ARTICLE pubs.acs.org/JPCC
Structure and Chemical Bonding of Binary Ytterbium Germanides, Yb3Ge5 and YbGe3, Prepared by High-Pressure and High-Temperature Reactions Momoko Harada,† Hiroshi Fukuoka,*,† Daiju Matsumura,‡ and Kei Inumaru† † ‡
Department of Applied Chemistry, Faculty of Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan Synchrotron Radiation Research Center, Japan Atomic Energy Agency, Sayo, Hyogo 679-5148, Japan
bS Supporting Information ABSTRACT: Two new ytterbium germanides, Yb3Ge5 and YbGe3, were obtained using high-pressure and high-temperature reactions. Yb3Ge5 crystallizes in the Pu3Pd5 structure (the , b = 7.5569(5) Å , space group Cmcm, No. 63) with a = 9.3739(8) Å 3 c = 9.5170(8) Å, and V = 674.16(9) Å . It is a new polymorph and contains Ge5 units with a square-pyramidal structure. COHP and ELF calculations revealed that the unit is constructed with strong Ge Ge covalent bonds. The XAS analysis showed that the mean oxidation state of Yb is +2.4. It is metallic and is an example of electron-rich Zintl phases. YbGe3 crystallizes in the Cu3Au structure (the space group Pm3m, No. 221) having a unit cell of a = 4.276(1) Å and V = 78.13(3) Å3. It is the first example for heavy rare-earth germanides having the Cu3Au-type structure. The mean oxidation state of Yb is +2.4. YbGe3 is metallic and is possibly a valence-fluctuating system.
’ INTRODUCTION Lanthanide germanides show various structures depending on the valences and ionic radii of lanthanides, as well as on reaction conditions. For 1:2 compounds, light rare-earth metals with large ionic radii often crystallize in the ThSi2 structure at ambient pressure, whereas heavy rare-earth metals tend to form layered compounds, such as the EuGe2 and the defect AlB2 structures.1 4 We have studied the synthesis of lanthanide germanides using reactions under high-pressure and high-temperature conditions and have successfully obtained some new germanides.5 11 By using the high-pressure techniques, we can effectively prepare new compounds with interesting Ge networks that cannot be produced at ambient pressure. For example, it was found that some light rare-earth metals form the LaGe5 structure with a tunnel structure and the Cu3Au-type structure.5,6,12 We also obtained new layered germanides with the YGe3 structure for some rare-earth elements composed of double Ge-squared meshes and one-dimensional Ge chains by high-pressure and high-temperature reactions.9 In this study, we focus on the reactions of the Yb Ge system under high-pressure and high-temperature conditions. Pani et al. proposed a phase diagram of Yb Ge compounds produced under ambient pressure.13 Among those compounds, Yb3Ge5 and Yb3Ge8 have unique Ge networks not found in other lanthanide germanides.13,14 The structural uniqueness of Yb germanides is mainly due to the fact that Yb readily forms divalent compounds, whereas other lanthanide elements except for Eu are usually in a 3+ oxidation state. Therefore, ytterbium sometimes forms mixed valence (or valence-fluctuating) compounds, which attract increasing attention from material scientists. Especially, r 2011 American Chemical Society
intermetallic compounds with 13, 14, and 15 elements exhibit unique structures as well as interesting physical properties, such as superconductivity and heavy-fermion behaviors. In view of these circumstances, we performed high-pressure and high-temperature reactions in the Yb Ge system and have successfully obtained two new ytterbium germanides, Yb3Ge5 and YbGe3. The former crystallizes in the Pu3Pd5 structure and contains unique Ge5 square-pyramidal units. YbGe3 is a new Cu3Au-type compound with metallic properties. We have comprehensively investigated the oxidation state of Yb and the charge distribution in the structure using physical properties measurements and theoretical calculations of electronic structures.
