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Raman spectrum and lattice dynamics of NbTe2
Solid ‘state Communications, Printed in Great Britain.
Vol.
70,
No.
7,
pp.
713-715,
1989.
0038-1098/89$3.00+.00 Pergamon Press plc
RAMANSPECTRUMAND LATTICE DYNAMICS OF NbTe2 Hasan Erdogan* and Roger D. Kirby Behlen Laboratory of Physics University of Nebraska - Lincoln Lincoln, NE 68588 (Received
January
23,
1989 by R.H.
Silsbee)
Raman scattering measurements on the layered-structure compound No evidence for a phase transition is found NbTe2 are reported. for temperatures between 80 K and 420 K. A group-theoretical analysis of the crystal structure predicts 51 optic phonon The observed Raman branches, with 24 of these being Raman-active. spectrum is interpreted in terms of the phonon branches of the much simpler Cd12 structure.
the Raman spectra, and a Spex model 1401 double spectrometer, in conjunction with photon counting electronics, was used to analyze the scattered light. For most measurements, approximately 50 mW of laser light was focussed on the surface of the sample at the pseudoBrewster angle, using a cylindrical lens to produce a line focus and hence reduce local The weak Raman heating by the laser beam. intensities precluded Stokes-antistokes estimates of the local heating, but such measurements on other transition-metal dichalcogenides revealed a local heating of 10 -4OC’ under similar experimental conditions. Raman spectra (resolution 4 cm-l) from an unoriented single crystal of NbTe2 at nominal temperatures of 80 K, 300 K, and 420 K are shown in Fig. 1. For these measurements, the incident laser beam was polarized in the plane of incidence and the scattered beam was unanalyzed to maximize the signal. The low-temperature spectrum shows at least fourteen Raman peaks which shift slightly downward in frequency and broaden as the temperature is increased. While the 420 K spectrum shows little detailed Raman structure, there is no convincing evidence for the occurance of a chargedensity-wave-induced phase transition, as suggested by Wilson et al.’ A number of lattice dynamical models have been applied to the transition-metal dichalcogenides.’ 2-15 In view of the complex crystal structure of NbTes. we will first treat it as if it had the undistorted Cd12 structure. We will then consider the changes in the phonon . dispersion curves brought about by the presence of the distortion. To do this, we use a simple nearest-neighbor force constant model for a single layer of the crystal, as has been discussed by Bromley12 for the 2H-structure transition-metal dichalcogenides and by Duffey and Kirby16 for the lT-structure polytypes. The nearest-neighbor force constant model discussed by Duffey and Kirby has three force constants: a = Nb-Nb force constant, B = Nb-Te force constant, and p = Te-Te force constant within a layer, as illustrated in Fig. 2. The Cd12 crystal structure is described by the D33d space group, and it has four optic phonon
In this paper, we report the results of Raman scattering measurements on the layeredstructure compound NbTe2, and we carry out an analysis of the optic phonons expected. NbTe2 is a member of the transition-metal dichalcogenides, a class of compounds which has been extensively studied because of their propensity towards the formation of charge-density waves.’ ~~~T~~~a~~
~,““,“&~~!??“,“~~
~~~~t~~t~~~:cture
is based upon the Cd12 structure, in which the transition metal atom is surrounded by a nearoctahedral arrangement of chalcogenide atoms.6*7 The presence of the charge-density wave in these materials results in a rather complex distorted Cd12 structure, with atomic displacements from the ideal Cd12 sites on the order of 0.1 A.’ The structural basis for NbTe2 is also the Cd12 structure, but the actual structure is quite distorted, with atomic displacements from the ideal Cd12 structure being as large as 0.5 ~8-10. The most complete structural analysis of NbTe2 has been carried out by Brown, who was able to index the x-ray data accordin to a monoclinic lattice of space units per group C2/m (C 3 2h), with six formula unit cell.lO Wilson et al1 speculated that NbTe2 may be a charge density wave system with a transition temperature above 300 K. This question is still unresolved, but it seems unlikely because of the large size of the distortion. Single crystals of NbTe2 were grown by the vapor phase transport method with iodine as the transporting agent.” The resulting crystals were thin elongated hexagons (typical dimensions 3 x 5 x 0.1 mm31 which could be cleaved using cellophane tape. These crystals were glued to a copper substrate and cleaved immediately prior to mounting in an exchange-gas coupled cryostat. A Spectra Physics argon ion laser operating at 514.5 nm was used to excite
*Permanent Address: Ataturk Universitesi K. Karabekir Egitim Fakultesi Fizik Bolumu Baskani Erzurum, Turkey 713
Vol.
