- Email: [email protected]
Electronic structure of one-dimensional bismuth oxide, BiCu2VO6
Solid State Sciences 17 (2013) 111e114
Contents lists available at SciVerse ScienceDirect
Solid State Sciences journal homepage: www.elsevier.com/locate/ssscie
Electronic structure of one-dimensional bismuth oxide, BiCu2VO6 Sungwoo Cho a, In-Ja Lee b, *, Dongwoon Jung a, * a b
Department of Chemistry, Wonkwang University, Iksan, Jeonbuk 570-749, Republic of Korea Department of Advanced Materials Chemistry, Dongguk University, Gyeongju, Gyeongbuk 780-714, Republic of Korea
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 November 2012 Received in revised form 30 November 2012 Accepted 6 December 2012 Available online 21 December 2012
Electronic structure of BiCu2VO6 was analyzed by adopting tight-binding band structure calculation based upon the extended Hückel method. Results show the contribution to the DOS at the Fermi energy is mostly from the Cu atoms. Therefore CueO chains running along the crystallographic b-direction are proved to be the pathways of electrons for conduction in BiCu2VO6. The Fermi surface calculated for BiCu2VO6 shows the compound is one-dimensional, so that the electrical conductivity is supposed to arise only along the b-direction. Ó 2012 Elsevier Masson SAS. All rights reserved.
Keywords: Bismuth oxide Phase transition Band calculation Dimensionality
1. Introduction Ternary bismuth oxides having general formula BiA2MO6 (A ¼ divalent metals; Cu, Mg, Zn, Pb: M ¼ pentavalent elements; V, P) have been prepared and their phase transitions to higher symmetry structures have been also reported subsequently [1e4]. One of these compounds, BiCu2VO6, was successfully synthesized in 1998 by Sleight group [5], and recently its structural and electrical properties were reported by Evans et al. [6]. This compound shows interesting magnetic properties that its singlet ground state is non-magnetic and there is a gap in the spin excitation spectrum [7]. According to the electrical resistivity measurement data, it is metallic within the experimental temperature range since the electrical resistivity decreases with decreasing temperature. The structure of BiCu2VO6 is primitive monoclinic with the space group of P21/n at room temperature which is referred to as a-BiCu2VO6. However, this compound shows a phase transition and a-BiCu2VO6 turns out to be b-BiCu2VO6 whose space group is I2/m at higher temperature. Electrical measurement data prove the phase transition that there is a noticeable slope change in conductivity vs. temperature plot at w450 K [6]. Changes in cell parameters of the compound at this temperature also prove the phase transition. So far, the origin of the phase transition in this compound and the physical properties are not fully studied yet. In this paper, we
* Corresponding authors. Tel.: þ82 63 850 6207. E-mail address: [email protected] (D. Jung). 1293-2558/$ e see front matter Ó 2012 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.solidstatesciences.2012.12.007
analyze the reason of the phase transition in a-BiCu2VO6 by examining the structureeproperty relationship. Also, the physical properties found in this compound are discussed. 2. Structure BiA2MO6 (A ¼ divalent metals; Cu, Mg, Zn, Pb: M ¼ pentavalent elements; V, P) show closely related structures that they all contain (BiO2) chains, and (MO4)3 tetrahedra. Besides the (BiO2) chains and (VO4)3 tetrahedra, additional (CuO5) square pyramids and (CuO6) distorted octahedra complete the whole structure in BiCu2VO6. (BiO2) chains run along the crystallographic c-direction as shown in Fig. 1. The distances between Bi and O range from 2.2 to 3.1 A, depending upon the different distinct site of Bi3þ. Cu2þ ions occupy six crystallographically distinct sites in the compound. Four of them construct Cu4O14 cluster whose projection view on ab-plane is shown in Fig. 2. In the cluster, two Cu atoms are fivecoordinated to form distorted square pyramids. These two pyramids share edges to construct Cu2O8 sub-cluster. Another two CuO5 square pyramids in the Cu4O14 cluster share corners and form another Cu2O9 sub-cluster. Two sub-clusters share a corner and an edge to construct final Cu4O14 cluster. Each of the remaining two copper atoms out of six distinct Cu atoms forms a distorted octahedron in which the CueO bond length is between 2.2 and 3.0 A. The distorted CueO octahedra alternatively share an edge and a corner, and finally construct a chain running along the crystallographic b-direction which is perpendicular to the (BiO2) chains, as shown in Fig. 3. Vanadium forms distorted tetrahedra in the
112
S. Cho et al. / Solid State Sciences 17 (2013) 111e114
Fig. 3. A CueO chain running along the b-direction. Distorted CuO6 octahedra form edge and corner sharing alternatively. Fig. 1. A (BiO2) chain running along the c-direction. Large and small circles represent bismuth and oxygen atoms, respectively.
