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On the origin of the anomalous electrical resistivity of LnMo5O8 (Ln=TRIVALENT rare earth)
Solid State Communications, Vol. 108, No. 8, pp. 539–544, 1998 䉷 1998 Elsevier Science Ltd. All rights reserved 0038–1098/98 $ - see front matter
Pergamon
PII: S0038–1098(98)00407-4
ON THE ORIGIN OF THE ANOMALOUS ELECTRICAL RESISTIVITY OF LnMo 5O 8 (Ln ¼ TRIVALENT RARE EARTH) H.-J. Koo, a M.-H. Whangbo, a ,* W.H. McCarroll, b M. Greenblatt, c R. Gautier, d J.-F. Halet d and P. Gougeon d a
Department of Chemistry, North Carolina State University, Raleigh, NC 27695-8204, U.S.A. b Department of Chemistry, Rider College, Lawrenceville, NJ 08648, U.S.A. c Department of Chemistry, Rutgers University, Piscataway, NJ 08855, U.S.A. d Laboratoire de Chimie du Solide et Inorganique Moleculaire, UMR CNRS 6511, Universite´ de Rennes 1, 35042 Rennes Cedex, France (Received 7 July 1998; accepted in revised form 11 August 1998 by F.J. Di Salvo) Electronic structures of AMo 5O 8 (A ¼ rare earth, alkaline earth) and the solid solution Sr 1¹xLa xMo 5O 8 (x ¼ 0–1) were examined using the extended Hu¨ckel tight binding method. AMo 5O 8 phases with divalent A cations (A ¼ Sr, Ca, Eu) are normal semiconductors with small band gap. The Fermi surfaces of Sr 1¹xLa xMo 5O 8 (0:0 ⬍ x ⱕ 1:0) and LnMo 5O 8 (Ln ¼ trivalent rare earth) do not exhibit any nesting. In the electronic structures of LnMo 5O 8 (Ln ¼ trivalent rare earth) phases, the Fermi level is dominated by the d-orbitals of the Mo(2) atoms of their Mo 10 clusters. With decreasing x from 1.0 in Sr 1¹xLa xMo 5O 8, the dominance of the Mo(2) atoms at the Fermi level sharply diminishes. Based on this observation, we proposed a probable reason for the weakly semiconducting state above 180 K and the metallic state below 180 K in LnMo 5O 8 (Ln ¼ trivalent rare earth). 䉷 1998 Elsevier Science Ltd. All rights reserved
1. INTRODUCTION The magnetic properties of reduced molybdenum oxides LnMo 5O 8 (Ln ¼ La, Ce, Pr, Nd) show that the La compound has a Pauli-type temperature independent susceptibility in the 50–300 K range, while the Ce, Pr and Nd phases have susceptibilities essentially corresponding to the rare-earth ions [1]. To characterize these properties further, Gall et al. examined the electrical resistivity of LnMo 5O 8 (Ln ¼ La, Ce, Pr, Nd, Sm, Eu, Gd) and their alkaline earth analogues CaMo 5O 8 and SrMo 5O 8 [2]. Upon lowering temperature, the LnMo 5O 8 (Ln ¼ trivalent rare earth) compounds exhibit a semiconductor-to-metal transition near 180 K and then a metal-to-semiconductor transition near 30 K [Fig. 1(a)]. However, the magnetic susceptibilities of these compounds show no anomaly at the temperatures of their metal–semiconductor transitions [Fig. 1(b)]. In contrast, AMo 5O 8 phases with divalent A cations (A ¼ Ca, Sr, Eu)
* Corresponding author.
are semiconducting in the 20–300 K range [2]. To elucidate these seemingly puzzling properties of AMo 5O 8 (A ¼ rare earth, alkaline earth), McCarroll et al. prepared single crystal samples of the solid solution between SrMo 5O 8 and LaMo 5O 8, i.e. Sr 1¹xLa xMo 5O 8 (x ¼ 0–1) and characterized their crystal structures and electrical resistivity [3]. The solid solution becomes metallic over the 20–300 K range when a few at.% of either La or Sr are present. Single crystal X-ray diffraction studies of the solid solution members show no significant structural changes that can be attributed to the semiconducting and metallic behaviors. Furthermore, powder neutron diffraction studies of LaMo 5O 8 at 200, 100, 50 and 5 K studies gave no evidence for structural changes that can be related to its resistivity anomaly [3]. Consequently, it appears that the electronic structures of LnMo 5O 8 (Ln ¼ trivalent rare earth) have a special feature leading to their resistivity anomaly. In the present work, we probe this question by performing electronic band structure calculations for AMo 5O 8 and Sr 1¹xLa xMo 5O 8 (x ¼ 0–1) using the extended Hu¨ckel tight binding method [4].