RAMANSPECTRDMAND LATTICE DYNAMICS OF NbTe,
70,
No. 7
L
I
420
I
I
NbTe,
K
branches, which at the Brillouin zone center transform as the A2u, Eu, Alg and Eg irreducible representations of the D3d point group. The zone-center frequencies calculated from the lattice dynamical model of Duffey and Kirby are given by:
w2(Alg)= 2 c
I87 + 1 $
w2(A2J
= 2 R
where I$i is the metal mass, MC is the chalcogen mass, and MR is the reduced mass given by MR = ~MCMM/(MM+ 2MC). Note that the A2u frequency is higher than the E, frequency by the factor J1.5. and that the zone-center frequencies are independent of the force constant a. In the case of NbTe2, the chalcogen mass is about twice the reduced mass, so we expect the oddparity (u) modes to be higher in frequency than Choosing the same the even-parity (g) modes. values of the force constants used by Duffey and Kirby for TaS2 (S = 9.7 x lo4 dyne/cm and u = 3.5 x lo4 dyne/cm) leads to the “undistorted” NbTe2 optical model frequencies:
FREQUENCY Fig.
1
240
160
80
cc m-l)
Raman spectrum of NbTe2 for three different temperatures. The incident laser beam was polarized in the plane of and the scattered light was incidence, No corrections to the unanalyzed. sample temperatures have been made for local heating by the incident laser beam.
4
0
0
a!
0
Fig.
2
P
c)
0
@
METAL
0
CHALCOGEN
Force constants used to lattice dynamics of the tur e compounds.
calculate the layered-struc-
m(Alg)
= 193 cm-’
w(A~~)
-1 = 249 cm
w(Eg)
= 120 cm-’
w(EU)
-1 = 203 cm
Note that the A2u and Eu mode frequencies fall quite close to the two highest frequency peaks observed in NbTe2. (See the 300 K spectrum in Fig. 1). we wish to make the connecAt this point, tion between the undistorted Cd12 phonon frequencies discussed above and the actual phonon The CdI2-structure phofrequencies in NbTe2. non dispersion curves are shown schematically in Fig. 3 for a general direction in k-space. There are three acoustic phonon branches and six, relatively dispersionless, optic branches. Adopting the crystal structure for NbTe2 proposed by Brown,l o we see that two of the Nb atoms in the unit cell are at sites of symmetry 2/m, while the other four are at sites of symmetry m. All twelve Te atoms are at sites of symmetry m. Using the methods described by Fately et al, ‘7 we have carried out a correlation analysis of this structure, and we find that there are 51 optic phonon branches, which at the Brillouin zone center transform as the 16Ag + 8Bg + 18B, + 9A, irreducible representations of the C2h point group. The Ag and Bg phonons are Raman-active, so that in principle 24 Raman peaks could be observed in the spectrum. Referring back to Fig. 3, when the NbTe2 type distortion is introduced. all nine phonon branches are “folded” to create five new zonecenter phonons for each branch, resulting in the 51 optic phonon branches predicted by group For each branch of the dispersion theory. curves of Fig. 3, one or more Raman-active To the extent that the phonons are predicted. distortions from the Cd12 structure are small
70,
ho.
7
RAMAN SPECTRUMAND LATTICE DYNAMICS OF NbTe,
L
k Fig.