compound with the bond angles ranging from 105 to 113 . The (VO4)3 tetrahedra sit between CueO chains and share their corners with the coppereoxygen polyhedra and BieO polyhedra. 3. Computational method Electronic structure calculations were performed by the extended Huckel method [8] within the framework of tight binding approximation [9]. Density of states (DOS) and crystal orbital overlap populations (COOP) were calculated based on the given crystal structure. The atomic orbital parameters employed in the calculation were the default values in the CAESAR program [10], which are listed in Table 1. The band structures were calculated along the special lines connecting the following high-symmetry points: G (0, 0, 0), X (0.5, 0, 0), Y (0, 0.5, 0), Z (0, 0, 0.5), M (0.5, 0.5, 0) and R (0.5, 0.5, 0.5) in terms of the reciprocal basis vectors [11]. Atomic and bond populations were evaluated via the Mulliken population analysis [12]. Within the Brillouin zone of the cell, 816 irreducible k points were selected. 4. Results and discussion The total density of states (DOS) and the projected density of states (PDOS) for the Cu, Bi, V, and O atoms in a-BiCu2VO6 are shown in Fig. 4. The vertical dashed line represents the Fermi energy of the compound. The solid line represents the total DOS of the compound. The dashed, dotted, dash-dot, and dash-dot-dot line represents the contribution of Cu, O, V, and Bi atoms, respectively. At the Fermi energy, the DOS value for the compound is not zero, which means that a-BiCu2VO6 is metallic. This result is consistent with the experimental data that the conductivity increases with increasing temperature. The conductivity of a-BiCu2VO6 at 450 C is reported to be about 5.5 102 S/m, which is raised up to 100 times at 700 C [6]. These conductivity values are bigger than that of silicon by more than 30 times. Upon the general oxidation scheme of Bi3þ, V5þ, Cu2þ, and O2, BiCu2VO6 cannot be metallic because there is no partially filled band. The PDOS result calculated for Cu, Bi, V, and O atoms provides the clue why this compound is metallic.
At the Fermi energy, the major contribution to DOS comes from Cu atoms, which means that electrons in Cu 3d-orbitals are most important charge carriers. The DOS of Bi p-orbitals contributes totally at 11.8 to 10.6 eV, which is just above the Fermi energy as shown in Fig. 4. The Bi p-orbitals are, therefore, totally empty and the oxidation state of Bi is þ3 as expected. The contribution to DOS from vanadium lies mostly in the region of 10 to 7 eV, which is far above the Fermi energy. Only small portion of contribution below the Fermi level from vanadium can be found at about 15 eV. This means that the d-orbitals of V are almost empty, but small amount of electrons still exist in the d-orbitals. The DOS peak of Cu d-orbitals is cut by the Fermi energy as illustrated in Fig. 4. It is clear from the figure that most of Cu d-orbitals are occupied, but small amount of d-orbitals are still unoccupied. The oxidation state of Cu is, therefore, þ(2 þ x). The small amount of electrons transfer from Cu to V is understandable from the PDOS data of Cu and V. Electron deficiencies in Cu atoms in the sample create the partially filled bands, thereby changing this compound be metallic. Band dispersions calculated for a-BiCu2VO6 are shown in Fig. 5. Only four bands near the Fermi energy are shown in the figure since the electrons in the bands around the Fermi energy are most important for the electrical conductivity. Two bands out of four are cut by the Fermi energy. G, X, Y, M, R, Z represent the wave vector points (0, 0, 0), (a*/2, 0, 0), (0, b*/2, 0), (a*/2, b*/2, 0), (a*/2, b*/2, c*/2), (0, 0, c*/2) in the first Brillouin zone of the reciprocal lattice, respectively. Bands are almost flat along the a-, and c-directions in a-BiCu2VO6 while they are strongly dispersive only along the b-direction. Structural features suggest that a-BiCu2VO6 may be 3-dimensional since BieO, CueO, and VeO polyhedra are repeated along the a-, b-, and c-directions by sharing their edges or corners. Band dispersion of this compound, however, tells us that this compound is 1-dimensional. From the PDOS analysis, the major contribution to the conductivity of this compound comes from Cu atoms. CueO chains act as charge carrier paths by forming strong interactions between copper and oxygen atoms along the b-direction (See Fig. 1). BieO chains running along the c-direction does not contribute to the conductivity in this compound since the DOS value of Bi atoms lie above the Fermi energy. Table 1 Atomic parameters used in EHTB calculationsa: Valence orbital ionization potential Hii (eV) and exponent of the Slater-type orbital z and the orbital coefficient c. Atom
Orbital
Hii (eV)
z1 (c1)
Bi
6s 6p 4s 4p 3d 4s 4p 3d 2s 2p
15.19 7.79 11.4 6.06 14.0 8.81 5.52 11.0 32.299 14.8
2.56 2.072 2.20 2.20 5.95 1.30 1.30 4.75 2.275 2.275
Cu
V
O
Fig. 2. The Cu4O14 cluster. Large and small circles represent copper and oxygen atoms, respectively.
