Primary Creep in Sn-3.8Ag-0.7Cu Solder, Part?II: Constitutive Creep Model Development and Finite Element Analysis

This article presents constant-load creep and stress relaxation data for Sn3.8Ag0.7Cu spanning a range of strain rates 10 ^{- 8} s ^{- 1} < [(e)\dot] < 10 ^{- 4} s ^{- 1} , 10^{ - 8}\, \hbox{s}^{ - 1} < \dot{\varepsilon } < 10^{ - 4}\, \hbox{s}^{ - 1} , and temperatures 25°C, 75°C, and 100°C. Creep and stress relaxation measurements showed that transient creep caused faster strain rates during stress relaxation for a given stress than the corresponding minimum creep rate from constant-load creep tests. The extent of strain hardening during primary creep was a function of temperature and strain rate. Data reduction incorporated a fast Fourier transform method to remove spurious data from stress relaxation corresponding to the period of partial strain relaxation during loading.     

An Alternative Approach to Improve the Thermoelectric Properties of Half-Heusler Compounds

In this report an alternative approach for optimization of the thermoelectric properties of half-Heusler compounds is presented. The common approaches are partial substitution of elements by elements of nearby groups and substitution with homologs. In this approach we substitute one element by one neighboring element with fewer valence electrons and by one with more electrons. The amounts of the substitutions are chosen such that the amount of deficiency and excess electrons are compensated. In the solid solution TiCo_x(Ni_0.5Fe_0.5)_1-xSb\hbox{TiCo}_{x}(\hbox{Ni}_{0.5}\hbox{Fe}_{0.5})_{1-x}\hbox{Sb}, Co was substituted equally by Fe and Ni. The aim of the substitution was to improve the figure of merit by a reduction of the thermal conductivity accompanied by an unchanged high Seebeck coefficient. The solid solution TiCo_x(Ni_0.5Fe_0.5)_1-xSb\hbox{TiCo}_{x}(\hbox{Ni}_{0.5}\hbox{Fe}_{0.5})_{1-x}\hbox{Sb} was synthesized by arc-melting. The structure of the as-cast samples was analyzed by x-ray diffraction. Rietveld refinements yielded the C1_bC1_b structure type with a small amount of antisite disorder between Co and Sb. The thermoelectric properties of the solid solution were investigated in the temperature range from 2 K to 400 K. A Seebeck coefficient of -260 mV K^-1-260\,\mu\hbox{V\,K}^{-1} at 400 K and a reduction of the thermal conductivity to 3 Wm^-1 K^-13\,\hbox{Wm}^{-1}\,\hbox{K}^{-1} were measured. The figure of merit was enhanced by a factor of about seven to a value of 0.04 at 400 K for TiCo_0.8(Ni_0.1Fe_0.1)Sb\hbox{TiCo}_{0.8}(\hbox{Ni}_{0.1}\hbox{Fe}_{0.1})\hbox{Sb}.     

Investigation of the Mθ/G/1/m system with service regime switchings and threshold blocking of the input flow

The M^θ/G/1/m queueing system with the group arrival of customers, switchings of service regimes, and threshold blocking of the flow of customers is studied. The input flow is blocked if, at the instant of the successive customer service start, the number of customers in the system exceeds specified threshold level h. If, at instant t of the customer service start, number of customers in the system ξ(t) satisfies the condition h_i < x(t) \leqslant h_{i + 1} (i = [`(1,r)] )h_i < \xi (t) \leqslant h_{i + 1} (i = \overline {1,r} ), then the service time for this customer corresponds to distribution function F _i (t). At 1 ≤ ξ(t) ≤ h = h ₁, the service time for a customer is distributed according to law F(t) (basic service time). The Laplace transforms for the distribution of the number of customers in the system on the busy period and for the distribution function of the busy period are found, the mean length of the busy period (including the case m = ∞) is determined and formulas for the ergodic distribution of the number of customers in the system (including the case m = ∞) are obtained. An effective algorithm for calculation of the ergodic distribution is proposed. The recurrence relations of the algorithm are not explicitly dependent on m.     

