Anisotropy in the resistivity of NbSe2

J. Phys. Chem. Solids

Pergamon Press 197 I. Vol. 32, pp. 2217-2221.

Printed in G r e a t Britain.

ANISOTROPY IN THE RESISTIVITY OF NbSe2 J. EDWARDS and R. F. FRINDT Department of Physics, Simon Fraser University, Burnaby, British Columbia, Canada

(Received 12 November 1970) A b s t r a c t - T h e resistivity of the metallic layer structure NbSe2 has been measured across the layers (lie) by a four probe technique which could be used for other layer structures. The temperature dependent part of the resistivity p~ was found to be linear in T from 300 to 80*K, and had a T 3 dependence below 60~ The rat o of the resistivities Pl~/P'~c was constant at 31 : I from 300 to 80*K and then fell linearly with temperature. 1. INTRODUCTION

NbSe._, IS a metallic compound that crystallises into a hexagonal layer structure[l]: each layer consists of a S e - N b - S e sheet, either two or four layers making up one unit cell. The details of the crystallography of NbSe2 and related layer structures may be found in the reviews by Hulliger [2] and Wilson and Yoffe [3]. The bonds between N b and Se within a layer are covalent, while bonds between layers are of the weak van der Waals type. As a result, many of the properties of NbSe2 should show anisotropic behaviour. Measurements of the resistivity of NbSe2 along the layers (_l_c) have been made[4,5], but in spite of recent interest in layer structures, no data has yet been published on the anisotropy in resistivity of a metallic layer structure such as N b S ~ . This work presents the results of resistivity measurements on the two layer modification of NbSe2 by a method that may also be extended to semiconducting layer structures.

N b and 99.999 per cent for the Se. The resulting crystal platelets were of all sizes up to 2 cm • 2 cm • 0-4 mm thick. The resistivity measurements were taken on as-grown samples, both parallel and perpendicular to the c-axis. The method for obtaining a four-terminal configuration for measurements parallel to the c-axis in layer structures is shown in Fig. 1. The voltage probes were partially cleaved from the body of the crystal. The connecting wires were attached using a conducting silver paste.

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2. EXPERIMENTAL

Single crystals of NbSe2 were prepared by generally following the method described by Kershaw et al. [4]. Chemical vapour transport, using iodine as the carder, was employed with charge and growth-zone temperatures of 750 and 700~ for all samples. The purity of the elements used was 99.93 per cent for the

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J. E D W A R D S and R. F. F R I N D T

T y p i c a l sample dimensions were 5 m m x 5 m m x 0 - 1 mm thick; the current c o n t a c t area was a b o u t 1 m m 2 and t h e \ v o l t a g e contacts were about 0-005 mm thick. Resistivity m e a s u r e m e n t s were made perpendicular to the c-axis on some crystals, using either a c o n v e n t i o n a l f o u r - p r o b e g e o m e t r y or the van der P a u w method. T e m p e r a t u r e s below 77~ were m e a s u r e d using a g o l d - i r o n - s i l v e r normal t h e r m o c o u p l e [6]: above 77~ standard freezing mixtures were used. 3. RESULTS

M e a s u r e m e n t s parallel to c were taken on nine samples, including a series o f six made by successive cleaving o f one o f the thicker single crystals. T h e thickness o f these nine ranged from 0.007 to 0-08 cm.

F o r a typical c u r r e n t c o n t a c t area (A) o f 1 mm 2 the m e a s u r e d resistivity (RA/t) o f the samples was i n d e p e n d e n t o f thickness (t) for thicknesses less than 0.02 cm, but a b o v e this thickness, the m e a s u r e d resistivity was red u c e d (Fig. 2). Results similar to those in Fig. 2 w e r e obtained by a two-dimensional analogue method, showing that shape effects w e r e detectable for l/t ~ 10, L being the c o n t a c t length. This c o r r e s p o n d s in o u r samples to t >~ 0.01 cm. O n e crystal (#1 in Fig. 2) was measured, first with a small c u r r e n t c o n t a c t ( - 30 per cent o f crystal area) and secondly with a larger c o n t a c t ( - 8 0 per cent o f crystal area). Results were obtained that were consistent with the sample resistance being a function o f the contact area, not the crystal area. Figure 3 shows the resistivity parallel to

