Influence of the static electron gas screening function on the lattice dynamics of sodium

1970 ◽  
Vol 48 (2) ◽  
pp. 183-192 ◽  
Author(s):  
D. J. W. Geldart ◽  
Roger Taylor ◽  
Y. P. Varshni
Keyword(s):  
Distribution Function ◽  
Lattice Dynamics ◽  
Phonon Frequency ◽  
Phonon Dispersion ◽  
Electron Gas ◽  
Phonon Dispersion Curves ◽  
X Ray ◽  
Debye Temperatures ◽  
Static Electron ◽  
Good Agreement

The static electron gas screening function calculated by Geldart and Taylor has been used in conjunction with the theory of Vosko, Taylor, and Keech to calculate the phonon dispersion curves, the effective calorimetric and X-ray Debye temperatures, and moments of the phonon frequency distribution function of sodium. The results which compare very favorably with those obtained using other screening functions give good agreement with experiment, indicating that the new screening function is reasonably adequate for calculations in sodium.

Atomistic simulation of phonon dispersion for body-centred cubic alkali metals

2008 ◽  
Vol 86 (6) ◽  
pp. 801-805 ◽  
Author(s):  
Y Xie ◽  
J -M Zhang
Keyword(s):  
Cohesive Energy ◽  
Atomistic Simulation ◽  
Alkali Metals ◽  
Phonon Frequency ◽  
Phonon Dispersion ◽  
Atomistic Simulations ◽  
Phonon Dispersion Curves ◽  
Embedded Atom ◽  
Atomic Force ◽  
Good Agreement

Atomistic simulations of phonon dispersion for body-centred cubic alkali metals were carried out using the modified analytic embedded atom potentials. The expressions for atomic force constants are derived, the cohesive energy and elastic constants are calculated, and the phonon dispersion curves of Li, Na, K, Rb, and Cs are calculated along five principal symmetry directions. The calculated results are in good agreement with the available experiments. For all of the five alkali metals, in the same direction, a similar phonon dispersion curve is obtained in spite of the successive phonon frequency decreases for Li, Na, K, Rb, and Cs, which may be related to the atom mass increases or the cohesive energy decreases. PACS Nos.: 63.20.Dj, 71.20.Dg, 31.15.Ct

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 of ZnTe, CdTe, GaP, and InP

1980 ◽  
Vol 58 (3) ◽  
pp. 351-358 ◽  
Author(s):  
M. S. Kushwaha ◽  
S. S. Kushwaha
Keyword(s):  
Lattice Dynamics ◽  
Present Model ◽  
Phonon Dispersion ◽  
Model Parameters ◽  
Force Model ◽  
Phonon Dispersion Curves ◽  
Bending Force ◽  
Zinc Blende ◽  
Bond Bending ◽  
Good Agreement

An eight-parameter bond-bending force model (BBFM), recently developed by us for zinc-blende (ZB) structure, has been used to study the lattice dynamics of other compounds of the II–VI and III–V groups. The model parameters were calculated using six critical point phonon frequencies, two elastic constants, and the lattice equilibrium condition. Phonon dispersion curves, phonon density of states, and Debye-characteristic temperatures have been calculated. The comparison of theoretical and the available experimental results reveals a fairly good agreement. The merits and demerits of the present model have been discussed in full.

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.

Temperature-dependent X-ray dynamical diffraction: Darwin theory simulations

1999 ◽  
Vol 55 (1) ◽  
pp. 14-19 ◽  
Author(s):  
Jin-Seok Chung ◽  
Stephen M. Durbin
Keyword(s):  
Phonon Dispersion ◽  
Lattice Vibrations ◽  
X Ray Diffraction ◽  
Temperature Dependent ◽  
Phonon Dispersion Curves ◽  
Dynamical Diffraction ◽  
X Ray ◽  
Ergodic Hypothesis ◽  
Thermal Vibrations ◽  
Good Agreement

Thermal vibrations destroy the perfect crystalline periodicity generally assumed by dynamical diffraction theories. This can lead to some difficulty in deriving the temperature dependence of X-ray reflectivity from otherwise perfect crystals. This difficulty is overcome here in numerical simulations based on the extended Darwin theory, which does not require periodicity. Using Si and Ge as model materials, it is shown how to map the lattice vibrations derived from measured phonon dispersion curves onto a suitable Darwin model. Good agreement is observed with the usual Debye–Waller behavior predicted by standard theories, except at high temperatures for high-order reflections. These deviations are discussed in terms of a possible breakdown of the ergodic hypothesis for X-ray diffraction.

scholarly journals Study of lattice dynamics of silicon

BIBECHANA ◽  
2012 ◽  
Vol 9 ◽  
pp. 13-17
Author(s):  
SRB Thapa
Keyword(s):  
Lattice Dynamics ◽  
Phonon Dispersion ◽  
Characteristic Temperature ◽  
Central Force ◽  
Phonon Dispersion Curves ◽  
Valence Force Field ◽  
Model Following ◽  
Bond Stretching ◽  
Bond Bending ◽  
Good Agreement

