Charge order and superconductivity in vanadium oxides

Charge order and superconductivity in vanadium oxides

Solid State Sciences 7 (2005) 874–881 www.elsevier.com/locate/ssscie Charge order and superconductivity in vanadium oxides Touru Yamauchi, Masahiko I...

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Solid State Sciences 7 (2005) 874–881 www.elsevier.com/locate/ssscie

Charge order and superconductivity in vanadium oxides Touru Yamauchi, Masahiko Isobe, Yutaka Ueda ∗ Materials Design and Characterization Laboratory, Institute for Solid State Physics, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan Received 1 October 2004; accepted 10 January 2005 Available online 28 April 2005

Abstract We have performed high-pressure experiments on β-vanadium bronzes, β-A0.33 V2 O5 (A = Li+ , Na+ , Ag+ , Ca2+ , Sr2+ and Pb2+ ) which are quasi-one-dimensional conductors. All of compounds except β-Pb0.33 V2 O5 show metal-insulator transitions accompanied by charge ordering. Under hydrostatic high pressure the charge ordered phase is suppressed and the superconducting phase appears. The superconducting phase adjacent to the charge ordered phase implies an important role for charge fluctuation in the superconductivity of β-A0.33 V2 O5 . The 2+ 4+ 5+ = 1/5) for the superpresence/absence of superconductivity in β-A+ 0.33 V2 O5 /β-A0.33 V2 O5 suggests an optimum doping level (V /V conductivity in β-vanadium bronzes.  2005 Elsevier SAS. All rights reserved. Keywords: Vanadium oxide; Charge order; Superconductivity; High-pressure

1. Introduction Vanadium element can take various valence states and consequently forms many oxides with various oxygencoordination such as octahedral, tetrahedral, square pyramidal and so on. In addition to such interest in solid state chemistry, vanadium oxides have been one of central substances in solid state physics because of strongly correlated electron system. There are many metallic oxides even in the binary V–O system. Many of them show Curie–Weiss behaviors in magnetic susceptibility, which is described as a localized picture, although the system is metallic [1]. One of the important properties of these metallic vanadium oxides is metal-insulator (MI) transition as a function of temperature [2]. These MI transitions, particularly in the mixed valent compounds, are accompanied by charge ordering [3–5]. In the low temperature insulating phases, there exist the clear charge separation and the charge ordering. One of the current topics of charge order is the charge order in the quarterfilled spin-ladder compound NaV2 O5 which is a compound * Corresponding author.

E-mail address: [email protected] (Y. Ueda). 1293-2558/$ – see front matter  2005 Elsevier SAS. All rights reserved. doi:10.1016/j.solidstatesciences.2005.01.024

of vanadium bronze family. In 1996, we found a spin Peierls like transition in NaV2 O5 [6]. The observed magnetic susceptibility is well described by Bonner–Fisher equation [7] characteristic of spin-1/2 one-dimensional (1D) antiferromagnetic Heisenberg linear chain system, and below 35 K it exponentially decreases with decreasing temperature [6]. This transition is accompanied by the formation of spin-gap and the superlattice of 2 × 2 × 4 [8]. The discovery of this transition triggered off the explosion of research. At present there is a general consensus that the transition of NaV2 O5 is not a spin-Peierls transition but a charge order transition in a quarter-filled ladder system [9,10]. The charge ordered manner determined by various experiments is a so-called zigzag-type of V4+ and V5+ within the a–b plane, and this zigzag-type charge ordered layers are stacked in a manner of AAA A with a four-fold periodicity along the c-axis [11]. The research activity of NaV2 O5 reached to a peak in the discovery of devil’s staircase-type phase transition under high pressure [12]. In NaV2 O5 , the charge ordered pattern (the zigzag-type) in the a–b plane is well maintained and the stacking manner along the c-axis has modulations with the devil’s staircase-type sequences. This is the first example of the devil’s flower type phase diagram on charge order. In

