Raman scattering from 2H and 3R–NbS2

0038-1098/83/070557-04503.00/0 Pergamon Press Ltd.

Solid State Communications, Vol. 45, No. 7, pp. 557-560, 1983. Printed in Great Britain.

RAMAN SCATTERING FROM 2H AND 3R-NbS2 W.G. McMullan and J.C. Irwin Physics Department, Simon Fraser University, Burnaby, BC V5A 1$6, Canada

(Received 23 September 1982 by R. Barrie)

Raman scattering experiments have been carried out on 2H-NbS2 crystals and 3R-NbS2 crystals. The spectra obtained from both compounds have been found to contain all the Raman active modes predicted by group theory. A nearest-neighbour lattice dynamics model has also been used to analyze the spectra and qualitative agreement with the experimental results is obtained. The results are also discussed in terms of the modifications expected in the Raman spectra obtained from different polytypes of the same layered compound. Some discrepancies with previously reported results are found.

1. INTRODUCTION NIOBIUM DISULPHIDE is a member of the large group of layered structure compounds in which the interaction between the individual layers is much weaker than the intralayer bonding [1 ]. These compounds have many interesting physical properties that in many cases arise from their quasi-two-dimensional structure [I]. In particular, the long wavelength phonons have been the subject of a number of investigations (see, for example, [2] and references therein) over the past several years that have provided a great deal of information on the structure and physical properties of the layered compounds. Although NbS2 is often designated as one of the prototypical structures [1] of the layered dichalcogenides it has been the subject of relatively few studies. For example, the only study of the vibrational modes of NbS2 known to the authors is a Raman scattering investigation of 3R-NbS2 [3, 16]. Presumably, this lack of interest results from the difficulties involved in growing NbS2 crystals with a well defined structure, particularly the 2H-polytype. However, Fisher and Sienko [4] have recently reported a technique for obtaining the desired polytype. They found that the 3R-structure prevailed in crystals of Nb~ +xS2 when x ~> 0.07 and that the 2H-polytype could be obtained by quenching crystals from 750°C after they had been annealed at this temperature in an excess sulfur atmosphere with sulphur pressures greater than 6 arm. The resulting 2H-NbS2 crystals were found to be stoichiometric but to have quite broad X-ray diffraction spots, in contrast to the non-stoichiometric 3R-crystals which provided quite sharp X-ray diffraction spots. The structural information provided by the work of Fisher and Sienko [3] now enables one to obtain samples of a known structure and thus provides a basis 557

for understanding the results of experiments carried out on these samples. This paper reports on the results of Raman scattering experiments carried out on both 3R-NbS2 and 2H-NbS2 crystals. The results obtained from the 3Rpolytype are compared with those obtained by Onari et al. [3] and a new interpretation of the spectra is presented. Spectra obtained from 2H-NbS2 are also presented and found to be consistent with group theoretical predictions. Finally, the results obtained from the two polytypes are checked for consistency by using a simple nearest neighbour lattice dynamics model [5]. 2. CRYSTAL SYMMETRY 2H-NbS2 crystals have a primitive unit cell that spans two layers of the crystal [1,2], The crystal symmetry can be described using the D~h space group and the long wavelength vibrational modes for such a structure have been discussed in detail by many workers [2, 6 - 9 ] . The long wavelength phonons are correlated with the irreducible representations of the D6h factor group:

P =-2A2u + 2B2e +Alu + Aae + 2Elu + 2E2e + E2u +Ele The acoustic modes are associated with A2u + E~ u, the remaining A2u and Exu are infrared active, B2u, Bxu and E2u are inactive and there are four Raman active modes, namely Alg + 2E2g + El~ where one of the E2~ modes (E~2ghereafter) is the "rigid layer mode" [8]. The crystallographic unit cell of the 3R-polytype (space group C3So)spans three layers

RAMAN SCATTERING FROM 2H AND 3R-NbS2

558

of the crystal but the primitive cell, that should be used for the enumeration of the modes contains only three atoms [2, I0, 11 ]. Thus there are three atoms per unit cell and nine vibrational modes at the zone center which can be represented by the irreducible representations of the factor group C3v:

lo0 -

r

[

,

q

i

P - 3A1 + 3E

2

Three of the modes are acoustic (A + E) are thus there are four nondengerate Raman active modes, namely

>i-~_

2A1 + 2E

z

In this case there is no rigid layer mode because the unit cell contains a single layer and all modes should be both Raman and Infrared active [2].