3
A schematic representation of the phonon dispersion curves in a IT-structure The transition-metal dichalcogenide. optical phonon branches will typically have more dispersion than is indicated here.
and to the extent that the optic phonon branches of Fig. 2 are dispersionless, these “distortion-created” k = 0 optic phonons will tend to fall in groups, depending on the sdistorted phonon branch of their origin.
In view of the above discussion, we propose at low that the 255 cm-’ Raman peak (a doublet temperature) arises from the undistorted-crystal A2u branch, and the 220 cm-’ peak arises These two from the undistorted E, branch. assignments seem quite certain because the odd-parity modes are expected to be higher in frequency than the even parity modes. The magnitude of the force constant B has to be increased from its TaS2 value to -1 .I x 105 dyne/cm to give the approximately correct frequencies. There is quite a large gap in the observed phonon frequencies between 175 and 220 cm-l. This suggests that the (undistorted) Alg branch lies lower than predicted by the lattice dynamical model with TaS2 force constants, with This it most likely falling near 160 cm-l. frequency for the Alg branch requires that the force constant u be reduced to -1.2 x lo4 The several Raman peaks near 160 cm-l dyne/cm. then would arise from the folded Alg branch. The above values of f? and u then give the Eg branch frequency as 116 cm-l, with the several Raman peaks in this region arising from the folded E -branch phonons. The remaining Raman peaks be Bow about 100 cm-l must then arise from the zone-folded acoustic phonon branches of there seems to be at Fig. 3. In this picture, most only a small gap between the acoustic and optic phonon branches. In summary, we have presented a plausible picture for the origins of the Raman spectrum of NbTe2. One should treat the details of this analysis with some caution because of the simplicity of the lattice dynamical model, but it would seem to offer a useful starting point for a more realistic calculation of the lattice dynamics of NbTe2. Acknowledgement - We wish to thank S.S. Jaswal and E.A. Pearlstein for helpful comments on the manuscript.
REFERENCES 1. 2. 3. 4. 5.
6. 7. a.
J.A. Wilson, F.J. DiSalvo, and S. Mahajan, Adv. Physics 2, 117 (1975). D.E. Moncton, J.D. Axe, and F.J. DiSalvo, Phys. Rev. Letters 2, 734 (1975). C.B. Scruby, P.M. Williams, and G.S. Parry, Phil. Mag. 3l_, 255 (1975). J.R. Duffey, R.D. Kirby, and R.V. Coleman, Solid State Commun. 2, 617 (1976). D.E. Moncton. F.J. DiSalvo. J.D. Axe. L.J. Sham, and B.R. Patton, Phys. Rev. B _, 3432 (1976). J.A. Wilson and A.D. Yoffe, Adv. Physics ‘8, 193 (1969). F.J. DiSalvo, Surface Science 5&, 297 (1976). E. Revolinsky, B.E. Brown, D.J. Beerntsen, and C.H. Armitage, J. Less Common Metals 8, 63 (1965).
9. 10. 11.
12. 13. 14. 15. 16. 17.
K. Selte, E. Bjerklund, and A. Kjekshus, J. Less Common Metals ll_, 14 (1966). B.E. Brown, Acta Cryst. 20, 264 (1966). F. Levy, 11 Nuovo Cimento 388, 359 (1977). R.A. Bromley, Phil. Mag. 2, 1417 (1971). H. Wakabayashi, H.G. Smith, K.C. Woo, and F.C. Brown, Solid State Commun. 2, 923 (1978). S.S. Jaswal, Phys. Rev. B 20, 5297 (1979). J.L. Feldman, Phys. Rev. B 2, 7132 (1982). J.R. Duffey and R.D. Kirby, Phys. Rev. B 2, 1534 (1981). W.G. Fateley, F.R. Dollish, N.T. McDevitt, and F.F. Bentley, in Infrared and Raman Selection Rules for Molecular and Lattice Vibrations: The Correlation Method, (Wiley-Interscience, New York), 1972.
