Force Constant Defects Research Articles

Inductive intrinsic localized modes in a one-dimensional nonlinear electric transmission line.

The experimental properties of intrinsic localized modes (ILMs) have long been compared with theoretical dynamical lattice models that make use of nonlinear onsite and/or nearest-neighbor intersite potentials. Here it is shown for a one-dimensional lumped electrical transmission line that a nonlinear inductive component in an otherwise linear parallel capacitor lattice makes possible a new kind of ILM outside the plane wave spectrum. To simplify the analysis, the nonlinear inductive current equations are transformed to flux transmission line equations with analog onsite hard potential nonlinearities. Approximate analytic results compare favorably with those obtained from a driven damped lattice model and with eigenvalue simulations. For this mono-element lattice, ILMs above the top of the plane wave spectrum are the result. We find that the current ILM is spatially compressed relative to the corresponding flux ILM. Finally, this study makes the connection between the dynamics of mass and force constant defects in the harmonic lattice and ILMs in a strongly anharmonic lattice.

Far-infrared spectroscopy of Cd1−xMnxS quantum dots

Far-infrared reflectivity spectra, in spectral region 50–600cm−1 and temperature region 80–300K, of CdS and Cd1−xMnxS nanocrystals embedded in hexametaphosphate, are presented. The analysis of the far-infrared experimental reflectivity spectrum was made by the fitting procedure. The Maxwell–Garnet effective medium theory is used for modeling an effective dielectric function as well as to separate respond from nanoparticles.To analyze spectra in CdS ωTO(≈238cm−1) to ωLO(≈305cm−1) spectral region, quantized dipolar modes in a spherical isotropic material quantum dot (QD) are considered in the framework of a continuum model. As to the mechanical boundary conditions rigid sphere is concerned. Experimental far-infrared reflectivity spectra of our samples are in general agreement with the predictions of this model.Experimentally registered and through fitting procedure located features for CdS nanoparticles in spectral region below CdS ωTO at: ≈102cm−1, ≈135cm−1, ≈170cm−1 and ≈210cm−1 are associated to defect induced modes, especially to defects located near the surface of CdS QD. In region over CdS ωLO, modes are identified as multiphonons. In Cd1−xMnxS QD spectra new reflectivity peaks are at: ≈85cm−1, ≈110cm−1 and ≈180cm−1 in spectral region below CdS ωTO, ≈270cm−1 inside CdS ωTO–ωLO spectral region and ≈356cm−1 and ≈376cm−1 in region over CdS ωLO. First two registered modes are associated to both mass and force constant defects at the surface, and rest four modes are consequence of MnS phases present in the sample.

Cd<sub>1-x</sub>Mn<sub>x</sub>S Nanoparticles: Far-Infrared Phonon Spectroscopy

Phonon spectra of Cd1-xMnxS (x = 0; 0.01; 0.05; 0.1; 0.15; 0.3) nanoparticles (d ~ 4.5 nm) have been investigated by far-infrared reflection (FIR) (spectral range 40 - 600 cm-1, temperature range 80 – 300 K) and Raman spectroscopy (100 – 700 cm-1, 300 K). Cd1-xMnxS nanoparticles have been synthesized by using aqueous solution precipitation. We obtained interesting features in FIR spectra: there are expected modes of bulk CdS (240 cm-1, 300 cm-1), new modes connected with nano-size of CdS (130 cm-1, 170 cm-1) and additional mode at 120 cm-1 in Cd1-xMnxS nanoparticles which can be assigned to the presence of Mn. The position of obtained modes is discussed in the frame of the linear chain model with both mass and force constant defects. Raman spectroscopy gives us only the mode at 300 cm-1 and its second harmonic.

Properties of IR-active lattice vibrations in the vicinity of kinks in the Frenkel-Kontorova model

The properties of infrared lattice vibrations in the presence of kinks in the Frenkel-Kontorova model are analyzed. Our results show that the vibration of particles involved in kink formation is very similar to that in a gap mode around a force-constant defect. We found that the IR phonon mode intensity possesses a universal dependence on a certain combination of system parameters and kink concentration. On the basis of these results a criterion is proposed for separating the regime of weakly interacting kinks in the system from the regime of a kink lattice.

Band-Theoretical Interpretation of Stationary Localized Modes in Pure Nonlinear Lattices-Ubiquity of Existence and Similarity to Force-Constant-Defect Modes-

A lattice Green's function theory is formulated to give a band-theoretical interpretation of stationary nonlinear localized modes (SNLM) in pure nonlinear lattices. In one-dimensional lattices and in its simplest form in higher-dimensional cases, the theory yields the eigenfrequency ω of the SNLM in terms of the frequency ω 0 ( q ) ( q is the wave vector) of the corresponding linear lattice in the form ω=ω 0 ( q 0 + i K ), where q 0 is an edge point of the Brillouin zone of ω 0 ( q ), and K ≡ K ( A ) is a parameter depending on the localized mode amplitude A. Such a result and more general ones involving lattice Green's functions lead to the ubiquity of the existence of the SNLM irrespective of the lattice dimensionality as approximate nonlinear modes in nonintegable lattices and its similarity to force-constant defect modes. Stationary solitons in the Ablowitz-Ladik lattice can be considered as an example of the SNLM in integrable lattices.