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Fig. 1. (a) Electrical resistivity of LaMo 5O 8 as a function of temperature. (b) Magnetic susceptibility of LaMo 5O 8 as a function of temperature. 2. CRYSTAL STRUCTURE OF AMo 5O 8 To facilitate our discussion, it is necessary to describe the essential structural features of AMo 5O 8. The building blocks of AMo 5O 8 are the Mo 10O 26 units [Fig. 2(a)] containing the bi-octahedral Mo 10 cluster. The Mo 10O 26 units are fused together to form one-dimensional (1D) chains along the crystallographic a-direction. In each 1D chain direct Mo–Mo bonding occurs between Mo 10 clusters [Fig. 2(b)]. Finally, the 1D chains share oxygen atoms to form the three-dimensional (3D) lattice of AMo 5O 8 [Fig. 2(c)]. In the 3D lattice there is no direct Mo–Mo bonding between the 1D chains and the A atoms are located in the channels between the 1D chains. AMo 5O 8 has two 1D chains per unit cell, so that a unit cell is given by the formula (AMo 5O 8) 4. As labeled in Fig. 2(a), there are five non-equivalent Mo atoms, i.e. Mo(1), Mo(2), Mo(3), Mo(4) and Mo(5). In the 1D chain, each Mo(1) of one Mo 10 cluster makes additional Mo–Mo bonding with the Mo(1), Mo(2) and Mo(3) atoms of its adjacent Mo 10 cluster (Fig. 2). As will be discussed below, this structural aspect has a profound consequence on the electronic structure of LnMo 5O 8
Fig. 2. (a) Perspective view of an isolated Mo 10O 26 unit in AMo 5O 8. (b) Perspective view of how two adjacent Mo 10O 26 units link together to form 1D chains in AMo 5O 8. Only the Mo 10 clusters are shown for simplicity. (c) Perspective view of the 3D lattice of AMo 5O 8. (Ln ¼ trivalent rare earth) in the energy region of the Fermi level and hence the resistivity anomaly of LnMo 5O 8.
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3. ELECTRONIC BAND STRUCTURE OF AMo 5O 8 Within the EHTB approximation, the Sr and La atoms of Sr 1¹xLa xMo 5O 8 (x ¼ 0–1) can be treated as Sr 2þ and La 3þ ions giving its valence electrons (2 and 3, respectively). Consequently, the electronic structure of Sr 1¹xLa xMo 5O 8 is approximated by that of the (Mo 5O 8) (2þx)¹ lattice. Since Sr 1¹xLa xMo 5O 8 has four formula units (i.e. two Mo 10 clusters) per unit cell, LaMo 5O 8 has four more electrons per unit cell than does SrMo 5O 8. That is, each Mo 10 cluster of LaMo 5O 8 has one more electron than does that of SrMo 5O 8. The electronic band structures of AMo 5O 8 and Sr 1¹xLa xMo 5O 8 (x ¼ 0–1) calculated for various values of x are very similar. As a representative example, Fig. 3(a)
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shows the dispersion relations of the low-lying d-block bands calculated for SrMo 5O 8 in the vicinity of the Fermi level. SrMo 5O 8 has a direct band gap of approximately 0.18 eV at the G point. This is consistent with the results of resistivity measurements [5] that AMo 5O 8 phases with divalent A cations (i.e. A ¼ Sr, Ca, Eu) are semiconductors with activation energies of 0.15 and 0.08 eV for the Sr and Eu analogues, respectively, although these energies may reflect defects rather than the underlying electronic structure. To discuss the electronic structure of Sr 1¹xLa xMo 5O 8 for x ⬎ 0 based on Fig. 3(a), it is necessary to raise the Fermi level by 4x electrons per unit cell from that of SrMo 5O 8. As a consequence, the conduction band of Fig. 3(a) becomes partially filled. A representative example is given in Fig. 3(b), which shows the dispersion relations of the low-lying d-block bands calculated for LaMo 5O 8 in the vicinity of the Fermi level. Thus Sr 1¹xLa xMo 5O 8 for x ⬎ 0 is predicted to be metallic from the viewpoint of one-electron theory. This prediction is correct as long as x is not close to 0.0 or 1.0 [3]. However, what is predicted to be a metal by oneelectron theory can be an insulator because of electron localization arising from electron–electron repulsion [6], electron–phonon interactions [7], or random potentials [7, 8]. Let us consider the non-metallic behavior of Sr 1¹xLa xMo 5O 8 for x close to 0.0. The carrier density for x ⬎ 0:0 is given by the amount of electrons in the conduction band of Fig. 3(a). When x is close to 0.0 so that the carrier density is below the critical value needed for metallic transport [7a], local distortions may take place in the 3D lattice to trap electrons (i.e. electron phonon interaction) thereby preventing metallic transport. To discuss why LnMo 5O 8 (Ln ¼ trivalent rare earth) exhibits the unusual resistivity anomaly, we need to examine its electronic structure in more detail (see below). 4. FERMI SURFACE
Fig. 3. Dispersion relations of the low-lying d-block bands calculated for the 200 K structure of (a) SrMo 5O 8 and (b) LaMo 5O 8. Only the bands in the vicinity of the Fermi level are shown for simplicity.