’ EXPERIMENTAL SECTION Synthesis and Characterization of Yb3Ge5. A mixture of Yb and Ge with an atomic ratio of 3:5 was placed in a Ta cell and was sealed in an Ar-filled stainless steel tube. The tube was heated in an electric furnace at 900 °C for 18 h. The product was hexagonal Yb3Ge5. It has a defect AlB2 structure.13 The obtained Yb3Ge5 was well ground with an agate mortar and was placed in an h-BN cell. The cell was placed in a MgO octahedral pressure medium and was heated at 750 1200 °C under 2 13 GPa using a Kawaitype multianvil press.15 After the reactions, the samples were Special Issue: Chemistry and Materials Science at High Pressures Symposium Received: July 1, 2011 Revised: September 21, 2011 Published: October 25, 2011 2153
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The Journal of Physical Chemistry C quenched to room temperature. The products were characterized by X-ray powder diffraction (XRD) measurements with a Bruker AXS D8 Advance diffractometer with Ni-filtered Cu Kα radiation. The crystal structure was analyzed using a single crystal with a size of 0.06 0.04 0.04 mm3. The X-ray diffraction data were collected using a Rigaku Rapid-Auto diffractometer with graphite-monochromated Mo Kα radiation. The structure was solved and refined using the Shelx97 Package.16 Synthesis and Characterization of YbGe3. A mixture of Yb (Nilaco, 99.9%) and Ge (Rare Metallic Co. Ltd., 99.999%) with a molar ratio of 1:3 was melted in an Ar-filled arc furnace. The product was a mixture of Ge and Yb3Ge8. The mixture was heated using a Kawai-type multianvil press. Reactions were performed varying the temperature (800 1100 °C) and the pressure (5 13 GPa). The products were characterized by X-ray powder diffraction (XRD) measurements with a Bruker AXS D8 Advance diffractometer with Ni-filtered Cu Kα radiation. The crystal structure was analyzed using a single crystal with a size of 0.058 0.038 0. 030 mm3. The X-ray diffraction data were collected using a Bruker APEX-II CCD diffractometer with graphitemonochromated Mo Kα radiation. The structure was solved and refined using the Bruker SHELXTL Software Package.16 Electric Resistivity, Magnetic Susceptibility, and X-ray Absorption Measurements. We polished the bulk product with sandpaper to prepare rectangular-shaped specimens. Electrical resistivity was measured on the specimen with the van der Pauw method using dc from room temperature to 2 K. Magnetic susceptibility measurements were performed with a SQUID magnetometer (Quantum Design MPMS-5) in a 5000 Oe field. X-ray absorption measurements using synchrotron radiation were carried out at the BL14B1 beamline of SPring-8. The photoabsorption of powder samples was measured around the Yb LIII edge at room temperature. Electronic Structure Analysis. The band structure calculation was performed using the WIEN2k package with a general potential APW+lo code.17,18 Some parameters used were as follows: RMT, 2.5 for Yb and 2.47 for Ge; Gmax, 12; RMT kmax, 7; number of k points, 5000. Chemical bond analysis using COHP (crystal overlapping Hamiltonian population) and ELF (electron localization function) were calculated and analyzed using a tight-binding linear muffin-tin orbital-atomic sphere approximation with TB-LMTO-ASA software.19
’ RESULTS AND DISCUSSION Crystal Structure of New Yb3Ge5. A new polymorph of Yb3Ge5 with the Pu3Pd5 structure was obtained by annealing hexagonal Yb3Ge5 (the ambient pressure phase) at 13 GPa and 1000 °C for 1 h. The new Yb3Ge5 forms silver brittle crystals with a metallic luster. It crystallizes in the monoclinic Cmcm having a , b = 7.5569(5) Å, c = 9.5170(8) Å, unit cell of a = 9.3739(8) Å 3 and V = 674.16(9) Å . The crystallographic data and atomic and thermal displacement parameters of Yb3Ge5 are listed in Tables S1, S3, and S4 of the Supporting Information. The new Yb3Ge5 is isotypic with another lanthanide germanide Eu3Ge5, stannides Sr3Sn5 and Ba3Sn5, and a plumbide Ba3Pb5.20 22 These compounds contain unique five-atom cluster units. The crystal structure of new Yb3Ge5 is shown in Figure 1a. For comparison, the structure of hexagonal Yb3Ge5 is presented in Figure 1b. The new phase of Yb3Ge5 (orthorhombic form) changed into the hexagonal form when it was annealed at 1000 °C in an evacuated silica ampule. Therefore, the phase
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Figure 1. (a) Crystal structure of the high-pressure phase Yb3Ge5. Yellow and blue spheres show Yb and Ge atoms, respectively. (b) Crystal structure of hexagonal Yb3Ge5. (c) The structure of the Ge5 unit of the high-pressure phase Yb3Ge5 with some interatomic distances.
