(s). The deviation from the linear trend is due to the contribution of the third-order anharmonic term in the lattice potential energy with a pure temperature effect. An estimated value of 1.5 for the Grüneisen parameter of the 
(s) band was found.]]>
(s)). La desviación se debe a la contribución del término anarmónico de tercer orden en la energía potencial. Se encontró un valor estimado de 1,5 para el parámetro de Grüneisen de la banda (s).]]>
Anharmonic properties of Raman modes in double wall carbon nanotubes
J. Marquinaa, CH. Powerb, J.M. Brotoc, E. Flahautd, and J. Gonzálezb,e
a Centro de Estudios Avanzados en Óptica, Facultad de Ciencias, Universidad de los Andes, Mérida 5101, Venezuela. e–mail: castella@ula.ve
b Centro de Estudios en Semiconductores, Facultad de Ciencias, Universidad de los Andes, Mérida 5101, Venezuela.
c Laboratoire National des Champs Magnétiques Intenses (LNCMI) – CNRS UPR 3228, Université de Toulouse, 31400 Toulouse, France.
d Laboratoire de Chimie des Matériaux Inorganiques (CIRIMAT), UMR CNRS 5085, Université Paul Sabatier, 31062 Toulouse, France.
]]> e DCITIMAC–Malta Consolider Team, Universidad de Cantabria, Facultad de Ciencias, Santander 69005, Spain.
Recibido el 23 de noviembre de 2010
Aceptado el 21 de octubre de 2011
Abstract
The temperature dependence of the radial breathing modes (RBMs) and the zone–center tangential optical phonons (G–bands) of double–walled carbon nanotubes (DWCNTs) has been investigated between 300 and 700 K using Raman scattering. As expected, with increasing temperature, the frequencies of the Raman peaks, including the RBMs and G–bands downshift simultaneously. We show here that the temperature dependence of the RBMs can be fitted by a simple linear dependence and different RBMs have different frequency shifts. We observe a noticeable nonlinearity in the temperature dependence of the G–band associated with the outer semiconducting tube 
(s). The deviation from the linear trend is due to the contribution of the third–order anharmonic term in the lattice potential energy with a pure temperature effect. An estimated value of 1.5 for the Grüneisen parameter of the (s) band was found.
Keywords: Raman spectroscopy; double wall carbon nanotubes; high–temperature; anharmonicity; Grüneisen parameter.
Resumen
]]> La variación con la temperatura de los modos de respiración radial (RBMs) y los fonones ópticos tangenciales de centro de zona (banda G) de los nanotubos de doble pared (DWCNTs) han sido investigados en el rango de 300 a 700 K utilizando dispersión Raman. Como era de esperarse, con el incremento de la temperatura las frecuencias de los picos Raman de los RBMs y las bandas G se desplazan hacia más bajas frecuencias. Nosotros demostramos que la variación con la temperatura de los RBMs puede ser ajustada mediante un modelo lineal y muestran diferentes desplazamientos en frecuencia. Nosotros observamos una no linealidad importante en la variación con la temperatura de la banda G asociada a los tubos semiconductores externos ((s)). La desviación se debe a la contribución del término anarmónico de tercer orden en la energía potencial. Se encontró un valor estimado de 1,5 para el parámetro de Grüneisen de la banda (s). Descriptores: Espectroscopía raman; nanotubos de carbono doble pared; altas temperaturas; anarmonicidad; parámetro Grüneisen.
PACS: 63.22.GH; 63.20.KG; 78.30.–J
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Acknowledgments
This research was supported in part by the Franco–Venezuelan Cooperation Program PCP "Nanotubos de Carbono" and by the CDCHT (code C–1720–11–05–B) of the Universidad de los Andes, Merida, Venezuela. J.G. acknowledge support of this research by the MALTA–Consolider Ingenio 2010 Program. J.M. would like to thank to reviewers and also to the Dr. M. Quintero for their interest in this work and the useful suggestions.
]]> References
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