Since the AMo 5O 8 compounds consist of 1D chains made up of Mo 10 clusters, one might wonder if Sr 1¹xLa xMo 5O 8 (0 ⬍ x ⬍ 1:0) possesses any charge density wave (CDW) instability often associated with metals with 1D structural components [9]. Figures 4(a)–(c) show three cross-section views of the Fermi surfaces calculated for LaMo 5O 8 [i.e. those associated with the partially filled bands of Fig. 3(b)]. In essence, the Fermi surfaces consist of electron and hole pockets so that LnMo 5O 8 (Ln ¼ trivalent rare earth) phases are semi-metals. In Figs 4(a)–(c) the Fermi surfaces are all closed in all three directions of the reciprocal space and exhibit no 1D character. Though not shown, the same is true for Sr 1¹xLa xMo 5O 8 (0 ⬍ x ⬍ 1:0). This result is consistent with the
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experimental observation that LaMo 5O 8 does not have a CDW instability and also with the fact that the magnetic susceptibility of LaMo 5O 8 exhibits no anomaly at the transition temperatures of its resistivity anomaly. 5. ATOM CHARACTER NEAR THE FERMI LEVEL OF LnMo 5O 8 (Ln ¼ TRIVALENT RARE EARTH) To gain insight into the resistivity anomaly of LnMo 5O 8, we now examine how strongly the d-orbitals of each kind of Mo contribute at the Fermi level by calculating the projected density of state (PDOS) plots for the five unique Mo atoms. Figure 5(a) shows the PDOS plots calculated based on the electronic band structure of LaMo 5O 8. It reveals that the Fermi level is strongly dominated by the d-electrons of the Mo(2) atoms. At the Fermi level, the relative contributions of
Fig. 4. Three cross-section views of the Fermi surface calculated for LaMo 5O 8. (a) on the aⴱ bⴱ plane at the cⴱ -height of 0, (b) on the aⴱ cⴱ -plane at the bⴱ height of 0 and (c) on the bⴱ cⴱ -plane at the aⴱ height of 0. G ¼ ð0; 0; 0Þ, X ¼ ðaⴱ =2; 0; 0Þ, Y ¼ ð0; bⴱ =2; 0Þ and Z ¼ ð0; 0; cⴱ =2Þ. In (a) the closed areas lying on the G–Y line are filled (i.e. electron pockets) and the remaining closed areas are empty (i.e. hole pockets). In (b) the closed areas are filled. In (c) the closed areas lying on the G–Y and G–Z lines are filled and the other closed areas are empty.
Fig. 5. PDOS plots calculated for the d-orbitals of the Mo(1), Mo(2), Mo(3), Mo(4) and Mo(5) atoms of (a) LaMo 5O 8 and (b) an isolated (Mo 10O 26) 26¹ unit taken from LaMo 5O 8. The legends are as follows: the solid line for Mo(1), the dotted line for Mo(2), the dashed line for Mo(3), the dash–dot line for Mo(4) and the dash–dot–dot line for Mo(5). The energy range covers all the t 2g-block energy levels. For simplicity, only a small energy region around the Fermi level is shown.
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the five Mo atoms decrease in the order Moð2Þ Ⰷ Moð1Þ ⬎ Moð5Þ ⬎ Moð4Þ ⬎ Moð3Þ [NðEf Þ ⬇ 21:5, 9.0, 7.5, 6.9 and 5.7 electrons/unit formula unit, respectively]. As the Fermi level is lowered, i.e. as the x value is decreased from 1.0 in Sr 1¹xLa xMo 5O 8, the dominance of the Mo(2) contribution to the Fermi level decreases sharply. To see why the Fermi level of LaMo 5O 8 is dominated by the d-orbitals of the Mo(2) atoms, we examine the electronic structure of an isolated Mo 10O 26 unit. The average oxidation state of Mo in LnMo 5O 8 is þ2.6. Thus, for the Mo atoms of the Mo 10O 26 unit to have the same oxidation state, the formal charge on the Mo 10O 26 unit should be ¹26. Figure 5(b) shows the PDOS plots calculated for the Mo(1), Mo(2), Mo(3), Mo(4) and Mo(5) atoms of an isolated (Mo 10O 26) 26¹ unit taken from LaMo 5O 8. Notice that the highest occupied level is strongly dominated by the Mo(1) atom and that the Mo(2) character is strong on the unoccupied levels lying immediately above the highest occupied level. This feature is easily explained by noting the extent of Mo–Mo bonding within each Mo 10 cluster and between Mo 10 clusters. In an isolated Mo 10O 26 unit, the Mo(1) and Mo(2) atoms each engage in four Mo–Mo bonds, the Mo(3) and Mo(4) atoms in five Mo–Mo bonds and the Mo(5) in seven Mo–Mo bonds. Thus the extent of direct metal– metal bonding is least for the Mo(1) and Mo(2) atoms. As an Mo atom engages in more Mo–Mo bonds, its d-orbitals contribute to lower-lying d-block energy levels of each Mo 10O 26 unit, i.e. their contributions to the PDOS plot occur at a lower energy. This explains why the contributions of the Mo(1) and Mo(2) atoms occur at higher energy levels than do those of the Mo(3), Mo(4) and Mo(5) atoms in the PDOS plot for an isolated (Mo 10O 26) 26¹ unit. When the Mo 10O 26 units fuse together to form 1D chains, the metal–metal bonding interaction between adjacent Mo 10 clusters occurs mainly through the Mo(1) atoms so that the Mo(1) contribution occurs at lower energy levels than does the Mo(2) contribution in the 3D lattice of LnMo 5O 8 [Fig. 5(a)]. The inter-cluster Mo–Mo distances of AMo 5O 8 decrease with increasing the electron count of its Mo 5O 8 anion lattice, because the energy levels accommodating the additional electrons are bonding between the inter-cluster Mo–Mo bonds [5]. For example, the inter-cluster Mo–Mo bond distances ˚ , Mo(1)–Moð2Þ ¼ are: Mo(1)–Moð1Þ ¼ 2:7651ð9Þ A ˚ ˚ in SrMo 5MO 8 3:0380ð6Þ A, Mo(1)–Moð3Þ ¼ 3:0869ð6Þ A ˚ and Mo(1)–Moð1Þ ¼ 2:6890ð7Þ A, Mo(1)–Moð2Þ ¼ ˚ , Mo(1)–Moð3Þ ¼ 3:0911ð5Þ A ˚ in LaMo 5MO 8. 2:9108ð5Þ A 6. DISCUSSION Let us now consider the resistivity anomaly of LaMo 5O 8 and its disappearance in Sr 1¹xLa xMo 5O 8 for
