Einstein Relation in n-Channel Inversion Layers of Nonlinear Optical, Optoelectronic and Related Materials: Simplified Theory, Relative Comparison and Suggestion for an Experimental Determination

In this paper, we study the Einstein relation for the diffusivity to mobility ratio (DMR) in n-channel inversion layers of non-linear optical materials on the basis of a newly formulated electron dispersion relation by considering their special properties within the frame work of k.p formalism. The results for the n-channel inversion layers of III-V, ternary and quaternary materials form a special case of our generalized analysis. The DMR for n-channel inversion layers of II-VI, IV-VI and stressed materials has been investigated by formulating the respective 2D electron dispersion laws. It has been found, taking n-channel inversion layers of CdGeAs2, Cd(3)AS(2), InAs, InSb, Hg1-xCdxTe, In1-xGaxAsyP1-y lattice matched to InP, CdS, PbTe, PbSnTe, Pb1-xSnxSe and stressed InSb as examples, that the DMR increases with the increasing surface electric field with different numerical values and the nature of the variations are totally band structure dependent. The well-known expression of the DMR for wide gap materials has been obtained as a special case under certain limiting conditions and this compatibility is an indirect test for our generalized formalism. Besides, an experimental method of determining the 2D DMR for n-channel inversion layers having arbitrary dispersion laws has been suggested.

Einstein relation in n-i-p-i and microstructures of nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestions for an experimental determination

We investigate the Einstein relation for the diffusivity-mobility ratio (DMR) for n-i-p-i and the microstructures of nonlinear optical compounds on the basis of a newly formulated electron dispersion law. The corresponding results for III-V, ternary and quaternary materials form a special case of our generalized analysis. The respective DMRs for II-VI, IV-VI and stressed materials have been studied. It has been found that taking CdGeAs2, Cd3As2, InAs, InSb, Hg1−xCdxTe, In1−xGaxAsyP1−y lattices matched to InP, CdS, PbTe, PbSnTe and Pb1−xSnxSe and stressed InSb as examples that the DMR increases with increasing electron concentration in various manners with different numerical magnitudes which reflect the different signatures of the n-i-p-i systems and the corresponding microstructures. We have suggested an experimental method of determining the DMR in this case and the present simplified analysis is in agreement with the suggested relationship. In addition, our results find three applications in the field of quantum effect devices.

Influence of crossed electric and quantizing magnetic fields on the Einstein relation in nonlinear optical, optoelectronic and related materials: Simplified theory, relative comparison and suggestion for experimental determination

An attempt is made to study the Einstein relation for the diffusivity-to-mobility ratio (DMR) under crossed fields' configuration in nonlinear optical materials on the basis of a newly formulated electron dispersion law by incorporating the crystal field in the Hamiltonian and including the anisotropies of the effective electron mass and the spin-orbit splitting constants within the framework of kp formalisms. The corresponding results for III-V, ternary and quaternary compounds form a special case of our generalized analysis. The DMR has also been investigated for II-VI and stressed materials on the basis of various appropriate dispersion relations. We have considered n-CdGeAs2, n-Hg1-xCdxTe, n-In1-xGaxAsyP1-y lattice matched to InP, p-CdS and stressed n-InSb materials as examples. The DMR also increases with increasing electric field and the natures of oscillations are totally band structure dependent with different numerical values. It has been observed that the DMR exhibits oscillatory dependences with inverse quantizing magnetic field and carrier degeneracy due to the Subhnikov-de Haas effect. An experimental method of determining the DMR for degenerate materials in the present case has been suggested. (C) 2010 Elsevier B.V. All rights reserved.

Simplified dispersion curves for circular cylindrical shells using shallow shell theory.

An alternative derivation of the dispersion relation for the transverse vibration of a circular cylindrical shell is presented. The use of the shallow shell theory model leads to a simpler derivation of the same result. Further, the applicability of the dispersion relation is extended to the axisymmetric mode and the high frequency beam mode.

Coupled amplitude theory of nonlinear surface acoustic waves

The nonlinear propagation characteristics of surface acoustic waves on an isotropic elastic solid have been studied in this paper. The solution of the harmonic boundary value problem for Rayleigh waves is obtained as a generalized Fourier series whose coefficients are proportional to the slowly varying amplitudes of the various harmonics. The infinite set of coupled equations for the amplitudes when solved exhibit an oscillatory slow variation signifying a continuous transfer of energy back and forth among the various harmonics. A conservation relation is derived among all the harmonic amplitudes.

