500600 K, suggesting the presence of a subtle structural transition not previously detected in any of the physical properties.5 The phase transition is not expected according to the thermal analysis, which indicates stability up to 1300 K.23 There is also no clear signature of this subtle transition in the unit cell parameters (Figure 3). A comparison of the PXRD data below 500 K and above 600 K does not reveal extra diffraction peaks, which indicates that it is a structural change in the Yb14MnSb11 crystal structure rather than some sort of decomposition. The most significant changes in interatomic distances involve the Sb2 atom, which is coordinated to the manganese atom in the tetrahedron, 3726
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Figure 6. Curvedness plotted on the atomic Hirshfeld surfaces and mapped from 1.4 (flat; red) to 0.3 (sphere-like; blue) for the atoms of the Yb14MnSb11 structure at 90 K. Panel (a) shows the coordination of the atoms of the distorted tetrahedron, i.e., a manganese atom and two of coordinated Sb2-atoms. In panels (b) and (c) the antimony atoms of the linear trimer (Sb4 and Sb1) are shown. Panel (d) shows the last isolated antimony atom (Sb3), while the AHS of all the ytterbium atoms are seen in panel (e). The labeling of the atoms in the unit cell is shown in Figure 1.
and it is especially the Sb2 y coordinate, which changes significantly. The angles in the tetrahedron develop toward a more ideal tetrahedral geometry (i.e., 109.5) as the temperature increases, but at 500600 K a remarkable change is observed. Currently, we do not have any suggestions for the origin of the effect. It may be related to the magnetic properties of the material, since the changes occur around the Mn atom, but no high temperature magnetic properties have been published previously or measured in this study.
’ ATOMIC HIRSHFELD SURFACES Because of the many bonding possibilities in intermetallic compounds, the atomic interactions are not easily understood.
To gain insight into these interactions the Hirshfeld surface partitioning scheme implemented in CrystalExplorer was used.39 Hirshfeld originally proposed to use the stockholder concept to divide the electron density of a molecule into atomic fragments.40 The concept was generalized to extract molecular fragments from a crystal by defining a molecular weight function, w(r) = Fpromolecule(r)/Fprocrystal(r). The promolecule density is a sum of spherically averaged atomic electron density functions centered on the atomic positions for the selected molecular fragment, whereas the procrystal density is the corresponding density of the surrounding crystal. Partitioning space into regions where the promolecule density dominates, for example, w(r) g 0.5, was suggested by Spackman and co-workers as a unique new scheme 3727
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Table 2. AHS Coordinations, Volumes, and Sphericities in the Yb14MnSb11 Structure at 90 Ka coordination number
volume [Å3]
atom
site
sphericity
Yb1
32 g
6
16.11
0.978
Yb2 Yb3
32 g 16e
6 (8) 6
18.01 15.68
0.979 0.985
Yb4
32 g
6
17.35
0.979
Sb1
16f
9
23.79
0.993
Sb2
32 g
7
24.21
0.990
Sb3
32 g
7
24.86
0.993
Sb4
8b
6 (10)
23.20
0.992
Mn
8b
4
12.49
0.958
The sphericity is defined as π1/3(6V)2/3/A, where V and A are the volume and surface area of the Hirshfeld atom, respectively.41. a
defining a Hirshfeld surface.41,42 The same concept can be applied to atoms in a crystal rather than to molecular fragments, and this is called the atomic Hirshfeld surface (AHS). AHS analysis is a useful tool for partitioning crystal space, and it provides insight into the interatomic interactions and also provides a somewhat rigorous structural analysis of the atomic volumes. This AHS approach provides a way of identifying plausible bonding patterns in nonmolecular crystal structures, as well as providing a tool for analyzing the atomic environments. One property that can reveal interesting details about the atomic environments is the curvedness of the AHS as defined by McKinnon et al.42 As shown by Skovsen et al.29 a low curvedness suggests close contacts and this is possibly indicative of covalent bonding interactions. However, currently the AHS are calculated using neutral spherical