Figure 2. Temperature dependence of the electrical resistivity of Yb3Ge5.
transition between these forms is reversible. The comparison of the density of the orthorhombic (8.69 g/cm3) and hexagonal (8.63 g/cm3) forms shows that the new phase is slightly denser than the hexagonal form. The new orthorhombic phase of Yb3Ge5, therefore, can be mentioned as a high-pressure phase. The hexagonal phase has a layered structure derived from the AlB2 structure (a defect AlB2 structure). The Ge layer is flat, and all Ge atoms have two- or three-bonded sp2 coordinations. On the other hand, the Ge atoms in the new phase form Ge5 squarepyramidal cluster units. Figure 1c shows the structural detail of the Ge5 unit in the high-pressure phase. The distances between neighboring Ge atoms are observed to be 2.634(1), 2.658(1), for Ge2 Ge3, Ge1 Ge2, and Ge1 Ge3, and 2.787(1) Å respectively. Each Ge5 unit is separated from other units with , which is about 0.2 Å the shortest Ge Ge distance of 2.957(1) Å longer than the maximal distance in the intra-unit. Electric and Magnetic Properties of New Yb3Ge5 and the Oxidation State of Yb Ions. The whole structure of new Yb3Ge5 is constructed by covalent and ionic interactions, that is, the Ge Ge and the unit guest interactions, respectively. The structure, therefore, has characteristics similar to those of the Zintl 2154
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Figure 3. Temperature dependence of the magnetic susceptibility of Yb3Ge5. Green circles show the observed points. The red line shows the fitting curve by a modified Curie Weiss equation.
phase compounds. However, new Yb3Ge5 is not a classical Zintl phase because it is metallic, as shown in Figure 2. The resistivity decreases with the decrease of temperature. To figure out the electronic structure of new Yb3Ge5, we have to determine the valence state of Yb ions first. Therefore, we tried to calculate the averaged oxidation state of Yb from magnetic susceptibility measurements. The temperature dependence of the magnetic susceptibility of Yb3Ge5 is presented in Figure 3. Yb3Ge5 shows paramagnetic properties. We fit the curve using a modified Curie Weiss equation; χ = χ0 + C/(T θ), where C and θ are the Curie constant and Weiss temperature, respectively. The calculated Weiss temperature is 5.03 K, suggesting that the magnetic interaction between Yb ions is antiferromagnetic. The effective magnetic moment μexp was calculated to be 1.33 μB from the Curie constant of 0.220 emu K mol 1. Because theoretical magnetic moments are 4.54 and 0 μB for Yb3+ and Yb2+ ions, respectively, the mean oxidation state of +2.09 is derived for ytterbium in Yb3Ge5. Most of the Yb ions are assigned to be in the 2+ oxidation state. However, Tsujii and Yamaoka et al. pointed out in their work on AlB2-type YbGaxSi2 x that Yb ions in metallic compounds can be in a valence-fluctuating state, Yb2+T3+, and show significant deviation from the Curie Weiss type susceptibility.23 We, therefore, measured X-ray absorption spectra (XAS) at the LIII edge of Yb because the technique enable one to resolve the 2+/3+ states of Yb even in fluctuating systems. Figure 4 shows the Yb LIII XAS spectrum of Yb3Ge5. The two peaks at 8941 and 8949 eV correspond to the Yb2+ and Yb3+ contributions, respectively. The observed spectrum is fit by two sets of Gaussian and error functions after the normalization. The averaged oxidation state of Yb estimated through fitting is +2.43, indicating that about 40% Yb is in the trivalent state. This value is quite different from the value of +2.09 derived from the magnetic susceptibility using the modified Curie Weiss law. This disagreement is probably due to the valence fluctuation of Yb as mentioned by Tsujii and Yamaoka et al.23 In the fluctuation system, it is difficult to obtain the averaged oxidation state from the magnetic susceptibility measurements applying the normal routine using the Curie Weiss law. We, therefore, concluded that Yb3Ge5 is a mixed valence compound containing about 40% Yb3+. Electronic Structure of New Yb3Ge5. We examined the electronic structure of new Yb3Ge5 to consider the charge
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Figure 4. X-ray absorption spectrum of Yb3Ge5 measured at the LIII edge of Yb. The observed spectrum presented with open circles is fitted using two sets of Gaussian and error functions for Yb2+ and Yb3+ as shown by red and blue lines, respectively. The green line is the fitting curve.