715
Vol.
70,
No.
7,
pp.
713-715,
1989.
0038-1098/89$3.00+.00 Pergamon Press plc
RAMANSPECTRUMAND LATTICE DYNAMICS OF NbTe2 Hasan Erdogan* and Roger D. Kirby Behlen Laboratory of Physics University of Nebraska - Lincoln Lincoln, NE 68588 (Received
January
23,
1989 by R.H.
Silsbee)
Raman scattering measurements on the layered-structure compound No evidence for a phase transition is found NbTe2 are reported. for temperatures between 80 K and 420 K. A group-theoretical analysis of the crystal structure predicts 51 optic phonon The observed Raman branches, with 24 of these being Raman-active. spectrum is interpreted in terms of the phonon branches of the much simpler Cd12 structure.
the Raman spectra, and a Spex model 1401 double spectrometer, in conjunction with photon counting electronics, was used to analyze the scattered light. For most measurements, approximately 50 mW of laser light was focussed on the surface of the sample at the pseudoBrewster angle, using a cylindrical lens to produce a line focus and hence reduce local The weak Raman heating by the laser beam. intensities precluded Stokes-antistokes estimates of the local heating, but such measurements on other transition-metal dichalcogenides revealed a local heating of 10 -4OC’ under similar experimental conditions. Raman spectra (resolution 4 cm-l) from an unoriented single crystal of NbTe2 at nominal temperatures of 80 K, 300 K, and 420 K are shown in Fig. 1. For these measurements, the incident laser beam was polarized in the plane of incidence and the scattered beam was unanalyzed to maximize the signal. The low-temperature spectrum shows at least fourteen Raman peaks which shift slightly downward in frequency and broaden as the temperature is increased. While the 420 K spectrum shows little detailed Raman structure, there is no convincing evidence for the occurance of a chargedensity-wave-induced phase transition, as suggested by Wilson et al.’ A number of lattice dynamical models have been applied to the transition-metal dichalcogenides.’ 2-15 In view of the complex crystal structure of NbTes. we will first treat it as if it had the undistorted Cd12 structure. We will then consider the changes in the phonon . dispersion curves brought about by the presence of the distortion. To do this, we use a simple nearest-neighbor force constant model for a single layer of the crystal, as has been discussed by Bromley12 for the 2H-structure transition-metal dichalcogenides and by Duffey and Kirby16 for the lT-structure polytypes. The nearest-neighbor force constant model discussed by Duffey and Kirby has three force constants: a = Nb-Nb force constant, B = Nb-Te force constant, and p = Te-Te force constant within a layer, as illustrated in Fig. 2. The Cd12 crystal structure is described by the D33d space group, and it has four optic phonon
In this paper, we report the results of Raman scattering measurements on the layeredstructure compound NbTe2, and we carry out an analysis of the optic phonons expected. NbTe2 is a member of the transition-metal dichalcogenides, a class of compounds which has been extensively studied because of their propensity towards the formation of charge-density waves.’ ~~~T~~~a~~
~,““,“&~~!??“,“~~
~~~~t~~t~~~:cture
is based upon the Cd12 structure, in which the transition metal atom is surrounded by a nearoctahedral arrangement of chalcogenide atoms.6*7 The presence of the charge-density wave in these materials results in a rather complex distorted Cd12 structure, with atomic displacements from the ideal Cd12 sites on the order of 0.1 A.’ The structural basis for NbTe2 is also the Cd12 structure, but the actual structure is quite distorted, with atomic displacements from the ideal Cd12 structure being as large as 0.5 ~8-10. The most complete structural analysis of NbTe2 has been carried out by Brown, who was able to index the x-ray data accordin to a monoclinic lattice of space units per group C2/m (C 3 2h), with six formula unit cell.lO Wilson et al1 speculated that NbTe2 may be a charge density wave system with a transition temperature above 300 K. This question is still unresolved, but it seems unlikely because of the large size of the distortion. Single crystals of NbTe2 were grown by the vapor phase transport method with iodine as the transporting agent.” The resulting crystals were thin elongated hexagons (typical dimensions 3 x 5 x 0.1 mm31 which could be cleaved using cellophane tape. These crystals were glued to a copper substrate and cleaved immediately prior to mounting in an exchange-gas coupled cryostat. A Spectra Physics argon ion laser operating at 514.5 nm was used to excite
*Permanent Address: Ataturk Universitesi K. Karabekir Egitim Fakultesi Fizik Bolumu Baskani Erzurum, Turkey 713
Vol.
