An extended mathematical model for failure kinetics

In practice we often observe some kind of ‘self-acceleration’ when degradation causes the local temperature to increase, and in turn the temperature accelerates degradation. In this paper an extended model for failure kinetics is proposed to describe the phenomenon mentioned above. It is a common belief that a non-linear relation between logarithmic lifetime and inverse temperature reveals a change of failure mechanisms. The results of the paper tell us that non-linearity may be produced by a single failure process with more complex failure kinetics than the simple reaction of the first order.     

Arrhenius and the temperature dependence of non-constant failure rate

This paper examines the temperature dependence of component hazard rate for the cases of log-normal and Weibull failure-time distributions and shows that the common belief that the temperature variation of component failure rate follows the Arrhenius rule can be substantially in error. Although most failures in present-day equipment are not due to defective components, the paper also examines the temperature dependence of equipment rate of occurrence of failure having a power-law or negative exponential variation with time for the temperature range where the majority of failures are due to rate processes obeying the Arrhenius equation. The consequences of a Gaussian distribution of failure-mechanism activation energy in a device population are also considered. Although the temperature dependence of failure rate can be very high, in most situations it is much less than that of the Arrhenius acceleration factor. It is very improbable that the temperature dependence of component failure rate can be meaningfully modelled for reliability prediction purposes or for the purpose of optimizing thermal design component layout. Attention is drawn to the invalidity of determining the failure activation energy from the average failure rates in accelerated high-temperature time-terminated life tests.     

Estimation and test for the parameters of the arrhenius model

Estimation and test procedures are given for the parameters of the Arrhenius model. The assumed failure distribution is of exponential or Weibull type with fixed and temperature independent shape parameter. The approach is based on failure terminated experiments on at least two different tempera-ture levels with pre-assigned and equal number of failures for each temperature level. Estimation consists of two steps, modified maximum likelihood estimation followed by ordinary least squares regression. Statistical tests are defined on acceptance regions given in the particular parameter space by circles or ellipses depending only on the experimental design.     

Variation of activation energy determined by a modified Arrhenius approach: Roles of dynamic recrystallization on the hot deformation of Ni-based superalloy

The hot deformation behaviors of Ni18Cr9Co9Fe5Nb3Mo superalloy were explored in the formation temperature range free ofγ'phase with various strain rates applied.The hot deformation behaviors are initially modeled with Arrhenius equation which gives an average activation energy of 581.1 kJ mol-1.A modified Arrhenius approach,including the updated Zener-Hollomon parameter is proposed to consider the change of activation energy under different deformation conditions which turns out a relatively accurate computation for activation energy of hot deformation,i.e.,the standard variance for modified model calculated in the covered deformation condition is just 35.4 ％ of that for Arrhenius equation.The modified model also proposes a map for activation energy which ranges from 571.5-589.0 kJ mol-1 for various deformation conditions.Microstructural features of the representative superalloy specimens were characterized by electron backscattered diffraction (EBSD) techniques in order to clarify the influence of activation energy on the microstructural formation.It is found that the Ni-based superalloy samples with higher activation energy are promoted by the degree of dynamic recrystallization which suggests that the rise in activation energy gives either a better recrystallization rate or finer grains.     

Cathode ray tube bleed resistor reliability—a case study

This paper describes, and gives a mathematical analysis of, the performance of two makes of CRT bleed resistors which exhibit markedly different characteristics under heat soak conditions. By examining the observed resistance changes with temperature, and relating these to the Arrhenius equation, the reaction activation energies can be determined. Further analysis of the power consumption characteristics of the resistors leads to the establishment of resistance-time curves for both makes of resistor. These indicate very different conclusions than might otherwise have been drawn from initial test data. Finally the Monte Carlo' simulation technique is used to determine the most likely survival characteristics in a field situation, and a quantitative assessment of the reliability of CRTs using these bleed resistors is given. The construction of the resistor body is common to both makes and comprises a resistor substrate enclosed within an overcoat which is in turn encapsulated in epoxy. One make (type A) is a glass thick film structure, whereas the other is a polymer thick film system.     