Some properties of order-Statistics filters

LetX ₁,X ₂,... be a stationary sequence of random variables with Pr{X _t, x}=F(x),t=1, 2,... Also let _i ^n,(t) ,i=1,...,n, denote the ith order statistic (OS) in the moving sample (X _t–N ,...,X _t,...,X _t+N) of odd sizen=2N+1. ThenY _t=a _i X _i ^n(t) with a _i=1 is an order-statistics filter. In practicea _i0,i=1,...,n. Fort>N, the sequence {Y _t} is also stationary. IfX ₁ X ₂, ... are independent, the autocorrelation function (r)=corr(Y _t,Y _t+r) is zero forr >n – 1 and forr n – 1 can be evaluated directly in terms of the means, variances, and covariances of the OS in random samples of sizen +r fromF(x).In special cases several authors have observed that the spectral density functionf() of {Y _t} is initially decreasing for > 0. This result is made more precise and shown to hold generally under white noise. The effect of outliers (impulses) is also discussed.This research was supported by the U.S. Army Research Office.     

Computation of minimal-order realizations of generalized state-space systems

In this paper we consider the problem of obtaining minimal-order representations of generalized state-space systems described by equations of the formE x(t)=A x(t)+B u(t),y(t)=C x(t)+D u(t) withE singular and det(sE–A)0. The underlying principle is that of removal of impulsive and exponential uncontrollable and unobservable modes. When this is followed by the removal of the remaining impulsive modes, we get a minimal-order generalized or standard state-space representation. Simple reduction procedures and numerical algorithms based on these principles are developed and illustrated by means of two numerical examples.P. Misra's research was supported in part by AFWAL, Wright Patterson Air Force Base under Grant F33615-88-C-3605. R. V. Patel's research was supported by NSERC of Canada under Grant A1345.     

Anomalous Peak in the Forward-Bias <Emphasis Type="Italic">C</Emphasis>–<Emphasis Type="Italic">V</Emphasis> Plot and Temperature-Dependent Behavior of Au/PVA (Ni,Zn-doped)/<Emphasis Type="Italic">n</Emphasis>-Si(111) Structures

In this study, the temperature-dependent mean density of interface states (N_SS)(N_{\rm SS}) and series resistance (R_S)(R_{\rm S}) profiles of Au/PVA (Ni,Zn-doped)/n-Si(111) structures are determined using current–voltage (I−V) and admittance spectroscopy [capacitance–voltage (C–V) and conductance–voltage G/ω–V] methods. The other main electronic parameters such as zero-bias barrier height (F_B0)(\Phi_{{\rm B}0}), ideality factor (n), and doping concentration (N _D) are also obtained as a function of temperature. Experimental results show that the values of F_B0\Phi_{\rm{B}0}, n, R _S, and N _SS are strongly temperature dependent. The values of F_B0\Phi_{\rm{B}0} and R _S increase with increasing temperature, while those of n and N _SS decrease. The C–V plots of Au/PVA (Ni,Zn-doped)/n-Si(111) structures exhibit anomalous peaks in forward bias (depletion region) at each temperature, and peak positions shift towards negative bias with increasing temperature. The peak value of C has been found to be strongly dependent on N _SS, R _S, and temperature. The experimental data confirm that the values of N _SS, R _S, temperature, and the thickness and composition of the interfacial polymer layer are important factors that influence the main electrical parameters of the device.     

Approximating linearizations for nonlinear systems

Given a nonlinear control system $$\dot x(t) = f(x(t)) + \sum\limits_{i = 1}^m {u_i (t)g_i (x(t))}$$ on ? ⁿ and a pointx ₀ in ? ⁿ , we want to approximate the system nearx ₀ by a linear system. Of course, one approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that we should construct a linear approximation based on Lie bracket matching atx ₀. In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, we show that there is a coordinate system for ? ⁿ nearx ₀ in which these two types of linearizations agree. We indicate the importance of this agreement by examining the time responses of the nonlinear system and its linear approximation and comparing the lower-order kernels in Volterra expansions of each.     

