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Phonon properties of graphene derived from molecular dynamics simulations.

Koukaras EN, Kalosakas G, Galiotis C, Papagelis K - Sci Rep (2015)

Bottom Line: The method is promising for systems with large scale periodicity, accounts for anharmonic effects and non-bonding interactions with a general environment, and it is applicable under finite temperatures.The potentials used show diverse behaviour.The Tersoff-2010 potential exhibits the most systematic and physically sound behaviour in this regard, and gives a first-order temperature coefficient of χ = -0.05 cm(-1)/K for the Γ-E2g shift in agreement with reported experimental values.

View Article: PubMed Central - PubMed

Affiliation: Institute of Chemical Engineering Sciences, Foundation of Research and Technology-Hellas (FORTH/ICE-HT), Stadiou Street, Platani, Patras, 26504 Greece.

ABSTRACT
A method that utilises atomic trajectories and velocities from molecular dynamics simulations has been suitably adapted and employed for the implicit calculation of the phonon dispersion curves of graphene. Classical potentials widely used in the literature were employed. Their performance was assessed for each individual phonon branch and the overall phonon dispersion, using available inelastic x-ray scattering data. The method is promising for systems with large scale periodicity, accounts for anharmonic effects and non-bonding interactions with a general environment, and it is applicable under finite temperatures. The temperature dependence of the phonon dispersion curves has been examined with emphasis on the doubly degenerate Raman active Γ-E2g phonon at the zone centre, where experimental results are available. The potentials used show diverse behaviour. The Tersoff-2010 potential exhibits the most systematic and physically sound behaviour in this regard, and gives a first-order temperature coefficient of χ = -0.05 cm(-1)/K for the Γ-E2g shift in agreement with reported experimental values.

No MeSH data available.


Related in: MedlinePlus

Phonon dispersion curves of graphene calculated using (a) the LCBOP, (b) the AIREBO, (c) the original Tersoff (1989), and (d) the reparameterised Tersoff-2010 potential, at T = 300 K. The reported MSE, MAE and RMSD values in Table 1 were obtained using these dispersion curves. Solid circles and squares correspond to numerical results of optical and acoustic branches, respectively. Open symbols correspond to experimental data taken from Refs 30,31.
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f2: Phonon dispersion curves of graphene calculated using (a) the LCBOP, (b) the AIREBO, (c) the original Tersoff (1989), and (d) the reparameterised Tersoff-2010 potential, at T = 300 K. The reported MSE, MAE and RMSD values in Table 1 were obtained using these dispersion curves. Solid circles and squares correspond to numerical results of optical and acoustic branches, respectively. Open symbols correspond to experimental data taken from Refs 30,31.

Mentions: In Fig. 2(a–d) we show the results of our calculations obtained for each of the potentials under consideration (Tersoff, Tersoff-2010, LCBOP, and AIREBO). The dispersion curves were calculated at a temperature of T = 300 K to facilitate the comparison with the experimental values which were measured at room temperature3031. In the Supplementary Information we compare the results derived through the presented method at low temperatures (T = 60 K) with the corresponding ones obtained by a direct diagonalization of the dynamical matrix for the Tersoff and Tersoff-2010 potentials. Excellent agreement is obtained, demonstrating the accuracy of the proposed method. In Fig. 2 the calculated results are given in solid circles for the optical modes and solid squares for the acoustic modes. Hollow symbols represent experimental data from Maultzsch et al.30 and Mohr et al.31, which we have included for comparison. As can be seen, each of the potentials succeeds on producing a good description of some branches, but none manages to do so for all branches. The best overall description is seemingly provided by LCBOP. In Table 1 we list for each potential the mean signed error (MSE), mean absolute error (MAE) and the root mean square deviation (RMSD) for each branch separately and also for the overall phonon dispersions, compared to the corresponding experimental values (the formulas used are provided in the Supplementary Information). The calculated frequencies used were taken at the k value of each experimental data point by interpolation between two sampling points in the specific k-region. Along with the original Tersoff potential, that properly describes the ZO branch, LCBOP also provides an acceptable description of the ZO branch. However, the Tersoff potential fails dramatically on the other two optical modes, while LCBOP provides rather accurate TO and LO branches, arguably the most accurate around the Γ point. A significant improvement in the description of the TO and LO branches is obtained by the reparameterisation of the Tersoff potential by Lindsay and Broido27. However, this is at the cost of a much worse description of the ZO branch (as compared to the original Tersoff potential). The AIREBO and Tersoff-2010 compete in accuracy depending on the specific branch. The AIREBO potential overestimates the TO and LO branches (especially around Γ) somewhat more than the Tersoff-2010 potential. Also, while AIREBO underestimates the ZO branch, Tersoff-2010 overestimates it. The description of the acoustic branches is more or less on equal footing, with the AIREBO providing a more accurate TA branch and Tersoff-2010 providing the most accurate ZA branch (of all the given potentials). What is very apparent in the dispersion curves from all of the potentials used here is their general failure in describing the highest optical mode around the K point.