Activation energy and grain growth in nanocrystalline Y-TZP ceramics

Grain growth of nanocrystalline yttria-stabilized tetragonal zirconia polycrystals (Y-TZP) was studied between 1250 and 1650 °C and compared to the Y-TZP data from the literature. All the results exhibited two distinctly different behaviour, where slow and fast grain growth regimes with activation energies 280 and 546 kJ mol⁻¹ prevail below and above 1400 °C, respectively. Analysis of the data with respect to the grain growth mechanisms and the diffusion kinetics was in agreement with limited Y³⁺ lattice diffusion within the cubic zirconia nano-grains below 1400 °C. This results in slow grain growth kinetics. Redistribution of Y³⁺ above 1400 °C together with the equilibrium phase assemblage lead to enhanced grain boundary diffusion of Y³⁺ and results in enhanced grain growth of the sub-micrometer tetragonal grains.     

利用主烧结曲线和Arrhenius曲线确定TiO_2陶瓷表观激活能

表观烧结激活能是研究陶瓷烧结机理的一个非常重要参量。采用纳米金红石相TiO2陶瓷坯体在空气中进行无压烧结,加热速率分别为1,2,5℃/min,用热膨胀仪记录试样收缩率,阿基米德法测量烧结体相对密度,分别用主烧结曲线法和Arrhenius法计算表观烧结激活能。结果表明:用主烧结曲线得到的激活能是一个定值,而用Arrhenius法得到的激活能是一个变化的值,激活能是相对密度的函数,随相对密度的增加而减小,且激活能和相对密度的变化趋势分成两段,当相对密度大于85%时,激活能随相对密度的增加而减小比小于85%时要快,这意味着在烧结过程中,控制烧结的扩散机制可能发生了变化。     

Motion and conversion energies of adatom and adatom clusters on gold (0 0 1) surface

Beginning of epitaxial growth of vapor deposition on (0 0 1) surface has been studied by use of molecular dynamics. The activation energies of motion and conversion can be calculated using an embedded atom potential at any temperatures. The activation energy of the motion of a gold adatom on (0 0 1) surface of gold is calculated to be 0.41 eV. The activation energies of dissociation in the direction of a di-adatom is 0.72 eV from the nearest neighbor to the next nearest neighbor, and 0.27 eV from the next nearest neighbor to the third neighbor. Butterfly motion of a di-adatom is 0.42+0.12 eV=0.54 eV. Tri-adatoms are classified by the angle between the two bonds in the adatoms and the lengths of the two bonds. The conversion energies of tri-adatoms have also been calculated. The activation energy for the motion of an adatom on (0 0 1) surface is much higher than those corresponding the motion on (1 1 1) surfaces.     

激活工艺和表面气体压强对一种改性锆石墨吸气剂吸气性能的影响

用粉末冶金工艺制备了一种改性的锆石墨类吸气剂,研究了激活工艺和吸气剂表面气体压强对该吸气剂吸气性能的影响。结果表明：该类吸气剂具有优越的室温吸气性能。高温短时间的激活效果优于低温长时间。增加吸气剂表面气体压强Pg有利于提高吸气剂的吸气速率和吸气量,且适当增加Pg比提高激活温度更有利于提高吸气剂的吸气性能。本文从吸气剂对气体分子的吸附和扩散作用机理解释了上述结果。     

Functional equation for the fading correction of imaging plates

Several experiments were performed to investigate the effects of temperature on the fading of the commercial imaging plate, IP (BAS-UR). The fading characteristics were measured under controlled temperatures between 0°C and 60°C after irradiation with ²³⁸U alpha-ray and ⁶⁰Co gamma-ray sources. Applying Arrhenius' equation to the experimental results, we calculated a universal functional equation that includes two variables: elapsed time (t) and temperature (K). The photo-stimulated luminescence (PSL) calculated by this equation showed good agreement with the results of our experimental ones between 0°C and 40°C. From this equation, the activation energies of the fading are estimated to be about 0.9 eV for both ²³⁸U alpha-ray and ⁶⁰Co gamma-ray sources.     