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Fig. 1. The monoclinic crystal structure of β-Ax V2 O5 . The V2 O5 framework consists of three crystallographically distinct vanadium atoms (V1, V2 and V3) and oxygen atoms, which are illustrated as chromatically different V3O5 pyramids and V1O6 and V2O6 octahedra. Each polyhedron forms three V chains running along the b-axis; the V1 zigzag chain, the V2 ladder chain and the V3 zigzag chain. This framework has a tunnel along the b-axis and A-cations are aligned in the tunnel.

the spin system, the origin of devil’s flower type phase diagram is a frustration of magnetic interactions, that is the nearest is ferromagnetic and the next nearest is antiferromagnetic [13]. In the charge system of NaV2 O5 , what is the microscopic mechanism for frustration has been open question. Our recent study [1,14–21] has revealed that β-vanadium bronzes are a new family of metallic vanadium oxide and show MI transitions accompanied by charge ordering. The chemical formula of β-vanadium bronze is represented as β-Ax V2 O5 (A: mono-valent Li+ , Na+ , Ag+ and di-valent Ca2+ , Sr2+ , Pb2+ ) and it is a vanadium oxide with a mixed valence of V4+ (d 1 ) and V5+ (d 0 ). The monoclinic crystal structure consists of a characteristic V2 O5 -framework and A-cations, as shown in Fig. 1. The V2 O5 -framework is formed by sharing the corners and edges of (V1)O6 , (V2)O6 octahedra and (V3)O5 pyramids, where V1, V2 and V3 are the three crystallographically distinct vanadium sites. Each polyhedron forms three V chains running along the b-axis; the V1 zigzag chain, the V2 ladder and the V3 zigzag chain. Thus formed V2 O5 framework has a tunnel surrounded by the three chains. The A-atoms occupy lattice positions (tunnel sites) which can be represented as a ladder along the b-axis. For the stoichiometric composition x = 1/3 (0.33) only 50% of these lattice sites is occupied in the zigzagtype manner with each rung hosting one A-atom alternately between the left- and right-hand sides of the ladder. All compounds have a considerable non-stoichiometric range of A-cations. In 2002, the superconductivity under high-pressure was first discovered in a member of β-vanadium bronze fam-

ily, β-Na0.33 V2 O5 [22]. Since the discovery of high-TC superconducting cuprates (HTSC), superconductivity has drawn much interest as the ground state of strongly correlated electron systems. The electronic states of vanadium oxides are similar to those of high Tc cuprates, for examples, spin 1/2 state, strong electron correlation, charge and spin fluctuation and so on, although the leading part is t2g -electron in vanadium oxides while it is eg -electron in cuprates; nevertheless superconductivity had never been found in vanadium oxides. As mentioned above, many metallic vanadium oxides show MI transitions as a function of temperature. The MI transition prevents us from studying ground states of the high temperature metallic phases because of the nature of first order transition. In some vanadium oxides the metallic phases were stabilized by high-pressure, and, however, superconductivity had never been found. The superconductivity under high-pressure in β-Na0.33 V2 O5 was the first observation of superconductivity in vanadium oxides. We have continued to perform highpressure experiments on β-A0.33 V2 O5 (A: Li+ , Na+ , Ag+ , Ca2+ , Sr2+ and Pb2+ ). In this paper, we report charge order and superconductivity under high-pressure in β-vanadium bronzes.

2. Experimental Powder samples of β-A0.33 V2 O5 (A = Li, Na, Ag, Ca, Sr and Pb) were synthesized by a solid-state reaction of V2 O5 , V2 O3 , AVO3 (A = Li, Na, Ag), AV2 O6 (A = Ca, Sr) and PbO [14,16–18,21]. Single crystals of β-A0.33 V2 O5

