Local normal modes and lattice dynamics

2018 ◽  
Vol 124 (4) ◽  
pp. 045102 ◽  
Author(s):  
Seyed H. Nasrollahi ◽  
Dimitri D. Vvedensky
Keyword(s):  
Lattice Dynamics ◽  
Normal Modes

Analysis of Heat Conduction in Silicon Using Molecular Dynamics Simulations

2006 ◽  
Author(s):  
Asegun S. Henry ◽  
Gang Chen
Keyword(s):  
Molecular Dynamics ◽  
Lattice Dynamics ◽  
Crystalline Silicon ◽  
Relaxation Times ◽  
Normal Modes ◽  
Md Simulations ◽  
Dynamics Simulations ◽  
Technological Significance ◽  
Fitting Parameters ◽  
Phonon Properties

Silicon's material properties, have been studied extensively because of its technological significance in a variety of industries, including microelectronics. Yet, questions surrounding the phonon relaxation times in silicon continue to linger.1,2 Previous theoretical works3-5 have generated qualitative expressions for phonon relaxation times, however these approaches require fitting parameters that cannot be determined reliably. This paper first discusses implementation issues associated with using the Green-Kubo method in molecular dynamics (MD) simulations. We compare various techniques used in similar works and discusses several implementation issues that have arisen in the literature. We then describe an alternative procedure for analyzing the normal modes of a crystal to extract phonon relaxation times. As an example material we study bulk crystalline silicon using equilibrium MD simulations and lattice dynamics. The environment dependent interatomic potential6 is used to model the interactions and frequency dependent phonon properties are extracted from the MD simulations.

scholarly journals Parameter-free predictions of the viscoelastic response of glassy polymers from non-affine lattice dynamics

Soft Matter ◽  
2018 ◽  
Vol 14 (42) ◽  
pp. 8475-8482 ◽  
Author(s):  
Vladimir V. Palyulin ◽  
Christopher Ness ◽  
Rico Milkus ◽  
Robert M. Elder ◽  
Timothy W. Sirk ◽  
...  
Keyword(s):  
Finite Temperature ◽  
Lattice Dynamics ◽  
Normal Modes ◽  
Glassy Polymers ◽  
Internal Stresses ◽  
Viscoelastic Response ◽  
Viscoelastic Moduli ◽  
P Parameter ◽  
Instantaneous Normal Modes

Parameter-free predictions of viscoelastic moduli at finite temperature are obtained by accounting for internal stresses and instantaneous normal modes within athermal non-affine theory.

LATTICE DYNAMICS OF α-LiIO3

1991 ◽  
Vol 05 (17) ◽  
pp. 1167-1173
Author(s):  
YIMIN JIANG ◽  
HONG LIN ◽  
CHENG GOU ◽  
SHIWEN NIU
Keyword(s):  
Lattice Dynamics ◽  
Molecular Crystal ◽  
Field Model ◽  
Phonon Dispersion ◽  
Normal Modes ◽  
Coulomb Force ◽  
Strong Mixing ◽  
Phonon Dispersion Curves ◽  
Good Agreement ◽  
Rigid Ion Model

The phonon dispersion curves of α- LiIO 3, which exhibit a characteristic molecular crystal behaviour, are calculated on the basis of a modified rigid-ion model in which a Born-Mayer potential is used for short-range repulsive interactions between Li ions and [Formula: see text] groups and a central force constant model is used for internal interactions in the [Formula: see text] group. The computed phonon frequencies are in good agreement with those of Raman, infrared and neutron measurements. The calculations show a strong mixing of the pre-normal modes given by Crettez et al.,4 therefore indicating that the long-range Coulomb force may change greatly the assignments previously obtained from a force-field model.

Theory of the lattice vibrations of germanium

1959 ◽  
Vol 253 (1273) ◽  
pp. 260-276 ◽  
Keyword(s):  
Elastic Constants ◽  
Lattice Dynamics ◽  
Normal Modes ◽  
Wave Number ◽  
Simple Explanation ◽  
Lattice Vibrations ◽  
Germanium Crystal ◽  
Frequency Wave ◽  
Oppositely Charged ◽  
Good Agreement

