Article

1998 ◽  
Vol 76 (2) ◽  
pp. 143-151
Author(s):  
J S Ononiwu
Keyword(s):  
Lattice Dynamics ◽  
Alkaline Earth ◽  
Phonon Dispersion ◽  
Earth Metal ◽  
Model Potential ◽  
Dispersion Curves ◽  
The Body ◽  
Symmetry Direction ◽  
Normal Ordering ◽  
Phonon Dispersion Curves

A phenomenological one-parameter model potential that includes sp-d hybridization and core--core exchange contributions is used to calculate the phonon dispersion curves in the lattice dynamics of the body-centered cubic alkaline-earth metal, barium. There is good overall agreement between theory and experiment, and in particular, in the [xi00] direction we obtained frequencies of the transverse dispersion curves that are lower than those of the longitudinal dispersion curves along the [100] symmetry direction thereby restoring the normal ordering of the branches.PACS Nos.: 63.20D

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.

Lattice dynamics and Debye–Waller factors of some compounds with the sodium chloride structure

1999 ◽  
Vol 55 (6) ◽  
pp. 1014-1025 ◽  
Author(s):  
H. X. Gao ◽  
L.-M. Peng ◽  
J. M. Zuo
Keyword(s):  
Sodium Chloride ◽  
Lattice Dynamics ◽  
Polynomial Regression ◽  
Phonon Dispersion ◽  
Harmonic Approximation ◽  
Dispersion Curves ◽  
Phonon Dispersion Curves ◽  
Shell Models ◽  
Downhill Simplex ◽  
Physical Quantities

The lattice dynamics of 19 compounds with the sodium chloride structure have been investigated using shell models. The models are compared with existing experimentally measured phonon-dispersion curves and refined using a multidimensional downhill simplex method. Debye–Waller factors for these compounds are calculated over the temperature range from 1 to 1000 K where appropriate and the results are fitted analytically using polynomial regression. The results are compared with experimentally measured room-temperature Debye–Waller factors and for most of the compounds the agreement is found to be better than 10%. At lower temperatures, it is expected that these results would be more accurate, since the harmonic approximation, which is crucial to the calculation of the Debye–Waller factors, works better. In choosing the models for particular applications, it is recommended that the model with the smallest standard error \sigma is used for fitting the experimentally measured phonon-dispersion curves, or the model that shows best agreement with reliable experimental measurements of more relevant physical quantities, such as Debye–Waller factors in crystallography.

Lattice Dynamics

2003 ◽  
Author(s):  
Toshiaki Enoki ◽  
Morinobu Endo ◽  
Masatsugu Suzuki
Keyword(s):  
Brillouin Zone ◽  
Lattice Dynamics ◽  
Degrees Of Freedom ◽  
Phonon Dispersion ◽  
Dispersion Curves ◽  
Primitive Cell ◽  
Phonon Dispersion Curves ◽  
Modes Of Vibration ◽  
Stage 1 ◽  
Three Degrees Of Freedom

Pristine graphite crystallizes according to the D46h space group. There are twelve modes of vibration associated with the three degrees of freedom of the four atoms in the primitive cell. The hexagonal Brillouin zone and the phonon dispersion curves of pristine graphite, calculated by Maeda et al. (1979), are shown in Figure 4.1. The zone-center (Γ point) modes are labeled as three acoustic modes (A2u + Elu), three infrared active modes (A2u + Elu), four Raman active modes (2E2g), and two silent modes (2Blg). The first calculation of phonon dispersion for the stage-1 compounds KC8 and RbC8 was presented by Horie et al. (1980) on the basis of the model of Maeda et al. (1979) for the lattice dynamics of pristine graphite. Although the calculated phonon energies do not agree well with the experimental data, the model has most of the ingredients for describing the lattice dynamics of stage-1 GICs. A simple review of their work is presented as follows. The primitive cell of KC8, having a p(2 × 2)R0° superlattice, contains 16 carbon atoms and two K atoms. Note that only an αβ stacking sequence is assumed here (see Section 3.6.1). The primitive translation vectors are given by t1 (0, a, 0), t2 = (−√3a/2, a/2, 0), and t3 = (−√3a/4, −a/4, c), where a = 2aG = 4.91 Å and c = 5.35 × 2 = 10.70 Å. The corresponding Brillouin zone is shown in Figure 4.2b. The phonon dispersion for KC8 has been calculated by Horie et al. (1980) on the basis of the Born-von Karman force constant model. This dispersion curve is compared with that of pristine graphite by folding the dispersion curves of graphite into the first Brillouin zone of KC8. Since the side of the Brillouin zone in KC8 is not flat in two directions, as shown in Figure 4.2b, it is a little difficult to transfer the information on the dispersion curves in the first Brillouin zone of graphite into the Brillouin zone of KC8. For simplicity, nevertheless, we assume that the side of the Brillouin zone in KC8 is flat like that of graphite.

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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