Adachi's Model Research Articles

Thermal Transport Properties of Cd1-x Mg x Se Mixed Crystals Measured by Means of the Photopyroelectric Method

The concentration dependence of the thermal conductivity and thermal diffusivity were determined for Cd1-xMgxSe mixed crystals in the temperature range between 20 ◦C and 40 ◦C. To determine the thermal transport properties, the photopyroelectric setup in the back detection configuration was constructed. In the concentration range 0< x <0.36, both thermal conductivity and thermal diffusivity were found to decrease with increasing magnesium concentration as well as with increasing temperature. The observed concentration dependence is discussed in the framework of the Adachi model.

Dielectric functions of CuIn1+2nSe2+3n and CuGa1+2nSe2+3n (n = 2.5, 3.0, 3.5)

AbstractThe dielectric functions ϵ(ω) = ϵ1(ω) +i ϵ2(ω) of CuIn1+2nSe2+3n and CuGa1+2nSe2+3n (n = 2.5, 3.0, 3.5) have been determined in the photon energy range from 0.8 to 4.7 eV by spectroscopic ellipsometry. The measurements reveal distinct structures at energies of the critical points in the Brillouin zone. The structure observed in the spectral dependence of the dielectric functions, the complex refractive index, the absorption coefficient and the normal‐incidence reflectivity has been modelled using a modification of the Adachi's model. The results are in a good agreement with the experimental data over the entire range of photon energies. The model parameters (strength, threshold energy and broadening) have been determined using the simulated annealing algorithm. (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Optical and X-ray characterization of ferroelectric strontium–bismuth–tantalate (SBT) thin films

Metal-organic chemical vapor deposition (MOCVD) made layers of strontium–bismuth–tantalate (SBT) were characterized by spectroscopic ellipsometry (SE) using the Adachi model [S. Adachi, Phys. Rev. B 35 (1987) 7454–7463]. The evaluated optical parameters were correlated with the physical and chemical behavior examined by X-ray diffraction (XRD). As a result, it was possible to fit the measured spectra with the Adachi model in a wide range covering the region of the band gap. The Adachi model provides electronic layer parameters like the transition energy E 0 and broadening Γ. Our investigations established a correlation between XRD-determined average grain size and the electronic layer parameters.

Carrier concentration dependent optical properties of wurzite InN epitaxial films on Si(111) studied by spectroscopic ellipsometry

The refractive index and optical absorption of wurzite InN epilayers grown on Si(111) substrates with a β-Si 3N 4/AlN(0001) double-buffer by nitrogen-plasma-assisted molecular-beam epitaxy were studied by employing spectroscopic ellipsometry (SE). The crystalline quality of the InN epilayers were investigated by cross-sectional transmission electron microscopy, X-ray diffraction, and scanning electron microscopy. SE results analyzed by the Adachi's model for the dielectric function show that the optical absorption edge of InN varies in the range of 0.76–0.83 eV depending on the carrier concentration, which in turn can be adjusted by the thickness of the AlN buffer layer.

An Elasto-viscoplastic Constitutive Model with Strain-softening for Soft Sedimentary Rocks

In general, soft sedimentary rocks exhibit strain-softening and time-dependent behavior. In the present paper, an elasto-viscoplastic constitutive model for soft rocks is proposed, that can universally describe time-dependent behavior such as creep, stress relaxation and strain rate sensitivity by extending Adachi and Oka's elasto-viscoplastic model for frozen sand. It is found that the proposed model can be applied to the time-dependent behavior of a soft tuffaceous rock called Tomuro Stone under the strain rate constant triaxial compression, drained triaxial creep and undrained triaxial stress relaxation.