atom charge densities, and intermetallic systems may be significantly ionic, which could alter the interpretation of the AHS. To investigate the chemical bonding in Yb14MnSb11 the curvedness of the different AHS are mapped over the range 1.4 to 0.3 (red is flat; blue is curved) in Figure 6. Furthermore, the volumes and the sphericity of the Hirshfeld atoms have been calculated for all the atoms in the 141-11 Zintl phase, and they are listed in Table 2. The most evident interatomic interactions are observed in the [MnSb4]9 tetrahedron (Figure 6a), which verifies this structural element as discussed in the previous studies of the 14-1-11 structure.11,20 The manganese atom is not spherical but almost completely tetrahedral and the flat red surfaces on the manganese atom toward the four antimony atoms indicate strong interactions confirming the proposed covalent bonding in this Zintl anion. The Sb2 atoms are more sphere-like, and besides the obvious interaction with the manganese atom, flat surfaces are also observed toward six ytterbium atoms (two Yb1, a Yb2, a Yb3, and two Yb4). The distance between the Sb2 atoms and the manganese atom is 2.732 Å, and the angles in the tetrahedron are 117.5 and 105.6. The two Yb2 atoms are actually also placed in a pseudotetrahedral arrangement around the manganese atom at a distance of 3.506 Å, but no interactions are observed on the AHS of manganese toward the Yb2 atoms. In Figure 6b the interactions in the linear [Sb3]7 polyanion are shown. The central Sb4 atom has quite flattened surfaces toward the two Sb1 atoms at a distance of 3.194 Å supporting the suggested trimer polyanion structure. Furthermore, interactions are observed between Sb4 and the four Yb1 atoms separated by 3.205 Å in addition to the weaker surface flattenings toward the four Yb2 atoms located 3.281 Å from Sb4.
The Sb1 atoms in the ends of the trimer (Figure 6c) show strong interactions with the Yb4 atoms, which are located slightly closer (3.152 Å) than the central Sb4 atom. Since the Sb1 atom has flattened surfaces toward all its nine neighbor atoms (Sb4 and two of each kind of ytterbium atoms), it is the most coordinated atom in the unit cell. The fact that the ends of the trimer (Sb1) shows so significant interaction with the surrounding Yb atoms rather than with the central Sb1 atom may indicate that the trimer structural unit is more complex than suggested in the simple Zintl picture. It could also indicate that the negative charges of the trimer are concentrated at the ends of the trimer to optimize ionic bonding with the positive Yb atoms. According to Figure 6d, the isolated Sb3 anions (denoted Sb3) are coordinated to all their seven neighboring ytterbium atoms (two Yb1, two Yb2, one Yb3, and two Yb4). All of the ytterbium atoms are almost octahedrally coordinated, hence the AHS of these atoms are practically cubic (Figure 6e). The Yb3 atom is almost completely octahedrally coordinated with angles between the antimony atoms of 87.1 to 96.8. Yb2 is the most distorted cube since it is virtually only 5-coordinated, probably because of the lack of interaction toward the tetrahedral manganese atom. The AHS of Yb4 is the most interesting of the ytterbium atoms. As mentioned Sb1 in the end of the trimer has a strong interaction with Yb4, but the AHS of Yb4 also shows a much flattened surface toward a Sb2 atom in the tetrahedron. Consequently, the Yb4 atoms are observed to “connect” the two different polyanion units of the 14-1-11 structure. As mentioned, the currently available atomic Hirshfeld surface approach is based on neutral spherical atom charge densities, which may not be fully valid for intermetallic systems like Yb14MnSb11. Although the interpretation of the values in Table 2 might not be completely straightforward, it is still possible to compare the relative values of the different AHS. From Table 2 and Figure 6 it is apparent that the antimony Hirshfeld atoms are larger than the ytterbium Hirshfeld atoms and that the manganese Hirshfeld atom is the smallest. This is in accordance with the expected ionic radii, since the negatively charged antinomy ions are larger than the divalent Yb2+ and Mn2+ cations. A comparison of the Yb2+ AHS volumes show that the least octahedrally