(1.0) (1.0) (1.0) (1.0) (0.5933) (1.0) (1.0) (0.4755) (1.0) (1.0)
z2 (c2)
2.30 (0.5744)
1.70 (0.7052)
a Parameters are collected from the following data: (a) E. Clementi, C. Roetti, Atomic Data Nuclear Data Tables 14 (1974) 177. (b) A.D. McLeen, R.S. McLeen, Atomic Data Nuclear Data Tables 26 (1981) 197. (c) J.W. Richardson, M.J. Blackman, J.E. Ranochak, J. Chem. Phys. 58 (1973) 3010.
S. Cho et al. / Solid State Sciences 17 (2013) 111e114
113
Fig. 4. Density of states calculated for a-BiCu2VO6. The solid line represents the total DOS of the compound. The dashed, dotted, dash-dot, and dash-dot-dot line represents the contribution of Cu, O, V, and Bi atoms, respectively.
The Fermi surface of a partially filled band is defined as the boundary surface of wave vectors that separate the wave vector region of filled band levels from that the wave vector region of unfilled band levels. Since there are two bands cut by the Fermi energy, two Fermi surfaces can be drawn for a-BiCu2VO6 as shown in Fig. 6a and b, respectively. Carriers responsible for electrical properties of metals are those electrons at the Fermi energy. When a certain wave vector direction does not cross a Fermi surface [e.g., G / X and G / Z in Fig. 6], there are no electrons at the Fermi level having momentum along that direction, so that the system is not metallic along that direction. Both Fermi surfaces in Fig. 6a and b are open along the a- and c-directions and there are no Fermi surface crossing along those directions. The dimensionality of a metal is given by the dimensionality of its Fermi surface. The Fermi surface crossing is shown only along the b-direction. Consequently, the Fermi surface of a-BiCu2VO6 is one-dimensional. Essentially two Fermi surfaces given in Fig. 6a and b are, therefore, one-dimensional in nature and conductivity is going to arise only along the b-direction. This is consistent with the structural feature that CueO chains run along the crystallographic b-direction. One piece of a Fermi surface may be superimposable, by translating it with wave vector q, onto another piece of the Fermi surface. In such a case, the two pieces are said to be nested by the wave vector q. A metallic system with a nesting vector q leads to a phase
Fig. 6. The Fermi surface associated with the bands cut by the Fermi energy. The Fermi surface associated with the (a) upper band and (b) the lower band. Fig. 5. The dispersion curves of four bands near the Fermi energy.