Capacity of data collection in randomly-deployed wireless sensor networks

Data collection is one of the most important functions provided by wireless sensor networks. In this paper, we study theoretical limitations of data collection and data aggregation in terms of delay and capacity for a wireless sensor network where n sensors are randomly deployed. We consider different communication scenarios such as with single sink or multiple sinks, regularly-deployed or randomly-deployed sinks, with or without aggregation. For each scenario, we not only propose a data collection/aggregation method and analyze its performance in terms of delay and capacity, but also theoretically prove whether our method can achieve the optimal order (i.e., its performance is within a constant factor of the optimal). Particularly, with a single sink, the capacity of data collection is in order of \Uptheta(W)\Uptheta(W) where W is the fixed data-rate on individual links. With k regularly deployed sinks, the capacity of data collection is increased to \Uptheta(kW)\Uptheta(kW) when k=O(\fracnlogn)k=O\left({\frac{n}{\log n}}\right) or \Uptheta(\fracnlognW)\Uptheta\left({\frac{n}{\log n}}W\right) when k=\Upomega(\fracnlogn)k=\Upomega\left({\frac{n}{\log n}}\right). With k randomly deployed sinks, the capacity of data collection is between \Uptheta(\fracklogkW)\Uptheta\left({\frac{k}{\log k}}W\right) and \Uptheta(kW)\Uptheta(kW) when k=O(\fracnlogn)k=O\left({\frac{n}{\log n}}\right) or \Uptheta(\fracnlognW)\Uptheta\left({\frac{n}{\log n}}W\right) when k=w(\fracnlogn)k=\omega\left({\frac{n}{\log n}}\right). If each sensor can aggregate its receiving packets into a single packet to send, the capacity of data collection with a single sink is also increased to \Uptheta(\fracnlognW)\Uptheta\left({\frac{n}{\log n}}W\right).     

Estimation of Energy Aliasing Error for Nonbandlimited Signals

In this paper, we investigate the problem of approximating a given (not necessarily bandlimited) signal, x(t), by a (bandlimited) interpolation or sampling series of the form:

Stationary characteristics of the Mθ/G/1/m system with the threshold functioning strategy

The M^θ/G/1 queueing system with the group arrival of customers, switchings of service regimes, and threshold blocking of the flow of customers is considered. The input flow is blocked if, at the instant of the beginning of the service of a successive customer, the number of customers in the system exceeds given threshold level h. If, at instant t of the beginning of the service of the customer, the number of customers in the system satisfies the condition h _i < ɛ(t) ≤ h _{i + 1} h_i < e(t) \leqslant h_{i + 1} (i = [`(1,r)] )h_i < \varepsilon (t) \leqslant h_{i + 1} (i = \overline {1,r} ), then, the service time of this customer is associated with distribution function F _i (t). When 1 ≤ ɛ(t) ≤ h = h ₁, the service time of the customer is distributed according to law F(t) (the basic service regime). For the case of a single switching (r = 1), the mean duration of the busy period intervals with the absence and presence of the input flow blocking, the probability of customer service, and the stationary characteristics of the queue are determined. The character of the dependences of the mean busy period duration and the probability of service on parameters m and h is investigated. For the case m = ∞, some problems of optimal synthesis of systems with given characteristics and the problem of minimization of the service cost are solved.     

Investigation of Trap States in AlInN/AlN/GaN Heterostructures by Frequency-Dependent Admittance Analysis

We present a systematic study on the admittance characterization of surface trap states in unpassivated and SiN _x -passivated Al_0.83In_0.17N/AlN/GaN heterostructures. C–V and G/ω–V measurements were carried out in the frequency range of 1 kHz to 1 MHz, and an equivalent circuit model was used to analyze the experimental data. A detailed analysis of the frequency-dependent capacitance and conductance data was performed, assuming models in which traps are located at the metal–AlInN surface. The density (D _t) and time constant (τ _t) of the surface trap states have been determined as a function of energy separation from the conduction-band edge (E _c − E _t). The D _st and τ _st values of the surface trap states for the unpassivated samples were found to be D_st @ (4 - 13) ×10¹² D_{\rm{st}} \cong (4 - 13) \times 10^{12}  eV ^{- 1} cm ^{- 2} {\hbox{eV}}^{ - 1} {\hbox{cm}}^{ - 2} and τ _st ≈ 3 μs to 7 μs, respectively. For the passivated sample, D _st decreased to 1.5 ×10¹² 1.5 \times 10^{12}  eV ^{- 1} cm ^{- 2} {\hbox{eV}}^{ - 1} {\hbox{cm}}^{ - 2} and τ _st to 1.8 μs to 2 μs. The density of surface trap states in Al_0.83In_0.17N/AlN/GaN heterostructures decreased by approximately one order of magnitude with SiN _x passivation, indicating that the SiN _x insulator layer between the metal contact and the surface of the Al_0.83In_0.17N layer can passivate surface states.     