coordinated ytterbium atom (Yb2) has the largest volume as expected, whereas the most octahedrally coordinated ytterbium atom (Yb3) has the smallest volume. Kim et al. studied doping site preferences in Eu13AMnSb11 (A = Ca, Sr, Ba, and Yb), and found that the Yb2 site is more favorable to larger dopants, whereas the Yb3 site with higher symmetry is preferred by smaller cations.43 This is in good agreement with the observed volumes of the atomic Hirshfeld surfaces. The volumes of the antimony atoms in Table 2 are also in good agreement with the previously reported Zintl anion structures. Thus, the isolated Sb3 anions (Sb3) are the largest, since they are not covalently bound, but coordinated to six ytterbium cations with ionic interactions. In the [Sb3]7 trimer the antimony ions only have a negative charge of 7/3, and therefore Sb1 and Sb4 are the smallest among the Sb atoms. However, the Yb atoms have larger ADPs than the Sb atoms (Figure 4) even though they have smaller Hirshfeld volumes. This corroborates that the Yb atoms are positively charged and therefore should have smaller ionic volumes in the AHS construction and more space for vibrational displacements. Regarding the shapes of the AHS, the dimensionless sphericity of a perfect sphere is unity, so the more deformed the Hirshfeld 3728
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’ CONCLUSIONS High quality synchrotron PXRD data were used to carry out crystal structure refinements of the complex thermoelectric Zintl phase Yb14MnSb11 from 90 to 900 K. A subtle structural transition is observed between 500 and 600 K, which primarily involved the [MnSb49] tetrahedron where the MnSb bond length is increased by about 0.015 Å, and the SbMnSb bond angles are changed by 0.17 and 0.35. The subtle transition has not previously been observed in neither transport nor thermal data, and its origin is yet unknown. It may be related to the magnetic properties of the system, but no high temperature magnetic properties have so far been measured. The ADPs of the Mn atom were found to be larger than for Sb and Yb reflecting the lower mass of Mn. On the other hand the heavy Yb atoms were found to vibrate significantly more than the lighter Sb atoms, and this presumably reflects the stronger chemical bonding of the covalently bonded anions relative to the isolated Yb cations. Modeling of the ADPs gives a Debye temperature of 168(2) K. The chemical bonding in Yb14MnSb11 was analyzed using the curvedness of Atomic Hirshfeld Surfaces. Overall, the analysis supports the presence of the structural elements of Yb cations, [MnSb49] tetrahedrons, linear [Sb37] trimers, and isolated Sb3 anions in case of Yb14MnSb11. There is, however, indication of a complex network of directional interactions between the Sb anions and the Yb cations, and as an example the Yb4 cation appears to connect the [MnSb49] tetrahedron with the linear [Sb37] trimer unit in Yb14MnSb11. This could have implications for the quite favorable electrical conductivity observed for this complex material. Analysis of chemical bonding in intermetallic compounds with the AHS approach is a new tool in structural chemistry, and its general applicability deserves to be further explored. One issue that merits further development is the use of non-neutral spherical electron densities that better reflect the actual charge transfer in systems such as these. ’ ASSOCIATED CONTENT
bS
Supporting Information. Full details on the Rietveld refinements from 90900 K, Debye fits for Uiso(T), selected bond distance table, selected PXRD data and Hirshfeld surfaces, comparison of low and high temperature atomic Hirshfeld surfaces. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This work was supported by the Danish National Research Foundation (Center for Materials Crystallography), the Danish
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Strategic Research Council (Center for Energy Materials), the Danish Research Council for Nature and Universe (Danscatt), the Australian Research Council, and NSF DMR-0600742. The synchrotron radiation experiment at the SPring-8 synchrotron was conducted with the approval of the Japan Synchrotron Radiation Research Institute.
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