Dynamics of phase-formation processes during self-propagating high-temperature synthesis in the thermal explosion regime

Specific features of formation of temperature and concentration fields during self-propagating high-temperature synthesis in the thermal explosion regime in a cylindrical reactor are studied by methods of mathematical modeling. The calculations are performed with allowance for melting of one (chemically active) component in the approximation with the high-melting component being non-soluble in the melt of the low-melting component. It is shown that the conditions of complete conversion of the original components in the volume of the reacting mixture depend on relations between the Biot criterion of the system, the ambient temperature, and the thermal effect of the reaction. After the thermal explosion, which occurs when the melting front reaches the geometric center of the reactor, a front of complete conversion is formed. This front moves from the cylinder centerline to the periphery with a gradually decreasing velocity. The diagram of the critical values of the Biot criterion at which the components burn down completely in the entire reaction volume is calculated. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 4, pp. 31–38, July–August, 2008.     

一类含多时滞和扩散项的非标准离散模型

建立了一类以媒体效应作为主要预防传染病传播手段、并且含有多时滞和扩散项的传染病连续模型，并证明了该连续模型平衡点的全局稳定性。其次，利用非标准有限差分方法对该连续模型进行离散，离散后的模型具有和原连续模型一致的动力学性质。通过构造适当的李雅普诺夫函数，证明离散模型的平衡点在一定条件下也都是全局渐近稳定的。最后，数值模拟验证了理论结果。     

A Computational Model of NBTI and Hot Carrier Injection Time-Exponents for MOSFET Reliability

Theories of interface trap generation in Negative Bias Temperature Instability (NBTI) and Hot Carrier Injection (HCI) mechanisms are unified under the geometric interpretation and computational modeling of Reaction-Diffusion (R-D) theoryframework. Analytical derivations that predict the degradation are shown, simulation methodology is explained and numerical solutions are obtained. Time-exponents and degradation behavior under dynamic bias in agreement with experimental observations are discussed. Implications regarding ultra-scaled surround-gate device structures are presented.     

具有边界摄动的反应扩散方程奇摄动Robin问题

研究具有边界摄动的非线性反应扩散方程奇摄动Robin问题,运用微分不等式理论,讨论原问题解在适当条件下的存在性、唯一性及其一致有效的渐近估计。     

具有边界摄动的反应扩散时滞方程奇摄动问题(英文)

本文研究了具有边界摄动的非线性时滞反应扩散方程奇摄动问题.首先得到了退化问题的解.其次构造了原问题的外部解.然后引入伸长变量构造了解的初始层校正项,得到了解的形式渐近展开式.最后在适当的假设下,利用微分不等式理论,证明了原初始边植问题解的渐近展开式的一致有效性.     

Numerical Solution of a Reaction-Diffusion Elliptic Interface Problem with Strong Anisotropy

We consider a singularly perturbed reaction-diffusion elliptic problem in two dimensions (x,y), with strongly anisotropic coefficients and line interface. The second order derivative with respect to x is multiplied by a small parameter ². We construct finite volume difference schemes on condensed Shihskin meshes and prove -uniform convergence in discrete energy and maximum norms. Numerical experiments that agree with the theoretical results are given.     

The effect of isothermal aging on the thickness of intermetallic compound layer growth between low melting point solders and Ni-plated Cu substrate

The growth kinetics of the intermetallic compound (IMC) layer formed between two low melting point solders and electrolytic Ni/Cu substrate by solid-state isothermal aging were examined. The solders were 100 In and In-48Sn. A quantitative analysis of the IMC layer thickness as a function of aging time and aging temperature was performed. Experimental results showed that the IMCs, such as In₂₇Ni₁₀ and Ni₃(In, Sn)₄), were observed for different solders. Additionally, the growth rate of these IMCs increased with the aging temperature and time. The layer growth of the IMC in the couples of indium solder alloy/electrolytic Ni system satisfied the parabolic law at a given temperature range. As a whole, because the values of the time exponent (n) are approximately 0.5, the layer growth of the IMC was mainly controlled by the diffusion mechanism over the temperature range studied. The apparent activation energies for IMC growth were 60.03 kJ/mol for In₂₇Ni₁₀ and 72.84 kJ/mol for Ni₃(In, Sn)₄.     

