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Chemical bonding and the dimensionality of NbSe3
Solid State Communications Vol. 26, pp. 563-565. © Pergamon Press Ltd. 1978. Printed in Great Britain
0038-1098/78/0601-0563502.00/0
CHEMICAL BONDING AND THE DIMENSIONALIT¥ OF NbSe 3 * D.W. Bullett Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, England (Received 3 January 1978 by C.W. McCombie) The electron energy band structure of NbSeq is presented for a single one-dimensional prismatic chain and for a Two-dimensional layer. In the former case the Fermi level falls in the middle of an isolated band. Interchain bonds in the 2-D crystal lead to semimetallic behaviour and a strong pressure dependence of n(EF).
The triselenide of niobium has recently been synthesised by Meerschaut and Rouxel I and displays many properties characteristic of systems of reduced dimensionality. The structure is very anisotropic. The crystals have a fibrous appearance and the microwave conductivity along the strands exceeds the transverse conductivity by a factor of between 350 and 1200 2 The crystal structure is made up of infinite chains of trigonal prisms extending parallel to the b-axis of the monoclinic cell and Li atoms may be intercalated between the chains without appreciable modification of the chairs themselves 3. The electrical resistivity along the chains shows phase transitions,at 145 and 59K, which can be interpreted in terms of charge density wave formation4, 5. These are all typical properties of one-dimensional materials and presented here are the results of an investigation to see to what extent the electronic structure of NbSe 3 is truly one-dimensional.
N ~il
- 10jf
S-! jf,k ~ ~k~,l
V!j I @il> = E i l ~ i l
where the.L 1 - s u f f i c e s d e n o t e a n g u l a r momentum number, Vj r e p r e s e n t s the p e r t u r b a t i o n f o r t h e o r b i t a l c e n t r e d on atom i due t o the p r e s e n c e of the atom a t j and t h e summation e x t e n d s over a l l v a l e n c e o r b i t a l s on s i t e s i and j . No t h r e e - c e n t r e terms were i n c l u d e d . A l l m a t r i x e l e m e n t s were r e t a i n e d f o r atomic s e p a r a t i o n s up to 4.5 ~. C r y s t a l e i g e n v a l u e s were t h e n calculated by setting up and diagonalising the non-hermitian secular determinant 6. Figure 2 illustrates the electron band structure and density of states n(E) calculated for an isolated chain taken from the structure as well as n(E) for an infinite layer of chains in the b-c plane. Because of the very large size of the unit cell (108 valence and conduction orbitals) a full 3-D calculation was not attempted.
The structure of NbSe31 is illustrated in Figure !. Each metal atom sits at the centre of a right triangular prism of Se atoms. Two of the Se atoms in the base of each prism are directly bonded together at a distance comparable to that in pure Se (2.30~). Successive NbSe 6 prisms stack linearly along the b-axis to form an infinite chain. Six prisms form the monoclinic unit cell whichomeasures 10.006x 3.478 x 15.626 ~ (~ =I09.3 ). The separation between Nb atoms is 3.48 ~ along the b-axis and 4.25-4.45 ~ in the a-c plane. Each Nb atom has two Se neighbours in adjacent chains at distances scarcely greater than those to its six intrachain ligands.
Differences between the I-D and 2-D pictures are quite marked. In the I-D case the Fermi level falls in the middle of an isolated band which does not overlap other bands, a situation ripe for a Peierls' distortion into an insulating state. No such isolated band occurs in the 2-D layer. Instead the chains stabilise themselves by creating a semimetal, with the Fermi level falling exactly in the middle of a valley separating bonding from antibonding states. Such a low density of states at the Fermi surface has already been deduced from the very small electronic contribution ST to the specific heat at low temperatures 3 (~ ~ 5 x I 0 - 4 J kg -I K-2).