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(A = Li, Na, Ag, Ca, Sr) were grown by a self-flux method using AVO3 (A = Li, Na, Ag) and AV2 O6 (A = Ca, Sr), respectively [14,16,18,21]. The typical size of obtained crystals is 1 mm in length (b-axis), 0.3 mm in width and 0.1 mm in thickness (a or c-axis). On the other hand, single crystal of β-Pb0.33 V2 O5 was grown by chemical transport reaction using HCl gas as a transport agent [21]. The typical size of obtained crystals is 1 mm in length (b-axis), 0.1 mm in width and 0.01 mm in thickness (a or c-axis). The obtained crystals were often off-stoichiometric in the A-cation composition. The stoichiometric single crystals with the composition x = 0.33 were prepared by heating asgrown crystals with a large amount of stoichiometric powder sample in an evacuated silica tube at 823 K for 2 days. The stoichiometry of the obtained crystals was checked by measuring electromagnetic properties because they (especially resistivity) were very sensitive to the composition of A-cation [14,21]. Electrical resistivity was measured by an ordinary DC four-probe method. Magnetic susceptibility and magnetization were measured by using a SQUID magnetometer. In high-pressure experiments, we used a cubic-anvil-type apparatus to apply hydrostatic pressure of up to 9 GPa [22]. We also used a pressure medium, composed of fluorinate and a methanol-ethanol mixture, to improve the hydrostatic pressure [22].

Fig. 2. Temperature dependence of resistivity measured along the a-, b- and c-axis in β-Na0.33 V2 O5 .

3. Results and discussion The β-vanadium bronzes are quasi-1D conductors. The typical example of β-Na0.33 V2 O5 is shown in Fig. 2. A metallic behavior is observed only along the b-axis, chain direction, while the resistivity behavior is semiconductive along the a- and c-axis. The resistivity along the c- or a-axis is higher about two orders than along the b-axis. Such quasi1D conductivity indicates the dominant intrachain charge transfer. This metallic property is very sensitive to A-cation stoichiometry. A slight nonstoichiometry changes the metallic property to a semiconductive one [14]. Such a degradation of metallic property caused by a disorder at the A-cation sites is also characteristic of quasi-1D-conductor. One important property of β-vanadium bronzes is MI transition. Except β-Pb0.33 V2 O5 all members show MI transitions at independent temperatures (TCO ), as shown in Fig. 3. These MI transitions are accompanied by charge separation and charge order. The nature of charge order on the transition was confirmed from NMR [15], X-ray diffraction [19,23] and neutron diffraction [24]. The NMR study on β-Na0.33 V2 O5 has revealed the charge (V4+ ) condensation to V1/V2 sites and the simultaneous charge ordering below TCO . The X-ray and neutron diffraction study has revealed a superstructure with a 6-fold periodicity along the b-axis in the all compounds except β-Pb0.33 V2 O5 . Some models of charge ordered manner have been proposed [19,23,24] but they have not been established yet.

Fig. 3. Temperature dependence of resistivity measured along the b-axis in β-A0.33 V2 O5 (A = Li, Na, Ag, Ca and Sr). All of compounds except β-Pb0.33 V2 O5 show metal-insulator transitions at TCO .

On the other hand, the magnetic properties are different 2+ between β-A+ 0.33 V2 O5 (A = Li, Na, Ag) and β-A0.33 V2 O5 (A = Ca, Sr). Fig. 4 shows the temperature dependence of

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Fig. 4. Temperature dependence of magnetic susceptibility for powdered β-A0.33 V2 O5 (A = Li, Na, Ag, Ca and Sr) except Pauli-paramagnetic β-Pb0.33 V2 O5 . The metal-insulator transitions at TCO are accompanied by slight changes of magnetic susceptibility. The insulating phases of β-A0.33 V2 O5 (A = Li, Na and Ag) antiferromagnetically order at TN .

magnetic susceptibility for various β-vanadium bronzes except Pauli-paramagnetic β-Pb0.33 V2 O5 . The MI transitions are accompanied by slight changes of magnetic susceptibility. The magnetic susceptibilities of β-A+ 0.33 V2 O5 (A = Li, Na, Ag) show Curie–Weiss like behaviors both above and below TCO , and the insulating phases order antiferromagnetically around 20 K below TCO . On the other hand, the magnetic susceptibilities of β-A2+ 0.33 V2 O5 (A = Ca, Sr) show spin gap behavior or low dimensional behavior below TCO , and the ground state has no long-range magnetic order. It is very interesting what ground state appears when the charge order collapses under high pressure. We have performed high-pressure study on β-vanadium bronzes using strictly stoichiometric single crystals with high quality. We first reported the pressure-induced superconductivity in β-Na0.33 V2 O5 [22]. The superconducting transition was observed from resistivity and ac susceptibility measurements under high-pressure [22]. With increasing pressure, the charge order transition is suppressed and the superconducting phase appears around 8 GPa and at TC = 8 K. In succession the high-pressure experiments have been carried out on β-A2+ 0.33 V2 O5 (A = Ca, Sr, Pb), expecting much higher TC , because the doping level of them is twice as high as βNa0.33 V2 O5 . However, any sign of superconductivity were not observed in all of β-A2+ 0.33 V2 O5 (A = Ca, Sr, Pb). Fig. 5 shows resistivity (ρ) vs. temperature (T ) curves under various pressures for β-A2+ 0.33 V2 O5 (A = Ca, Sr, Pb). It is clearly observed in β-Ca0.33 V2 O5 that the MI transition temperature (TCO ) gradually decreases with increasing pressure, which is