两种群竞争非线性反应扩散系统奇摄动Robin问题

研究了一类生物数学中新的非线性两种群竞争反应扩散系统奇摄动Rob in问题,在适当的假设下,对此问题解的存在性及渐近性态作了较深入的讨论,利用伸长变量构造了问题解的形式展开式,并用微分不等式理论,证明了问题解渐近展开式的一致有效性.     

Interface reactions and reaction synthesis of a high temperature composite system

Reactive diffusion during isothermal annealing was examined in a Ti−Al−Si temary system. When a TiAl/TiSi₂ reaction couple was annealed at 1373 K for 200 h, the product phase sequence was observed as TiAl/TiAl₂/Ti₂Al₅/TiAl₃/Ti₅Si₄/TiSi/TiSi₂, in which the integrated diffusion coefficient of Ti₂Al₅ showed the lowest value. A Ti-rich Ti₅Si₃ phase appeared when an additional Ti flux was provided between the TiAl/TiSi₂ reaction. The growth kinetics for both the TiAl/TiSi₂ (direction reaction) and TiAl/Ti/TiSi₂ reactions (Ti biased reaction) were identified, and a comparison of the morphology of the product phases was provided. The chemical potential variation and mass balance exhibited guidance in predicting the diffusion pathway during isothermal annealing. It appears that a biasing reaction (i.e., controlling component flux) is an effective tool for the phase selection and morphology changes during isothermal annealing.     

铌对65SiCrV6弹簧钢氧化增重的影响

 铌对Si-Cr-V系弹簧钢强度和脱碳层特征的影响已受到较多关注,但铌对该系弹簧钢氧化增重影响的研究还较少。以65SiCrV6弹簧钢为研究对象,在其中添加质量分数约0.017%的铌(65SiCrV6Nb)。采用SEM+EDS、XRD、TEM、FactSage化学热力学软件、反应扩散理论和数理统计相结合的方法,从研究铌加入是否会对该弹簧钢在炉氧化增重和氧化铁皮物相组成等产生明显影响的角度,对铌加入是否会对该弹簧钢高压水除鳞难易度产生影响进行评价。结果表明,铌的加入提高了锻态65SiCrV6钢中的珠光体和未溶M(C,N)的相对含量,降低了铁素体的相对含量,并细化了组织。在氧气浓度为2%~7%(体积分数)、加热速度为8~20 ℃/min、保温温度为1 050~1 150 ℃和保温时间为60~90 min等工艺条件下,铌的加入使65SiCrV6钢的氧化增重明显提高,提高幅度为2.54%~27.82%且具有统计学意义。影响试验钢在炉氧化增重的主次效应依次为保温温度>保温时间>加热速度>氧气浓度,保温温度和保温时间对试验钢在炉氧化增重的影响为正相关,氧气浓度和加热速度对试验钢在炉氧化增重的影响为负相关。65SiCrV6钢在炉氧化增重达最小值的工艺为氧气浓度为7%、加热速度为14 ℃/min、保温温度为1 050 ℃和保温时间为60 min;65SiCrV6 Nb钢在炉氧化增重达最小值的工艺为氧气浓度为7%、加热速度为8 ℃/min、保温温度为1 050 ℃和保温时间为60 min。影响铌对65SiCrV6钢在炉氧化增重提高幅度的主次效应为保温时间>保温温度>加热速度>氧气浓度。铌的加入使65SiCrV6钢在炉氧化增重提高幅度最小的工艺为氧气浓度为2%、加热速度为8 ℃/min、保温温度为1 050 ℃和保温时间为75 min。由反应扩散控制的氧化固态相变是造成保温温度、保温时间、加热速度和氧气浓度对试验钢在炉氧化增重产生不同影响的主要原因。铌的加入未改变65SiCrV6钢表面氧化铁皮的3层结构特征,氧化铁皮由外向钢基体主要由Fe₂O₃、Fe₃O₄和FeO(或FeO+Fe₂SiO₄)等构成。铌的加入降低了65SiCrV6钢氧化铁皮中Fe₂SiO₄的相对含量,对高压水除鳞有利。