distribution in the structure. When electronic structures of Zintl anions are discussed, Wade’s rule is often used. In the present case, there are two possible structure models for Ge5 units: nido and arachno structures. Their mother (closo-) deltahedra are the octahedral and pentagonal bipyramidal structures, respectively. We have to choose either model taking into account the structural distortion of the Ge5 units from a regular squarepyramidal structure as well as from the character of local orbitals of the unit (i.e., bonding or antibonding). For isotypic compounds of Ba/Sr3Sn5, La3In5, and Eu3Ge5, detailed electronic structures of Sn5, In5, and Ge5 units were investigated.20 22 By reference to those work, we also calculated the molecular orbitals of a naked Ge5 unit having the identical structure in Yb3Ge5 using the DV-Xα method.24 We performed calculations for three ionic valence states, that is, Ge54 , Ge56 , and Ge57 . The nido and arachno cluster models of the Ge5 unit correspond to Ge54 and Ge56 , respectively. The state of Ge57 is a model of the estimated formal charge of Ge57.2 from the XAS measurement. All calculations gave very similar results to those obtained for the Sn5 unit in Ba/Sr3Sn5. The intrinsic electrons of five Ge atoms fill up to the 80th molecular orbital (MO) (Supporting Information, Figure S1). The HOMO and SOMO of the hypothetical Ge57 unit are, therefore, the MOs 84 and 83. These orbitals have antibonding natures for all pairs of neighboring Ge atoms. The MO 82 has an antibonding property for the pair of basal apical Ge pairs, but has a bonding property for the pairs of Ge atoms on the basal plane. Therefore, the three electrons in MOs 84 and 83 seem very unstable and possibly become itinerant electrons if those antibonding orbitals can form conduction bands. These calculations are a bit simple to determine the electronic structure of the Ge5 unit in Yb3Ge5, but it is a good guess that the Ge5 unit can be considered as a nido cluster that obeys the electron counting rule of 2n + 4 = 14 skeletal electrons with 10 lone pair electrons. The HOMO of the nido-Ge5 cluster is MO 82, and the formal ionic valence of the unit is 4 . This model shows that Yb3Ge5 is not a classical Zintl phase compound and is consistent with the observation that Yb3Ge5 is metallic. We calculated COHP diagrams for each bond to confirm the strength of the Ge Ge bonds in the unit. The diagrams are 2155
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Figure 6. ELF diagrams of Yb3Ge5 for the planes parallel to the a b plane (a), to the a c plane (b), and to the b c plane (c).
Figure 5. COHP diagrams of Ge Ge bonds in Yb3Ge5: (a) Ge1 Ge3, ; (c) Ge2 Ge3, 2.787 Å ; (d) Ge2 Ge2 2.634 Å; (b) Ge1 Ge2, 2.658 Å (interunit), 2.957 Å.
presented in Figure 5. The values of COHP at the Fermi level (EF) are negative for Ge1 Ge2 and Ge2 Ge3 pairs but is positive for Ge1 Ge3. The ICOHP (integrated COHP) diagrams at EF show high positive values (about 1 eV/bond or larger) for all Ge Ge pairs in the Ge5 unit. This shows the presence of strong covalency for each bond. It is notable that the ICOHP diagram of the 2.975 Å Ge2 Ge2 pair, which is the shortest distance between adjacent Ge5 units, also shows a relatively high value of 0.68 eV/bond. This shows the presence of considerable covalent interactions between the units. The Ge5 units are electronically interconnected through the Ge2 Ge2 interactions, forming a one-dimensional chain structure of Ge5 units, which can provide the conduction path for itinerant electrons. We performed the ELF analysis to confirm the interactions of those Ge Ge pairs. Figure 6a shows a vertical slice of Ge5 units by a plane parallel to the a b plane. Ge1, Ge3, and Yb2 atoms reside on the plane. Each Ge atom has one or two area(s) with high ELF values (η > 0.6) displayed in red. They probably correspond to localized electrons, such as lone pairs. There are areas with η > 0.55 between Ge1 and Ge3 atoms, too. They presumably show the covalent electrons of the Ge Ge bonds.