Optical characterization of ferroelectric strontium–bismuth–tantalate (SBT) thin films

Strontium–bismuth–tantalate (SBT) is a new kind of dielectric layer material for use in semiconductor devices. The optical layer parameters of SBT were characterized by spectroscopic ellipsometry using the well-known Cauchy model as well as the Adachi model (Phys. Rev. B 35 (1987) 7454–7463). A comparison of both models was performed. Furthermore, these optical data were compared with the physical and chemical behavior examined by Rutherford backscattering (RBS) and X-ray diffraction (XRD). As a result, it was possible to fit the measured spectra with both optical models. But with the Adachi model, it was possible to evaluate the optical layer parameters in a wider range than in the measured spectral range covering the region of the band gap. The Adachi model provides electronic layer parameters like the transition energy E 0. Our investigations also include the determination of the stoichiometry dependence of the optical layer parameters.

An Elasto-Viscoplastic Constitutive ModelIncorporating Pore Air Compressibility DuringPowder Compression Process

A new elasto-viscoplastic constitutive model (PSU-EVP) was developed for predicting a dry powder's mechanical behavior during compaction. The PSU-EVP model was developed in two stages. In the first stage, an elastoplastic model was formulated by using the fundamentals of critical state theory and key elements of the modified Cam-clay model. In the second stage, the elasto-viscoplastic model was formulated using the elastoplastic model developed in the first stage and the approach used by and given in the Adachi and Oka model. Based on these considerations, the PSU-EVP model explicitly incorporates the work done in volumetric compression of pore air during powder compaction. This aspect of the PSU-EVP model is different from the modified Cam-clay model that assumes the interparticle pore space in a powder mass to be filled with fluid. This key feature of the PSU-EVP model helps in isolating the effect of entrapped pore air on the mechanical properties of powders undergoing compression. The key parameter that quantifies the effect of pore air compression is known as the voids compression ratio parameter ( f ). The parameter a varies with pressure and can take on values between 0 and 1. A compatibility parameter (φ) was also proposed to facilitate the explicit computation of the work dissipated during compaction. Incorporation of these new concepts overcomes the major limitations of existing constitutive models. Additionally, the procedure to quantify the various parameters of the PSU-EVP constitutive model is outlined.

Microcrystalline silicon thin films studied using spectroscopic ellipsometry

We used spectroscopic ellipsometry to characterize four different microcrystalline silicon (μc-Si) films, which were fabricated by crystallizing a-Si:H films predeposited on glass substrates using solid phase crystallization (SPC), excimer laser annealing (ELA), Ni induced silicide-mediated crystallization (Ni-SMC), and field enhanced silicide-mediated crystallization (FESMC) method, respectively. A linear regression analysis, which took the effective dielectric function of μc-Si layer into account using effective medium approximation, showed that all these films were homogeneous throughout their thickness except the oxide overlayers, and completely crystallized regardless of the crystallization method. In our linear regression analysis, the complex dielectric function of silicon microcrystallites was represented by the Adachi model dielectric function (MDF) [T. Suzuki and S. Adachi, Jpn. J. Appl. Phys., Part1 32, 4900 (1993)], and the broadening parameters of the critical points (CPs) in MDF were allowed to vary. The dielectric function of silicon microcrystallites showed systematic broadening and shrinking of the peak features corresponding to the E1 and E2 CPs, from which we concluded that the average microcrystallite size increased in the order of SPC, ELA, Ni-SMC, and FESMC μc-Si. The Raman spectra and the transmission-electron-microscopy images of these films also supported the idea of systematic variation in the microcrystallite size.

Modelling the optical constants of SixGe1-x alloys in therange 1.7-5.6 eV

Optical constants of SixGe1-x alloys are modelled overthe spectral range from 0.7 eV to 5.6 eV for all compositions 0⩽x⩽1. The employed model is the modified Adachi's model, which utilizesvariable line broadening instead of the conventional Lorentzian one. Themodel takes into account transitions at the indirect band gap Egid,and critical points E0, E0 + Δ0, E1, E1 + Δ1,E0', E2(X), and E2(Σ). Excitonic effects are not considered. Themodel parameters are determined using a global optimization routine, namelyan acceptance-probability-controlled simulated annealing algorithm.Excellent agreement with the experimental data is obtained in the entireinvestigated energy and composition ranges. The obtained relative root meansquare errors are below 4.5% and 6.5% for the real and imaginary parts ofthe index of refraction, respectively.