RAMANSPECTRDMAND LATTICE DYNAMICS OF NbTe,
70,
No. 7
L
I
420
I
I
NbTe,
K
branches, which at the Brillouin zone center transform as the A2u, Eu, Alg and Eg irreducible representations of the D3d point group. The zone-center frequencies calculated from the lattice dynamical model of Duffey and Kirby are given by:
w2(Alg)= 2 c
I87 + 1 $
w2(A2J
= 2 R
where I$i is the metal mass, MC is the chalcogen mass, and MR is the reduced mass given by MR = ~MCMM/(MM+ 2MC). Note that the A2u frequency is higher than the E, frequency by the factor J1.5. and that the zone-center frequencies are independent of the force constant a. In the case of NbTe2, the chalcogen mass is about twice the reduced mass, so we expect the oddparity (u) modes to be higher in frequency than Choosing the same the even-parity (g) modes. values of the force constants used by Duffey and Kirby for TaS2 (S = 9.7 x lo4 dyne/cm and u = 3.5 x lo4 dyne/cm) leads to the “undistorted” NbTe2 optical model frequencies:
FREQUENCY Fig.
1
240
160
80
cc m-l)
Raman spectrum of NbTe2 for three different temperatures. The incident laser beam was polarized in the plane of and the scattered light was incidence, No corrections to the unanalyzed. sample temperatures have been made for local heating by the incident laser beam.
4
0
0
a!
0
Fig.
2
P
c)
0
@
METAL
0
CHALCOGEN
Force constants used to lattice dynamics of the tur e compounds.
calculate the layered-struc-
m(Alg)
= 193 cm-’
w(A~~)
-1 = 249 cm
w(Eg)
= 120 cm-’
w(EU)
-1 = 203 cm
Note that the A2u and Eu mode frequencies fall quite close to the two highest frequency peaks observed in NbTe2. (See the 300 K spectrum in Fig. 1). we wish to make the connecAt this point, tion between the undistorted Cd12 phonon frequencies discussed above and the actual phonon The CdI2-structure phofrequencies in NbTe2. non dispersion curves are shown schematically in Fig. 3 for a general direction in k-space. There are three acoustic phonon branches and six, relatively dispersionless, optic branches. Adopting the crystal structure for NbTe2 proposed by Brown,l o we see that two of the Nb atoms in the unit cell are at sites of symmetry 2/m, while the other four are at sites of symmetry m. All twelve Te atoms are at sites of symmetry m. Using the methods described by Fately et al, ‘7 we have carried out a correlation analysis of this structure, and we find that there are 51 optic phonon branches, which at the Brillouin zone center transform as the 16Ag + 8Bg + 18B, + 9A, irreducible representations of the C2h point group. The Ag and Bg phonons are Raman-active, so that in principle 24 Raman peaks could be observed in the spectrum. Referring back to Fig. 3, when the NbTe2 type distortion is introduced. all nine phonon branches are “folded” to create five new zonecenter phonons for each branch, resulting in the 51 optic phonon branches predicted by group For each branch of the dispersion theory. curves of Fig. 3, one or more Raman-active To the extent that the phonons are predicted. distortions from the Cd12 structure are small
70,
ho.
7
RAMAN SPECTRUMAND LATTICE DYNAMICS OF NbTe,
L
k Fig.