114
S. Cho et al. / Solid State Sciences 17 (2013) 111e114
transition. Let us discuss why a Fermi surface nesting is important in introducing a phase transition by investigating the orbital mixing between an occupied and unoccupied levels [13]. For a 1D metal, an occupied wave vector k and an unoccupied wave vector k0 form an occupied orbital F(k) and an unoccupied orbital F(k0 ), respectively. An orbital mixing between F(k) and F(k0 ) produces new orbitals J(k) and J(k0 ),
JðkÞ f FðkÞ þ gFðk0 Þ Jðk0 Þ f gFðkÞ þ Fðk0 Þ where g is a mixing coefficient. The extent of the orbital mixing is determined by the energy difference between the original orbitals F(k) and F(k0 ). At the Fermi level, by definition, two orbitals F(k) and F(k0 ) are degenerate. Therefore, the orbital mixing between them is significant and so is the interaction energy. When a Fermi surface is nested by a vector q, the orbital mixing can be performed for all wave vectors in the nested region of the First Brillouin Zone (FBZ), thereby leading to the sets of new orbitals {F(k)} and {F(k)} differing in their wave vectors by q ¼ k k0 . As the nesting area is large, therefore, the amount of orbital mixing is large and so is the extent of interaction energy. This large amount of energy becomes the driving force to change the structure which leads to a phase transition even at low temperature. Generally, a compound that possesses one-dimensional property shows well nested Fermi surfaces and therefore exhibits higher susceptibility to a phase transition. The electronic instability induced by these Fermi surface nestings may cause the charge density waves (CDWs) or the spin density waves (SDWs) depending upon how their orbitals are mixed [13e15]. These are well known as the metal-insulator (M I) transition or the Mott transition [16,17]. On the other hand, when the change in the crystal structure caused by the phase transition associated from the nested Fermi surfaces is strong enough, the compound after the phase transition may have partially filled bands. Sometimes the Fermi surface nesting area is collapsed by the mixing between the occupied and unoccupied orbitals in the vicinity of the Fermi energy, and a new Fermi surface is formed again. In this case, the electronic instability caused by the Fermi surface nesting in the compound may result in the metalemetal transition. According to the experimental results, the metalemetal transition is more reasonable for a-BiCu2VO6. The unnested Fermi surface associated with the highest bands in the compound may exhibit some metallic character even after the phase transition. To verify the dimensionality in a-BiCu2VO6 more clearly, the electrical measurements along three directions are needed.
5. Conclusions Electronic structure of BiCu2VO6 was examined by adopting tight-binding band structure calculation based upon the extended Hückel method. Structurally this compound seems to be a threedimensional material. (BiO2) chains run along the crystallographic c-direction, while CueO chains run along the crystallographic b-direction which is perpendicular to the (BiO2) chains. The (VO4)3 tetrahedra sit between CueO chains and share their corners with the CueO polyhedra and BieO polyhedra along the adirection. The DOS results calculated for BiCu2VO6 show that the contribution to the DOS at the Fermi energy is mostly from the Cu atoms. Therefore CueO chains running along the crystallographic bdirection are proved to be the pathways of electrons for conduction in BiCu2VO6. The band dispersion curve illustrates that the orbitale orbital mixing along the b-direction is stronger than that along the a- and c-direction. The Fermi surface calculated for BiCu2VO6 shows that the Fermi surfaces are open along the a- and c-directions and there are no Fermi surface crossing along those directions. Consequently, the compound is one-dimensional and the electric conductivity is going to arise only along the b-direction. The electronic instability caused by the low dimensionality may be the reason why this compound shows the phase transition at w450 K. Acknowledgment This work was supported by Wonkwang University Research Fund of 2012. References [1] I. Radosavljevic, A.W. Sleight, J. Solid State Chem. 149 (2000) 143. [2] I. Radosavljevic Evans, J.S.O. Evans, J.A.K. Howard, J. Mater. Chem. 12 (2002) 2648. [3] I. Radosavljevic, J.A.K. Howard, A.W. Sleight, Int. J. Inorg. Mater. 2 (2000) 543. [4] E.M. Ketatni, B. Memari, F. Abraham, O. Mentre, J. Solid State Chem. 153 (2000) 48. [5] I. Radosavljevic, J.S.O. Evans, A.W. Sleight, J. Solid State Chem. 141 (1998) 149. [6] I. Radosavljevic Evans, S. Tao, J.T.S. Irvine, J. Solid State Chem. 178 (2005) 2927. [7] T. Masuda, A. Zheludev, H. Kageyama, A.N. Vasilyev, Europhys. Lett. 63 (2003) 757. [8] R. Hoffmann, J. Chem. Phys. 39 (1963) 1397. [9] J.H. Ammeter, H.-B. Bergi, J. Thibeault, R. Hoffmann, J. Am. Chem. Soc. 100 (1978) 3686. [10] J. Ren, W. Liang, M.-H. Whangbo, CAESAR, Primecolor Software Inc., Cary, NC, 1999. [11] C.J. Bradley, A.P. Cracknell, The Mathematical Theory of Symmetry in Solids. Representation Theory for Point Groups and Space Groups, Clarendon Press, Oxford, 1972. [12] R.S. Mulliken, J. Chem. Phys. 23 (1955) 1833. [13] M.-H. Whangbo, J. Chem. Phys. 75 (1981) 4983. [14] M.-H. Whangbo, J. Chem. Phys. 70 (1979) 4963. [15] M.-H. Whangbo, J. Chem. Phys. 73 (1980) 3854. [16] N.F. Mott, R. Peierls, Proc. Phys. Soc. Lond. 49 (4S) (1937) 72. [17] N.F. Mott, Proc. Phys. Soc. Lond. Ser. A 62 (7) (1949) 416.
