Ultrasonic Velocity Studies of Graphite and Its Intercalation Compounds
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D. M. HWANG Department of Physics,
University of Illinois at Chicago,
ABSTRACT The c-axis sound velocities and attenuations for HOPG, stage 3 and stage 4 SbCl 5 -graphite were determined by ultrasonic techniques in the temperature range between 4 and 325 OK. The temperature variation of C3 3 for HOPG agrees closely with the theoretical prediction based on the LennardJones interlayer potential. In SbCl 5 -graphite, the longitudinal sound attenuation increases sharply and the transverse sound cannot propagate for temperatures above 200 OK, indicating a commensurate-to-incommensurate in-plane phase transition. The stage dependence of C 3 3 at low temperatures indicates that the interlayer forces beyond the nearest layers can not be neglected.
INTRODUCTION One of the fundamental questions in condensed matter physics is "How do the atoms interact with each other?" There have been only a few GIC investigations focused on this aspect. The nature of the intralayer forces within the intercalation layer and the interlayer forces among the intercalation layers and the graphite layers is not well understood. Room The interlayer forces in graphi.e have been studied for many years. temperature elastic constants for HOPG [1-3] and their pressure dependence [3, 4] have been determined by ultrasonic techniques. The c-axis compressional elastic constant C 3 3 is found to be sample independent. Its magnitude can be interpreted by the Lennard-Jones interlayer potential [5,6] or by both the Lennard-Jones contribution (89%) and the electronic contribution (11%) . The c-axis shear elastic constant C44 , on the other hand, is sample dependent. There has been considerable controversy over the true value of C4 4 . The low frequency ultrasonic measurements yield a low value which is of the same order of magnitude as predicted by the Lennard-Jones potential [1-2]. The high frequency experimental methods, and the ultrasonic measurements from neutron or boron irradiated specimens, yield a value which is -20 times higher . This constant high value has been accounted for by the electronic contribution . Assuming the Lennard-Jones potential between the nearest graphite layers, Kelly  has formulated a simple relation between the temperature dependence of C33 and the c-axis thermal expansion. The neutron scattering data are not accurate enough to justify this theory . The ultrasonic results reported by Gauster and Fritz  is -2 times larger than Kelly's prediction . C33 for several donor GIC's [9-11] and stage 2 FeCl3-graphite  have been derived from inelastic neutron scattering data. Some of them have also been determined by pressure dependent X-ray scattering . C 3 3 for stage I and stage 2 FeCl3-graphite have been measured by ultrasonic techniques . The relation between C33 and the intercalation species or the stage number is not yet established. In this study, the c-axis longitudinal sound velocity for HOPG, stage 3 and stage 4 SbCl 5 -graphite specimens between 4 and 325 "K was measur