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x ⬍ 1:0 in terms of their electronic structures near the Fermi level. The fact that the Fermi level of LaMo 5O 8 is strongly dominated by the d-orbitals of the Mo(2) atoms means that the carriers of LaMo 5O 8 are largely localized around the Mo(2) sites. Note from Fig. 2(b) that the Mo(2) atoms are well separated within each Mo 10 cluster and also between adjacent Mo 10 clusters. In other words, the carriers of LaMo 5O 8 are well localized spatially. Above 180 K LaMo 5O 8 exhibits a semiconducting character with very small activation energy [Fig. 1(a)], while its magnetic susceptibility in the 50–300 K region is nearly temperature independent [Fig. 1(b)]. The latter implies that the carrier density does not change in this temperature region. Then, the slight increase in resistivity observed when lowering the temperature down to 180 K is due most likely to certain lattice vibrations that disappear below 180 K, because the compound becomes metallic below 180 K. The kinds of vibrations that retard the carrier movement above 180 K would be some kinds of local vibrations involving the Mo(2) sites. On lowering temperature below 30 K, LaMo 5O 8 shows a sharp increase in resistivity as well as in magnetic susceptibility, that is, the metal–insulator transition near 30 K increases the amount of unpaired spin density. A possible cause for the metal-to-insulator transition near 30 K is electron localization resulting from electron–electron repulsion [6]. This mechanism increases the amount of unpaired spin density and is therefore consistent with the observed increase in the magnetic susceptibility, although impurities in the samples may contribute to it as well. When x is slightly smaller than 1.0 in Sr 1¹xLa xMo 5O 8, such resistivity anomaly as found for LaMo 5O 8 (Ln ¼ trivalent rare earth) disappears. This is understandable because the dominance of the Mo(2) character at the Fermi level diminishes sharply as x decreases from 1.0. 7. CONCLUDING REMARKS The present electronic structure study shows that the AMo 5O 8 phases with divalent A cations (A ¼ Ca, Sr, Eu) are normal semiconductors with small band gap. The Fermi surfaces of Sr 1¹xLa xMo 5O 8 (0:0 ⬍ x ⱕ 1:0) are 3D in nature and do not exhibit any nesting. The electronic structure of LaMo 5O 8 and its rare earth analogues have a special feature that the Fermi level is dominated by the Mo(2) atoms of their Mo 10 clusters. As x decrease from 1.0 in Sr 1¹xLa xMo 5O 8, the dominance of the Mo(2) atoms at the Fermi level diminishes sharply. We speculate that the weakly semiconducting state of LnMo 5O 8 (Ln ¼ La, Ce, Pr, Nd and Sm) above 180 K is caused by local vibrations of the Mo 10 clusters involving the spatially isolated Mo(2) atoms. It would
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be interesting to carry out reflectance Raman experiments on LnMo 5O 8 to see if any vibrational modes disappear as the temperature is lowered below 180 K. Acknowledgements—The work at North Carolina State University was supported by the Office of Basic Energy Sciences, Division of Materials Sciences, U.S. Department of Energy, under Grant DE-FG05-86ER45259. H.-J. Koo’s visit to North Carolina State University was in part supported by Grant BSRI-97-3421 from the Ministry of Education, South Korea. REFERENCES 1. Gall, P., Noe¨l, H. and Gougeon, P., Mater. Res. Bull., 28, 1993, 1225. 2. Gall, P., Gougeon, P., Greenblatt, M., Jones, B.B., McCarroll, W.H. and Ramanujachary, K.V., Croatica Chem. Acta, 68, 1995, 849. 3. McCarroll, W.H., Borgia, M., Ramanujachary, K.V., Gougeon, P. and Greedan, J.E., J. Solid State Chem., 138, 1998, 7.
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4. Whangbo, M.-H. and Hoffmann, R., J. Am. Chem. Soc., 100, 1978, 6093. 5. Gall, P., Gautier, R., Gougeon, P. and Halet, J.-F., Unpublished results. 6. (a) Mott, N.F., Metal–Insulator Transitions, Barnes and Noble, New York, 1977. (b) Brandow, B.H., Adv. Phys., 26, 1977, 651. (c) Whangbo, M.-H., J. Chem. Phys., 70, 1979, 4963. 7. (a) Mott, N.F., Conduction in Non-Crystalline Materials, Oxford University Press, New York, 1987. (b) Lakkis, S., Schlenker, C., Chakraverty, B.K., Buder, R. and Marezio, R., Phys. Rev., B14, 1976, 1429. 8. Hays, W. and Stoneham, A.M., Defects and Defect Processes in Nonmetallic Solids, Ch. 8. Wiley, New York, 1985. 9. For reviews, see: (a) Electronic Properties of Inorganic Quasi-One Dimensional Compounds (Edited by P. Monceau), Parts 1 and 2. Reidel, Dordrecht, The Netherlands, 1985. (b) Crystal Chemistry and Properties of Materials with QuasiOne-Dimensional Structures (Edited by J. Rouxel). The Netherlands, 1986. (c) Canadell, E. and Whangbo, M.-H., Chem. Rev., 91, 1991, 965.
