Direct Observation of Pressure-Driven Valence Electron Transfer in

May 17, 2016 - School of Chemistry, The University of Sydney, Sydney 2006, Australia ... Our data also support the highly unusual “4+” nominal oxi...
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Direct Observation of Pressure-Driven Valence Electron Transfer in Ba3BiRu2O9, Ba3BiIr2O9, and Ba4BiIr3O12 Peter E.R. Blanchard,† Karena W. Chapman,‡ Steve M. Heald,‡ Mohamed Zbiri,§ Mark R. Johnson,§ Brendan J. Kennedy,∥ and Chris D. Ling*,∥ †

Canadian Light Source, 44 Innovation Boulevard, Saskatoon, Saskatchewan S7N 2V3, Canada X-ray Science Division, Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, United States § Institute Laue Langevin, 71 avenue des Martyrs, Grenoble 38042, France ∥ School of Chemistry, The University of Sydney, Sydney 2006, Australia ‡

ABSTRACT: The hexagonal perovskites Ba3BiIr2O9, Ba3BiRu2O9, and Ba4BiIr3O12 all undergo pressure-induced 1% volume collapses above 5 GPa. These first-order transitions have been ascribed to internal transfer of valence electrons between bismuth and iridium/ruthenium, which is driven by external applied pressure because the reduction in volume achieved by emptying the 6s shell of bismuth upon oxidation to Bi5+ is greater in magnitude than the increase in volume by reducing iridium or ruthenium. Here, we report direct observation of these valence transfers for the first time, using high-pressure X-ray absorption near-edge spectroscopy (XANES) measurements. Our data also support the highly unusual “4+” nominal oxidation state of bismuth in these compounds, although the possibility of local disproportionation into Bi3+/Bi5+ cannot be definitively ruled out. Ab initio calculations reproduce the transition, support its interpretation as a valence electron transfer from Bi to Ir/Ru, and suggest that the high-pressure phase may show metallic behavior (in contrast to the insulating ambient-pressure phase).



curiosities of these compounds: Bi4+ is an otherwise unknown cation in solid-state compounds, which is not expected to be stable due to its nominal [Xe]4f145d106s1 electronic configuration. “Bi4+” oxides such as BaBiO316−23 normally disproportionate into Bi3+/Bi5+. However, in the case of Ba3BiRu2O9 and Ba3BiIr2O9, we could find no evidence for long-range-ordered Bi3+/Bi5+ disproportionation in high-resolution neutron and synchrotron X-ray diffraction data or for short-range disproportionation peak broadening or anisotropic atomic displacement parameters. Analysis of Bi−O bond lengths using the bond valence sum (BVS) method22 support a discrete Bi4+ state,9,11 as does X-ray absorption near-edge spectroscopy (XANES).23 A possible reason for the failure to disproportionate (or, at least, to do so on a sufficient length scale that it can be observed) is the fact that the BiO6 octahedra in these compounds are distributed on a triangular lattice in the pseudohexagonal unit cell, such that long-range Bi3+/Bi5+ ordering is geometrically frustrated in a manner analogous to spin frustration on triangular magnetic lattices. Ba4BiIr3O1224 is a 12L-type perovskite whose structure is closely related to that of Ba3BiIr2O9 but with face-sharing octahedral Ir3O12 trimers in place of Ir2O9 dimers. For Ba3BiRu2O9 and Ba3BiIr2O9, BVS analysis22 and comparison to isostructural Ba4LnIr3O12 (Ln = lanthanides)25−27 support

INTRODUCTION There has been a recent upsurge of interest in the magnetism of 4d and 5d transition-metal oxides, due to an increasing recognition that the broad, spatially extended nature of 4d and 5d electronic wave functions, with their relatively weak electronic correlations, strong crystal field effects, and spin− orbit coupling, can result in surprisingly complex electronic and magnetic properties. That the heavier transition metals can adopt long-range-ordered magnetic states is not new; SrRuO3 was first identified as ferromagnetic over 50 years ago.1 However, in recent times there has been a dramatic increase in the number of examples, including the discovery of superconductivity in the defect pyrochlore KOs2O6,2 the experimental realization of a Jeff = 1/2 Mott insulator in Sr2IrO4,3 and ferromagnetism in the Mott insulator Ba2NaOsO6.4 Mixed valency has also been observed in a number of Os and Ru perovskites,5−7 reflecting the spatially dispersed d orbitals. Ba3BiIr2O98,9 and Ba3BiRu2O910,11 are hexagonal 6H-type perovskites (Figure 1a), the structures of which can be understood in terms of face-sharing octahedral M2O9 dimers that share corners with BiO6 octahedra, while Ba2+ cations occupy the high-coordinate perovskite A sites. Comparison of the lattice parameters of Ba3BiM2O9 (M = Ir, Ru) with those of the isostructural series Ba3LnM2O9 (Ln = lanthanides) shows that they resemble the 4+ valent lanthanides (Ce, Pr, Tb)12,13 more than the 3+ valent lanthanides.14,15 This suggests oxidation states of Bi4+ and M4+, which is one of the principal © XXXX American Chemical Society

