Computing Phonon Dispersion using Fast Zero-Point Correlations of Conjugate Variables

MRS Advances ◽  
2018 ◽  
Vol 3 (10) ◽  
pp. 531-536 ◽  
Author(s):  
Anant Raj ◽  
Jacob Eapen
Keyword(s):  
Normal Mode ◽  
Phonon Dispersion ◽  
Zero Point ◽  
Time Correlation ◽  
Initial Time ◽  
Phonon Modes ◽  
Phonon Dispersion Curves ◽  
Time Correlations ◽  
Anharmonic Interactions ◽  
Equipartition Of Energy

ABSTRACTTime correlations of dynamic variables in the reciprocal space offer a rich theoretical setting for computing the phonon dispersion curves, particularly for systems with marked anharmonic interactions. Present techniques primarily rely either on the equipartition of energy between the phonon modes or on the oscillation of the time correlation of the normal mode projections. The former can lead to numerical errors due to deviation from equipartition while the latter usually requires long simulations for computing the time correlations. We investigate a different approach using the ratio of the normal mode expectation value of two conjugate variables – velocity and acceleration. Since only the correlations at the initial time (t=0) are needed, this approach is computationally attractive. In this work, we employ this method to extract the full Brillouin zone phonon dispersion for graphene.

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.

Structural, elasto-mechanical and phonon-related properties of MnCrP: A DFT Study

2020 ◽  
Vol 34 (21) ◽  
pp. 2050200
Author(s):  
A. Afaq ◽  
Abu Bakar ◽  
Muhammad Shoaib ◽  
Rashid Ahmed ◽  
Anila Asif
Keyword(s):  
Mechanical Stability ◽  
Phonon Dispersion ◽  
Structural Parameters ◽  
Far Infrared ◽  
Phonon Modes ◽  
Phonon Dispersion Curves ◽  
Anisotropic Factor ◽  
Cauchy Pressure ◽  
The Stability ◽  
Thermal Vibrations

The Half Heusler alloy (HHA) MnCrP has been studied theoretically for structural, elasto-mechanical and phonon properties. The structure is optimized and the calculated structural parameters are close to the literature. This optimized data is used to estimate three independent second-order cubic elastic constants [Formula: see text], [Formula: see text] and [Formula: see text]. The mechanical stability criteria are explored by these constants and further used to estimate the elastic moduli; Young’s, bulk and shear modulus. The mechanical parameters like Poisson’s ratio, Pugh’s ratio, anisotropic factor, Cauchy pressure, shear constant, Lame’s constants, Kleinman parameter are also calculated and discussed. Discussions reveal the ductile nature, ionic behavior, anisotropic nature and mechanical stability of MnCrP. The metallic nature, compressibility, stiffness and interatomic forces of material are also described. Furthermore, the Debye temperature, where the collective vibrations shifts to an independent thermal vibrations, is also calculated. Longitudinal and transverse sound velocities are also obtained to investigate the phonon modes of oscillation. These phonon modes confirm the stability of the alloy as no negative phonon frequencies in the phonon-dispersion curves. These curves are used to estimate the reststrahlen band where light reflects 100% and the suitability of material is checked for Far Infrared (FIR), photographic, optoelectronic devices and sensors.

scholarly journals Phonon dynamics of Zr67Ni33 AND Fe80B20 binary glassy alloys

BIBECHANA ◽  
2021 ◽  
Vol 18 (1) ◽  
pp. 33-47
Author(s):  
Aditya M Vora ◽  
Alkesh L Gandhi
Keyword(s):  
Amorphous Alloys ◽  
Phonon Dispersion ◽  
Phonon Modes ◽  
Phonon Dispersion Curves ◽  
Pseudopotential Theory ◽  
Glassy Alloys ◽  
Phonon Dynamics ◽  
Different Temperatures ◽  
Alloy Atom ◽  
Acceptable Agreement

