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On the Force Constants of Graphene
Authors: S. Yu. Davydov
Ioffe Physical-Technical Institute, Russian Academy of Sciences, Politekhnicheskaya ul. 26, St. Petersburg, 194021 Russia
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Summary
In this paper, the force constant for graphene has been computed. Different researchers have used Harrison bond-orbital method to compute the central force constant k_{0} and non-central force constant k_{1}. In this paper, the author has not used a simplified version of Harrison method. In other studies, short range part of the repulsion energy was not included which lead to a too small central force constant for graphene. In this study, short range part of repulsion energy was included which gave a reasonable value. The authors used the following model to calculate the short range repulsion energy
where S is the overlap integral and V_{2 }is the covalent energy. To compute the central force constant, following model was used
Using the method proposed by the author, the central force constant was found to be 305 N/m. However, the non-central force constant was found to be very less. The comparison of central force constant computed in this study has been compared to previous studies in table shown below.
Reference |
k_{0} |
k_{1} |
---|---|---|
This work |
305 |
39 |
M. Maeda and Y. Kuramoto et al. |
307 |
281 |
R. AL-Jishi and G. Dresselhaus |
313 |
267 |
L. A. Falkovsky |
290 |
79 |
The non-central force constant is considerably smaller than the results of other researchers because in this work model of rigid orbital was used.
Using the value of central force constant k0 found in this study, the frequency of atomic vibrations in the plane of graphene sheet at the point was computed to be 1598 cm^{-1}. The frequencies for graphite lie in the range of 1565 to 1590 cm^{-1} which shows good agreement with the frequency for graphene.
Reviewer: Aamir Alaud Din