Calculating the Phonon Modes of Graphene Using the 4th Nearest Neighbor Force Constant Method

2008 ◽  
Author(s):  
Mikiyas S. Tsegaye ◽  
Patrick E. Hopkins ◽  
Avik W. Ghosh ◽  
Pamela M. Norris
Keyword(s):  
Force Constant ◽  
Nearest Neighbor ◽  
Phonon Dispersion ◽  
Physical Structure ◽  
Dispersion Curves ◽  
Low Noise ◽  
Phonon Modes ◽  
Phonon Dispersion Curves ◽  
Molecular Systems ◽  
Potential Applications

Graphite has always been a very important material both industrially and academically due to its physical structure. But ever since the isolation of Graphene (a single sheet of Graphite) a few years ago, it’s been one of the most widely studied molecular systems for its potential applications in nano-electronics and other break-through areas. Some of the desirable traits of Graphene are its high thermal and electronic mobility, and its low noise properties. This paper outlines a standard method for calculating phonon dispersion curves in Graphene by making use of force constant measurements. This information is usually obtained from approximations of inter-atomic potentials, which involve derivatives of simplified potential approximations between every atom in Graphene to get the force constant tensors. In this paper, the measured values for the force constants are used in a mathematically rigorous way to calculate the Graphene phonon dispersion curves.

scholarly journals Lattice dynamics in CePd2Al2 and LaPd2Al2

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Petr Doležal ◽  
Petr Cejpek ◽  
Satoshi Tsutsui ◽  
Koji Kaneko ◽  
Dominik Legut ◽  
...  
Keyword(s):  
Lattice Dynamics ◽  
Phonon Dispersion ◽  
Elastic Interaction ◽  
Bound State ◽  
Dispersion Curves ◽  
Phonon Modes ◽  
Phonon Dispersion Curves ◽  
X Ray Scattering ◽  
Oppenheimer Approximation ◽  
Good Agreement

AbstractThe interaction between phonons and 4f electrons, which is forming a new quantum state (quasi-bound state) beyond Born-Oppenheimer approximation, is very prominent and lattice dynamics plays here a key role. There is only a small number of compounds in which the experimental observation suggest such a scenario. One of these compounds is CePd2Al2. Here the study of phonon dispersion curves of (Ce,La)Pd2Al2 at 1.5, 7.5, 80 and 300 K is presented. The inelastic X-ray scattering technique was used for mapping the phonon modes at X and Z points as well as in Λ and Δ directions, where the symmetry analysis of phonon modes was performed. The measured spectra are compared with the theoretical calculation, showing very good agreement. The measurements were performed in several Brillouin zones allowing the reconstruction of phonon dispersion curves. The results are discussed with respect to the magneto-elastic interaction and are compared with other cerium compounds. The phonon mode symmetry A1g was found to be unaffected by the interaction, which is in contrast to previous assumptions.

scholarly journals Phase Stability of the Tin Monochalcogenides SnS and SnSe: A Quasi-Harmonic Lattice-Dynamics Study

2021 ◽  
Author(s):  
Ioanna Pallikara ◽  
Jonathan Skelton
Keyword(s):  
Lattice Dynamics ◽  
Potential Energy Surfaces ◽  
Phonon Dispersion ◽  
Free Energies ◽  
Phonon Modes ◽  
Elastic Band ◽  
Phonon Dispersion Curves ◽  
Potential Applications ◽  
Band Method ◽  
Energy Surfaces

The tin monochalcogenides SnS and SnSe adopt four different crystal structures, <i>viz.</i> orthorhombic <i>Pnma</i> and <i>Cmcm</i> and cubic rocksalt and π-cubic (P2<sub>1</sub>3) phases, each of which has optimal properties for a range of potential applications. This rich phase space makes it challenging to identify the conditions under which the different phases are obtained. We have performed first-principles quasi-harmonic lattice-dynamics calculations to assess the relative stabilities of the four phases of SnS and SnSe. We investigate dynamical stability through the presence or absence of imaginary modes in the phonon dispersion curves, and we compute Helmholtz and Gibbs free energies to evaluate the thermodynamic stability. We also consider applied pressures from 0-15 GPa to obtain temperature-pressure phase diagrams. Finally, the relationships between the different crystal phases are investigated by explicitly mapping the potential-energy surfaces along the imaginary phonon modes and by using the climbing-image nudged elastic-band method.

scholarly journals Phase Stability of the Tin Monochalcogenides SnS and SnSe: A Quasi-Harmonic Lattice-Dynamics Study

2021 ◽  
Author(s):  
Ioanna Pallikara ◽  
Jonathan Skelton
Keyword(s):  
Lattice Dynamics ◽  
Potential Energy Surfaces ◽  
Phonon Dispersion ◽  
Free Energies ◽  
Phonon Modes ◽  
Elastic Band ◽  
Phonon Dispersion Curves ◽  
Potential Applications ◽  
Band Method ◽  
Energy Surfaces