Pergamon
PII: S0038–1098(98)00407-4
ON THE ORIGIN OF THE ANOMALOUS ELECTRICAL RESISTIVITY OF LnMo 5O 8 (Ln ¼ TRIVALENT RARE EARTH) H.-J. Koo, a M.-H. Whangbo, a ,* W.H. McCarroll, b M. Greenblatt, c R. Gautier, d J.-F. Halet d and P. Gougeon d a
Department of Chemistry, North Carolina State University, Raleigh, NC 27695-8204, U.S.A. b Department of Chemistry, Rider College, Lawrenceville, NJ 08648, U.S.A. c Department of Chemistry, Rutgers University, Piscataway, NJ 08855, U.S.A. d Laboratoire de Chimie du Solide et Inorganique Moleculaire, UMR CNRS 6511, Universite´ de Rennes 1, 35042 Rennes Cedex, France (Received 7 July 1998; accepted in revised form 11 August 1998 by F.J. Di Salvo) Electronic structures of AMo 5O 8 (A ¼ rare earth, alkaline earth) and the solid solution Sr 1¹xLa xMo 5O 8 (x ¼ 0–1) were examined using the extended Hu¨ckel tight binding method. AMo 5O 8 phases with divalent A cations (A ¼ Sr, Ca, Eu) are normal semiconductors with small band gap. The Fermi surfaces of Sr 1¹xLa xMo 5O 8 (0:0 ⬍ x ⱕ 1:0) and LnMo 5O 8 (Ln ¼ trivalent rare earth) do not exhibit any nesting. In the electronic structures of LnMo 5O 8 (Ln ¼ trivalent rare earth) phases, the Fermi level is dominated by the d-orbitals of the Mo(2) atoms of their Mo 10 clusters. With decreasing x from 1.0 in Sr 1¹xLa xMo 5O 8, the dominance of the Mo(2) atoms at the Fermi level sharply diminishes. Based on this observation, we proposed a probable reason for the weakly semiconducting state above 180 K and the metallic state below 180 K in LnMo 5O 8 (Ln ¼ trivalent rare earth). 䉷 1998 Elsevier Science Ltd. All rights reserved
1. INTRODUCTION The magnetic properties of reduced molybdenum oxides LnMo 5O 8 (Ln ¼ La, Ce, Pr, Nd) show that the La compound has a Pauli-type temperature independent susceptibility in the 50–300 K range, while the Ce, Pr and Nd phases have susceptibilities essentially corresponding to the rare-earth ions [1]. To characterize these properties further, Gall et al. examined the electrical resistivity of LnMo 5O 8 (Ln ¼ La, Ce, Pr, Nd, Sm, Eu, Gd) and their alkaline earth analogues CaMo 5O 8 and SrMo 5O 8 [2]. Upon lowering temperature, the LnMo 5O 8 (Ln ¼ trivalent rare earth) compounds exhibit a semiconductor-to-metal transition near 180 K and then a metal-to-semiconductor transition near 30 K [Fig. 1(a)]. However, the magnetic susceptibilities of these compounds show no anomaly at the temperatures of their metal–semiconductor transitions [Fig. 1(b)]. In contrast, AMo 5O 8 phases with divalent A cations (A ¼ Ca, Sr, Eu)
* Corresponding author.
are semiconducting in the 20–300 K range [2]. To elucidate these seemingly puzzling properties of AMo 5O 8 (A ¼ rare earth, alkaline earth), McCarroll et al. prepared single crystal samples of the solid solution between SrMo 5O 8 and LaMo 5O 8, i.e. Sr 1¹xLa xMo 5O 8 (x ¼ 0–1) and characterized their crystal structures and electrical resistivity [3]. The solid solution becomes metallic over the 20–300 K range when a few at.% of either La or Sr are present. Single crystal X-ray diffraction studies of the solid solution members show no significant structural changes that can be attributed to the semiconducting and metallic behaviors. Furthermore, powder neutron diffraction studies of LaMo 5O 8 at 200, 100, 50 and 5 K studies gave no evidence for structural changes that can be related to its resistivity anomaly [3]. Consequently, it appears that the electronic structures of LnMo 5O 8 (Ln ¼ trivalent rare earth) have a special feature leading to their resistivity anomaly. In the present work, we probe this question by performing electronic band structure calculations for AMo 5O 8 and Sr 1¹xLa xMo 5O 8 (x ¼ 0–1) using the extended Hu¨ckel tight binding method [4].