Previous attempts to explain the frequency-wave number relations for the normal modes of germanium, which have been determined experimentally by Brockhouse & Iyengar, have required the assumption of force constants between atoms which are relatively far apart. The theory then involves a large number of undetermined parameters which have no obvious physical justification, and the fact that the elastic constants of germanium satisfy an identity which might suggest that only interactions between adjacent atoms are important, has to be dismissed as a coincidence. In this paper we extend the Born-von Kármán theory of lattice dynamics to apply to a simple model of the germanium crystal, in which each atom is regarded as a charged core coupled to an oppositely charged shell. This gives the atom the property of polarizability, not only in an electric field but also under the influence of bonding interactions between adjacent atoms. On the basis of this model, the frequency-wave number relations can be reasonably well accounted for with only two disposable parameters, and a simple explanation is provided of the fact that the elastic constants satisfy Born’s identity. The value deduced for the polarizability of a germanium atom, using the neutron spectroscopy data of Brockhouse & Iyengar, is in good agreement with that determined directly from the dielectric constant. An extension of the theory of Mashkevich & Tolpygo provides some theoretical justification for the use of a shell model for germanium.

scholarly journals Lattice Dynamics of YBa2Cu3O6+x (x = 0·25, 0·5, 0.75)

1993 ◽  
Vol 46 (4) ◽  
pp. 535 ◽  
Author(s):  
KK Yim ◽  
J Oitmaa ◽  
MM Elcombe
Keyword(s):  
Oxygen Concentration ◽  
Density Of States ◽  
Coulomb Potential ◽  
Lattice Dynamics ◽  
Short Range ◽  
Phonon Dispersion ◽  
Normal Modes ◽  
Phonon Density ◽  
Phonon Density Of States ◽  
Phonon Dispersion Curves

The lattice dynamics of YBa2Cu306+x with partially filled 0(4) sites is investigated using a supercell method. The model used is the lattice-dynamical shell model, which incorporates the short-range interactions and the long-range Coulomb potential as well as the polarisabilities of ions. Varying the oxygen content produces small changes throughout the spectrum of normal modes, as well as major changes in those modes with large 0(4) amplitudes. Selected phonon dispersion curves are presented, with emphasis on the variation of frequency with oxygen concentration. The nature of new modes, which appear with an increase in oxygen concentration, is investigated. The overall phonon density of states is also presented.

A new model for the lattice dynamics of Zn–Cd chalcogenides

1985 ◽  
Vol 63 (4) ◽  
pp. 494-497 ◽  
Author(s):  
R. K. Ram ◽  
S. S. Kushwaha ◽  
S. P. Singh
Keyword(s):  
Satisfactory Agreement ◽  
Wave Vector ◽  
Lattice Dynamics ◽  
Normal Modes ◽  
Ionic Model ◽  
Frequency Wave ◽  
New Model ◽  
Zinc Blende ◽  
Cd Chalcogenides ◽  
Zinc Blende Structure

A noncentral second neighbour ionic model is proposed for calculating frequency wave vector dispersion relations for the normal modes of vibrations for zinc and cadmium tellurides crystallizing in the zinc blende structure. The model takes into account the change in energy owing to rotation of bonds. The calculated phonon frequencies show a reasonably satisfactory agreement with the available optic data.

The lattice dynamics of thallous bromide

1967 ◽  
Vol 300 (1460) ◽  
pp. 45-61 ◽  
Keyword(s):  
Single Crystal ◽  
Lattice Dynamics ◽  
Room Temperature ◽  
Inelastic Neutron Scattering ◽  
Normal Modes ◽  
Inelastic Neutron ◽  
Sum Rule ◽  
Shell Models ◽  
Modes Of Vibration ◽  
Higher Temperature

We have measured the frequencies of a representative set of normal modes of vibration of a single crystal of thallous bromide at room temperature and at 100°K using inelastic neutron scattering techniques. Most of the frequencies are almost independent of temperature, but some modes seem to display marked broadening of the neutron groups at the higher temperature. Various rigid-ion and shell models have been fitted to the results obtained at 100°K. A shell model involving 14 adjustable parameters is reasonably successful in describing the dispersion curves, although some discrepancies remain which are best revealed by an analysis utilizing Rosenstock’s sum rule. Extensive calculations have been made of the properties of the best model and for comparison some of the properties of other models have also been calculated.

Crystal structure and lattice dynamics of hydrogen-loaded austenitic steel

2003 ◽  
Vol 112 ◽  
pp. 407-410
Author(s):  
S. A. Danilkin ◽  
M. Hölzel ◽  
H. Fuess ◽  
H. Wipf ◽  
T. J. Udovic ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Austenitic Steel ◽  
Lattice Dynamics
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