Fig. 5. Temperature dependence of resistivity under high pressures for (a) β-Ca0.33 V2 O5 , (b) β-Sr0.33 V2 O5 and (c) β-Pb0.33 V2 O5 . The inset in the top panel exhibits a log T behavior of resistivity under 4.5 GPa and below 15 K.

similar to the case of β-Na0.33 V2 O5 [22]. The critical pressure where the charge order phase completely collapses is estimated as about 3.7 GPa, which is relatively lower than that (7 GPa) of β-Na0.33 V2 O5 [22]. Within the range measured, that is down to 2 K (the lowest temperature of this apparatus) and up to 4.5 GPa (the enough high pressure to suppress the charge order phase), β-Ca0.33 V2 O5 does not show superconductivity. Neither β-Sr0.33 V2 O5 nor β-Pb0.33 V2 O5 have a superconducting phase within the range measured (up to 9 GPa for β-Pb0.33 V2 O5 ). Here the resistivity behaviors under high-pressure will be discussed in more detail. A small upturn of resistivity curve under enough high pressure ∼ 4.5 GPa and below 15 K in β-Ca0.33 V2 O5 could be attributed to Anderson weak localization (AWL) caused by

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Fig. 6. Temperature dependence of resistivity under high pressures for β-Pb0.33 V2 O5 . (a) A T −1/2 -plot. (b) A T −1/3 -plot. (c) A log T -plots.

defects and/or a slight off-stoichiometry of the sample crystals. It is natural that sample crystals include some inevitable crystal defects and a very slight off-stoichiometry which causes insulating behaviors in low dimensional conductors. It should be noted that the crystallinity of A2+ -compounds was relatively poorer than that of A+ -compounds. As seen in the inset of Fig. 5(a), this upturn exhibits a log-T behavior which is well observed in two-dimensional (2D) systems such as disordered interface in hetero-structure like a Si-MOS [25]. The log-T behavior allows us to suppose a dimension crossover from 1D- to 2D-electronic system in these compounds as increasing pressure. This crossover is fairly observed in β-Pb0.33 V2 O5 , as shown in Fig. 6. Fig. 6 shows various plots of the data of Fig. 5(c) to identify the manner of temperature dependence of resistivity such

