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ELASTIC PROPERTIES OF THE
ONE-DIMENSIONAL METAL Mo2 S3
Alova, G. Mozurkewich
To cite this version:
ELASTIC PROPERTIES OF THE ONE-DIMENSIONAL METAL Mo,S,
ALOVA
AND G.MOZURKEWICH
Physics
Department, University of Illinois a t Urbana-Champaign 1110W.
Green Street, Urbana, IL 61801, U.S.AAbstract
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The elastic properties of Mo2S3 were measured by the vibrating reed technique. The Young's modulus increased by 0.5% below the monoclinic- triclinic phase transition. A thermally activated internal friction peak not associated with a phase transition was found at a lower temperature.Mo2S3 is a quasi-one-dimensional metal whose monoclinic structure contains two inequivalent zigzag chains of Mo atoms extending along the b direction
111.
The compound contains about 3% Mo atoms in excess of the ideal chemical formula. Structural studies have shown the existence of periodic lattice distortions (PLDs) on both types of chain / 2 / . The PLUS exhibit several phase transitions between 100 K and 400 K, and the effects of these transitions on resistance, Hall effect, and magnetic susceptibility suggest charge density wave (CDW) formation 131. Here we examine the low-frequency elastic behavior of Mo2S3.Samples were grown by D. J. Holmgren by vapor transport in the presence of Sn. In spite of possible incorporation of Sn, two-probe measurements of the temperature dependent resistance were consistent with previous reports /1,3/. A vibrating reed technique with electrostatic drive and modulated radiofrequency detection 141 was used with samples of typical dimensions 2 mm x 1000 1.1m2 vibrating in air. A phase- locked loop allowed simultaneous determination of Young's modulus Y from the mechanical resonance frequency v , and internal friction Q - ~ from the resonance amplitude A'. The temperature was generally changed by a few degrees per minute. Higher rates led to irreproducible results.
I1
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MODULUSThe room temperature Young's modulus along the direction was Y = 2 x 1012 dyn/cm2, but this value has a large uncertainty from the difficulty of measuring the small sample dimensions.
The modulus results depended on direction and rate of temperature variation. Several examples are shown in Fig. 1. Upon warming (curves a, b, and d), the resonance frequency v always dropped discontinuously just above 200 K. The drop corresponded to a fractional change in Young's modulus, AYIY, of approximately
C10-686 JOURNAL DE PHYSIQUE
5 x This drop was preceded by a stiffening near 180 K, whose shape depended on the heating rate. For relatively rapid temperature increases the stiffening was sudden (curve b), but for slower heating (a, d) the increase was progressively more gradual. Upon cooling (curve c) no sudden changes were found. Instead of the sudden softening at 200 K on warming, a gradual stiffening occurred near 180 K on cooling.
TEMPERATURE
(K)
Fig. 1
-
Temperature dependence of mechanical resonance frequency. (a) and (b): sample / / 4 , warming. (c): sample 1/4, cooling. .(d): sample t 6 , warming.Both the sudden drop of Y at 200 K on warming and the gradual increase at 180 K on cooling are connected with a hysteretic phase transition, as revealed in electrical and magnetic measurements by ourselves and others / 1 , 3 / . This transition has been identified as an incommensurate-commensurate change of the PLD along b in
association with a monoclinic-triclinic structure modification. In light of the electrical results, it is tempting to attribute AY to the change in carrier density at the transition, but this explanation seems untenable. The change may be crudely estimated from the Bohm-Staver expression for the metallic part of the stiffness: Ymetal =
(*)
eF/R,
where 0 is the volume per carrier. Hemmel et al. / 3 / deduced0.0856 holes/Mo above the transition, 0.0302 holes/Mo below it and a Fermi energy
2
cF = 0.1 eV, from which we estimate AY = 2 x lo8 dyn/cm2 = 10- Y, nearly two orders of magnitude smaller than the experimental result.
The dominant feature in the internal friction was a large peak between 130 and 150 K. It is illustrated in Fig. 2 as a dip in the temperature dependence of the mechanical resonance amplitude. The temperature at which the maximum loss was found did not depend on the direction of temperature variation nor on the strain
amplitude, but it did depend on measuring frequency, increasing with increasing v.
A second, smaller internal friction peak was found near 170 K, but only when the sample was being cooled (Fig. 2c). The origin of this second peak has not been established, but it is probably connected with the gradual stiffening on cooling (Fig. Ic).
The absence of a friction peak at the hysteretic monoclinic-triclinic phase transition is surprising. Perhaps it was too small to observe because the lattice parameters change only slightly at the transition / 2 / . However a friction peak would also be expected from the "lock-in" transition between the incommensurate and commensurate phases 151. A ul
.-
.-
C M02S3 3 ( 0 ) 33 kHz TEMPERATURE(K)
Fig. 2
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Temperature dependence of mechanical resonance amplitude. (a) and (b): sample ik4, warming. (c): sample # 4 , cooling. (d): sample f 6 , warming.The larger friction peak had magnitude A(Q-~) = 8 x and width about twice chat expected for a Debye relaxation. It occurred in a region in which no phase
transition was expected, and its frequency dependence indicated relaxational
character. Since the loss is maximum when 2n v T = 1, the temperature dependence of the relaxation rate T-' could be determined by plotting mechanical resonance
frequency % the temperature at which the smallest amplitude occurred. Fig. 3 shows that T - ~ is activated:
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Although this relaxation peak is reminiscent of a Bordoni peak, vo is much too large for dislocation motion. A second possibility is activated motion of excess Mo atoms or of Sn impurities, but then we would expect E to be higher. We may speculate about a third explanation: if the PLD is associated with a charge density wave, the friction peak could be due to thermal motion of "dislocations" or domain boundaries in the CDW array /5,6/. This mechanism could be tested if the CDW could be induced to slide by applying an external electric field. However we have not succeeded in inducing CDW mot ion.
TEMPERATURE (K)
Fig. 3 - Log(v) vs. T-' for data obtained from four different samples. The solid line is v = (1 x 1016 Hz)exp(-0.33 eV/kT).
We are grateful to D. J. Holmgren for providing the samples. This work was supported by a grant from the University of Illinois Research Board. REFERENCES
/1/ de Jonge, K., Popma, T. J. A., Wiegers, G. A. and Jellinek, F., Solid State Chem.
2,
(1970) 188./2/ Deblieck, R., Wiegers, G. A., Bronsema, K. D., van Uyck, D., van Tendeloo, G., van Landuyt, J. and Amelinckx, S., Phys. Stat. Solidi ( a ) Z , (1983) 249. /3/ Hemmel, R., van der Heide, H., van Bruggen, C. F., Haas, C. and Wiegers, G. A.,
in "Solid State Chemistry 1982," Proc. 2nd European Conf. Solid State Chem., Veldhoven, The Netherlands, Elsevier, 1982; page 691.