A quantum field theory of localized and resonant modes in 3D nonlinear lattices at finite temperatures II

We solve the eigenvalue equation derived in paper I under the assumption that a localized or resonant mode is well-localized at a lattice site. Localized modes appear above the top of the phonon band for an appropriate positive quartic potential at any temperatures. Resonant modes appear in the middle of the phonon band for an appropriate negative quartic potential at low temperatures due to the frequency dependent coupling of the mode. This fact is essentially different from that in the force constant defect, where resonant modes appear in the lower frequency regions due to the frequency independent couplings. Both modes are investigated numerically using the tables of the Green's functions for monoatomic simple cubic lattices in terms of the Bessel functions. Resonant modes are also investigated in the Debye approximation.

A quantum field theory of resonant modes in 3-d nonlinear lattices at finite temperatures

We establish the Heisenberg equation for phonon operators in 3-d nonlinear lattices at finite temperatures. Applying the one loop approximation to the nonlinear potential in the Heisenberg equation, we obtain a dynamical equation with a self-consistent potential created by a spatially localized mode. Under the assumption that the mode is well-localized at a lattice site, we obtain an eigenvalue equation with the frequency dependent couplings corresponding to that for the force constant defects in linear lattices. However, the frequency dependent couplings allow only frequencies near the middle of the phonon bands, while the constant couplings allow low frequencies.

Lattice Dynamics of the Force Constant Defect System Pd0.95Ru0.05

AbstractThe lattice dynamics of a Pd0.95Ru0.05 single crystal is investigated at room temperature. The phonon dispersion relations along the directions [100], [110], and [111] are measured using the inelastic neutron scattering technique. The seven‐neighbour Born‐von‐Kármán model is fitted to the experimental branches and the force constants and elastic constants are calculated. The phonon frequency shifts, Δω(q), and the self‐energy functions, Σj (q, ωj(q)), are determined. From the comparison of the self‐energy functions for 5 and 10 at% Ru contents in Pd matrix the evolution of the self‐energy with the Ru concentration is clearly seen.

Computer simulation of intrinsic localized modes in one-dimensional and two-dimensional anharmonic lattices.

The properties of stable and movable intrinsic localized vibrations (ILV's) have been investigated by the particle method. It is shown primarily with the help of computer experiments that an ILV in an anharmonic lattice is identical to a localized vibration near a force-constant defect in a harmonic lattice. The temperature dependence of the localization threshold is presented. The differences between ILV's and solitons are discussed. A brief study is also made on the existence of ILV in a two-dimensional square lattice.

Dynamique de reseau et frequences des modes de vibration pour des impuretes substitutionnelles dans InP, GaP et ZnS

The model used is a rigid-ion model with an effective ionic charge including general interactions for nearest and next nearest neighbours and long range Coulomb interactions. It provides a good fit with available neutron data and with IR absorption results for InP. In this model, no hypothesis is made a priori on the interatomic forces and the eleven parameters given by the model are used. A mathematical model which employs a Green's function technique in the mass defect and the nearest neighbour force constant defect approximation is used to calculate the lattice dynamics of the imperfect crystal. The frequencies of the local modes, the gap modes and the band modes, are given for isolated substitutional impurities. The same calculation is achieved for GaP and ZnS and the results are compared with IR data.

Phonon bands in disordered systems with both mass and force constant defects: Isotopic mixed ice Ih

An isotopic mixed crystal study is conducted on the 226.5 cm−1 phonon band in ice Ih. The result shows an amalgamation limit for this band with no significant clustering effect and indicates the absence of any isotope selectivity of the hydrogen bonds. The experimentally obtained self-energy when plotted against the mole fraction of the impurity (D2O) yields a symmetric curve pointing out that the additional disorder in the mixed crystals is purely dynamic. The self-energy curve is fitted into a polynomial of the mole fraction of the impurity using regression analysis. The polynomial obtained reveals the importance of both the mass defect and the force constant defect. The result obtained is also shown to provide information regarding the dispersion of this phonon band.

A new method for calculating the influence of force constant changes on the mean square displacements of surface atoms

The temperature dependence of the mean square displacements and the mean square momenta of surface atoms is studied using a series expansion. The elements of the series are calculated—even in the high temperature limit—by inverting dynamical matrices. Two parallel crystal surfaces are considered as a ‘force constant defect’ of a crystal with cyclic boundary conditions. Only elements of the dynamical matrices corresponding to atoms in the first two layers parallel to the surfaces are affected by the surfaces. As a consequence matrix partitioning permits a calculation of the inverse dynamical matrices by inverting matrices of much smaller dimension. Calculations are performed for the (100) surface of f.c.c. lattices using two Born-von Karman models with interactions up to third nearest neighbours. In the high temperature limit the influence of a change in the coupling constants for central forces between nearest neighbours at the surface is investigated. The coupling constant for central forces between an atom in the first layer and its nearest neighbours in the same layer and the coupling constant for central forces between an atom in the first layer and its nearest neighbours in the second layer are varied independently. A comparison between theoretical results and experimental data from low-energy electron diffraction is given.