as variable range hopping (VRH) and log-T behaviors. In Fig. 6(a) and (b), log-ρ vs. T −1/2 and T −1/3 are plotted because the resistivity of 1D and 2D VRH obeys formulae ρ ∼ exp(T −1/2 ) and ρ ∼ exp(T −1/3 ), respectively. The linear behaviors in these plots demonstrate 1D and 2D conductor of the system, respectively. The resistivity curves gradually deviate from a T −1/2 -dependence under ambient pressure with increase of pressure below 2 GPa (Fig. 6(a)), and then they approach to T −1/3 -dependence above 2 GPa (Fig. 6(b)) and finally to log-T behavior (Fig. 6(c)). This is a good evidence for pressure-induced dimension crossover from 1D to 2D as increasing pressure on β-Pb0.33 V2 O5 . As another observation, the critical pressure, where the charge order phase collapses, is lower in β-Sr0.33 V2 O5 (∼ 1.5 GPa) than in β-Ca0.33 V2 O5 (∼ 4.5 GPa). This low critical pressure in β-Sr0.33 V2 O5 is explained by relatively large crystallographic volume change at the charge order transition (V /V ∼ 1% in β-Sr0.33 V2 O5 , ∼ 0.2% in β-Ca0.33 V2 O5 ). Now the high-pressure experiments go back to the remaining A+ -compounds. Fig. 7 shows ρ vs. T curves under various pressures for β-Ag0.33 V2 O5 . The charge order transition is gradually suppressed with increasing pressure and a sharp drop of resistivity toward to zero-resistivity is observed around 7.5 GPa and at 6.5 K. This sharp drop of resistivity is attributed to a superconducting transition from the similar behavior in β-Na0.33 V2 O5 [22]. We carefully measured resistivity around the critical region by changing the pressure little by little. The resistivity shows a T 2 dependence above 6 GPa, that is Fermi liquid behavior, as shown in Fig. 8(a). Furthermore a reentrant behavior that the resistivity slightly drops at TC and then shows the upturn below TC , as shown in Fig. 8(b), is clearly recognized, which suggests the coexistence of the charge order phase with the superconducting phase. In the coexistence region, the TC is sharp and gradually rises with increasing pressure. If the coexistence of the two phases were due to inhomogeneous distribution of pressure, the superconducting transition would become broad. Such intrinsic coexistence behavior suggests a first order transition from the charge order to the superconducting phases. The increase of TC with increase of pressure in the coexistence region may be explained by the development of the superconducting phase in its domain size. Very recently we have done high-pressure experiments on the last compound β-Li0.33 V2 O5 . Among β-vanadium bronzes, βLi0.33 V2 O5 has the highest charge order transition temperature about TCO = 200 K. The charge order phase is persistent and is not suppressed completely even over 9 GPa which is the limit of our apparatus. However we have observed a drop of resistivity around 24 K and over 9 GPa. Interestingly a possible superconducting transition temperature about 24 K is very high among the superconductors except high TC cuprates. We have a plan of high-pressure experiments using sintered-diamond-anvil by which it is possible to measure under much higher pressure (∼ 13 GPa). The results of β-Ag0.33 V2 O5 are summarized in Fig. 9(a), a pressure-temperature (P –T ) diagram, with the P –T di-

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Fig. 7. Temperature dependence of resistivity under highs pressures for β-Ag0.33 V2 O5 . (a) An overall range view. (b) A macrograph of the low-temperature region below 20 K.

Table 1 Various properties of β-vanadium bronzes Compounds

V4+ /V5+

TCO (K)

TN (K)

TC (K)

β-Li0.33 V2 O5 β-Na0.33 V2 O5 β-Ag0.33 V2 O5 β-Ca0.33 V2 O5 β-Sr0.33 V2 O5 β-Pb0.33 V2 O5

1/5 1/5 1/5 2/4 2/4 2/4

200 136 90 150 170 –

7 24 24 Spin gap Spin gap Pauli para.

24? (P > 9 GPa) 8 (P ∼ 8 GPa) 6.5 (P ∼ 7.5 GPa) Non-super. Non-super. Non-super.

agram of β-Na0.33 V2 O5 (Fig. 9(b)) [22]. Furthermore the results of charge order transition and superconducting transition in β-vanadium bronzes are summarized in Table 1. Both phase diagrams in Fig. 9 have a common feature that is the superconducting phase adjacent to the charge order phase. The charge order phase is gradually suppressed with increasing pressure and the superconducting phase appears when the charge order phase melts. These phase diagrams should

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Fig. 8. Temperature dependence of resistivity under high pressures for β-Ag0.33 V2 O5 . (a) A T 2 -plot. (b) A T -plot.