z :~

The Raman spectra o f 2H-NbS2 are shown in Fig. 1 and four features have been identified. On the basis of their polarization dependence they have been correlated with the irreducible representations o f D6h as indicated in the first row of Table 1. In making the assignments it has been assumed that the E~e mode

lg

50

[

200 3 0 FREQUENCY SHIFT

3. RESULTS AND DISCUSSION

3.1.2H-NbS2

A

E~g

100

Raman spectra were excited with the 514.5 nm line of an argon ion laser. The exciting light was passed through a narrow-bandpass filter before hitting the sample. The scattered light was analyzed with a Spex triple monochromator, and detected with an RCA 31034A photomultiplier. The photomultiplier output was processed using standard photon counting techniques. The samples were mounted in a Displex refrigerator and spectra were obtained at temperatures from 15 to 300 K. The resulting spectra were found to be essentially independent of crystal temperature. Spectra were obtained from the faces of the crystals with angles of incidence varying from approximately 20 ° (backscattering geometry) to about 80 ° (right angle geometry). The z-axis was taken parallel to the c-axis of the crystal and x and y are two perpendicular axes in the basal plane of the crystal (after Loudon [12]). The crystals were oriented visually using cleavage facets that were found to exist on fresltly cleaved faces of the crystal. In all cases x lies in the plane of incidence and y was oriented perpendicular to the plane of incidence. The spectra shown in Figs. 1 and 2 were obtained with angles of incidence of approximately 20 ° . The polarization dependence and relative intensities in all the spectra were essentially independent o f angle o f incidence except that the zy (angle of incidence near 90 ° ) spectra were very weak and qualitatively similar to the xy spectra.

2 H - NbS 2

E22g

~1t ~-

.g3

Vol. 45, No. 7

400 (crn-')

5OO

Fig. 1. Room temperature Raman spectra of 2H-NbS2 with incident and scattered polarizations parallel (xx) and crossed (xy). The inset is a spectrum obtained with no analyzer showing the rigid layer layer mode at 31 ± 2 c m -1. J

i

loo

r

i

3R- NbS 2

"E

A1

E2

I

o E1 5o ~u

z :E

i

0

l(30

200 360 FREQUENCY SHIFT

4()0 (cm-~)

560

Fig. 2. Room temperature Raman spectra of 3 R - N b S ~ with incident and scattered polarizations parallel (xx) and crossed (xy). appears in the xx spectrum because of zx "leakage" made possible by crystal imperfections and nonnormal incidence. In this context the Ele mode assignment must be considered to be somewhat tentative. 2H-NbSe2 is a very similar compound to 2H-NbS2 and its Raman spectrum has been studied by Wang and Chen [7] and Duffey etaL [13]. Wang and Chen [7] determined the force constants between nearest neighbour atoms in 2 H - N b S % by using models

Vol. 45, No. 7

RAMAN SCATTERING FROM 2H AND 3R-NbS2

developed by Bromley [5] and Verble et al. [9]. These models predict that co2 (E~g) = 4Ks/M, 602(Elg)

-

co2(Alg) -

63' 7m2 '

w2(E~g ) = 123'

93' + 14/3 7m2

7# '

and

co2(A2u) =

183' 7/1

where K s is the interlayer force constant, 3' is the m e t a l ligand force constant,/3 is the ligand-ligand force constant,/a is the reduced mass, m2 is the ligand mass and M = Mr~ + 2m2. If data from the two compounds are compared one first notes that the fiequencies of the rigid layer mode (Egg) in the two compounds are equal to within the experimental accuracy and thus the interlayer force constant K s is approximately equal in the two compounds. If one further assumes that the force constants 3' and 13are the same for the two materials one can calculate the frequencies of the remaining three modes in 2 H - N b S 2 . The resulting values for the NbS2 frequencies are shown in Table 1 for comparison purposes. The agreement with the measured values is quite good given the assumptions involved. This indicates that the force constants in the two materials, although certainly not identical, are surprisingly similar. The reasonable agreement also lends confidence to the assignments given in Table 1 for 2 H - N b S 2 .

Table 1. Measured and calculated frequencies o f the

559

features at 290 and 3 3 0 c m -1 as the two E modes expected for the 3R-structure. Table 2 contains a comparison of these assignments with the frequencies predicted Bromley's model [5] using the 330 cm -1 mode for normalization. For this purpose the 330 cm -~ peak (E2) is assumed to correspond to the E~g mode of the 2H-compound and E1 and A2 with the Elg and A2u modes respectively. As can be seen fromTable 2 one obtains qualitative agreement but the quantitative agreement is poor. The peak at 158 cm -1 could arise from two-phonon scattering. A careful investigation of both the Stokes and antistokes spectrum was carried out, however, and the intensity of the 158 cm -~ was found to be essentially independent of temperature. Thus it is perhaps more likely that this feature is due to an impurity or defect mode, similar to the feature observed in the Raman spectrum of impure NbSe2 crystals [ 14]. The expected deviation from stoichiometry of the 3R-NbS2 crystals [4] also makes the existence of an impurity mode plausible.