Contents lists available at SciVerse ScienceDirect
Solid State Sciences journal homepage: www.elsevier.com/locate/ssscie
Electronic structure of one-dimensional bismuth oxide, BiCu2VO6 Sungwoo Cho a, In-Ja Lee b, *, Dongwoon Jung a, * a b
Department of Chemistry, Wonkwang University, Iksan, Jeonbuk 570-749, Republic of Korea Department of Advanced Materials Chemistry, Dongguk University, Gyeongju, Gyeongbuk 780-714, Republic of Korea
a r t i c l e i n f o
a b s t r a c t
Article history: Received 10 November 2012 Received in revised form 30 November 2012 Accepted 6 December 2012 Available online 21 December 2012
Electronic structure of BiCu2VO6 was analyzed by adopting tight-binding band structure calculation based upon the extended Hückel method. Results show the contribution to the DOS at the Fermi energy is mostly from the Cu atoms. Therefore CueO chains running along the crystallographic b-direction are proved to be the pathways of electrons for conduction in BiCu2VO6. The Fermi surface calculated for BiCu2VO6 shows the compound is one-dimensional, so that the electrical conductivity is supposed to arise only along the b-direction. Ó 2012 Elsevier Masson SAS. All rights reserved.
Keywords: Bismuth oxide Phase transition Band calculation Dimensionality
1. Introduction Ternary bismuth oxides having general formula BiA2MO6 (A ¼ divalent metals; Cu, Mg, Zn, Pb: M ¼ pentavalent elements; V, P) have been prepared and their phase transitions to higher symmetry structures have been also reported subsequently [1e4]. One of these compounds, BiCu2VO6, was successfully synthesized in 1998 by Sleight group [5], and recently its structural and electrical properties were reported by Evans et al. [6]. This compound shows interesting magnetic properties that its singlet ground state is non-magnetic and there is a gap in the spin excitation spectrum [7]. According to the electrical resistivity measurement data, it is metallic within the experimental temperature range since the electrical resistivity decreases with decreasing temperature. The structure of BiCu2VO6 is primitive monoclinic with the space group of P21/n at room temperature which is referred to as a-BiCu2VO6. However, this compound shows a phase transition and a-BiCu2VO6 turns out to be b-BiCu2VO6 whose space group is I2/m at higher temperature. Electrical measurement data prove the phase transition that there is a noticeable slope change in conductivity vs. temperature plot at w450 K [6]. Changes in cell parameters of the compound at this temperature also prove the phase transition. So far, the origin of the phase transition in this compound and the physical properties are not fully studied yet. In this paper, we
* Corresponding authors. Tel.: þ82 63 850 6207. E-mail address: [email protected] (D. Jung). 1293-2558/$ e see front matter Ó 2012 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.solidstatesciences.2012.12.007
analyze the reason of the phase transition in a-BiCu2VO6 by examining the structureeproperty relationship. Also, the physical properties found in this compound are discussed. 2. Structure BiA2MO6 (A ¼ divalent metals; Cu, Mg, Zn, Pb: M ¼ pentavalent elements; V, P) show closely related structures that they all contain (BiO2) chains, and (MO4)3 tetrahedra. Besides the (BiO2) chains and (VO4)3 tetrahedra, additional (CuO5) square pyramids and (CuO6) distorted octahedra complete the whole structure in BiCu2VO6. (BiO2) chains run along the crystallographic c-direction as shown in Fig. 1. The distances between Bi and O range from 2.2 to 3.1 A, depending upon the different distinct site of Bi3þ. Cu2þ ions occupy six crystallographically distinct sites in the compound. Four of them construct Cu4O14 cluster whose projection view on ab-plane is shown in Fig. 2. In the cluster, two Cu atoms are fivecoordinated to form distorted square pyramids. These two pyramids share edges to construct Cu2O8 sub-cluster. Another two CuO5 square pyramids in the Cu4O14 cluster share corners and form another Cu2O9 sub-cluster. Two sub-clusters share a corner and an edge to construct final Cu4O14 cluster. Each of the remaining two copper atoms out of six distinct Cu atoms forms a distorted octahedron in which the CueO bond length is between 2.2 and 3.0 A. The distorted CueO octahedra alternatively share an edge and a corner, and finally construct a chain running along the crystallographic b-direction which is perpendicular to the (BiO2) chains, as shown in Fig. 3. Vanadium forms distorted tetrahedra in the
112
S. Cho et al. / Solid State Sciences 17 (2013) 111e114
Fig. 3. A CueO chain running along the b-direction. Distorted CuO6 octahedra form edge and corner sharing alternatively. Fig. 1. A (BiO2) chain running along the c-direction. Large and small circles represent bismuth and oxygen atoms, respectively.
