Measuring the Dielectric Properties of Nanostructures using Optical Reflection and Transmission: Bismuth Nanowires in Porous Alumina

1999 ◽  
Vol 581 ◽  
Author(s):  
M. R. Black ◽  
Y. M. Lin ◽  
M. S. Dresselhaus ◽  
M. Tachibama ◽  
S. Fang ◽  
...  
Keyword(s):  
Dielectric Function ◽  
Filling Factor ◽  
Effective Medium Theory ◽  
Porous Alumina ◽  
Reflection And Transmission ◽  
Medium Theory ◽  
Porous Alumina Template ◽  
Theoretical Predictions ◽  
Bismuth Nanowires ◽  
Transmission Measurements

ABSTRACTThis paper develops a method to deduce the dielectric function of nanostructures smaller than the chosen wavelength of light. It modifies the Maxwell - Garnett Effective Medium Theory equations to calculate the dielectric function of a metal embedded inside a dielectric. Specifically, reflection and transmission measurements of an array of bismuth nanowires in an anodized porous alumina template are used to calculate the frequency - dependent di-electric function of the nanowires. The spectra are taken using Fourier transform infrared spectroscopy covering the 500 to 4000 cm−1 frequency range. These data are used to determine the real and imaginary parts of the dielectric function of the composite materials. Next, the percentage of the total volume occupied by either Bi or air in the porous alumina (the “filling factor”) was found by scanning electron microscopy. The modified Maxwell-Garnett (M-G) equations specify how to use the filling factor and the dielectric function of the composite material to calculate the dielectric function of the alumina. Finally, the modified M-G equations are used a second time to calculate the dielectric function of Bi nanowires using the dielectric function of alumina, the dielectric function of the filled template, and the filling factor. The resulting dielectric function of Bi nanowires is then compared to theoretical predictions.

scholarly journals A proof that multiple waves propagate in ensemble-averaged particulate materials

2019 ◽  
Vol 475 (2229) ◽  
pp. 20190344 ◽  
Author(s):  
Artur L. Gower ◽  
I. David Abrahams ◽  
William J. Parnell
Keyword(s):  
Acoustic Waves ◽  
Volume Fraction ◽  
Effective Medium Theory ◽  
Effective Medium ◽  
Inhomogeneous Material ◽  
Ensemble Averaging ◽  
Reflection And Transmission ◽  
Medium Theory ◽  
Transmission Coefficients ◽  
Cylindrical Inclusions

Effective medium theory aims to describe a complex inhomogeneous material in terms of a few important macroscopic parameters. To characterize wave propagation through an inhomogeneous material, the most crucial parameter is the effective wavenumber . For this reason, there are many published studies on how to calculate a single effective wavenumber. Here, we present a proof that there does not exist a unique effective wavenumber; instead, there are an infinite number of such (complex) wavenumbers. We show that in most parameter regimes only a small number of these effective wavenumbers make a significant contribution to the wave field. However, to accurately calculate the reflection and transmission coefficients, a large number of the (highly attenuating) effective waves is required. For clarity, we present results for scalar (acoustic) waves for a two-dimensional material filled (over a half-space) with randomly distributed circular cylindrical inclusions. We calculate the effective medium by ensemble averaging over all possible inhomogeneities. The proof is based on the application of the Wiener–Hopf technique and makes no assumption on the wavelength, particle boundary conditions/size or volume fraction. This technique provides a simple formula for the reflection coefficient, which can be explicitly evaluated for monopole scatterers. We compare results with an alternative numerical matching method.