Optical dielectric function of semiconductors

The optical constants of a range of semiconductors, from wide bandgap materials (GaN and AlN) over mid-bandgap materials (GaAs and InP) to narrow bandgap materials (InSb and HgTe) have been modeled over a wide spectral range. We compare several models in terms of accuracy, intricacy of model equations and the number of adjustable parameters. It has been found that a modified Adachi's model with adjustable broadening function obtains the best agreement with the experimental data for all investigated materials. An adjustable broadening function enables greater flexibility of the model, since no broadening mechanism is specified a priori and inhomogeneous broadening can be taken into account.

Modeling the optical properties of AlSb, GaSb, and InSb

Optical constants of AlSb, GaSb, and InSb are modeled in the 1-6 eV spectral range. We employ an extension of Adachi's model of the optical constants of semiconductors. The model takes into account transitions at E-0, E-0 + Delta(0), E-1, and E-1 + Delta(1) critical points, as well as higher-lying transitions which are modeled with three damped harmonic oscillators. We do not consider indirect transitions contribution, since it represents a second-order perturbation and its strength should be low. Also, we do not take into account excitonic effects at E-1, E-1 + Delta(1) critical points, since we model the room temperature data. In spite of fewer contributions to the dielectric function compared to previous calculations involving Adachi's model, our calculations show significantly improved agreement with the experimental data. This is due to the two main distinguishing features of calculations presented here: use of adjustable line broadening instead of the conventional Lorentzian one, and employment of a global optimization routine for model parameter determination.

DETERMINATION OF TIME-DEPENDENT CONSTITUTIVE MODEL PARAMETERS FOR MICROCRYSTALLINE CELLULOSE

ABSTRACT Material parameters of a time-dependent elasto-viscoplaslic constitutive model, proposed by Adachi and Oka, have been determined for microcrystalline cellulose. Adachi and Oka model has eight material parameters, with five of them (i.e., consolidation index, swelling index, critical index, shear modulus, and Poisson's ratio) same as those in the more commonly used in time-independent modified Cam-clay model, and remaining three parameters account for time-dependency. To measure the time-dependent parameters, constant strain-rate conventional triaxial compression (CTC) test was designed and conducted using Penn Slate's flexible-boundary cubical triaxial tester (CTT) with microcrystalline cellulose as the test material. To deposit the powder, the sprinkle filling method was used in a layer by layer fashion with a small spoon. The three time-dependent Adachi and Oka parameters were determined from these tests. Adachi and Oka model was verified by comparing the predicted values from the model with measured values from the CTT at 0.05 level of significance. Results showed that: 1) there were no significant differences (p > 0.05) between measured and predicted HTC responses at all loading rates; 2) failure values were predicted accurately (p > 0.05); and 3) there were significant differences (p < 0.05) between measured and predicted CTC responses at all loading rates.

Optical Constants of AlxGa1—xN: Modeling over a Wide Spectral Range

The optical constants of AlxGa1—xN have been modeled over a wide spectral range (up to 10 eV) and for all compositions 0 ≤ x ≤ 1. The employed model is the modified Adachi model for the dielectric function of hexagonal materials which utilizes an adjustable broadening function instead of the conventional Lorentzian one. The broadening function can vary over a range of functions including Lorentzian and Gaussian, enabling the model to deal with inhomogeneous broadening. Excellent agreement with the experimental data is obtained for all compositions. Obtained relative rms errors for all individual compositions are below 1.5% for the real part and below 2.5% for the imaginary part of the index of refraction.