The Ge5 units seem to be well separated from the view of this direction. Figure 6b shows the ELF diagram for the bottom plane of a Ge5 unit. There are areas with η > 0.55 between Ge1 and Ge2 atoms, suggesting the existence of strong bonds between them. These results agree well with the results of the COHP analysis mentioned above. Figure 6c shows the wide view of the crystal parallel to the b c plane. Ge2, Ge3, and Yb2 atoms are on this plane. There is no high-ELF area between Ge2 and Ge3 atoms. This would agree with the relatively low ICOHP value compared with those for Ge1 Ge3 and Ge1 Ge2 pairs. We tried to find the evidence for the covalent interaction between Ge2 Ge2 atoms of adjacent units, but there is no remarkable high-ELF area between the units. However, the appearance of the ELF around Ge5 units in Figure 6c is clearly different from that in Figure 6a. The separation of Ge5 units between Ge2 and Ge2 atoms of adjacent units is not so clear. From the results of COHP analysis, we conclude that there are significant interactions between Ge5 units, despite the ELF analysis. We will discuss the importance of the interunit interactions for the electrical resistivity of this structure in a later section. The collective results above provide information about the electronic structure for new Yb3Ge5. The Ge5 unit can be understood as a nido-Tt4 cluster, and the excess electrons (3.2 electrons) probably become itinerant electrons. The interunit interaction through the Ge2 Ge2 path along the Ge5 units plays an important role for the metallic properties. The formalism of the electron distribution in this compound should be described as Yb2.4+3 [Ge5]4 3 3.2e ; here, the 3.2e are itinerant electrons. This compound is a rare case of electron-rich Zintl phases like La3Sn5.22,25 Comparison with Eu3Ge5. Unlike in the case of usual rareearth elements, ytterbium and europium readily form divalent compounds. This is a reason why these elements often form 2156
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Figure 7. Crystal structure of YbGe3. Yellow and blue spheres represent Yb and Ge atoms, respectively.
isotypic compounds. For the Pu3Pd5 structure, europium forms an isotypic compound Eu3Ge5. The lattice parameters of this , b = 7.9681(3) Å , and c = compound are a = 9.7675(4) Å 9.8562(3) Å. The oxidation state of Eu was determined to be +2.0 from the XAS analysis.20 The cell volume of Yb3Ge5 (674 Å3) is much smaller than that of Eu3Ge5 (767 Å3). This is probably due to the large difference in the ionic radii. The ionic radius of Eu2+ is about 0.1 and 0.26 Å larger than those of Yb2+ and Yb3+, respectively.26 Taking into account the mean oxidation state of +2.4 for Yb, the averaged smaller than that of Eu2+. ionic radii of Yb in Yb3Ge5 is 0.16 Å The unit cell of the Pu3Pd5 structure contains two rows of guest atoms along each axis. The estimated elongation of the cell for each axis, which is in good parameters is about 0.32 Å agreement with the observed values. We compared the volumes of the Ge5 unit in those compounds because the size of the unit should be affected by the number of donated electrons from guest ions. For simple comparison, we calculated the volumes of pyramidal units without thinking of the atomic volumes, that is, the volume of a pyramid of which five vertices are at the center of the Ge atoms of the Ge5 unit. The calculation gave volumes of 4.82 and 4.62 Å3 for Yb3Ge5 and Eu3Ge5, respectively. Contrary to their cell volumes, the volume of the Ge5 unit for Yb3Ge5 is larger than that of Eu3Ge5. This is probably due to the difference of mean oxidation states. In the case of Eu3Ge5, europium donates 6 electrons, while ytterbium donates 7.2 electrons to their host Ge network. Therefore, more electrons are accommodated in orbitals or bands composed of Ge Ge antibonding properties in Yb3Ge5 than in Eu3Ge5. This is the main reason for the large volume for the Ge5 unit in the ytterbium compound. The electrical resistivity of Yb3Ge5 is more than 10 times as small as that of Eu3Ge5 below 50 K.20 This can be explained by the small unit cell volume as well as the large number of donated electrons of the Yb compound. Because of the small ionic radii of Yb, the shortest interunit distances (Ge2 Ge2) of the Yb ) is much smaller than that of Eu compounds compound (2.787 Å (3.303 Å). The smaller interunit distance suggests the stronger interaction between units. The stronger interaction between the Ge5 units as well as the larger carrier concentration of the Yb compound enhanced the metallic property. Crystal Structure of YbGe3. According to the phase diagram of the Yb Ge system at ambient pressure, Yb3Ge8 is the
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Figure 8. Temperature dependence of the magnetic susceptibility of YbGe3. Green circles show the observed points. The red line shows the fitting curve by a modified Curie Weiss equation.