Quantum Effects on the Dielectric Function of Porous Silicon

2000 ◽  
Vol 638 ◽  
Author(s):  
M. Cruz ◽  
S. F. Díaz ◽  
C. Wang ◽  
Y. G. Rubo ◽  
J. Tagüeña-Martínez
Keyword(s):  
Porous Silicon ◽  
Dielectric Function ◽  
Imaginary Part ◽  
Effective Medium Theory ◽  
Tight Binding ◽  
Exact Result ◽  
Effective Medium ◽  
Tight Binding Approximation ◽  
Medium Theory ◽  
Microscopic Models

AbstractIn this work, the imaginary part of the dielectric function of porous silicon is studied by means of both the tight-binding and the effective medium approaches, in the latter exact result is obtained for the case of 50% porosity. Within the tight-binding approximation, the dielectric function is calculated by using the interconnected and chessboard-like supercell models for the Si skeleton. These microscopic models give quantitatively similar results, which are by a factor of three larger than those from the effective medium theory.

The magnetoresistance of polycrystalline copper

1979 ◽  
Vol 291 (1385) ◽  
pp. 569-598 ◽  
Keyword(s):  
Fermi Surface ◽  
Effective Medium Theory ◽  
Dominant Role ◽  
Effective Medium ◽  
Polycrystalline Copper ◽  
High Symmetry ◽  
Medium Theory ◽  
Angle Scattering ◽  
Theoretical Predictions ◽  
Observed Behaviour

The effective medium theory has been applied to calculate the transverse magnetoresistance of random polycrystalline copper on the basis of the known Fermi surface, in order to explain the nearly linear variation of resistance with magnetic field up to very high values. Ziman’s (1958) conjecture that the conductivity tensor should be averaged over all orientations is shown to be a good first approximation, though it does suggest that the resistance should have been observed to approach saturation in some experiments, when the open orbits might play a dominant role at large values of w c T. The effective medium theory, by raising the saturation level considerably, eliminates this difficulty. The conductivity due to open and highly extended orbits, when calculated by geometrical analysis of the Fermi surface, is found to be quite sufficient to account for the observed behaviour. Certain residual discrepancies, especially a deficit in conductivity in very pure samples at large w c T, are explained as arising partly from size effects and small angle scattering, but mainly from the markedly non-random texture of drawn and annealed wires; it is concluded that there is no reason to doubt that standard theories of magnetoresistance are capable of interpreting the observations. Most of the calculations of conductivity due to open and extended orbits are straightforward in principle and remarkably insensitive to the least well known parameters involved, the relaxation time and the angular distribution of scattering, so that the theoretical predictions are reasonably secure. Only in dealing with the extended orbits in the vicinity of high symmetry directions are approximations of dubious validity invoked, and even they are provided with more or less plausible justification. For the most part, however, the work represents a drawing together of well established concepts, and their application to a real Fermi surface rather than to convenient but imprecise approximate models.

Effective Medium Theory of DNA-linked Gold Nanoparticle Aggregates:Effect of Aggregate Shape

2001 ◽  
Vol 635 ◽  
Author(s):  
Anne A. Lazarides ◽  
K. Lance Kelly ◽  
George C. Schatz
Keyword(s):  
Dielectric Function ◽  
Effective Medium Theory ◽  
Effective Medium ◽  
Absorption Feature ◽  
Medium Theory ◽  
Spectral Changes ◽  
Comparison With Experiment ◽  
Nanoparticle Aggregates ◽  
Aggregate Shape ◽  
Good Agreement

AbstractWe present a dynamical effective medium theory (EMT) of the dielectric properties of nanoparticle aggregates formed from DNA-linked gold nanoparticles. Experimental measurements show that such aggregateshave reduced UV extinction and plasmon bands that are considerably red-shifted and broadened relative to the plasmon absorption feature observed in spectra of dispersed colloid. The EMT, which can be used to reproduce the observed spectral changes, is tested by comparing aggregate spectra calculated using the EMT dielectric function with spectra from explicit coupled particle calculations, and good agreement is found. The EMT dielectric function is used as well in discrete dipole calculations to calculate extinction spectra for a variety of aggregate shapes not amenable to analytic solution, and the sensitivity of the spectra to aggregate shape is examined. We find that the spectra are only weakly sensitive to aggregate shape, and conclude that, when calculating extinction of the DNA-linked aggregates for comparison with experiment, spherical shapes can be assumed.