Received: March 22, 2016

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evidence for the valence transfer between Bi and Ir/Ru. Here, we report direct observation of this valence transfer by highpressure X-ray absorption near-edge spectroscopy (XANES) measurements.



EXPERIMENTAL SECTION

All XANES spectra were collected in fluorescence mode using an unfocused beam with a 50 μm spot size on beamline 20-ID-C at the APS. Bi, Ir, and Ru metal foils were inserted as references for the respective edges. Data were treated using the Athena software.35 Ambient-pressure spectra were collected from films on Kapton tape. High-pressure spectra were collected using a diamond-anvil cell (DAC) with a 120 μm hole drilled in the gasket, which was then filled with sample, pressure-transmitting medium (a standard 4/1 methanol/ ethanol mixture), and several ruby chips for pressure calibration using the ruby fluorescence line. Data were collected on increasing pressure. For Ba3BiIr2O9 and Ba4BiIr3O12, we ran four repeats at the Bi L3, Bi L2, and Ir L3 edges. Spectra were collected at 0, 1.88, 3.81, 5.06, and 6.18 GPa for Ba3BiIr2O9 and at 0, 0.76, 1.96, 3.75, 5.39, 6.18, 7.59, and 8.76 GPa for Ba4BiIr3O12 over 2(1) s per point for Bi(Ir) edges. For Ba3BiRu2O9, we ran four repeats of all spectra at the Bi L3, Bi L2, and Ru K edges. Spectra were collected at 1.91, 5.06, 7.63, 9.04, and 9.61 GPa over 2(1) s per point for Bi(Ru) edges. Spin-polarized ab initio (density functional theory, DFT) geometry optimization calculations were carried out for Ba3BiIr2O9 using the VASP36 code. A Hubbard correction for the Ir d electrons (U = 3 eV and J = 1 eV) was applied. All calculations used the GGA-PBE functional and were converged with respect to k-point sampling and plane-wave energy cutoff.

Figure 1. Structures of (a) 6H-type Ba3BiRu2O9 and (b) 12L-type Ba4BiIr3O12. O atoms are shown as small red spheres and Ba atoms as large green spheres; isolated BiO6 octahedra are shown in purple and face-sharing RuO6/IrO6 octahedra in silver and gold, respectively. Ba3BiIr2O9 is isostructural with Ba3BiRu2O9.



oxidation states of Bi4+ and Ir4+. Note that an isostructural Ru (for Ir) phase exists for a wide range of Ba4LnRu3O12 (Ln = lanthanides) phases,26−29 but Ba4BiRu3O12 could not be stabilized.24 Ba3BiRu2O9, Ba3BiIr2O9, and Ba4BiIr3O12 all undergo lowtemperature first-order magnetostructural transitions,9,11,22,30 but we have shown that these do not involve any change or disproportionation of the oxidation states of Bi or Ir/Ru. However, they also undergo apparently unrelated first-order pressure-induced ∼1% volume collapses above ∼5 GPa, as observed in synchrotron X-ray and neutron powder diffraction patterns.31 Like the temperature-induced transition, this does not appear to be accompanied by a change in the space group symmetry (C2/c). We have proposed that these transitions are due to valence transfer between Bi and Ir/Ru, whereby the reduction in volume from oxidizing “Bi4+” (or mixed Bi3+/Bi5+, as the case may be) to Bi5+ outweighs the increase in volume of Ir/Ru reducing to 4+. While it is intuitively obvious that external applied pressure should favor such transitions, in practice, they are extremely rare. Comparable pressure-induced valence transitions had only been observed three times before: in LaCu3Fe4O12 (between Cu and Fe),32 BiNiO3,33 and FeTiO3.34 Ba4BiIr3O12, Ba3BiIr2O9, and Ba3BiRu2O9 appear to be the first cases involving 4d (Ru) or 5d (Ir) transition metals. Analysis of bond lengths refined against neutron powder diffraction (NPD) data using the bond valence sum (BVS) method supported the hypothesis of a pressure-induced valence transition. We also carried out ab initio (density functional theory, DFT) calculations simulating applied pressure, which showed that the experimentally observed ambient and highpressure forms are both stable from 5 to 15 GPa, with the form of the optimized structure depending only on the initial form chosen (i.e., consistent with the observed first-order transition) and a 0.71e decrease in the Bi s-electron population in the highpressure phase in comparison to the low-pressure phase.31 Nevertheless, despite the agreement between empirical BVS and ab initio electronic calculations, both are only indirect