Approximation of nonlinear systems having outputs

Suppose we have a nonlinear system with output $$\begin{gathered} \dot x = f(x) + g(x)u, \hfill \\ y = h(x), \hfill \\ \end{gathered}$$ an open setO of state spaceR ⁿ , and a positive integerk. We find conditions onf,g, andh so that for eachx ₀ ε O there is ann-dimensional affine linear system, which depends onx ₀ but not onu, having the property that the output time responses (starting at the statex ₀ of the original nonlinear system and this approximating linear system agree through orderk for any admissable controlu. Several possible applications of our results are examined.     

Microstructure coarsening during static annealing of 60Sn40Pb solder joints: II eutectic coarsening kinetics

The eutectic coarsening kinetics for 60Sn40Pb solder joints annealed at 50°C to 150° C was determined to be of the form

Critical Layer Thickness in Exponentially Graded Heteroepitaxial Layers

Exponentially graded semiconductor layers are of interest for use as buffers in heteroepitaxial devices because of their tapered dislocation density and strain profiles. Here we have calculated the critical layer thickness for the onset of lattice relaxation in exponentially graded In _x Ga_1?x As/GaAs (001) heteroepitaxial layers. Upwardly convex grading with \( x = x_{\infty } \left( {1 - {\rm e}^{ - \gamma /y} } \right) \) was considered, where y is the distance from the GaAs interface, γ is a grading length constant, and x _∞ is the limiting mole fraction of In. For these structures the critical layer thickness was determined by an energy-minimization approach and also by consideration of force balance on grown-in dislocations. The force balance calculations underestimate the critical layer thickness unless one accounts for the fact that the first misfit dislocations are introduced at a finite distance above the interface. The critical layer thickness determined by energy minimization, or by a detailed force balance model, is approximately \( h_{\rm{c}} \approx <Exponentially graded semiconductor layers are of interest for use as buffers in heteroepitaxial devices because of their tapered dislocation density and strain profiles. Here we have calculated the critical layer thickness for the onset of lattice relaxation in exponentially graded In _x Ga_1−x As/GaAs (001) heteroepitaxial layers. Upwardly convex grading with x = x_￥ ( 1 - e ^{- g/y} ) x = x_{\infty } \left( {1 - {\rm e}^{ - \gamma /y} } \right) was considered, where y is the distance from the GaAs interface, γ is a grading length constant, and x _∞ is the limiting mole fraction of In. For these structures the critical layer thickness was determined by an energy-minimization approach and also by consideration of force balance on grown-in dislocations. The force balance calculations underestimate the critical layer thickness unless one accounts for the fact that the first misfit dislocations are introduced at a finite distance above the interface. The critical layer thickness determined by energy minimization, or by a detailed force balance model, is approximately h_c ? < h_{\rm{c}} \approx < Although these results were developed for exponentially graded In _x Ga_1−x As/GaAs (001), they may be generalized to other material systems for application to the design of exponentially graded buffer layers in metamorphic device structures such as modulation-doped field-effect transistors and light-emitting diodes.     

APPROXIMATION ANALYSES FOR FUZZY VALUED FUNCTIONS IN L_1(μ)-NORM BY REGULAR FUZZY NEURAL NETWORKS

 By defining fuzzy valued simple functions and giving L1(μ) approximations of fuzzy valued integrably bounded functions by such simple functions, the paper analyses by L1(μ)-norm the approximation capability of four-layer feedforward regular fuzzy neural networks to the fuzzy valued integrably bounded function F : Rn → FcO(R). That is, if the transfer functionσ: R→R is non-polynomial and integrable function on each finite interval, F may be innorm approximated by fuzzy valued functions defined as to anydegree of accuracy. Finally some real examples demonstrate the conclusions.     