Studies of the Dielectric Constant of Thin Film Bismuth Nanowire Samples Using Optical Reectometry

2001 ◽  
Vol 635 ◽  
Author(s):  
M. R. Blacka ◽  
Y.-M. Lin ◽  
S. B. Cronin ◽  
O. Rabin ◽  
M. P adi ◽  
...  
Keyword(s):  
Dielectric Constant ◽  
Energy Range ◽  
Dielectric Function ◽  
Composite System ◽  
Incident Light ◽  
Light Polarization ◽  
Alumina Template ◽  
Medium Theory ◽  
Bismuth Nanowires ◽  
Amorphous Alumina

AbstractArrays of 10 to 120 nm diameter single crystalline bismuth nanowires havebeen formed inside amorphous alumina templates. ince bismuth has a small e ective mass compared to other materials, signi cant quantum mechanical con nement is expected to occur in wires with diameter less than 50nm. he subbands formed b yquantum con nement cause in teresting modi cations to the dielectric function of bismuth. his study measures the dielectric function of bismuth nanowires in an energy range where the e ects of quantum con nement are predicted (0.05 to 0.5e). Using F ourier transforminfrared re ectometry, the dielectric constant as a function of energy is obtained for the alumina/bismuth composite system. E ective medium theory is used to subtract the e ect of the alumina template from the measurement of the composite material, thus yielding the dielectric function of bismuth nanowires. A strong absorption peak is observed at ∼1000cm−1 in the frequency dependent dielectric function in the photon energy range measured. he dependence of the frequency and intensity of this oscillator on incident light polarization and wire diameter are reviewed. n addition, the dependence of the optical absorption on antimony and tellurium doping of the nanowires are reported.

Effective medium theory characterization of Au/Ag nanoalloy-porous alumina composites

1997 ◽  
Vol 9 (1-8) ◽  
pp. 571-574 ◽  
Author(s):  
G.L. Hornyak ◽  
C.J. Patrissi ◽  
E.B. Oberhauser ◽  
C.R. Martin ◽  
J-C Valmalette ◽  
...  
Keyword(s):  
Effective Medium Theory ◽  
Porous Alumina ◽  
Effective Medium ◽  
Medium Theory ◽  
Alumina Composites

scholarly journals Thermal conductivity of silicone elastomer with a porous alumina continuum

e-Polymers ◽  
2021 ◽  
Vol 21 (1) ◽  
pp. 845-853
Author(s):  
Qichao Song ◽  
Bo Wang ◽  
Zhiyu Han ◽  
Zhidong Han
Keyword(s):  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Effective Medium Theory ◽  
Porous Alumina ◽  
Theoretical Models ◽  
Silicone Elastomer ◽  
Interfacial Thermal Resistance ◽  
X Ray Diffraction ◽  
Medium Theory ◽  
Gel Casting

Abstract In this paper, porous alumina continuum (PAC) was prepared with alumina powders (APs) by the gel-casting method and was applied to obtain silicone elastomer (SR) composites (PAC/SR) by the impregnating process. The structure was investigated by X-ray diffraction (XRD) and scanning electron microscopy (SEM). The influences of PAC on thermal conductivity and dielectric permittivity of PAC/SR composites were studied in comparison with AP/SR composites. When the alumina content was 14 vol%, the thermal conductivity of the PAC/SR composites reached 0.84 W·(m·K)−1, which was 3.1 times higher than that of the AP/SR composites. The thermal conductivity of PAC/SR and AP/SR was simulated by theoretical models, and the interfacial thermal resistance was calculated by effective medium theory, which indicated the advantages of PAC in enhancing the thermal conductivity of SR-based composites and the reduced interfacial thermal resistance between PAC and SR.

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