The electronic structure of the crystal was calculated by a non-empirical localized orbital method similar to that applied elsewhere 6. Orbitals computed for isolated atoms in the Hartree-Fock-Slater approximation were used to represent solutions to the localized orbital pseudopotential equations
I have not attempted a detailed analysis of the Fermi surface since more than one band appears to be involved and interlayer effects are likely to be non-negligible. However, it is clear that while CDW distortions are to be expected in this system, they are unlikely to destroy the Fermi surface completely. In this
*
SRC Advanced Research Fellow
563
564
CHEMICAL BONDING AND THE DIMENSIONALITY OF NbSe 3
Vol. 26, No. 9
2-D
I
T c
x
0
Nb
O
se
E o
~
T
3
x
Se
>
S -bonds
Se I p-bonds
Nb d
!' i
2
I-D 0 U~
J ,
I
0~ O,
r
kb
Figure
].
Structure of NbSe 3 projected on the a-c plane and the arrangement of triangular prisms along the b-axis (after Ref. I). Open circles: atoms at 0, I; filled circles: atoms at ± ~.
sense the material is not one-dimensional and will continue to behave as a metal at temperatures below the resistive anomalies 4,5. Also, the density of states at the Fermi energy n(EF) must depend very sensitively on the distance between the layers in the crystal. Any increase in pressure inevitably reduces this distance and may also strengthen some of the interchain bonds within a layer, thus tending to wash out the semimetallic valley and increase n(E F) (as well as suppressing the CDW phase transitions) by increasing the effective dimenslonality of the system. Such a band structure effect was proposed by Monceau et al. 2 to explain the strong pressure dependence of the superconducting transition temperature T c. The main features of Figure 2 have a simple interpretation in terms of chemical bond formation. Two of the three Se atoms in the base of each triangular prism are strongly bonded together. This is why in the Se s-band for the I-D chain we see three peaks: a bonding peak at -19eV and an antibonding peak at ~17eV separated by a non-bonding band. The next higher states may be loosely
~/b
,1,\
-20
Figure 2.
..,41k,.l.II
, ,
-15
-I0 eV
-5
Electron band structure and density of states for a single NbSe 3 chain and the density of states for a two-dimensional layer of NbSe 3.
labelled as either Se p-states or Nb d-states as in Figure 2.(The Nb siband lies even higher in energy after strong hybridisation with the chalcogen orbitals.) Of course, these states are not purely p- or d-like, but because the atomic Se p-level lies much lower in energy than the Nb d-level (Table I) the more strongly bound states are predominantly on the chalcogens. Split off Table I. Atomic levels used in the band calculations (eV). Nb E Es
-4.0
Se
-17.8 -7.4
50 from this lower group for the I-D chain and centred at -4.3 eV is a band derived from the antibonding p-orbitals of the closely spaced Se neighbours. The available electrons half fill this band. In the 2-D layer the fibres arrange themselves so that, as far as is compatible with other competing bonding considerations, a gap opens up in the middle of this Se-Se antibonding p-band.
Vol. 26, No. 9
CHEMICAL BONDING AND THE DIMENSIONALITY OF NbSe 3
REFERENCES
I. 2. 3. 4. 5. 6.
MEERSCHAUT A. and ROUXEL J., Journal of Less-Common Metals 39, 197 (1975). MONCEAU P., PEYRARD J.,RICHARD J. and MOLINIE P., Physical Review Letters 39, 161 (1977). MOLINIE P., MEERSCHAUT A., ROUXEL J., MONCEAU P. and HAEN P., Nouveau Journal de Chimie i, 205(1977). CHAUSSY J., HAEN p., LASJAUNIAS J.C., MONCEAU P. ,WAYSAND G. , WAINTAL A., MEERSCHAUT A., MOLINIE P. and ROUXEL J., Solid State Con~nunications 20, 759 (1976). MONCEAU P., ONG N.P., PORTIS A.M., MEERSCHAUT A. and ROUXEL J. , Physical Review Letters 37, 602 (1976). BDI.LETT D.W., Physical Review Letters 39, 664 (1977); Journal of Physics C IO, 2083 (1977).