be compared to those of (TMTSF)2 PF6 [26] (π -electron system) or CeCu2 Ge2 [27] and UGe2 [28] (f -electron system). Recently it has been elucidated that various ground states compete with each other and considerably change in thermodynamic parameters such as magnetic field and pressure. For instance, the superconducting phases that compete with either the CDW/SDW or magnetic ordered phase have been discovered in (TMTSF)2 PF6 [26] (π -electron system) or CeCu2 Ge2 [27] and UGe2 [28] (f -electron system). The obtained electronic phase diagrams of β-A0.33 V2 O5 (A = Na, Ag) are similar to the diagrams of these other systems. There is, however, a significant difference between β-A0.33 V2 O5 and other systems. The β-A0.33 V2 O5 has a charge order phase instead of an SDW phase in (TMTSF)2 PF6 , or instead of magnetic ordered metallic phase in CeCu2 Ge2 and UGe2 . This implies an important role for charge fluctuation in the superconductivity of β-A0.33 V2 O5 , as opposed to spin fluctuation in (TMTSF)2 PF6 , CeCu2 Ge2 and UGe2 . This could be supported by the result that the TC becomes

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fortunately we could not determine whether the charge order phase adjacent to the superconducting phase is antiferromagnetic or paramagnetic. In spite of the differences between the present system and π -electron and f -electron systems, we emphasize the existence of a feature common to all classes of materials in the electronic phase diagrams. That feature is superconductivity near the transition of charge localization/delocalization. Here it should be noticed that superconductivity is present 2+ in β-A+ 0.33 V2 O5 compounds but is absent in β-A0.33 V2 O5 compounds, although the charge order transition exists in all β-A0.33 V2 O5 compounds except β-Pb0.33 V2 O5 . The im2+ portant difference between β-A+ 0.33 V2 O5 and β-A0.33 V2 O5 compounds is that β-A2+ 0.33 V2 O5 has twice carrier number as much as β-A+ V O 2 5 . The presence/absence of super0.33 2+ V conductivity in β-A+ 0.33 2 O5 /β-A0.33 V2 O5 suggests an optimum doping level (V4+ /V5+ = 1/5) for the superconductivity in β-vanadium bronzes.

4. Conclusion

Fig. 9. The pressure-temperature (P –T ) phase diagram of (a) β-Ag0.33 V2 O5 and (b) β-Na0.33 V2 O5 . CO: charge ordered phase, SC: superconducting phase, PI: paramagnetic insulator phase, AFI: antiferromagnetic insulator phase, TCO (square): charge order transition temperature, TSC (circle): superconducting transition temperature, TN (triangle): AF transition temperature.

In conclusion, we have performed high-pressure experiments on β-vanadium bronzes. The β-vanadium bronze family has six members, β-A0.33 V2 O5 (A = Li, Na, Ag, Ca, Sr and Pb). The β-vanadium bronzes are quasi-1D conductors with a metallic conductivity along the b-axis of monoclinic structure. All members except β-Pb0.33 V2 O5 have metal-insulator transitions accompanied by the charge separation and charge ordering. The ground states of the insulating phases are antiferromagnetic ordered states in β-A+ 0.33 V2 O5 (A = Li, Na, Ag) and spin-gapped states in β-A2+ 0.33 V2 O5 (A = Ca, Sr). The charge order phase is gradually suppressed with increasing pressure and the superconducting phase appears when the charge order melts. The superconducting phase adjacent to the charge order phase implies an important role for charge fluctuation in the superconductivity of β-vanadium bronzes, as opposed to spin fluctuation in (TMTSF)2 PF6 (π -electron system), CeCu2 Ge2 and UGe2 (f -electron system). The presence/absence of superconductivity in β-A+ 0.33 V2 O5 / V O suggests an optimum doping level (V4+ / β-A2+ 2 5 0.33 5+ V = 1/5) for the superconductivity in β-vanadium bronzes.

Acknowledgements high in proportion to the TCO , as seen in Table 1. In other word, the more the charge order is persistent, the higher the TC is. On the other hand, we may not exclude a role for spin correlation in superconductivity of β-A0.33 V2 O5 , because the β-A0.33 V2 O5 (A = Li, Na, Ag) which shows pressure-induced superconductivity has magnetic ordered ground states in the insulator phases, as seen in Table 1. Un-

The authors thank H. Yamada, H. Ueda, J. Yamaura, S. Nagai, N. Môri, Y. Uwatoko, T. Ohama and M. Itoh for valuable discussions. This work was supported by Grant-inAid for Scientific Research (No. 407 and 14340205) and for Creative Scientific Research (No. 13NP0201) from the Ministry of Education, Science, Sports and Culture.

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