RESULTS AND DISCUSSION Direct evidence of Bi to Ir electron transfer in Ba3BiIr2O9 and Ba4BiIr3O12 can be seen in the Bi L2 edge and Ir L3 edge. The

Figure 2. Bi L2-edge XANES spectra of (a) Ba3BiIr2O9 and (b) Ba4BiIr3O12 collected at 0 GPa (black) and high pressure (red).

Figure 3. Bi L2-edge XANES spectra of Ba3BiIr2O9 (black) in comparison to Bi2O3 (Bi3+; red), BaBiO3 (Bi4+; green), and Ba2LuBiO6 (Bi5+; green). Features A−C corresponds to features characteristic of Bi5+.

Bi L2-edge XANES spectra of Ba3BiIr2O9 and Ba4BiIr3O12 are shown in Figure 2. Attempts to analyze the Bi L3 edge were B

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hampered by the overlapping Ir L1 edge. As both edges correspond to the transition of a 2p electron into unoccupied states, the Bi L3 edge and L2 edge will exhibit similar trends. The line shape of the Bi L edge is influenced by both the Bi oxidation state and local structure.37,38 This is evident on comparison of the appropriate Bi L2 edge spectra for Bi2O3 (Bi3+), BaBiO3 (Bi4+), and Ba1.5Sr0.5LuBiO6 (Bi5+) in Figure 3. The Bi L2 edge of Ba2LuBiO6 consists of three well-defined features (labeled A−C) in comparison to the single broad peak observed in Bi2O3. The same features are present in BaBiO3. However, feature C is found at lower energy in comparison to Ba1.5Sr0.5LuBiO6. The single broad peak in Bi2O3 corresponds to a dipole-allowed transition of a 2p electron into unoccupied 5d states. In Ba1.5Sr0.5LuBiO6, feature A corresponds to a dipole-allowed transition of a 2p electron into 6s states due to the unoccupied 6s states in Bi5+.38 The broad feature observed for Bi3+ splits into two features (labeled A and B) due to the transition of the 2p electron into bonding (feature B) and antibonding (feature C) 5d states.38 At 0 GPa, the Bi L2-edge line shapes and absorption edge energies of Ba3BiIr2O9 (Figure 2a) and Ba4BiIr3O12 (Figure 2b) are similar to those of BaBiO3, consistent with the presence of Bi4+. Applying a pressure of 6.18 GPa (Ba3BiIr2O9) and 8.76 GPa (Ba4BiIr3O12) results in changes in the line shape of both spectra. In particular, three features (labeled A−C) appear that are similar to the features observed in the Bi L2 edge of Ba1.5Sr0.5LuBiO6, suggesting that the high-pressure phase contains exclusively Bi5+ (note that feature A is only visible in Ba4BiIr3O12, suggesting that the increase in Bi oxidation state is greater in Ba4BiIr3O12 in comparison to Ba3BiIr2O9). This change in the line shape is consistent with an increase in the oxidation state of Bi at high applied pressures. The Ir L 3 -edge XANES spectra of Ba 3 BiIr 2 O 9 and Ba4BiIr3O12 are shown in Figure 4. Like the Bi L2 edge, the Ir L3 edge corresponds to a dipole-allowed transition of a 2p electron into unoccupied 5d states and appears as a broad white line peak. Generally, the Ir L3 absorption edge energy is sensitive to the oxidation state of Ir cations,39,40 which we observed in our previous studies of these materials.9,23 In this case, we observed no energy shift as a function of pressure (Figure 4). The anticipated energy shift for Ir4+ to Ir3+ is ∼1.0 eV.40 This may be a consequence of self-absorption effects in the DAC samples (note that there was no evidence for significant self-absorption effects at the other edges measured). We did observe a change in the peak areaat high pressure, the Ir L3-edge peak area decreases for both Ba3BiIr2O9 and Ba4BiIr3O12which may be due to a decrease in the number of unoccupied Ir 5d states (i.e., a lowering of oxidation state). However, we note that this could also, in principle, be due to change in Ir−Ir or Ir−O bond distances at high pressure. Alternatively, previous ab initio calculations indicated that the transferred electron is delocalized over the Ir2O9 (or Ir3O12) dimer,31 which would result in a smaller than expected energy shift in the Ir L3 edge. Therefore, while the Ir L3-edge data are not in themselves conclusive evidence of an oxidation state change, they are consistent with the Bi L2-edge data. Similar evidence of electron transfer at high pressure was observed for Ba3BiRu2O9. As illustrated in Figure 5a, the line shape of the Bi L3 edge of Ba3BiRu2O9 is similar to that of BaBiO3 at ambient pressures, indicating that the Bi oxidation state is close to +4. Applying a pressure of 9.61 GPa results in the appearance of features characteristic of Bi5+ (Figure 5b), suggesting an increase in the oxidation state of Bi at high