565
0038-1098/78/0601-0563502.00/0
CHEMICAL BONDING AND THE DIMENSIONALIT¥ OF NbSe 3 * D.W. Bullett Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, England (Received 3 January 1978 by C.W. McCombie) The electron energy band structure of NbSeq is presented for a single one-dimensional prismatic chain and for a Two-dimensional layer. In the former case the Fermi level falls in the middle of an isolated band. Interchain bonds in the 2-D crystal lead to semimetallic behaviour and a strong pressure dependence of n(EF).
The triselenide of niobium has recently been synthesised by Meerschaut and Rouxel I and displays many properties characteristic of systems of reduced dimensionality. The structure is very anisotropic. The crystals have a fibrous appearance and the microwave conductivity along the strands exceeds the transverse conductivity by a factor of between 350 and 1200 2 The crystal structure is made up of infinite chains of trigonal prisms extending parallel to the b-axis of the monoclinic cell and Li atoms may be intercalated between the chains without appreciable modification of the chairs themselves 3. The electrical resistivity along the chains shows phase transitions,at 145 and 59K, which can be interpreted in terms of charge density wave formation4, 5. These are all typical properties of one-dimensional materials and presented here are the results of an investigation to see to what extent the electronic structure of NbSe 3 is truly one-dimensional.
N ~il
- 10jf
S-! jf,k ~ ~k~,l
V!j I @il> = E i l ~ i l
where the.L 1 - s u f f i c e s d e n o t e a n g u l a r momentum number, Vj r e p r e s e n t s the p e r t u r b a t i o n f o r t h e o r b i t a l c e n t r e d on atom i due t o the p r e s e n c e of the atom a t j and t h e summation e x t e n d s over a l l v a l e n c e o r b i t a l s on s i t e s i and j . No t h r e e - c e n t r e terms were i n c l u d e d . A l l m a t r i x e l e m e n t s were r e t a i n e d f o r atomic s e p a r a t i o n s up to 4.5 ~. C r y s t a l e i g e n v a l u e s were t h e n calculated by setting up and diagonalising the non-hermitian secular determinant 6. Figure 2 illustrates the electron band structure and density of states n(E) calculated for an isolated chain taken from the structure as well as n(E) for an infinite layer of chains in the b-c plane. Because of the very large size of the unit cell (108 valence and conduction orbitals) a full 3-D calculation was not attempted.
The structure of NbSe31 is illustrated in Figure !. Each metal atom sits at the centre of a right triangular prism of Se atoms. Two of the Se atoms in the base of each prism are directly bonded together at a distance comparable to that in pure Se (2.30~). Successive NbSe 6 prisms stack linearly along the b-axis to form an infinite chain. Six prisms form the monoclinic unit cell whichomeasures 10.006x 3.478 x 15.626 ~ (~ =I09.3 ). The separation between Nb atoms is 3.48 ~ along the b-axis and 4.25-4.45 ~ in the a-c plane. Each Nb atom has two Se neighbours in adjacent chains at distances scarcely greater than those to its six intrachain ligands.
Differences between the I-D and 2-D pictures are quite marked. In the I-D case the Fermi level falls in the middle of an isolated band which does not overlap other bands, a situation ripe for a Peierls' distortion into an insulating state. No such isolated band occurs in the 2-D layer. Instead the chains stabilise themselves by creating a semimetal, with the Fermi level falling exactly in the middle of a valley separating bonding from antibonding states. Such a low density of states at the Fermi surface has already been deduced from the very small electronic contribution ST to the specific heat at low temperatures 3 (~ ~ 5 x I 0 - 4 J kg -I K-2).