A phase space approach to generalized Hamilton–Jacobi theory

Generalizations of H–J theory have been discussed before in the literature. The present approach differs from others in that it employs geometrical ideas on phase space and classical transformation theory to derive the basic equations. The relation between constants of motion and symmetries of the generalized H–J equations is then clarified. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Energy identities in water wave theory for free-surface boundary condition with higher-order derivatives

A modified form of Green's integral theorem is employed to derive the energy identity in any water wave diffraction problem in a single-layer fluid for free-surface boundary condition with higher-order derivatives. For a two-layer fluid with free-surface boundary condition involving higher-order derivatives, two forms of energy identities involving transmission and reflection coefficients for any wave diffraction problem are also derived here by the same method. Based on this modified Green's theorem, hydrodynamic relations such as the energy-conservation principle and modified Haskind–Hanaoka relation are derived for radiation and diffraction problems in a single as well as two-layer fluid.

Hamilton’s theory of turns and a new geometrical representation for polarization optics

Hamilton’s theory of turns for the group SU(2) is exploited to develop a new geometrical representation for polarization optics. While pure polarization states are represented by points on the Poincaré sphere, linear intensity preserving optical systems are represented by great circle arcs on another sphere. Composition of systems, and their action on polarization states, are both reduced to geometrical operations. Several synthesis problems, especially in relation to the Pancharatnam-Berry-Aharonov-Anandan geometrical phase, are clarified with the new representation. The general relation between the geometrical phase, and the solid angle on the Poincaré sphere, is established.

On the relation between rotation increments in different tangent spaces

In computational mechanics, finite rotations are often represented by rotation vectors. Rotation vector increments corresponding to different tangent: spaces are generally related by a linear operator, known as the tangential transformation T. In this note, we derive the higher order terms that are usually left out in linear relation. The exact nonlinear relation is also presented. Errors via the linearized T are numerically estimated. While the concept of T arises out of the nonlinear characteristics of the rotation manifold, it has been derived via tensor analysis in the context of computational mechanics (Cardona and Geradin, 1988). We investigate the operator T from a Lie group perspective, which provides a better insight and a 1-1 correspondence between approaches based on tensor analysis and the standard matrix Lie group theory. (C) 2010 Elsevier Ltd. All rights reserved.

Novel Algorithm for estimation of Swell Pressure of Fine Grained Soils Based on Diffuse Double Layer (DDL) Theory

Use of engineered landfills for the disposal of industrial wastes is currently a common practice. Bentonite is attracting a greater attention not only as capping and lining materials in landfills but also as buffer and backfill materials for repositories of high-level nuclear waste around the world. In the design of buffer and backfill materials, it is important to know the swelling pressures of compacted bentonite with different electrolyte solutions. The theoretical studies on swell pressure behaviour are all based on Diffuse Double Layer (DDL) theory. To establish a relation between the swell pressure and void ratio of the soil, it is necessary to calculate the mid-plane potential in the diffuse part of the interacting ionic double layers. The difficulty in these calculations is the elliptic integral involved in the relation between half space distance and mid plane potential. Several investigators circumvented this problem using indirect methods or by using cumbersome numerical techniques. In this work, a novel approach is proposed for theoretical estimations of swell pressures of fine-grained soil from the DDL theory. The proposed approach circumvents the complex computations in establishing the relationship between mid-plane potential and diffused plates’ distances in other words, between swell pressure and void ratio.

Activities and their relation to cation distribution in NiAl2O4 MgAl2O4 spinel solid solutions

The activity of NiAl2O4 in NiAl2O4MgAl2O4 solid solutions has been measured by using a solid oxide galvanic cell of the type, Pt, Ni + NiAl2O4 + Al2O3(α)/CaOZrO2/Ni + NixMg1−xAl2O4 + Al2O3(α). Pt, in the temperature range 750–1150°C. The activities in the spinel solid solutions show negative deviations from Raoult's law. The cation distribution in the solid solutions has been calculated using site preference energies independent of composition for Ni2+, Mg2+, and Al3+ ions obtained from crystal field theory and measured cation disorder in pure NiAl2O4 and MgAl2O4, and assumi g ideal mixing of cations on the tetrahedral and octahedral positions. The calculated values correctly predict the decrease in the fraction, α, of Ni2+ ions on tetrahedral sites for 1>x>0.25, observed by Porta et al. [J. Solid State Chem.11, 135 (1974)] but do not support their tentative evidence for an increase in α for x < 0.25. The measured excess free energy of mixing can be completely accounted for by using either the calculated or the measured cation distributions. This suggests that the Madelung energy is approximately a linear function of composition in the solid solutions. The composition of NiOMgO solid solutions in equilibrium with NiAl2O4MgAl2O4 solid solutions has been calculated from the results and information available in literature.