Modeling the optical constants of GaP, InP, and InAs

An extension of the Adachi model with the adjustable broadening function, instead of the Lorentzian one, is employed to model the optical constants of GaP, InP, and InAs. Adjustable broadening is modeled by replacing the damping constant with the frequency-dependent expression. The improved flexibility of the model enables achieving an excellent agreement with the experimental data. The relative rms errors obtained for the refractive index equal 1.2% for GaP, 1.0% for InP, and 1.6% for InAs.

Modeling the optical constants of 6H-SiC in the energy region 1–30 eV

Optical properties of 6H-SiC in the range from 1 eV to 30 eV for the component perpendicular to the c axis are modeled using the modified Adachi model. Model parameters are determined by acceptance-probability-controlled simulated annealing. The main distinguishing feature of the model employed here is the use of variable broadening instead of the conventional Lorentzian one. The type of broadening is determined by the ratio of two adjustable model parameters, so that greater flexibility of the model is achieved. In such a way, excellent agreement with experimental data is obtained, giving relative rms error of 3.5% for the real part of the index of refraction and 5.2% for the imaginary part.

Modeling the optical constants of diamonds from 006 to 30 eV

The optical properties of diamonds are modeled over a wide spectral range with the modified Adachi's model. Model parameters were estimated by use of the acceptance-probability-controlled simulated annealing algorithm. The employed model is quite flexible, as it uses an adjustable broadening function at each critical point. The broadening function can vary over a range of functions with similar kernels but different wings, so that extended absorption tails inherent to the conventional Lorentzian broadening can be eliminated. Good agreement with the experimental data is obtained in the entire investigated range. The obtained relative rms error for the real part of the index of refraction equals 4.7%, whereas for the imaginary part of the index-of-refraction relative rms error is 3.6%.

Two-dimensional flow of a liquid sheet under gravity

An iterative FD technique is developed to simulate the free surface flow relative to a two-dimensional gravitational (or vertically falling) liquid sheet. Its features are: it is based on an orthogonal boundary fitted coordinate transformation; a streamfunction-vorticity formulation is adopted; the normal stress boundary condition is employed to update the free interface shape within an iterative process. Inertia, viscous, gravity and surface tension forces are all taken into account in the present model and it is shown that different simplified flow regimes can be conveniently identified according to the values of Reynolds and Stokes numbers. Indeed, the main peculiarity of the present paper just lies in the relatively wider range of simulated Stokes values with respect to previous papers. Computed results (interface profiles, pressure distributions) well agree with available literature data for flows with and without gravity. From one hand the classical die-swell problem phenomenology is recovered, from the other one a discussion about the validity of the Adachi's theoretical model is yielded.

Strain localization analysis by elasto‐viscoplastic softening model for frozen sand

AbstractThe aim of the present paper is to numerically analyse the behaviour of frozen sand by using a viscoplastic constitutive model with strain softening. A constitutive model has been developed introducing the stress history tensor which is a functional of the stress history, with respect to a generalized time measure. It is shown that Adachi and Oka's model is applicable to the results of triaxial tests on a frozen Toyoura sand at different strain rates. First, the instability of the model is discussed within the framework of bifurcation theory. The model is then implemented into a FEM code to numerically simulate the behaviour under plane strain conditions. From the numerical results, it is revealed that the formation of shear bands is possible and the characteristics of strain localization, such as shear banding, depend on the strain rates.

Mathematical Structure of an Overstress Elasto-Viscoplastic Model for Clay

The mathematical structure of the overstress type elasto-viscoplastic constitutive model is discussed. Derived is the analytical solution of undrained strength for Adachi and Oka model, a typical overstress type model. It has been recognized that this type of model cannot describe acceleration creep. This disadvantage was overcome on the basis of the assumption that viscoplastic parameter for Adachi and Oka model depends on the effective stress state and check it with experimental findings. The modified overstress type of elasto-viscoplastic constitutive model is found to be able to the creep rupture including acceleration creep of normally consolidated clay.