Evaluation of UHPFRC activation energy using empirical models

The influence of thermal curing on the evolution of the material properties and the UHPFRC behaviour was investigated. Tests results showed a beneficial effect of a high temperature curing on the early age material properties due to the thermo-activation effect on the hydration process. However, an inverse effect was observed at long-term. In our study, activation energy of UHPFRC was evaluated from experimental data by means of empirical models. The traditional maturity-function based on Arrhenius law, generally used to describe thermally activated physical or chemical processes, was used to predict the evolution of the UHPFRC autogenous shrinkage and to validate the applicability of this concept for such cement-based materials. Results showed that the concept based on Arrhenius law could describe correctly temperature effects on UHPFRC for temperature lower than 30°C.

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Résumé  L’influence de la cure thermique sur l’évolution des propriétés et du comportement du Béton Fibré Ultra Performant (BFUP) a été étudiée. Les résultats d’essais ont montré l’effet bénéfique des températures élevées sur les propriétés du matériau au jeune age à cause de la thermo-activation du processus d’hydratation. Néanmoins, un effet inverse a été observé à long terme. Dans cette étude, l’énergie d’activation du BFUP a été évaluée à partir des résultats expérimentaux par le biais de modèles empiriques. Le concept de maturité traditionnel basé sur la loi d’Arrhenius, généralement utilisé pour décrire l’activation thermique des processus physiques et chimiques, a été utilisé pour prédire l’évolution du retrait endogène du BFUP et pour valider l’application de ce concept pour de tels matériaux cimentaires. Les résultats ont montré que le concept basé sur la loi d’Arrhenius décrit correctement l’effet thermique sur le BFUP pour des températures inférieures à 30°C.

     

Integrated circuits for submarine communication systems,their design and development

Digital optical systems represent the current advance in submarine communications. Modern system designs require rapid evaluation of new components without relaxation of the stringent reliability requirements demanded for submarine applications. This article describes the development of integrated circuits (ICs) for submarine use. It goes on to show the design methodology, and discusses some limitations and the demanding reliability assurance aspects. The current IC designs are being used in both long-haul and short-haul links. The technology discussed is providing a major role in the future development of high-capacity optical submarine systems.     

Gibbs Free Energy and Activation Energy of ZrTiAlNiCuSn Bulk Glass Forming Alloys

The Gibbs free energy differences between the supercooled liquid and the crystalline mixture for the (Zr_(52.5)Ti_5Al_(10)-Ni_(14.6)Cu_(17.9))_((100-x)/100)Sn_x (x=0, 1, 2, 3, 4 and 5) glass forming alloys are estimated by introducing the equationproposed by Thompson, Spaepen and Turnbull. It can be seen that the Gibbs free energy differences decrease firstas the increases of Sn addition smaller than 3, then followed by a decrease due to the successive addition of Snlarger than 3, indicating that the thermal stabilities of these glass forming alloys increase first and then followed by adecrease owing to the excessive addition of Sn. Furthermore, the activation energy of Zr_(52.5)Ti_5Al_(10)Ni_(14.6)Cu_(17.9) and(Zr_(52.5)Ti_5Al_(10)Ni_(14.6)Cu_(17.9))_(0.97)Sn_3 was evaluated by Kissinger equation. It is noted that the Sn addition increases theactivation energies for glass transition and crystallization, implying that the higher thermal stability can be obtainedby appropriate addition of Sn.     

The Al-1 per cent Si/TiN/Ti interconnection scheme: Electromigration and reliability extrapolations

The electromigration performance of the Al-1 per cent Si/TiN/Ti metal scheme is investigated both for contacts and for stripes and compared with the results for the standard Al-1 per cent Si metallization. Statistical extrapolations at the operating conditions for a device have been performed to calculate the useful life of contacts and stripes. The results indicate that the most severe limitation to the interconnection reliability is given by the contacts without the diffusion barrier layer.     