Figure 4. Ir L3-edge XANES spectra of (a) Ba3BiIr2O9 and (b) Ba4BiIr3O12 collected at 0 GPa (black) and high pressure (red).

Figure 5. (a) Bi L3-edge XANES spectra of Ba3BiRu2O9 at 0 GPa (black) and 9.61 GPa (red). Characteristic features of Bi5+ are labeled as A and B in the Bi L3 edge. (b) Bi L3-edge XANES spectra of Ba3BiRu2O9 (black) in comparison to Bi2O3 (Bi3+; red), BaBiO3 (Bi4+; green), and Ba2LuBiO6 (Bi5+; green). The line shape of Ba3BiRu2O9 is similar to that of BaBiO3, consistent with a Bi oxidation state of +4. (c) Ru K-edge XANES spectra and (d) first-derivative spectra of Ba3BiRu2O9 at 0 GPa (black) and 9.61 GPa (red). The dashed lines in (d) correspond to the Ru K-edge absorption edge energies.

Figure 6. Calculated total electronic density of states (eDOS) per unit cell for Ba3BiIr2O9 at ambient and 10 GPa pressure. The Fermi level is set to zero-energy.

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Figure 7. Calculated site-projected eDOS (per unit cell) for Ba3BiIr2O9 at (a) 0 and (b) 10 GPa. Both figures are plotted on a common y-axis scale to facilitate comparison of n(E).

Figure 8. Calculated l-projected eDOS (per atom) for Bi in Ba3BiIr2O9 at (a) 0 and (b) 10 GPa and for Ir at (c) 0 and (d) 10 GPa, plotted on common y-axis scales to facilitate comparison of n(E).

the Bi L3 edge and Ru K edge suggest that Ru to Bi charge transfer occurs at high pressures, similar to that observed in Ba3BiIr2O9 and Ba4BiIr3O12. Ab initio geometry optimization calculations for Ba3BiIr2O9 shed further light on the nature of the pressure-induced transition. As we previously reported,31 these calculations reproduce two stable isostructural phases whose volumes differ by ∼1%, with the relative stability of the smaller-volume phase increased as a function of simulated pressure (the PSTRESS parameter in VASP36); i.e., they are consistent with the experimentally observed pressure-induced first-order transition. We are now in a position to look more closely at the calculated electronic structures of the high- and low-pressure phases and compare them to the experimental XANES data presented above, in order to gain further insight concerning the nature of

pressure. The change in the Bi L3 edge of Ba3BiRu2O9 is similar to the changes observed in the Bi L2 edge of Ba3BiIr2O9 and Ba4BiIr3O12. Likewise, a corresponding decrease in the oxidation state of Ru can be observed in the Ru K-edge XANES spectra of Ba3BiRu2O9 (Figure 5c). The Ru K edge corresponds to a dipole-allowed transition of a 1s electron into 5p states. The line shape and absorption edge energy are dependent on the oxidation state of Ru.41 At ambient pressures, the line shape of the Ru K edge of Ba3BiRu2O9 is similar to that or RuO2, suggesting the presence of Ru4+.41 At high pressures (9.61 GPa), there is a small shift to lower absorption energy (Figure 5d), consistent with a decrease in the Ru oxidation states. However, the energy shift (0.5 eV) is smaller than expected for Ru3+ (∼3 eV),42 which is likely due to electron delocalization within the Ru2O9 dimer. Overall, the trends in D