XXVI. The relation between thermo-optic and piezo-optic phenomena in crystals

It is pointed out that the change in refractive index with temperature of a crystal is different from what is calculated from the accompanying change in volume and the piezo-optic coefficients. The difference, which is a pure temperature effect, is explained as being due to the change in polarizability of the atoms produced by a change in the amplitude of vibration. The polarizability (α) can be expanded as a Taylor series in the changes of the distance (r) between the atoms and it is found that while the piezo-optic coefficient depends only on ∂α/∂r, the pure temperature effect is a function of ∂ 2 a/∂r 2. Making use of the experimental data, the values of a and its first two derivatives can be determined. These values are foundto be of the same order as those deduced from the intensities of Rayleigh and Raman scattering of light. The theory predicts that dn/dT should vary as the coefficient of cubical expansion at different temperatures and this is verified to be true. Finally, calculations are made of the thermo- and piezo-optic coefficients, considering the electrostatic interaction between the atoms. These do not adequately explain the observed facts, since no provision is made for the distortion of electron atmospheres around the atoms and the consequent changes in polarizability.

On the two dimensional effective electron mass in quantum wells, inversion layers and NIPI superlattices of Kane type semiconductors in the presence of strong light waves: Simplified theory and relative comparison

An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures. (C) 2011 Elsevier Ltd. All rights reserved.

A Revisit to Capture the Entire Behavior of Ultrasonic Wave Dispersion Characteristics of Single Walled Carbon Nanotubes Based on Nonlocal Elasticity Theory and Flugge Shell Model

In this paper, an ultrasonic wave propagation analysis in single-walled carbon nanotube (SWCNT) is re-studied using nonlocal elasticity theory, to capture the whole behaviour. The SWCNT is modeled using Flugge's shell theory, with the wall having axial, circumferential and radial degrees of freedom and also including small scale effects. Nonlocal governing equations for this system are derived and wave propagation analysis is also carried out. The revisited nonlocal elasticity calculation shows that the wavenumber tends to infinite at certain frequencies and the corresponding wave velocity tends to zero at those frequencies indicating localization and stationary behavior. This frequency is termed as escape frequency. This behavior is observed only for axial and radial waves in SWCNT. It has been shown that the circumferential waves will propagate dispersively at higher frequencies in nonlocality. The magnitudes of wave velocities of circumferential waves are smaller in nonlocal elasticity as compared to local elasticity. We also show that the explicit expressions of cut-off frequency depend on the nonlocal scaling parameter and the axial wavenumber. The effect of axial wavenumber on the ultrasonic wave behavior in SWCNTs is also discussed. The present results are compared with the corresponding results (for first mode) obtained from ab initio and 3-D elastodynamic continuum models. The acoustic phonon dispersion relation predicted by the present model is in good agreement with that obtained from literature. The results are new and can provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave propagation properties of single-walled carbon nanotubes.

Novel procedure for the estimation of swelling pressures of compacted bentonites based on diffuse double layer theory

Bentonite clays are proven to be attractive as buffer and backfill material in high-level nuclear waste repositories around the world. A quick estimation of swelling pressures of the compacted bentonites for different clay-water-electrolyte interactions is essential in the design of buffer and backfill materials. The theoretical studies on the swelling behavior of bentonites are based on diffuse double layer (DDL) theory. To establish theoretical relationship between void ratio and swelling pressure (e versus P), evaluation of elliptic integral and inverse analysis are unavoidable. In this paper, a novel procedure is presented to establish theoretical relationship of e versus P based on the Gouy-Chapman method. The proposed procedure establishes a unique relationship between electric potentials of interacting and non-interacting diffuse clay-water-electrolyte systems. A procedure is, thus, proposed to deduce the relation between swelling pressures and void ratio from the established relation between electric potentials. This approach is simple and alleviates the need for elliptic integral evaluation and also the inverse analysis. Further, application of the proposed approach to estimate swelling pressures of four compacted bentonites, for example, MX 80, Febex, Montigel and Kunigel V1, at different dry densities, shows that the method is very simple and predicts solutions with very good accuracy. Moreover, the proposed procedure provides continuous distributions of e versus P and thus it is computationally efficient when compared with the existing techniques.