Lattice Dynamical Model for Graphite-Bromine Intercalation Compounds
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LATTICE DYNAMICAL MODEL FOR GRAPHITE-BROMINE INTERCALATION COMPOUNDS
R.
AL-JISHI*§ and G. DRESSELHAUSt
Massachusetts Institute of Technology,
Cambridge, MA 02139, USA
ABSTRACT A Born-von Kirmin lattice dynamical model for the graphite Br2 intercalation compounds is presented. The low frequency bromine branches are calculated using a commensurate (U3x /13)R(30 0 ,13.9*) unit cell with two Br 2 molecules/unit cell. In-plane zone folding is used to calculate the high frequency graphitic modes at the Brillouin zone center. INTRODUCTION Graphite intercalation compounds (GIC) are formed by introducing atomic or molecular layers of a different chemical species, the intercalate, between graphite layers. This process results in compounds of a well defined stage, whereby for a stage n compound, there are n graphite layers between consecutive intercalate layers. In addition, some GIC, such as graphite-Br 2 form well-ordered in-plane commensurate superlattices [1]. A calculation of the phonon dispersion relations in GIC is motivated by the need to explain the results of Raman and infrared spectroscopy [2,31 and inelastic neutron scattering [4]. The results of the calculation are then used to explain the observed anomalies in the specific heat [5,61. The calculation of the phonon dispersion relations in GIC also provides a valuable tool for the interpretation of phase transitions in the intercalate layer which have recently been observed in the Raman spectra of the graphite-Rb [21 and graphite-Br 2 [7] systems. The commensurate intercalate phase introduces additional in-plane superlattice periodicities which result in the zone-folding of specific phonon modes into the Brillouin zone center. In some cases, commensurate-incommensurate phase transitions can be detected by Raman scattering experiments [7] and a detailed knowledge of the phonon dispersion relations can therefore be used to help identify the superlattice structure [1]. The staging periodicity associated with the intercalation process allows zone folding of the pristine graphite dynamical matrix along kz to obtain the dynamical matrix of the GIC [8,91. The zone-folded dynamical matrix is then transformed from the site into the layer representation through a unitary transformation [8]. In this representation, each row and column of the dynamical matrix is identified with a graphite layer. The effect of intercalation is explicitly taken into account by replacing certain graphite layers with the corresponding intercalate layers in accordance with the particular stage of the compounds under investigation. This kz-axis zone-folding technique was successfully applied to the study of alkali-metal GIC [91 and potassium-amalgam GIC [10]. Phonon data derived from inelastic neutron, light scattering, and specific heat measurements were all accounted for by this model. In this work we shall be concerned with a parallel study of the graphite-Br 2 compounds where Raman spectroscopy has been used to study the vibrational and *Department of Physics. §Center for Materials Science
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