Lattice dynamics of Si has been investigated by using a Urey-Bradley Valence Force Field (UVFF) model which is a phenomenological model. In this model following interactions are taken into account: (i) the central force due to bond-stretching (ii) the angular force due to bond bending (iii) central force between non-bonded atoms (iv) the force due to interaction of one internal co-ordinate to adjacent internal coordinate. Calculated results of phonon dispersion curves, Debye Characteristic temperature, microscopic elastic constants and Bulk modulus of Si are compared with experimental results giving fairly good agreement. DOI: http://dx.doi.org/10.3126/bibechana.v9i0.7145BIBECHANA 9 (2013) 13-17

Calculation of Phonon Dispersion for 3d Transition Metals Cr and Fe by Modified Analytic Embedded Atom Method

2011 ◽  
Vol 411 ◽  
pp. 532-536
Author(s):  
You Xie ◽  
Jian Min Zhang
Keyword(s):  
Experimental Data ◽  
Transition Metals ◽  
Phonon Frequency ◽  
Phonon Dispersion ◽  
Phonon Dispersion Curve ◽  
Embedded Atom Method ◽  
Body Centered Cubic ◽  
Phonon Dispersion Curves ◽  
Embedded Atom ◽  
Good Agreement

The modified analytical embedded atom method is applied to calculate the phonon dispersion of body-centered cubic 3d transition metals Cr and Fe along five symmetry directions [q 0 0], [1 q q], [q q q], [q q 0] and [1/2 1/2 q]. Our results of phonon dispersion curves are in good agreement with the available experimental data. For the two transition metals Cr and Fe, along the same direction, a similar phonon dispersion curve is obtained in spite of the phonon frequency decreases for Cr and Fe due to the atom mass increases. There are no experimental results for comparison along the directions [1 q q] and [1/2 1/2 q], further experimental measurement are needed.

Lattice Dynamics and Short Range Correlations in B.C.C. 3He

1971 ◽  
Vol 49 (23) ◽  
pp. 2997-3009 ◽  
Author(s):  
H. R. Glyde ◽  
F. C. Khanna
Keyword(s):  
Effective Potential ◽  
Lattice Dynamics ◽  
Phonon Dispersion ◽  
Phonon Branch ◽  
Phonon Dispersion Curves ◽  
Hartree Fock ◽  
Debye Temperatures ◽  
Upward Curvature ◽  
Scattering Response ◽  
T Matrix

A T-matrix method for determining the effective potential appropriate to the correlated Gaussian functions employed in lattice dynamics is developed. The method is similar to those discussed by Guyer and Horner for single particle functions. The T matrix and the correlated functions are then computed iteratively, much as suggested for the Brueckner–Hartree–Fock method for nuclear matter, to obtain an internally consistent result. Employing the T matrix, phonon dispersion curves, elastic constants, and Debye temperatures which include the cubic anharmonic term are calculated. The cubic contribution is larger for the T matrix than for the Nosanow effective potential and this leads to upward curvature of the T2[110] phonon branch, as noted by Horner, and thus a possible explanation of the anomalous Debye temperature observed at low temperatures. No resolvable second peaks in the scattering response functions were found.

CALCULATION OF PHONON DISPERSION FOR TRANSITION METALS V, Nb AND Ta

2011 ◽  
Vol 25 (29) ◽  
pp. 4047-4053 ◽  
Author(s):  
YOU XIE ◽  
JIAN-MIN ZHANG
Keyword(s):  
Transition Metals ◽  
Lattice Dynamics ◽  
Phonon Frequency ◽  
Phonon Dispersion ◽  
Atomic Mass ◽  
The Other ◽  
Embedded Atom Method ◽  
High Symmetry ◽  
Embedded Atom ◽  
Good Agreement

Combining the modified analytic embedded atom method (MAEAM) with lattice dynamics theory, the phonon dispersion along five symmetry directions have been calculated for three transition metals V, Nb and Ta . A good agreement between calculations and experiments along three high symmetry directions [q00], [qqq] and [qq0] implies that the predicted phonon dispersion along the other two directions [1qq] and [Formula: see text] are well behaved. Along each direction, the phonon frequency decreases for V, Nb and Ta successively may be related to the ratio of the cohesive energy to atomic mass.

The crystal dynamics of cuprous halides

1982 ◽  
Vol 60 (11) ◽  
pp. 1589-1594 ◽  
Author(s):  
Manvir S. Kushwaha
Keyword(s):  
Phonon Dispersion ◽  
Characteristic Temperature ◽  
Force Model ◽  
Phonon Dispersion Curves ◽  
Debye Characteristic Temperature ◽  
Zinc Blende ◽  
Crystal Dynamics ◽  
Bond Bending ◽  
Dynamical Description ◽  
Good Agreement

The lattice dynamics of cuprous halides have been thoroughly investigated by means of an 8-parameter bond-bending force model (BBFM), recently developed and applied successfully to study phonons in various II–VI and III–V compound semiconductors having zinc-blende (ZB) structure. The application of BBFM is made to calculate the phonon dispersion relations, phonon density of states, and temperature variation of the Debye characteristic temperature [Formula: see text] of CuCl, CuBr, and CuI. The room-temperature neutron scattering measurements for phonon dispersion curves along three principal symmetry directions and calorimetric experimental data for the Debye characteristic temperature have been used to check the validity of BBFM for the three crystals. The overall good agreement between theoretical and experimental results supports its use as an appropriate model for the dynamical description of ZB crystals.

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