Table 2. Frequencies observed for 3 R - N b S 2 compared with predictions o f the Bromley Model [5]. The force constant obtained in this manner is." 7 = 13.4 (104) dyn cm -~ .

Measured Calc:

E1

E2

A1

A2

290 + 5 223

330 -+ 3 330

386 + 2 -

458 + 3 404

2H-NbS2 modes shown in Fig. 1. The calculated

frequencies were obtained with the values o f 7 and/3 given by Wangand Chen[7]: 3' = 11.4 × 104 d y n c m -1, /3 = 5.07 × 104 dyn cm -1 andK s = 0 . 3 2 4 x 104 d y n c m -1.

Measured Calc:

E~g

Elg

EIg

A lg

31 + 2 -

260 + 5 227

304 + 3 296

379 +- 2 363

3.2.3R-NbS2 Room temperature Raman spectra obtained from single crystals of 3 R - N b S 2 are shown in Fig. 2. The feature at 386 cm -~ can be clearly identified as an A mode. In addition, the mode at 458 cm -~ has diagonal symmetry and is thus assigned as an A mode. The identification of the E modes is much less certain. Two prominent features at 158 and 330 cm -1 both have polarization properties appropriate to an E mode as does the shoulder at 290 cm -x . Additional information can be obtained from a comparison with the 2H-spectra since the E modes should have approximately the same frequencies in the two compounds [2]. This would lead to the assignment of the two

Several aspects of the results remain somewhat puzzling. On the basis of previous predictions [2, 8] and observations on GaSe [10, 15] one would not have expected the different stacking arrangements to give rise to the large shifts observed here for the intralayer modes. In addition, the Elu mode frequency in 2H-NbS2 and the 3 R - N b S 2 assignments are in rather poor agreement with Bromley's model [5 ]. To clarify these aspects, additional investigations are planned on 3R-crystals with various known stoichiometries in conjunction with the application of a more sophisticated lattice dynamics model.

Acknowledgements - The authors would like to thank Dr F. Levy for providing the 3 R - N b S 2 crystals used in this work. The 2H-NbS2 crystals were provided by Dr R.F. Frindt and Mr. P. Joensen of the SFU Physics Department. The financial support of the Natural Sciences and Engineering Council of Canada is gratefully acknowledged. REFERENCES 1.

J.A. Wilson & A.D. Yoffe, Advances in Physics 18, 193 (1969).

560 2.

3. 4. 5. 6. 7. 8.

RAMAN SCATTERING FROM 2H AND 3R-NbS2 T.J. Wieting & J.L. Verble, Electrons and Phonons in Layered Crystal Structures (edited by T.J. Wieting & M. Schulter), p. 321. Published by D. Reidel (1979). S. Onari, T. Arai, R. Aoki & S. Nakamura, Solid State Commun. 31,577 (1979). M.W.Fisher & M.J. Sienko, Inorg. Chem. 19, 39 (1980). R.A. Bromley, Phil. Mag. 23, 1417 (1971). J.M. Chen & C.S. Wang, Solid State Commun. 14, 857 (1974). C.S.Wang & J.M. Chen, Solid State Commun. 14, 1145 (1974). J.L. Verble & T.J. Wieting, Phys. Rev. Lett. 25, 362 (1970); T.J. Wieting & J.L. Verble, Phys. Rev. BS, 1473 (1972).

9. 10. 11.

12. 13. 14. 15.

Vol. 45, No. 7

J.L. Verble, T.J. Wieting & P.R. Reed, Solid State Commun. 11,941 (1972). A. Polian, K. Kunc & A. Kuhn, Solid State Commun. 19, 1079 (1976). W.G.Fately, F.R. Dollish, N.T. McDevitt & F.F. Bentley, Infrared and Raman Selection Rules for Molecular and Lattice Vibrations, pp. 2-4, Wiley (1972). R. London,Adv. Phys. 13,423 (1972). J.R. Duffey, R.D. Kirby & R.V. Coleman,Light Scattering in Solids, (edited by M. Balkanskii, R. Leite & S. Porto), p. 383. Flammarion (1976). R. Sooryakumar, M.V. Klein & R.F. Frindt,Phys. Rev. B23, 3222 (1981). R.M.Hoff, J.C. Irwin & R.M.A. Lieth, Can. J. Phys. 53, 1606 (1975).

NOTE ADDED IN PROOF A paper by S. Nakashima, Y. Tokuda, A. Mitsuishi, R. Aoki & V. Hamaue, Solid State Commun. 42, 601 (1982) has been brought to our attention. This paper presents results on 2H-NbS2 which are in partial agreement with the present findings.