Phonon properties of graphene derived from molecular dynamics simulations.

Koukaras EN, Kalosakas G, Galiotis C, Papagelis K - Sci Rep (2015)

Phonon dispersion curves of graphene calculated using (a) the LCBOP, (b) the AIREBO, (c) the original Tersoff (1989), and (d) the reparameterised Tersoff-2010 potential, at T = 300 K. The reported MSE, MAE and RMSD values in Table 1 were obtained using these dispersion curves. Solid circles and squares correspond to numerical results of optical and acoustic branches, respectively. Open symbols correspond to experimental data taken from Refs 30,31.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4551956&req=5

f2: Phonon dispersion curves of graphene calculated using (a) the LCBOP, (b) the AIREBO, (c) the original Tersoff (1989), and (d) the reparameterised Tersoff-2010 potential, at T = 300 K. The reported MSE, MAE and RMSD values in Table 1 were obtained using these dispersion curves. Solid circles and squares correspond to numerical results of optical and acoustic branches, respectively. Open symbols correspond to experimental data taken from Refs 30,31.
Mentions: In Fig. 2(a–d) we show the results of our calculations obtained for each of the potentials under consideration (Tersoff, Tersoff-2010, LCBOP, and AIREBO). The dispersion curves were calculated at a temperature of T = 300 K to facilitate the comparison with the experimental values which were measured at room temperature3031. In the Supplementary Information we compare the results derived through the presented method at low temperatures (T = 60 K) with the corresponding ones obtained by a direct diagonalization of the dynamical matrix for the Tersoff and Tersoff-2010 potentials. Excellent agreement is obtained, demonstrating the accuracy of the proposed method. In Fig. 2 the calculated results are given in solid circles for the optical modes and solid squares for the acoustic modes. Hollow symbols represent experimental data from Maultzsch et al.30 and Mohr et al.31, which we have included for comparison. As can be seen, each of the potentials succeeds on producing a good description of some branches, but none manages to do so for all branches. The best overall description is seemingly provided by LCBOP. In Table 1 we list for each potential the mean signed error (MSE), mean absolute error (MAE) and the root mean square deviation (RMSD) for each branch separately and also for the overall phonon dispersions, compared to the corresponding experimental values (the formulas used are provided in the Supplementary Information). The calculated frequencies used were taken at the k value of each experimental data point by interpolation between two sampling points in the specific k-region. Along with the original Tersoff potential, that properly describes the ZO branch, LCBOP also provides an acceptable description of the ZO branch. However, the Tersoff potential fails dramatically on the other two optical modes, while LCBOP provides rather accurate TO and LO branches, arguably the most accurate around the Γ point. A significant improvement in the description of the TO and LO branches is obtained by the reparameterisation of the Tersoff potential by Lindsay and Broido27. However, this is at the cost of a much worse description of the ZO branch (as compared to the original Tersoff potential). The AIREBO and Tersoff-2010 compete in accuracy depending on the specific branch. The AIREBO potential overestimates the TO and LO branches (especially around Γ) somewhat more than the Tersoff-2010 potential. Also, while AIREBO underestimates the ZO branch, Tersoff-2010 overestimates it. The description of the acoustic branches is more or less on equal footing, with the AIREBO providing a more accurate TA branch and Tersoff-2010 providing the most accurate ZA branch (of all the given potentials). What is very apparent in the dispersion curves from all of the potentials used here is their general failure in describing the highest optical mode around the K point.

Bottom Line: The method is promising for systems with large scale periodicity, accounts for anharmonic effects and non-bonding interactions with a general environment, and it is applicable under finite temperatures.The potentials used show diverse behaviour.The Tersoff-2010 potential exhibits the most systematic and physically sound behaviour in this regard, and gives a first-order temperature coefficient of χ = -0.05 cm(-1)/K for the Γ-E2g shift in agreement with reported experimental values.

View Article: PubMed Central - PubMed

Affiliation: Institute of Chemical Engineering Sciences, Foundation of Research and Technology-Hellas (FORTH/ICE-HT), Stadiou Street, Platani, Patras, 26504 Greece.

ABSTRACT
A method that utilises atomic trajectories and velocities from molecular dynamics simulations has been suitably adapted and employed for the implicit calculation of the phonon dispersion curves of graphene. Classical potentials widely used in the literature were employed. Their performance was assessed for each individual phonon branch and the overall phonon dispersion, using available inelastic x-ray scattering data. The method is promising for systems with large scale periodicity, accounts for anharmonic effects and non-bonding interactions with a general environment, and it is applicable under finite temperatures. The temperature dependence of the phonon dispersion curves has been examined with emphasis on the doubly degenerate Raman active Γ-E2g phonon at the zone centre, where experimental results are available. The potentials used show diverse behaviour. The Tersoff-2010 potential exhibits the most systematic and physically sound behaviour in this regard, and gives a first-order temperature coefficient of χ = -0.05 cm(-1)/K for the Γ-E2g shift in agreement with reported experimental values.

No MeSH data available.


Related in: MedlinePlus