3
A schematic representation of the phonon dispersion curves in a IT-structure The transition-metal dichalcogenide. optical phonon branches will typically have more dispersion than is indicated here.
and to the extent that the optic phonon branches of Fig. 2 are dispersionless, these “distortion-created” k = 0 optic phonons will tend to fall in groups, depending on the sdistorted phonon branch of their origin.
In view of the above discussion, we propose at low that the 255 cm-’ Raman peak (a doublet temperature) arises from the undistorted-crystal A2u branch, and the 220 cm-’ peak arises These two from the undistorted E, branch. assignments seem quite certain because the odd-parity modes are expected to be higher in frequency than the even parity modes. The magnitude of the force constant B has to be increased from its TaS2 value to -1 .I x 105 dyne/cm to give the approximately correct frequencies. There is quite a large gap in the observed phonon frequencies between 175 and 220 cm-l. This suggests that the (undistorted) Alg branch lies lower than predicted by the lattice dynamical model with TaS2 force constants, with This it most likely falling near 160 cm-l. frequency for the Alg branch requires that the force constant u be reduced to -1.2 x lo4 The several Raman peaks near 160 cm-l dyne/cm. then would arise from the folded Alg branch. The above values of f? and u then give the Eg branch frequency as 116 cm-l, with the several Raman peaks in this region arising from the folded E -branch phonons. The remaining Raman peaks be Bow about 100 cm-l must then arise from the zone-folded acoustic phonon branches of there seems to be at Fig. 3. In this picture, most only a small gap between the acoustic and optic phonon branches. In summary, we have presented a plausible picture for the origins of the Raman spectrum of NbTe2. One should treat the details of this analysis with some caution because of the simplicity of the lattice dynamical model, but it would seem to offer a useful starting point for a more realistic calculation of the lattice dynamics of NbTe2. Acknowledgement - We wish to thank S.S. Jaswal and E.A. Pearlstein for helpful comments on the manuscript.
REFERENCES 1. 2. 3. 4. 5.
6. 7. a.
J.A. Wilson, F.J. DiSalvo, and S. Mahajan, Adv. Physics 2, 117 (1975). D.E. Moncton, J.D. Axe, and F.J. DiSalvo, Phys. Rev. Letters 2, 734 (1975). C.B. Scruby, P.M. Williams, and G.S. Parry, Phil. Mag. 3l_, 255 (1975). J.R. Duffey, R.D. Kirby, and R.V. Coleman, Solid State Commun. 2, 617 (1976). D.E. Moncton. F.J. DiSalvo. J.D. Axe. L.J. Sham, and B.R. Patton, Phys. Rev. B _, 3432 (1976). J.A. Wilson and A.D. Yoffe, Adv. Physics ‘8, 193 (1969). F.J. DiSalvo, Surface Science 5&, 297 (1976). E. Revolinsky, B.E. Brown, D.J. Beerntsen, and C.H. Armitage, J. Less Common Metals 8, 63 (1965).
9. 10. 11.
12. 13. 14. 15. 16. 17.
K. Selte, E. Bjerklund, and A. Kjekshus, J. Less Common Metals ll_, 14 (1966). B.E. Brown, Acta Cryst. 20, 264 (1966). F. Levy, 11 Nuovo Cimento 388, 359 (1977). R.A. Bromley, Phil. Mag. 2, 1417 (1971). H. Wakabayashi, H.G. Smith, K.C. Woo, and F.C. Brown, Solid State Commun. 2, 923 (1978). S.S. Jaswal, Phys. Rev. B 20, 5297 (1979). J.L. Feldman, Phys. Rev. B 2, 7132 (1982). J.R. Duffey and R.D. Kirby, Phys. Rev. B 2, 1534 (1981). W.G. Fateley, F.R. Dollish, N.T. McDevitt, and F.F. Bentley, in Infrared and Raman Selection Rules for Molecular and Lattice Vibrations: The Correlation Method, (Wiley-Interscience, New York), 1972.
715