The tin monochalcogenides SnS and SnSe adopt four different crystal structures, <i>viz.</i> orthorhombic <i>Pnma</i> and <i>Cmcm</i> and cubic rocksalt and π-cubic (P2<sub>1</sub>3) phases, each of which has optimal properties for a range of potential applications. This rich phase space makes it challenging to identify the conditions under which the different phases are obtained. We have performed first-principles quasi-harmonic lattice-dynamics calculations to assess the relative stabilities of the four phases of SnS and SnSe. We investigate dynamical stability through the presence or absence of imaginary modes in the phonon dispersion curves, and we compute Helmholtz and Gibbs free energies to evaluate the thermodynamic stability. We also consider applied pressures from 0-15 GPa to obtain temperature-pressure phase diagrams. Finally, the relationships between the different crystal phases are investigated by explicitly mapping the potential-energy surfaces along the imaginary phonon modes and by using the climbing-image nudged elastic-band method.

Phonons in chiral nanorods and nanotubes: A Cosserat-rod-based continuum approach

2019 ◽  
Vol 24 (12) ◽  
pp. 3897-3919
Author(s):  
Prakhar Gupta ◽  
Ajeet Kumar
Keyword(s):  
Phonon Dispersion ◽  
Coefficient Matrix ◽  
Molecular Data ◽  
Dispersion Curves ◽  
Mode Shapes ◽  
Wave Form ◽  
Phonon Modes ◽  
Continuum Approach ◽  
Phonon Dispersion Curves ◽  
Cosserat Rod

A Cosserat-rod-based continuum approach is presented to obtain phonon dispersion curves of flexural, torsional, longitudinal, shearing, and radial breathing modes in chiral nanorods and nanotubes. Upon substituting the continuum wave form in the linearized dynamic equations of stretched and twisted Cosserat rods, we obtain an analytical expression of a coefficient matrix (in terms of the rod’s stiffnesses, induced axial force, and twisting moment) whose eigenvalues and eigenvectors give us frequencies and mode shapes, respectively, for each of the above phonon modes. We show that, unlike the case of achiral tubes, these phonon modes are intricately coupled in chiral tubes owing to extension–torsion–inflation and bending–shear couplings inherent in them. This coupling renders the conventional approach of obtaining stiffnesses from the long wavelength limit slope of dispersion curves redundant. However, upon substituting the frequencies and mode shapes (obtained independently from phonon dispersion molecular data) in the eigenvalue–eigenvector equation of the above-mentioned coefficient matrix, we are able to obtain all the stiffnesses (bending, twisting, stretching, shearing, and all coupling stiffnesses corresponding to extension–torsion, extension–inflation, torsion–inflation, and bending–shear couplings) of chiral nanotubes. Finally, we show unusual effects of the single-walled carbon nanotube’s chirality as well as stretching and twisting of the nanotube on its phonon dispersion curves obtained from the molecular approach. These unusual effects are accurately reproduced in our continuum formulation.

scholarly journals Phase Stability of the Tin Monochalcogenides SnS and SnSe: A Quasi-Harmonic Lattice-Dynamics Study

2021 ◽  
Author(s):  
Ioanna Pallikara ◽  
Jonathan Skelton
Keyword(s):  
Lattice Dynamics ◽  
Potential Energy Surfaces ◽  
Phonon Dispersion ◽  
Free Energies ◽  
Phonon Modes ◽  
Elastic Band ◽  
Phonon Dispersion Curves ◽  
Potential Applications ◽  
Band Method ◽  
Energy Surfaces

The tin monochalcogenides SnS and SnSe adopt four different crystal structures, <i>viz.</i> orthorhombic <i>Pnma</i> and <i>Cmcm</i> and cubic rocksalt and π-cubic (P2<sub>1</sub>3) phases, each of which has optimal properties for a range of potential applications. This rich phase space makes it challenging to identify the conditions under which the different phases are obtained. We have performed first-principles quasi-harmonic lattice-dynamics calculations to assess the relative stabilities of the four phases of SnS and SnSe. We investigate dynamical stability through the presence or absence of imaginary modes in the phonon dispersion curves, and we compute Helmholtz and Gibbs free energies to evaluate the thermodynamic stability. We also consider applied pressures from 0-15 GPa to obtain temperature-pressure phase diagrams. Finally, the relationships between the different crystal phases are investigated by explicitly mapping the potential-energy surfaces along the imaginary phonon modes and by using the climbing-image nudged elastic-band method.

Phonon Dispersion Curves of aBC3Honeycomb Epitaxial Sheet

2004 ◽  
Vol 93 (17) ◽  
Author(s):  
H. Yanagisawa ◽  
T. Tanaka ◽  
Y. Ishida ◽  
M. Matsue ◽  
E. Rokuta ◽  
...  
Keyword(s):  
Phonon Dispersion ◽  
Dispersion Curves ◽  
Phonon Dispersion Curves
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