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work used facilities at GeoSoilEnviroCARS (The University of Chicago, Sector 13), Advanced Photon Source (APS), Argonne National Laboratory. GeoSoilEnviroCARS is supported by the National Science Foundation - Earth Sciences (EAR-1128799) and Department of Energy- GeoSciences (DE-FG0294ER14466).

the transition. Figure 6 shows the calculated total electronic density of states (eDOS) per unit cell for Ba3BiIr2O9 at ambient and 10 GPa pressure. At ambient pressure, the estimated band gap is ∼0.2 eV, while at 10 GPa the gap is suppressed. This suggests that the high-pressure phase could show metallic-like behavior, consistent with the valence-transfer model for the transition. Figure 7 compares the site-projected eDOS (per unit cell) at 0 and 10 GPa. Ir and O bands dominate the electron distribution both above and below the Fermi level. There is a strong overlap with Bi bands; i.e., the calculations are consistent with Ir−O bonding, Bi−O bonding, and Bi−Ir charge transfer. The Ba bands exhibit an ionic-like character: i.e., (decoupled) core bands. Figure 8 compares the l-projected eDOS of Bi and Ir (per atom) at 0 and 10 GPa. For Bi, applying pressure leads to a decrease in the s-shell electron density of the valence band in the vicinity of the Fermi level, while for Ir, it leads to an increase of the d-shell electron density of the valence band and a decrease in the conduction band near the Fermi level.