compound with the bond angles ranging from 105 to 113 . The (VO4)3 tetrahedra sit between CueO chains and share their corners with the coppereoxygen polyhedra and BieO polyhedra. 3. Computational method Electronic structure calculations were performed by the extended Huckel method [8] within the framework of tight binding approximation [9]. Density of states (DOS) and crystal orbital overlap populations (COOP) were calculated based on the given crystal structure. The atomic orbital parameters employed in the calculation were the default values in the CAESAR program [10], which are listed in Table 1. The band structures were calculated along the special lines connecting the following high-symmetry points: G (0, 0, 0), X (0.5, 0, 0), Y (0, 0.5, 0), Z (0, 0, 0.5), M (0.5, 0.5, 0) and R (0.5, 0.5, 0.5) in terms of the reciprocal basis vectors [11]. Atomic and bond populations were evaluated via the Mulliken population analysis [12]. Within the Brillouin zone of the cell, 816 irreducible k points were selected. 4. Results and discussion The total density of states (DOS) and the projected density of states (PDOS) for the Cu, Bi, V, and O atoms in a-BiCu2VO6 are shown in Fig. 4. The vertical dashed line represents the Fermi energy of the compound. The solid line represents the total DOS of the compound. The dashed, dotted, dash-dot, and dash-dot-dot line represents the contribution of Cu, O, V, and Bi atoms, respectively. At the Fermi energy, the DOS value for the compound is not zero, which means that a-BiCu2VO6 is metallic. This result is consistent with the experimental data that the conductivity increases with increasing temperature. The conductivity of a-BiCu2VO6 at 450 C is reported to be about 5.5 102 S/m, which is raised up to 100 times at 700 C [6]. These conductivity values are bigger than that of silicon by more than 30 times. Upon the general oxidation scheme of Bi3þ, V5þ, Cu2þ, and O2, BiCu2VO6 cannot be metallic because there is no partially filled band. The PDOS result calculated for Cu, Bi, V, and O atoms provides the clue why this compound is metallic.