Binary amorphous alloys are the primary bulk metallic glasses (BMGs). Two binary BMGs Zr67Ni33 and Fe80B20 have been studied in the present work using the pseudo- alloy-atom (PAA) model based on the pseudopotential theory. Some important thermodynamic properties like Debye temperature and elastic properties like elasticity moduli and Poisson’s ratio at room temperature are theoretically computed with the help of pseudopotential theory from the elastic limit of the phonon dispersion curves (PDCs). The collective dynamics of longitudinal and transverse phonon modes are investigated in terms of eigenfrequencies of the localized collective modes. The presently computed results are compared with the other such data including theoretically generated results from the molecular dynamics at different temperatures as available in the literature and an acceptable agreement is found. BIBECHANA 18 (2021) 33-47 

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.

Effect of polarizability on the vibrational and thermal properties of rare gas solids

1978 ◽  
Vol 56 (7) ◽  
pp. 849-858 ◽  
Author(s):  
S. K. Jain ◽  
G. P. Srivastava
Keyword(s):  
Lattice Dynamics ◽  
Interatomic Potential ◽  
Phonon Dispersion ◽  
Zero Point ◽  
Rare Gas ◽  
Model Parameters ◽  
Point Energy ◽  
Phonon Dispersion Curves ◽  
Boundary Frequency ◽  
Experimental Values

A simple shell model theory has been developed for the study of lattice dynamics of monatomic crystals. The phonon dispersion curves and variations of heat capacities with temperature are reported for solidified krypton and argon. The model parameters have been evaluated using the recent experimental values of elastic constants, polarizability of atoms, and a zone boundary frequency in each case. The zero point effects are also included by expressing the zero point energy in terms of the interatomic potential. The agreement between the theoretical and experimental results is found to improve appreciably by incorporating polarizability of atoms.

scholarly journals Dispersion of Phonons in Ideal Crystals

1969 ◽  
Vol 22 (4) ◽  
pp. 471 ◽  
Author(s):  
NP Gupta
Keyword(s):  
Experimental Data ◽  
Phonon Dispersion ◽  
Zero Point ◽  
Lattice Vibrations ◽  
Rare Gases ◽  
Point Energy ◽  
Phonon Dispersion Curves ◽  
Debye Theory ◽  
Specific Heats ◽  
Theoretical Frequency

A quasiharmonic central force rigid-atom model has been used to study the lattice vibrations of frozen rare gases. The model takes care of interactions up to fourth neighbour and estimates zero-point energy and its volume derivatives by the Debye theory of specific heats. The theoretical frequency distribution and phonon dispersion curves are found to compare reasonably well with the available experimental data. Various causes of the discrepancies and possibilities of improvement of the results are discussed.

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.

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.

Long-wavelength phonons in 2H–NbS2, 2H–TaS2, and AgxTaS2

1984 ◽  
Vol 62 (8) ◽  
pp. 789-795 ◽  
Author(s):  
W. G. McMullan ◽  
J. C. Irwin
Keyword(s):  
Raman Spectrum ◽  
Phonon Dispersion ◽  
Phonon Modes ◽  
Phonon Dispersion Curves ◽  
Long Wavelength ◽  
Valence Force Field ◽  
Phonon Spectra ◽  
Analytic Expressions ◽  
Zone Centre ◽  
Zone Folding

The Raman spectra of 2H–NbS2 and 2H–TaS2 have been analyzed in terms of a valence-force-field (VFF) model that incorporates four parameters. Analytic expressions for the Brillouin-zone-centre phonon frequencies have been obtained from the model and used in conjunction with the Raman frequencies to evaluate the four force constants for the two compounds. The results are compared with the known phonon spectra of similar compounds. The Raman spectrum of AgxTaS2 has also been investigated as a function of silver concentration x. Three new phonon modes appear in the Raman spectrum of AgxTaS2 with x < 1/3 and these new modes are attributed to a zone-folding mechanism. The plausibility of this interpretation has been investigated using phonon dispersion curves calculated from the VFF model.

Sign in / Sign up

Export Citation Format

Share Document