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Fig. 1. (a) Electrical resistivity of LaMo 5O 8 as a function of temperature. (b) Magnetic susceptibility of LaMo 5O 8 as a function of temperature. 2. CRYSTAL STRUCTURE OF AMo 5O 8 To facilitate our discussion, it is necessary to describe the essential structural features of AMo 5O 8. The building blocks of AMo 5O 8 are the Mo 10O 26 units [Fig. 2(a)] containing the bi-octahedral Mo 10 cluster. The Mo 10O 26 units are fused together to form one-dimensional (1D) chains along the crystallographic a-direction. In each 1D chain direct Mo–Mo bonding occurs between Mo 10 clusters [Fig. 2(b)]. Finally, the 1D chains share oxygen atoms to form the three-dimensional (3D) lattice of AMo 5O 8 [Fig. 2(c)]. In the 3D lattice there is no direct Mo–Mo bonding between the 1D chains and the A atoms are located in the channels between the 1D chains. AMo 5O 8 has two 1D chains per unit cell, so that a unit cell is given by the formula (AMo 5O 8) 4. As labeled in Fig. 2(a), there are five non-equivalent Mo atoms, i.e. Mo(1), Mo(2), Mo(3), Mo(4) and Mo(5). In the 1D chain, each Mo(1) of one Mo 10 cluster makes additional Mo–Mo bonding with the Mo(1), Mo(2) and Mo(3) atoms of its adjacent Mo 10 cluster (Fig. 2). As will be discussed below, this structural aspect has a profound consequence on the electronic structure of LnMo 5O 8
Fig. 2. (a) Perspective view of an isolated Mo 10O 26 unit in AMo 5O 8. (b) Perspective view of how two adjacent Mo 10O 26 units link together to form 1D chains in AMo 5O 8. Only the Mo 10 clusters are shown for simplicity. (c) Perspective view of the 3D lattice of AMo 5O 8. (Ln ¼ trivalent rare earth) in the energy region of the Fermi level and hence the resistivity anomaly of LnMo 5O 8.
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3. ELECTRONIC BAND STRUCTURE OF AMo 5O 8 Within the EHTB approximation, the Sr and La atoms of Sr 1¹xLa xMo 5O 8 (x ¼ 0–1) can be treated as Sr 2þ and La 3þ ions giving its valence electrons (2 and 3, respectively). Consequently, the electronic structure of Sr 1¹xLa xMo 5O 8 is approximated by that of the (Mo 5O 8) (2þx)¹ lattice. Since Sr 1¹xLa xMo 5O 8 has four formula units (i.e. two Mo 10 clusters) per unit cell, LaMo 5O 8 has four more electrons per unit cell than does SrMo 5O 8. That is, each Mo 10 cluster of LaMo 5O 8 has one more electron than does that of SrMo 5O 8. The electronic band structures of AMo 5O 8 and Sr 1¹xLa xMo 5O 8 (x ¼ 0–1) calculated for various values of x are very similar. As a representative example, Fig. 3(a)
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shows the dispersion relations of the low-lying d-block bands calculated for SrMo 5O 8 in the vicinity of the Fermi level. SrMo 5O 8 has a direct band gap of approximately 0.18 eV at the G point. This is consistent with the results of resistivity measurements [5] that AMo 5O 8 phases with divalent A cations (i.e. A ¼ Sr, Ca, Eu) are semiconductors with activation energies of 0.15 and 0.08 eV for the Sr and Eu analogues, respectively, although these energies may reflect defects rather than the underlying electronic structure. To discuss the electronic structure of Sr 1¹xLa xMo 5O 8 for x ⬎ 0 based on Fig. 3(a), it is necessary to raise the Fermi level by 4x electrons per unit cell from that of SrMo 5O 8. As a consequence, the conduction band of Fig. 3(a) becomes partially filled. A representative example is given in Fig. 3(b), which shows the dispersion relations of the low-lying d-block bands calculated for LaMo 5O 8 in the vicinity of the Fermi level. Thus Sr 1¹xLa xMo 5O 8 for x ⬎ 0 is predicted to be metallic from the viewpoint of one-electron theory. This prediction is correct as long as x is not close to 0.0 or 1.0 [3]. However, what is predicted to be a metal by oneelectron theory can be an insulator because of electron localization arising from electron–electron repulsion [6], electron–phonon interactions [7], or random potentials [7, 8]. Let us consider the non-metallic behavior of Sr 1¹xLa xMo 5O 8 for x close to 0.0. The carrier density for x ⬎ 0:0 is given by the amount of electrons in the conduction band of Fig. 3(a). When x is close to 0.0 so that the carrier density is below the critical value needed for metallic transport [7a], local distortions may take place in the 3D lattice to trap electrons (i.e. electron phonon interaction) thereby preventing metallic transport. To discuss why LnMo 5O 8 (Ln ¼ trivalent rare earth) exhibits the unusual resistivity anomaly, we need to examine its electronic structure in more detail (see below). 4. FERMI SURFACE
Fig. 3. Dispersion relations of the low-lying d-block bands calculated for the 200 K structure of (a) SrMo 5O 8 and (b) LaMo 5O 8. Only the bands in the vicinity of the Fermi level are shown for simplicity.