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c obtained for two crystals as a function of temperature. These results were typical of those obtained with all seven crystals of thickness less than 0.02 cm. A logarithmic plot of the ideal resistivity p ' ( T ) both parallel and perpendicular to c is shown in Fig. 4. Because of the superconducting transition at 7 ~ there is an uncertainty in the value of the residual resistivity p(0). The value for p(0) was taken to be p(7~ and p' (T) was consequently given by p'(T) = p(T)--O(7~ Our results " for P~_~ are in good agreement with the results of Lee et aL[5], also shown in Fig. 4. The resistivity P,i~ has a T 3 temperature dependence below approximately 60~ while p;c follows a T 2 law below 45~ The error in the exponents is estimated to be ___0-2. We feel that the data is not accurate enough to specify the temperature dependence below about 20~ Our value for p(7~177 was 10 x 10-6 ~'~cm. The ratio of ideal resistivities pti~/p'~c is plotted in Fig. 5 as a function of temperature.

The error bars in Fig. 5 mainly reflect the error in the estimates of p(0) and the crystal dimensions. The superconducting transition temperature was measured to be 7.0~ with current parallel or perpendicular to c. The measurements showed that any departures of the NbSe2 from stoichiometry were small since it has been shown [7] that Tc is very sensitive to minor variations in niobium concentration. 4. DISCUSSION

The anisotropic behaviour of N b S ~ shows itself in the ratio Pl'lc/P',c being considerably greater than one, and also in the ratio being a function of temperature. The ideal resistivities Prlc and p;~ are both linear in T at temperatures above 100~ (Fig. 4). Since 0~ = 210~ for NbSe2[8], this behaviour is typical of most metals [9]. A full explanation of the 10w temperature observations that ~t'~ ~ T3 and p ~ ~ T ~- will require a knowledge of both the Fermi surface and the phonon spectrum of NbSe._,.

2220

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2221

Some conjectures about the Fermi surface Acknowledgements-We thank Dr. D. J. Huntley and have been made [3] but, as yet, there have been Dr. S. Gygax for helpful comments and acknowledge the financial support of the National Research Council of no experimental determinations carried out. Canada. With regard to the phonon spectrum, it has been suggested by Krumhansl and Brooks [10] in the case of graphite, and for layer REFERENCES structures in general by N e w e l l [ l l ] that at 1. R E V O L I N S K Y E., S P I E R I N G G. A. and BEERNthe lowest temperatures the phonon spectrum T S E N D. J., J. Phys. Chem. Solids 26, 1029 (1965). 2. H U L L I G E R F., In Structure and Bonding (Edited resembles that of an anisotropic threeby C. Jorgenson) Vol. 4, p. 83. Springer Verlag, dimensional Debye solid, while at higher Berlin (I 968). temperatures, the spectrum will, to a good 3. W I L S O N J. A. and Y O F F E A. D., Adv. Phys. I8, 193 (1969). approximation, resemble that of a two4. K E R S H A W R., V L A S S E M. and W O L D A., dimensional Debye solid. Experimental lnorg. Chem. 6, 1599 (1967). confirmations of the theory given by [10] and 5. L E E H. N. S., M C K E N Z I E H., T A N N H A U S E R D. S. and W O L D A.,J. appl. Phys. 40,602 (1969). [11] have been provided by the low-tempera6. B E R M A N R., B R O C K J. C. F. and H U N T L E Y ture specific heat of graphite[12, 13]. A T 3 D. J., Cryogenics 4, 233 (1964). dependence has been observed for the lattice 7. A N T O N O V A E. A., M E D E E V C. A. and SHEBA L I N I. Yu., Zh. eks. teor. Fiz. 57 (2), 329 (1969). specific heat of NbSe2 and other related layer 8. V A N M A A R E N M. H. and H A R L A N D H. B., structures below 10~ so that NbSe., may Phys. Lett. 29A, 571 (1969). resemble a two-dimensional Debye solid in 9. M E A D E N G. T., In Electrical Resistance of Metals, p. 59, Plenum Press, New York (1965). some temperature range above 10~ 10. K R U M H A N S L J. A. and BROOKS H., J. chem. The Hall coefficient for NbSe., for current Phys. 21, 1663 (1954). _l_c is observed to change sign at 26~ the 11. N E W E L L G. F.,J. chem. Phys. 23, 2431 (1955). samples going from p-type to n-type on 12. D E SORBO W. J. and T Y L E R W. W., J. chem. Phys. 21, 1660 (1954). cooling [5]. It would be of interest to see if 13. D E SORBO W. J. and N I C H O L S G. E., J. Phys. Chem. Solids 6,352 (1958). similar behaviour is observed for current parallel to the c-axis.