The electronic structure of the crystal was calculated by a non-empirical localized orbital method similar to that applied elsewhere 6. Orbitals computed for isolated atoms in the Hartree-Fock-Slater approximation were used to represent solutions to the localized orbital pseudopotential equations
I have not attempted a detailed analysis of the Fermi surface since more than one band appears to be involved and interlayer effects are likely to be non-negligible. However, it is clear that while CDW distortions are to be expected in this system, they are unlikely to destroy the Fermi surface completely. In this
*
SRC Advanced Research Fellow
563
564
CHEMICAL BONDING AND THE DIMENSIONALITY OF NbSe 3
Vol. 26, No. 9
2-D
I
T c
x
0
Nb
O
se
E o
~
T
3
x
Se
>
S -bonds
Se I p-bonds
Nb d
!' i
2
I-D 0 U~
J ,
I
0~ O,
r
kb
Figure
].
Structure of NbSe 3 projected on the a-c plane and the arrangement of triangular prisms along the b-axis (after Ref. I). Open circles: atoms at 0, I; filled circles: atoms at ± ~.
sense the material is not one-dimensional and will continue to behave as a metal at temperatures below the resistive anomalies 4,5. Also, the density of states at the Fermi energy n(EF) must depend very sensitively on the distance between the layers in the crystal. Any increase in pressure inevitably reduces this distance and may also strengthen some of the interchain bonds within a layer, thus tending to wash out the semimetallic valley and increase n(E F) (as well as suppressing the CDW phase transitions) by increasing the effective dimenslonality of the system. Such a band structure effect was proposed by Monceau et al. 2 to explain the strong pressure dependence of the superconducting transition temperature T c. The main features of Figure 2 have a simple interpretation in terms of chemical bond formation. Two of the three Se atoms in the base of each triangular prism are strongly bonded together. This is why in the Se s-band for the I-D chain we see three peaks: a bonding peak at -19eV and an antibonding peak at ~17eV separated by a non-bonding band. The next higher states may be loosely
~/b
,1,\
-20
Figure 2.
..,41k,.l.II
, ,
-15
-I0 eV
-5
Electron band structure and density of states for a single NbSe 3 chain and the density of states for a two-dimensional layer of NbSe 3.
labelled as either Se p-states or Nb d-states as in Figure 2.(The Nb siband lies even higher in energy after strong hybridisation with the chalcogen orbitals.) Of course, these states are not purely p- or d-like, but because the atomic Se p-level lies much lower in energy than the Nb d-level (Table I) the more strongly bound states are predominantly on the chalcogens. Split off Table I. Atomic levels used in the band calculations (eV). Nb E Es
-4.0
Se
-17.8 -7.4
50 from this lower group for the I-D chain and centred at -4.3 eV is a band derived from the antibonding p-orbitals of the closely spaced Se neighbours. The available electrons half fill this band. In the 2-D layer the fibres arrange themselves so that, as far as is compatible with other competing bonding considerations, a gap opens up in the middle of this Se-Se antibonding p-band.
Vol. 26, No. 9
CHEMICAL BONDING AND THE DIMENSIONALITY OF NbSe 3
REFERENCES
I. 2. 3. 4. 5. 6.
MEERSCHAUT A. and ROUXEL J., Journal of Less-Common Metals 39, 197 (1975). MONCEAU P., PEYRARD J.,RICHARD J. and MOLINIE P., Physical Review Letters 39, 161 (1977). MOLINIE P., MEERSCHAUT A., ROUXEL J., MONCEAU P. and HAEN P., Nouveau Journal de Chimie i, 205(1977). CHAUSSY J., HAEN p., LASJAUNIAS J.C., MONCEAU P. ,WAYSAND G. , WAINTAL A., MEERSCHAUT A., MOLINIE P. and ROUXEL J., Solid State Con~nunications 20, 759 (1976). MONCEAU P., ONG N.P., PORTIS A.M., MEERSCHAUT A. and ROUXEL J. , Physical Review Letters 37, 602 (1976). BDI.LETT D.W., Physical Review Letters 39, 664 (1977); Journal of Physics C IO, 2083 (1977).
565