Figure 9. Temperature dependence of the electrical resistivity of YbGe3.
Ge-richest compound.13 We found that high-pressure reactions of Yb3Ge8 and Ge at 800 1200 °C under pressures higher than 2 GPa yield a new binary compound, YbGe3. It crystallizes in the and V = Cu3Au structure with a unit cell of a = 4.276(1) Å 3 78.17(3) Å . The crystallographic data and atomic and thermal displacement parameters of YbGe3 are listed in Tables S1 and S2 of the Supporting Information. The crystal structure of YbGe3 is presented in Figure 7. Ce forms a Cu3Au-type germanide by high-pressure and high-temperature reactions.6 YbGe3 is the second example of germanides having this type of structure. Heavy rare-earth elements, such as Gd, Tb, Dy, Ho, and Er, are known to form layered compounds with the DyGe3 structure.27 32 Because the Yb2+ ion is much larger than the heavy rare-earth 3+ ions of elements, ytterbium forms trigermanide with the Cu3Au structure. The temperature dependence of the magnetic susceptibility of YbGe3 is presented in Figure 8. YbGe3 shows a paramagnetic property. The fitting using a modified Curie Weiss equation, χ = χ0 + C/(T θ), gave the mean oxidation state of +2.02 for Yb, where C and θ are 0.05445 emu K mol 1 and 5.76 K, respectively. However, XAS measurements (Supporting Information, Figure S2) showed that YbGe3 is also a mixed valence compound with about 40% Yb3+ ions. Because there is no evidence of any superstructure for YbGe3, Yb2+, and Yb3+ ions occupy the same site. Therefore, YbGe3 is possibly a valencefluctuating compound. The charge distribution can be described as Yb2.4+ [Ge0.8 ]3. 2157
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The Journal of Physical Chemistry C The temperature dependence of the electrical resistivity of YbGe3 is shown in Figure 9. As expected from the charge distribution, it is a metal. The resistivity monotonically decreases down to around 20 K and shows almost constant values from 20 to 2 K.
’ CONCLUSIONS We successfully synthesized new ytterbium germanides Yb3Ge5 and YbGe3 using high-pressure and high-temperature synthesis. The high-pressure phase of Yb3Ge5 with the Pu3Pd5 structure contains Ge5 units with a square-pyramidal shape. COHP and ELF calculations revealed that the unit is composed of strong Ge Ge covalent bonds. Yb3Ge5 is a metal. The interaction between the Ge5 units strongly affects the metallic property. The XAS analysis showed that the mean oxidation state of Yb is +2.4. The formalism of the electron distribution is described as Yb2.4+3 [Ge5]4 3 3.2e ; here, the 3.2e are itinerant electrons. This compound is an example of electron-rich Zintl phases. YbGe3 is the first example of germanides with the Cu3Au-type structure for heavy rare-earth elements. The mean oxidation state of Yb is +2.4. YbGe3 is metallic and is possibly a valencefluctuating system. ’ ASSOCIATED CONTENT
bS
Supporting Information. Crystallographic data, atomic coordinates and thermal displacement parameters of YbGe3 and Yb3Ge5, molecular orbitals (MOs) for the naked Ge57 unit calculated by the DVX-α method, and X-ray absorption spectrum of YbGe3 measured at the LIII edge of Yb. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*Tel: +81-824-24-7742. Fax: +81-824-24-5494. E-mail: hfukuoka@ hiroshima-u.ac.jp.
’ ACKNOWLEDGMENT We are grateful to Dr. Kenji Yoshii of Japan Atomic Energy Agency for his help with the XAS measurements. The X-ray absorption measurements were performed under the CommonUse Facility Program of JAEA. This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, and Culture of Japan, Grant Nos. 16037212, 16750174, 18750182, 18027010, and 20550178.
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