Oscar D. Crisalle

Application of Measurement Models to Impedance Spectroscopy II . Determination of the Stochastic Contribution to the Error Structure

Development of appropriate models for the interpretation of impedance spectra in terms of physical properties requires, in addition to insight into the chemistry and physics of the system, an understanding of the measurement error structure. The time-varying character of electrochemical systems has prevented experimental determination of the stochastic contribution to the error structure. A method is presented by which the stochastic contribution to the error structure can be determined, even for systems for which successive measurements are not replicate. Although impedance measurements are known to be heteroskedastic in frequency (i.e., have standard deviations that are functions of frequency) and time varying over the duration of the experiment, the analysis conducted in the impedance plane suggests that the standard deviations for the real and imaginary parts of the impedance have the same magnitude, even at frequencies at which the imaginary part of the impedance asymptotically approaches zero. On this basis, a general model for the error structure was developed which shows good agreement for a broad variety of experimental measurements.

Influence of zero locations on the number of step-response extrema

Abstract A new bounding theorem for the number of extrema that may occur in the step-response of a stable linear system is presented. The derivation of an easily-computed upper bound is given to complement literature results which have previously established the existence of a lower bound. The theorem requires knowledge of the pole-zero configuration of the transfer-function and is applicable to stable systems with real zeros and real poles.

Epitaxial growth and characterization of CuInSe2 crystallographic polytypes

Migration-enhanced epitaxy (MEE) has been successfully employed to grow epitaxial films of the ternary compound CuInSe2 on (001) GaAs that exhibit distinct coexisting domains of both a nonequilibrium crystallographic structure characterized by CuAu (CA) cation ordering, and the compound’s equilibrium chalcopyrite structure. X-ray diffraction, transmission electron diffraction, and Raman scattering data provide evidence for this structural polytype. Distinctive signatures of the CA polytype are found in the data from each of these methods, and their analyses are consistent with assignment of this crystallographic structure to the P4m2 space group. This structure is found to preferentially segregate into domains that constitute a distinct metastable phase, which may be stabilized by surface kinetic effects favored by the MEE growth process.

Reaction kinetics of CuInSe2 thin films grown from bilayer InSe/CuSe precursors

The reaction kinetics for the formation of CuInSe2 thin films from a stacked bilayer precursor consisting of InSe and CuSe was studied by means of in situ high-temperature x-ray diffraction. In particular, the isothermal phase evolution of the glass/InSe/CuSe precursor was observed at different temperatures. The pathway produces a CuInSe2 diffusion barrier layer that also functions as a nucleation barrier. Hence, amorphous and crystalline phases simultaneously grow during isothermal processing. The shape of the time-resolved fractional reaction curve exhibits a deceleratory behavior, consistent with the presence of a diffusion-controlled reaction mechanism. Analyses based on Avrami and parabolic-rate laws were conducted. The Avrami exponent for each isothermal reaction is in the range 0.5–0.8, which indicates that the growth reaction is dominantly one-dimensional diffusion controlled. The estimated apparent activation energy for this reaction is 66.0 kJ/mol. The results based on the parabolic rate model a...

THE NYQUIST ROBUST STABILITY MARGIN—A NEW METRIC FOR THE STABILITY OF UNCERTAIN SYSTEMS

The Nyquist robust stability margin kN is proposed as a new tool for analysing the robustness of uncertain systems. The analysis is done using Nyquist arguments involving eigenvalues instead of singular values, and yields exact necessary and sufficient conditions for robust stability. The concept of a critical line on the Nyquist plane is defined and used to calculate a critical perturbation radius which in turn is used to produce kN. The new approach gives alternatives to computing exact stability margins in some cases of highly directional uncertainty templates where other models are not applicable.

An approach to stabilize linear systems with state and input delay

A sliding mode control scheme has been designed to ensure the asymptotic stability of a linear system with delay in both the input and state variables. A key step is the use of a transformation that eliminates the input delay. The resulting state-delay system is controlled through a sliding mode approach, where the equivalent control term uses state feedback and the discontinuous control term involves the sign and value of the switching function. It is shown that the sliding mode is reached in finite time. Stability conditions are derived using a Lyapunov technique combined with a Razumikhin approach to bound the difference between the original and the transformed states. The result is a set of sufficient conditions for asymptotic stability. The theoretical developments are illustrated via an example.

Sliding mode control of uncertain input-delay systems

A sliding mode control design is proposed for a class of uncertain input-delay systems based on transformation that converts the original system into a delay-free form. It is shown that asymptotic stability of the transformed system guarantees the asymptotic stability of the original system. The reaching condition and the asymptotic stability are assured through a proper choice of the switching function and the controller parameters. The advantages over state feedback are discussed along with an approach for reducing the problem of chattering.

Robustness analysis for systems with ellipsoidal uncertainty

SUMMARY This note derives an explicit expression for computing the robustness margin for aƒne systems whose real and complex coeƒcients are related by an ellipsoidal constraint. The expression, which is an application of a result by Chen, Fan, and Nett for rank-one generalized structured singular-value problems, extends and unifies previous results on robustness margin computation for systems with ellipsoidal uncertainty. ( 1998 John Wiley & Sons, Ltd.

On the Error Structure of Impedance Measurements Simulation of FRA Instrumentation

A new paradigm is introduced for the investigation of errors in frequency-domain measurements. The propagation of errors from time-domain measurements to the desired complex variables in the frequency domain was analyzed for the frequency response analysis (FRA) algorithm, one of two techniques commonly used for spectroscopy measurements. Errors in the frequency domain were found to be normally distributed, even when the errors in the time-domain were not normally distributed and when the measurement technique introduced bias errors. For additive errors in time-domain signals, the errors in the real and imaginary impedance were found to be uncorrelated, and the variances of the real and imaginary parts of the complex impedance were equal. The equality of variances was realized except for cases where the time-domain signals contained proportional errors. The statistical characteristics of the results were in good agreement with experimental observations.

Role of sodium in the control of defect structures in CIS [solar cells]

The authors have grown CIS epitaxial films on single-crystal GaAs substrates under conditions that enhance the influence of surface effects on the resulting structures and their properties. There is a pronounced morphological dichotomy between indium-rich and copper-rich films. In addition, epilayers with nominally identical compositions and morphologies can exhibit fundamentally different ordering of the lattice in either the equilibrium chalcopyrite (CH) or metastable CuAu (CA) structure. The addition of sodium to In-rich CulnSe/sub 2/ epilayers during the initial stages of epitaxy both suppresses the formation of metastable Cu-CuInSe/sub 2/ and dramatically changes the film morphology. They discuss these results in the context of recent theories of island nucleation and their hypothesis that sodium acts as a surfactant during the growth of CuInSe/sub 2/ by destabilizing the (ln/sub Cu/+2V/sub Cu/) defect associate-complex in the near-surface transition layer, rejecting excess indium from the bulk of the growing film.