Since the AMo 5O 8 compounds consist of 1D chains made up of Mo 10 clusters, one might wonder if Sr 1¹xLa xMo 5O 8 (0 ⬍ x ⬍ 1:0) possesses any charge density wave (CDW) instability often associated with metals with 1D structural components [9]. Figures 4(a)–(c) show three cross-section views of the Fermi surfaces calculated for LaMo 5O 8 [i.e. those associated with the partially filled bands of Fig. 3(b)]. In essence, the Fermi surfaces consist of electron and hole pockets so that LnMo 5O 8 (Ln ¼ trivalent rare earth) phases are semi-metals. In Figs 4(a)–(c) the Fermi surfaces are all closed in all three directions of the reciprocal space and exhibit no 1D character. Though not shown, the same is true for Sr 1¹xLa xMo 5O 8 (0 ⬍ x ⬍ 1:0). This result is consistent with the
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experimental observation that LaMo 5O 8 does not have a CDW instability and also with the fact that the magnetic susceptibility of LaMo 5O 8 exhibits no anomaly at the transition temperatures of its resistivity anomaly. 5. ATOM CHARACTER NEAR THE FERMI LEVEL OF LnMo 5O 8 (Ln ¼ TRIVALENT RARE EARTH) To gain insight into the resistivity anomaly of LnMo 5O 8, we now examine how strongly the d-orbitals of each kind of Mo contribute at the Fermi level by calculating the projected density of state (PDOS) plots for the five unique Mo atoms. Figure 5(a) shows the PDOS plots calculated based on the electronic band structure of LaMo 5O 8. It reveals that the Fermi level is strongly dominated by the d-electrons of the Mo(2) atoms. At the Fermi level, the relative contributions of
Fig. 4. Three cross-section views of the Fermi surface calculated for LaMo 5O 8. (a) on the aⴱ bⴱ plane at the cⴱ -height of 0, (b) on the aⴱ cⴱ -plane at the bⴱ height of 0 and (c) on the bⴱ cⴱ -plane at the aⴱ height of 0. G ¼ ð0; 0; 0Þ, X ¼ ðaⴱ =2; 0; 0Þ, Y ¼ ð0; bⴱ =2; 0Þ and Z ¼ ð0; 0; cⴱ =2Þ. In (a) the closed areas lying on the G–Y line are filled (i.e. electron pockets) and the remaining closed areas are empty (i.e. hole pockets). In (b) the closed areas are filled. In (c) the closed areas lying on the G–Y and G–Z lines are filled and the other closed areas are empty.
Fig. 5. PDOS plots calculated for the d-orbitals of the Mo(1), Mo(2), Mo(3), Mo(4) and Mo(5) atoms of (a) LaMo 5O 8 and (b) an isolated (Mo 10O 26) 26¹ unit taken from LaMo 5O 8. The legends are as follows: the solid line for Mo(1), the dotted line for Mo(2), the dashed line for Mo(3), the dash–dot line for Mo(4) and the dash–dot–dot line for Mo(5). The energy range covers all the t 2g-block energy levels. For simplicity, only a small energy region around the Fermi level is shown.
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ANOMALOUS ELECTRICAL RESISTIVITY OF LnMo 5O 8
the five Mo atoms decrease in the order Moð2Þ Ⰷ Moð1Þ ⬎ Moð5Þ ⬎ Moð4Þ ⬎ Moð3Þ [NðEf Þ ⬇ 21:5, 9.0, 7.5, 6.9 and 5.7 electrons/unit formula unit, respectively]. As the Fermi level is lowered, i.e. as the x value is decreased from 1.0 in Sr 1¹xLa xMo 5O 8, the dominance of the Mo(2) contribution to the Fermi level decreases sharply. To see why the Fermi level of LaMo 5O 8 is dominated by the d-orbitals of the Mo(2) atoms, we examine the electronic structure of an isolated Mo 10O 26 unit. The average oxidation state of Mo in LnMo 5O 8 is þ2.6. Thus, for the Mo atoms of the Mo 10O 26 unit to have the same oxidation state, the formal charge on the Mo 10O 26 unit should be ¹26. Figure 5(b) shows the PDOS plots calculated for the Mo(1), Mo(2), Mo(3), Mo(4) and Mo(5) atoms of an isolated (Mo 10O 26) 26¹ unit taken from LaMo 5O 8. Notice that the highest occupied level is strongly dominated by the Mo(1) atom and that the Mo(2) character is strong on the unoccupied levels lying immediately above the highest occupied level. This feature is easily explained by noting the extent of Mo–Mo bonding within each Mo 10 cluster and between Mo 10 clusters. In an isolated Mo 10O 26 unit, the Mo(1) and Mo(2) atoms each engage in four Mo–Mo bonds, the Mo(3) and Mo(4) atoms in five Mo–Mo bonds and the Mo(5) in seven Mo–Mo bonds. Thus the extent of direct metal– metal bonding is least for the Mo(1) and Mo(2) atoms. As an Mo atom engages in more Mo–Mo bonds, its d-orbitals contribute to lower-lying d-block energy levels of each Mo 10O 26 unit, i.e. their contributions to the PDOS plot occur at a lower energy. This explains why the contributions of the Mo(1) and Mo(2) atoms occur at higher energy levels than do those of the Mo(3), Mo(4) and Mo(5) atoms in the PDOS plot for an isolated (Mo 10O 26) 26¹ unit. When the Mo 10O 26 units fuse together to form 1D chains, the metal–metal bonding interaction between adjacent Mo 10 clusters occurs mainly through the Mo(1) atoms so that the Mo(1) contribution occurs at lower energy levels than does the Mo(2) contribution in the 3D lattice of LnMo 5O 8 [Fig. 5(a)]. The inter-cluster Mo–Mo distances of AMo 5O 8 decrease with increasing the electron count of its Mo 5O 8 anion lattice, because the energy levels accommodating the additional electrons are bonding between the inter-cluster Mo–Mo bonds [5]. For example, the inter-cluster Mo–Mo bond distances ˚ , Mo(1)–Moð2Þ ¼ are: Mo(1)–Moð1Þ ¼ 2:7651ð9Þ A ˚ ˚ in SrMo 5MO 8 3:0380ð6Þ A, Mo(1)–Moð3Þ ¼ 3:0869ð6Þ A ˚ and Mo(1)–Moð1Þ ¼ 2:6890ð7Þ A, Mo(1)–Moð2Þ ¼ ˚ , Mo(1)–Moð3Þ ¼ 3:0911ð5Þ A ˚ in LaMo 5MO 8. 2:9108ð5Þ A 6. DISCUSSION Let us now consider the resistivity anomaly of LaMo 5O 8 and its disappearance in Sr 1¹xLa xMo 5O 8 for