On the robustness of stability for uncertain large-scale systems subjected to multiple time delays

The robustness problem of stability for large-scale uncertain systems with a class of multiple time delays is addressed in this paper. By applying the complex Lyapunov stability theorem, the matrix measure techniques, and norm inequalities, a new approach for solving a general case of the above problem is proposed. Several robust stability conditions, delay-dependent or delay-independent, are derived to guarantee the asymptotic stability and exponential stability of the uncertain large-scale time-delay systems. Moreover, these obtained results can also be applied to the stabilization design.Notation real number field - complex number field - x x=(x ₁,x ₂,...,x _n ) ^T R ⁿ - x ^T transpose of vectorx - x* complex conjugate transpose of vectorx - Re(·) real part of (·) - x norm of vectorx; x=(x*x)^1/2 - A ^T transpose of matrixA - A* complex conjugate transpose of matrixA - ¯(·) maximal absolute value of eigenvalue of matrixA - (A) matrix measure of matrixA; (A)=¯((A + A*)/2) - A induced norm of matrix A; A=[¯(A*A)]^1/2 - ¦a_ij ¦ absolute value of element a_ij - ¦ A¦ {¦a_ij¦} for matrix A={a_ij} - A >B a_ij > b_ij for alli andj where A={a_ij} andB={b_ij} - z complex number - ¯z complex conjugate ofz Supported by National Science Council, Taiwan, Republic of China, Grant NSC83-0404-E006-001.     

Symmetry relations in multidimensional Fourier transform pairs

A relation between the types of symmetries that exist in signal and Fourier transform domain representations is derived for continuous as well as discrete domain signals. The symmetry is expressed by a set of parameters, and the relations derived in this paper will help to find the parameters of a symmetry in the signal or transform domain resulting from a given symmetry in the transform or signal domain respectively. A duality among the relations governing the conversion of the parameters of symmetry in the two domains is also brought to light. The application of the relations is illustrated by a number of two-dimensional examples.Notation R the set of real numbers - R ^m R × R × ... × R m-dimensional real vector space - continuous domain real vector - L {¦ – _i , i = 1,2,..., m} - m-dimensional frequency vector - W { – _i ,i=1,2,..., m} - m-dimensional normalized frequency vector - _P {¦ – _i , i=1,2,...,m} - g(ol) g (₁,₂,..., _m ) continuous domain signal - () ( _{1 2},..., _m )=G (j ₁,j ₂,..., j _m ) Fourier transform ofg (ol) - (A,b,,,) parameters ofT- symmetry - N the set of integers - N ^m N × N × ... × N m-dimensional integer vector spacem-dimensional lattice - h(n) h (n ₁,.,n _m ) discrete domain signal - H() Fourier transform ofh (n) - v ₁,v ₂,..., v_m m sample-direction and interval vectors - V (v ₁ v ₂ ...v _m ) sampling basis matrix - [x]^* complex conjugate ofx - detA determinant ofA - X {x¦ – x _i , i=1,2,..., m} - A ^–t [A ^–1] ^t ,t stands for transpose This work was supported in part by the Natural Sciences and Engineering Research Council of Canada under Grant A-7739 to M. N. S. Swamy and in part by Tennessee Technological University under its Faculty Research support program to P. K. Rajan.     

Measurement of Complex Permittivity of Lossy Materials in Free Space Using Matched THz Power Meter

The complex permittivity of lossy materials is measured at 330 GHz by matched THz power meter. Such a power meter operates near the Brewster’s angle of its absorbing film resulting in an own reflection coefficient close to zero. It permits to reduce an uncertainty associated with parasitic reflections created by conventional power meters. The measured power transmission coefficient of the dielectric slab as a function of the incident angle is used for estimating the dielectric constant. Its evaluation is based on the root-finding procedure applied to the proper formulated system of two non-linear equations. Convergence and sensitivity of this system in the space of { e￠_\textr,e"_\textr } \left\{ {{{\varepsilon '}_{\text{r}}},{{\varepsilon '}_{\text{r}}}} \right\} are investigated in order to formulate recommendations how guess values providing the unique solution must be chosen. The results are useful for estimating sheilding effects caused by dielectric losses in the sub-mm range with application to detecting hidden objects as well as other homeland security purposes.