Nanocrystalline Growth Activation Energy of Zirconia Polymorphs Synthesized by Mechanochemical Technique

The synthesis of ZrO_2 by mechanochemical reaction using ZrCI_4 and CaO as raw materials and subsequent annealing of the products were investigated.The effect of thermal treatment on the structural evolution and morphological characteristics of the nanopowders was studied by X-ray diffractometry,Raman spectroscopy,transmission electron microscopy,scanning electron microscopy,differential thermal analysis and Rietveld refinement.The results showed that the average crystallite size of ZrO_2 was less than 100 nm up to around1100 ℃.The activation energy for ZrO_2 nanocrystallite growth during calcination was calculated to be about13,715 and 27,333 J/mol for tetragonal(t-ZrO_2) and monoclinic(m-ZrO_2) polymorphs,respectively.Mechanism of the nanocrystallite growth of the ZrO_2 polymorphs during annealing is primarily investigated.     

A general model for age acceleration during thermal cycling

Conventional practice in evaluating the effect of elevated temperature upon electronic devices in either accelerated testing or stress screening is the use of the Arrhenius reaction rate equation. This equation fails to represent several key aspects of the stress. A general model that includes the reaction rate effects during heating and cooling, the mechanical effects of heating and cooling, and non-constant activation energies is provided here. The model is based upon a general representation of a thermal cycle. Once the general model is constructed, it is shown to accommodate as special cases, acceleration when one or more of the features is assumed absent. An example illustrates this point. Then several uses for the model beyond the computation of the acceleration factor are discussed. It is suggested that the general model can be used to support test design and equipment selection decisions. The model therefore provides a more realistic portrayal of the effects of a thermal cycle and increased decision flexibility in defining thermal stress regimens.     

Reliability and robustness of thin film composite resistor networks

Reliability of composite NiCr–tantalum nitride resistors was tested according to MIL STD 883 procedures. It was shown analytically and experimentally that these resistors are robust and stable, and they can thus be recommended for use in precise and reliable integrated circuits.     

The Activation Energy <Emphasis Type="Italic">U</Emphasis>(<Emphasis Type="Italic">T</Emphasis>,<Emphasis Type="Italic">H</Emphasis>) in Y-based Superconductors

Based on the Arrhenius equation, a method to calculate the activation energy from the resistance transition is proposed for high temperature superconductors. This method is applied to the Y-based superconductors. The activation energy is found to be U(T,H)∼(1−T/T _c )^4.8(H/H ₀)^−3.8 of YBCO crystal, and U(T,H)∼(1−T/T _c )^3.3(H/H ₀)^−2.2 of Er doped MTG YBCO crystal, respectively. With the obtained activation energy U(T,H), the lower part of the experimental curve ρ(T,H) and its derivative can be reproduced.      

Integrated optics — technology and applications

The emergence of optoelectronics and photonics as viable alternatives to electronics in many key areas of engineering relevance is indeed significant. This paper presents a tutorial review of integrated optics — a technologically important development in photonics. Materials, processes, device technology and applications are highlighted.     

Kinetics of the glass transition in As22S78 chalcogenide glass: Activation energy and fragility index

Differential scanning calorimetry (DSC) has been used to probe the dynamics of the glass transition in As₂₂S₇₈ chalcogenide glass. Non-isothermal measurements were performed at different heating rates (5–35 K min⁻¹). The experimental result of this kinetic glass transition phenomenon was analyzed on the basis of the relaxation process occurring in the transition temperature range. The activation energy of the glass transition was determined from the heating rate dependence of the glass transition temperature. The fragility index m of the glass was estimated from the measurements of the activation energy of the relaxation process, which characterizes the glass transition. Different kinetic methods as well as isoconversional methods were used. Isoconversional analysis of the experimental data shows that the activation energy of glass transition process is varying with the degree of transformation (and hence with temperature) from the glassy to the supercooled phase.