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x ⬍ 1:0 in terms of their electronic structures near the Fermi level. The fact that the Fermi level of LaMo 5O 8 is strongly dominated by the d-orbitals of the Mo(2) atoms means that the carriers of LaMo 5O 8 are largely localized around the Mo(2) sites. Note from Fig. 2(b) that the Mo(2) atoms are well separated within each Mo 10 cluster and also between adjacent Mo 10 clusters. In other words, the carriers of LaMo 5O 8 are well localized spatially. Above 180 K LaMo 5O 8 exhibits a semiconducting character with very small activation energy [Fig. 1(a)], while its magnetic susceptibility in the 50–300 K region is nearly temperature independent [Fig. 1(b)]. The latter implies that the carrier density does not change in this temperature region. Then, the slight increase in resistivity observed when lowering the temperature down to 180 K is due most likely to certain lattice vibrations that disappear below 180 K, because the compound becomes metallic below 180 K. The kinds of vibrations that retard the carrier movement above 180 K would be some kinds of local vibrations involving the Mo(2) sites. On lowering temperature below 30 K, LaMo 5O 8 shows a sharp increase in resistivity as well as in magnetic susceptibility, that is, the metal–insulator transition near 30 K increases the amount of unpaired spin density. A possible cause for the metal-to-insulator transition near 30 K is electron localization resulting from electron–electron repulsion [6]. This mechanism increases the amount of unpaired spin density and is therefore consistent with the observed increase in the magnetic susceptibility, although impurities in the samples may contribute to it as well. When x is slightly smaller than 1.0 in Sr 1¹xLa xMo 5O 8, such resistivity anomaly as found for LaMo 5O 8 (Ln ¼ trivalent rare earth) disappears. This is understandable because the dominance of the Mo(2) character at the Fermi level diminishes sharply as x decreases from 1.0. 7. CONCLUDING REMARKS The present electronic structure study shows that the AMo 5O 8 phases with divalent A cations (A ¼ Ca, Sr, Eu) are normal semiconductors with small band gap. The Fermi surfaces of Sr 1¹xLa xMo 5O 8 (0:0 ⬍ x ⱕ 1:0) are 3D in nature and do not exhibit any nesting. The electronic structure of LaMo 5O 8 and its rare earth analogues have a special feature that the Fermi level is dominated by the Mo(2) atoms of their Mo 10 clusters. As x decrease from 1.0 in Sr 1¹xLa xMo 5O 8, the dominance of the Mo(2) atoms at the Fermi level diminishes sharply. We speculate that the weakly semiconducting state of LnMo 5O 8 (Ln ¼ La, Ce, Pr, Nd and Sm) above 180 K is caused by local vibrations of the Mo 10 clusters involving the spatially isolated Mo(2) atoms. It would
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be interesting to carry out reflectance Raman experiments on LnMo 5O 8 to see if any vibrational modes disappear as the temperature is lowered below 180 K. Acknowledgements—The work at North Carolina State University was supported by the Office of Basic Energy Sciences, Division of Materials Sciences, U.S. Department of Energy, under Grant DE-FG05-86ER45259. H.-J. Koo’s visit to North Carolina State University was in part supported by Grant BSRI-97-3421 from the Ministry of Education, South Korea. REFERENCES 1. Gall, P., Noe¨l, H. and Gougeon, P., Mater. Res. Bull., 28, 1993, 1225. 2. Gall, P., Gougeon, P., Greenblatt, M., Jones, B.B., McCarroll, W.H. and Ramanujachary, K.V., Croatica Chem. Acta, 68, 1995, 849. 3. McCarroll, W.H., Borgia, M., Ramanujachary, K.V., Gougeon, P. and Greedan, J.E., J. Solid State Chem., 138, 1998, 7.
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4. Whangbo, M.-H. and Hoffmann, R., J. Am. Chem. Soc., 100, 1978, 6093. 5. Gall, P., Gautier, R., Gougeon, P. and Halet, J.-F., Unpublished results. 6. (a) Mott, N.F., Metal–Insulator Transitions, Barnes and Noble, New York, 1977. (b) Brandow, B.H., Adv. Phys., 26, 1977, 651. (c) Whangbo, M.-H., J. Chem. Phys., 70, 1979, 4963. 7. (a) Mott, N.F., Conduction in Non-Crystalline Materials, Oxford University Press, New York, 1987. (b) Lakkis, S., Schlenker, C., Chakraverty, B.K., Buder, R. and Marezio, R., Phys. Rev., B14, 1976, 1429. 8. Hays, W. and Stoneham, A.M., Defects and Defect Processes in Nonmetallic Solids, Ch. 8. Wiley, New York, 1985. 9. For reviews, see: (a) Electronic Properties of Inorganic Quasi-One Dimensional Compounds (Edited by P. Monceau), Parts 1 and 2. Reidel, Dordrecht, The Netherlands, 1985. (b) Crystal Chemistry and Properties of Materials with QuasiOne-Dimensional Structures (Edited by J. Rouxel). The Netherlands, 1986. (c) Canadell, E. and Whangbo, M.-H., Chem. Rev., 91, 1991, 965.