(1) Callaghan, A.; Moeller, C. W.; Ward, R. Inorg. Chem. 1966, 5, 1572−1576. (2) Yonezawa, S.; Muraoka, Y.; Matsushita, Y.; Hiroi, Z. J. J. Phys.: Condens. Matter 2004, 16, L9−12. (3) Kim, B. J.; Jin, H.; Moon, S. J.; Kim, J.-Y.; Park, B.-G.; Leem, C. S.; Yu, J.; Noh, T. W.; Kim, C.; Oh, S.-J.; Park, J.-H.; Durairaj, V.; Cao, G.; Rotenberg, E. Phys. Rev. Lett. 2008, 101, 076402. (4) Erickson, A. S.; Misra, S.; Miller, G. J.; Gupta, R. R.; Schlesinger, Z.; Harrison, W. A.; Kim, J. M.; Fisher, I. R. Phys. Rev. Lett. 2007, 99, 016404. (5) Stitzer, K. E.; Smith, M. D.; Gemmill, W. R.; zur Loye, H.-C. J. Am. Chem. Soc. 2002, 124, 13877−13885. (6) Shimoda, Y.; Doi, Y.; Wakeshima, M.; Hinatsu, Y. Inorg. Chem. 2009, 48, 9952−9957. (7) Stitzer, K. E.; El Abed, A.; Smith, M. D.; Kim, S.-J.; Darriet, J.; zur Loye, H.-C. Inorg. Chem. 2003, 42, 947−949. (8) Ling, C. D.; Kennedy, B. J.; Zhou, Q.; Spencer, J. R.; Avdeev, M. J. Solid State Chem. 2010, 183, 727−735. (9) Miiller, W.; Avdeev, M.; Zhou, Q.; Kennedy, B. J.; Sharma, N.; Ling, C. D. J. Am. Chem. Soc. 2012, 134, 3265−3270. (10) Darriet, J.; Bontchev, R.; Dussarrat, C.; Weill, F.; Darriet, B. Eur. J. Solid State Inorg. Chem. 1993, 30, 287−296. (11) Miiller, W.; Avdeev, M.; Zhou, Q.; Studer, A. J.; Kennedy, B. J.; Kearley, G. J.; Ling, C. D. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 220406. (12) Doi, Y.; Hinatsu, Y. J. Phys.: Condens. Matter 2004, 16, 2849− 2860. (13) Doi, Y.; Wakeshima, M.; Hinatsu, Y.; Tobo, A.; Ohoyama, K.; Yamaguchi, Y. J. Mater. Chem. 2001, 11, 3135−3140. (14) Doi, Y.; Hinatsu, Y. J. Phys.: Condens. Matter 2004, 16, 2849− 2860. (15) Doi, Y.; Hinatsu, Y. J. Mater. Chem. 2002, 12, 1792−1796. (16) Cox, D. E.; Sleight, A. W. Solid State Commun. 1976, 19, 969. (17) Thornton, G.; Jacobson, A. J. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1978, 34, 351−354. (18) Balzarotti, A.; Menushenkov, A. P.; Motta, N.; Purans, J. Solid State Commun. 1984, 49, 887−890. (19) Chaillout, C.; Santoro, P.; Remeika, A.; Cooper, A. S.; Espinosa, G. P.; Marezio, M. Solid State Commun. 1988, 65, 1363−1369. (20) Flavell, W. R.; Mian, M.; Roberts, A. J.; Howlett, J. F.; Sarker, M. M.; Wincott, P. L.; Bilsborrow, R. L.; van Dorssen, G. J. Mater. Chem. 1997, 7, 357−364. (21) Kennedy, B. J.; Howard, C. J.; Knight, K. S.; Zhang, Z.; Zhou, Q. Acta Crystallogr., Sect. B: Struct. Sci. 2006, 62, 537−546. (22) Brese, N. E.; O'Keeffe, M. Acta Crystallogr., Sect. B: Struct. Sci. 1991, 47, 192−197. (23) Blanchard, P. E. R.; Huang, Z.; Kennedy, B. J.; Liu, S.; Miiller, W.; Reynolds, E.; Zhou, Q.; Avdeev, M.; Zhang, Z.; Aitken, J. B.; Cowie, B. C. C.; Jang, L.-Y.; Tan, T. T.; Li, S.; Ling, C. D. Inorg. Chem. 2014, 53, 952−960. (24) Miiller, W.; Dunstan, M. T.; Huang, Z.; Mohamed, Z.; Kennedy, B. J.; Avdeev, M.; Ling, C. D. Inorg. Chem. 2013, 52, 12461−12467. (25) Shimoda, Y.; Doi, Y.; Wakeshima, M.; Hinatsu, Y. J. Solid State Chem. 2009, 182, 2873−2879. (26) Shimoda, Y.; Doi, Y.; Wakeshima, M.; Hinatsu, Y. Inorg. Chem. 2009, 48, 9952−9957. (27) Shimoda, Y.; Doi, Y.; Wakeshima, M.; Hinatsu, Y. J. Solid State Chem. 2010, 183, 1962−1969. (28) Shimoda, Y.; Doi, Y.; Wakeshima, M.; Hinatsu, Y.; Ohoyama, K. Chem. Mater. 2008, 20, 4512−4518.



CONCLUSIONS High-pressure XANES measurement at Bi, Ir, and Ru X-ray absorption edges confirm that the volume collapses observed in Ba3BiRu2O9, Ba3BiIr2O9, and Ba4BiIr3O12 above ∼5 GPa are due to the transfer of valence electrons from Bi to Ir/Ru. As with previous XANES experiments carried out at ambient pressure, the spectra are consistent with (although do not unequivocally confirm) an intermediate 4+ oxidation state for Bi. This implies significant instability in the electronic structures of these compounds, reinforced by our ab initio calculations, which imply that external applied pressure should lead to a change from insulating to metallic behavior. In future experimental studies it would therefore be worthwhile to investigate their magnetic and electronic properties close to the transition. It will also be worthwhile to look for other systems similarly poised to undergo an interelemental valence transition under pressure. The most likely candidates will involve heavy-metal cations with 6s2 lone pairs (Tl+, Pb2+, Bi3+) or possibly those with 5s2 lone pairs (Sn2+, Sb3+, Te4+), the radii of which could be greatly reduced by vacating those lone pairs, in conjunction with a transition-metal cation in a relatively high oxidation state. This is not a commonly encountered situation because the relative redox potentials of these cations mean that they are usually incompatible, but it seems certain that further candidates can be found, especially among the 4d and 5d transition metals.



REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail for C.D.L.: [email protected]. Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS This work was supported by the Australian Research Council (Discovery Projects) and the Australian Synchrotron (International Synchrotron Access Program). This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. Portions of this E

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