At the Fermi energy, the major contribution to DOS comes from Cu atoms, which means that electrons in Cu 3d-orbitals are most important charge carriers. The DOS of Bi p-orbitals contributes totally at 11.8 to 10.6 eV, which is just above the Fermi energy as shown in Fig. 4. The Bi p-orbitals are, therefore, totally empty and the oxidation state of Bi is þ3 as expected. The contribution to DOS from vanadium lies mostly in the region of 10 to 7 eV, which is far above the Fermi energy. Only small portion of contribution below the Fermi level from vanadium can be found at about 15 eV. This means that the d-orbitals of V are almost empty, but small amount of electrons still exist in the d-orbitals. The DOS peak of Cu d-orbitals is cut by the Fermi energy as illustrated in Fig. 4. It is clear from the figure that most of Cu d-orbitals are occupied, but small amount of d-orbitals are still unoccupied. The oxidation state of Cu is, therefore, þ(2 þ x). The small amount of electrons transfer from Cu to V is understandable from the PDOS data of Cu and V. Electron deficiencies in Cu atoms in the sample create the partially filled bands, thereby changing this compound be metallic. Band dispersions calculated for a-BiCu2VO6 are shown in Fig. 5. Only four bands near the Fermi energy are shown in the figure since the electrons in the bands around the Fermi energy are most important for the electrical conductivity. Two bands out of four are cut by the Fermi energy. G, X, Y, M, R, Z represent the wave vector points (0, 0, 0), (a*/2, 0, 0), (0, b*/2, 0), (a*/2, b*/2, 0), (a*/2, b*/2, c*/2), (0, 0, c*/2) in the first Brillouin zone of the reciprocal lattice, respectively. Bands are almost flat along the a-, and c-directions in a-BiCu2VO6 while they are strongly dispersive only along the b-direction. Structural features suggest that a-BiCu2VO6 may be 3-dimensional since BieO, CueO, and VeO polyhedra are repeated along the a-, b-, and c-directions by sharing their edges or corners. Band dispersion of this compound, however, tells us that this compound is 1-dimensional. From the PDOS analysis, the major contribution to the conductivity of this compound comes from Cu atoms. CueO chains act as charge carrier paths by forming strong interactions between copper and oxygen atoms along the b-direction (See Fig. 1). BieO chains running along the c-direction does not contribute to the conductivity in this compound since the DOS value of Bi atoms lie above the Fermi energy. Table 1 Atomic parameters used in EHTB calculationsa: Valence orbital ionization potential Hii (eV) and exponent of the Slater-type orbital z and the orbital coefficient c. Atom
Orbital
Hii (eV)
z1 (c1)
Bi
6s 6p 4s 4p 3d 4s 4p 3d 2s 2p
15.19 7.79 11.4 6.06 14.0 8.81 5.52 11.0 32.299 14.8
2.56 2.072 2.20 2.20 5.95 1.30 1.30 4.75 2.275 2.275
Cu
V
O
Fig. 2. The Cu4O14 cluster. Large and small circles represent copper and oxygen atoms, respectively.
(1.0) (1.0) (1.0) (1.0) (0.5933) (1.0) (1.0) (0.4755) (1.0) (1.0)
z2 (c2)
2.30 (0.5744)
1.70 (0.7052)
a Parameters are collected from the following data: (a) E. Clementi, C. Roetti, Atomic Data Nuclear Data Tables 14 (1974) 177. (b) A.D. McLeen, R.S. McLeen, Atomic Data Nuclear Data Tables 26 (1981) 197. (c) J.W. Richardson, M.J. Blackman, J.E. Ranochak, J. Chem. Phys. 58 (1973) 3010.
S. Cho et al. / Solid State Sciences 17 (2013) 111e114
113
Fig. 4. Density of states calculated for a-BiCu2VO6. The solid line represents the total DOS of the compound. The dashed, dotted, dash-dot, and dash-dot-dot line represents the contribution of Cu, O, V, and Bi atoms, respectively.
The Fermi surface of a partially filled band is defined as the boundary surface of wave vectors that separate the wave vector region of filled band levels from that the wave vector region of unfilled band levels. Since there are two bands cut by the Fermi energy, two Fermi surfaces can be drawn for a-BiCu2VO6 as shown in Fig. 6a and b, respectively. Carriers responsible for electrical properties of metals are those electrons at the Fermi energy. When a certain wave vector direction does not cross a Fermi surface [e.g., G / X and G / Z in Fig. 6], there are no electrons at the Fermi level having momentum along that direction, so that the system is not metallic along that direction. Both Fermi surfaces in Fig. 6a and b are open along the a- and c-directions and there are no Fermi surface crossing along those directions. The dimensionality of a metal is given by the dimensionality of its Fermi surface. The Fermi surface crossing is shown only along the b-direction. Consequently, the Fermi surface of a-BiCu2VO6 is one-dimensional. Essentially two Fermi surfaces given in Fig. 6a and b are, therefore, one-dimensional in nature and conductivity is going to arise only along the b-direction. This is consistent with the structural feature that CueO chains run along the crystallographic b-direction. One piece of a Fermi surface may be superimposable, by translating it with wave vector q, onto another piece of the Fermi surface. In such a case, the two pieces are said to be nested by the wave vector q. A metallic system with a nesting vector q leads to a phase
Fig. 6. The Fermi surface associated with the bands cut by the Fermi energy. The Fermi surface associated with the (a) upper band and (b) the lower band. Fig. 5. The dispersion curves of four bands near the Fermi energy.
114
S. Cho et al. / Solid State Sciences 17 (2013) 111e114
transition. Let us discuss why a Fermi surface nesting is important in introducing a phase transition by investigating the orbital mixing between an occupied and unoccupied levels [13]. For a 1D metal, an occupied wave vector k and an unoccupied wave vector k0 form an occupied orbital F(k) and an unoccupied orbital F(k0 ), respectively. An orbital mixing between F(k) and F(k0 ) produces new orbitals J(k) and J(k0 ),
JðkÞ f FðkÞ þ gFðk0 Þ Jðk0 Þ f gFðkÞ þ Fðk0 Þ where g is a mixing coefficient. The extent of the orbital mixing is determined by the energy difference between the original orbitals F(k) and F(k0 ). At the Fermi level, by definition, two orbitals F(k) and F(k0 ) are degenerate. Therefore, the orbital mixing between them is significant and so is the interaction energy
5. Conclusions Electronic structure of BiCu2VO6 was examined by adopting tight-binding band structure calculation based upon the extended Hückel method. Structurally this compound seems to be a threedimensional material. (BiO2) chains run along the crystallographic c-direction, while CueO chains run along the crystallographic b-direction which is perpendicular to the (BiO2) chains. The (VO4)3 tetrahedra sit between CueO chains and share their corners with the CueO polyhedra and BieO polyhedra along the adirection. The DOS results calculated for BiCu2VO6 show that the contribution to the DOS at the Fermi energy is mostly from the Cu atoms. Therefore CueO chains running along the crystallographic bdirection are proved to be the pathways of electrons for conduction in BiCu2VO6. The band dispersion curve illustrates that the orbitale orbital mixing along the b-direction is stronger than that along the a- and c-direction. The Fermi surface calculated for BiCu2VO6 shows that the Fermi surfaces are open along the a- and c-directions and there are no Fermi surface crossing along those directions. Consequently, the compound is one-dimensional and the electric conductivity is going to arise only along the b-direction. The electronic instability caused by the low dimensionality may be the reason why this compound shows the phase transition at w450 K. Acknowledgment This work was supported by Wonkwang University Research Fund of 2012. References [1] I. Radosavljevic, A.W. Sleight, J. Solid State Chem. 149 (2000) 143. [2] I. Radosavljevic Evans, J.S.O. Evans, J.A.K. Howard, J. Mater. Chem. 12 (2002) 2648. [3] I. Radosavljevic, J.A.K. Howard, A.W. Sleight, Int. J. Inorg. Mater. 2 (2000) 543. [4] E.M. Ketatni, B. Memari, F. Abraham, O. Mentre, J. Solid State Chem. 153 (2000) 48. [5] I. Radosavljevic, J.S.O. Evans, A.W. Sleight, J. Solid State Chem. 141 (1998) 149. [6] I. Radosavljevic Evans, S. Tao, J.T.S. Irvine, J. Solid State Chem. 178 (2005) 2927. [7] T. Masuda, A. Zheludev, H. Kageyama, A.N. Vasilyev, Europhys. Lett. 63 (2003) 757. [8] R. Hoffmann, J. Chem. Phys. 39 (1963) 1397. [9] J.H. Ammeter, H.-B. Bergi, J. Thibeault, R. Hoffmann, J. Am. Chem. Soc. 100 (1978) 3686. [10] J. Ren, W. Liang, M.-H. Whangbo, CAESAR, Primecolor Software Inc., Cary, NC, 1999. [11] C.J. Bradley, A.P. Cracknell, The Mathematical Theory of Symmetry in Solids. Representation Theory for Point Groups and Space Groups, Clarendon Press, Oxford, 1972. [12] R.S. Mulliken, J. Chem. Phys. 23 (1955) 1833. [13] M.-H. Whangbo, J. Chem. Phys. 75 (1981) 4983. [14] M.-H. Whangbo, J. Chem. Phys. 70 (1979) 4963. [15] M.-H. Whangbo, J. Chem. Phys. 73 (1980) 3854. [16] N.F. Mott, R. Peierls, Proc. Phys. Soc. Lond. 49 (4S) (1937) 72. [17] N.F. Mott, Proc. Phys. Soc. Lond. Ser. A 62 (7) (1949) 416.