Long-range chemical interactions in solid-state reactions: effect of an inert Ag interlayer on the formation of L10-FePd in epitaxial Pd(0 0 1)/Ag(0 0 1)/Fe(0 0 1) and Fe(0 0 1)/Ag(0 0 1)/Pd(0 0 1) trilayers

The effect of 0, 0.5, and 1?μm-thick Ag interlayers on the chemical interaction between Pd and Fe in epitaxial Pd(0?0?1)/Ag(0?0?1)/Fe(0?0?1)/MgO(0?0?1) and Fe(0?0?1)/Ag(0?0?1)/Pd(0?0?1)/MgO(0?0?1) trilayers has been studied using X-ray diffraction, ⁵⁷Fe Mössbauer spectroscopy, X-ray photoelectron spectroscopy, and magnetic structural measurements. No mixing of Pd and Fe occurs via the chemically inert Ag layer at annealing temperatures up to 400?°C. As the annealing temperature is increased above 400?°C, a solid-state synthesis of an ordered L1₀-FePd phase begins in the Pd(0?0?1)/Ag(0?0?1)/Fe(0?0?1) and Fe(0?0?1)/Ag(0?0?1)/Pd(0?0?1) film trilayers regardless of the thickness of the buffer Ag layer. In all samples, annealing above 500?°C leads to the formation of a disordered Fe_xPd_1?x(0?0?1) phase; however, in samples lacking the Ag layer, the synthesis of Fe_xPd_1?x is preceded by the formation of an ordered L1₂-FePd₃ phase. An analysis of the X-ray photoelectron spectroscopy results shows that Pd is the dominant moving species in the reaction between Pd and Fe. According to the preliminary results, the 2.2?μm-thick Ag film does not prevent the synthesis of the L1₀-FePd phase and only slightly increases the phase’s initiation temperature. Data showing the ultra-fast transport of Pd atoms via thick inert Ag layers are interpreted as direct evidence of the long-range character of the chemical interaction between Pd and Fe. Thus, in the reaction state, Pd and Fe interact chemically even though the distance between them is about 10⁴ times greater than an ordinary chemical bond length.     

Athermal migration of vacancies in iron and copper induced by electron irradiation

Abstract

Irradiation with high-energy particles induces athermal migration of point defects, which affects defect reactions at low temperatures where thermal migration is negligible. We conducted molecular dynamics simulations of vacancy migration in iron and copper driven by recoil energies under electron irradiation in a high-voltage electron microscope. Minimum kinetic energy required for migration was about 0.8 and 1.0 eV in iron and copper at 20 K, which was slightly higher than the activation energy for vacancy migration. Around the minimum energy, the migration succeeded only when a first nearest neighbour (1NN) atom received the kinetic energy towards the vacancy. The migration was induced by higher kinetic energies even with larger deflection angles. Above several electron-volts and a few 10s of electron-volts, vacancies migrated directly to 2NN and 3NN sites, respectively. Vacancy migration had complicated directional dependence at higher kinetic energies through multiple collisions and replacement of atoms. The probability of vacancy migration increased with the kinetic energy and remained around 0.3–0.5 jumps per recoil event for 20–100 eV. At higher temperatures, thermal energies slightly increased the probability for kinetic energies less than 1.5 eV. The cross section of vacancy migration was 3040 and 2940 barns for 1NN atoms in iron and copper under irradiation with 1.25 MV electrons at 20 K: the previous result was overestimated by about five times.     

Rates of diffusion controlled reactions for one-dimensionally-moving species in 3D space

ABSTRACT

The asymmetry in diffusion dimensionality between self-interstitial atom (SIA) clusters and vacancies is a fundamental feature of irradiation damage in crystals, leading to a defect buildup imbalance that manifests itself as measurable dimensional and mechanical property changes. It is well known that, while vacancies and mobile vacancy clusters diffuse in a three-dimensional (3D) fashion, SIA clusters perform one-dimensional motion along mostly rectilinear trajectories. Despite this, a complete set of kinetic coefficients, including coagulation reaction rates and sink strengths, does not exist for 1D-moving objects. In this paper, we derive analytical expressions for these coefficients from continuum diffusion theory particularised to 1D motion. Moreover, we carry out kinetic Monte Carlo simulations of numerical replicas of the geometry of diffusing particles and sinks to validate the proposed solutions. Our simulations, which are conducted entirely independently from the analytical derivations, reveal excellent agreement with the proposed expressions, adding confidence to their validity. We compare the 1D and 3D cases and discuss their relevance for kinetic codes for damage accumulation calculations.     

Solvable models of temporally correlated random walk on a lattice

We seek the conditional probability functionP(m,t) for the position of a particle executing a random walk on a lattice, governed by the distributionW(n, t) specifying the probability ofn jumps or steps occurring in timet. Uncorrelated diffusion occurs whenW is a Poisson distribution. The solutions corresponding to two different families of distributionsW are found and discussed. The Poissonian is a limiting case in each of these families. This permits a quantitative investigation of the effects, on the diffusion process, of varying degrees of temporal correlation in the step sequences. In the first part, the step sequences are regarded as realizations of an ongoing renewal process with a probability densityψ(t) for the time interval between successive jumps.W is constructed in terms ofψ using the continuous-time random walk approach. The theory is then specialized to the case whenψ belongs to the class of special Erlangian density functions. In the second part,W is taken to belong to the family of negative binomial distributions, ranging from the geometric (most correlated) to the Poissonian (uncorrelated). Various aspects such as the continuum limit, the master equation forP, the asymptotic behaviour ofP, etc., are discussed.     

Monitoring cooperative equilibria in a stochastic differential game

This paper deals with a class of equilibria which are based on the use of memory strategies in the context of continuous-time stochastic differential games. In order to get interpretable results, we will focus the study on a stochastic differential game model of the exploitation of one species of fish by two competing fisheries. We explore the possibility of defining a so-called cooperative equilibrium, which will implement a fishing agreement. In order to obtain that equilibrium, one defines a monitoring variable and an associated retaliation scheme. Depending on the value of the monitoring variable, which provides some evidence of a deviation from the agreement, the probability increases that the mode of a game will change from a cooperative to a punitive one. Both the monitoring variable and the parameters of this jump process are design elements of the cooperative equilibrium. A cooperative equilibrium designed in this way is a solution concept for a switching diffusion game. We solve that game using the sufficient conditions for a feedback equilibrium which are given by a set of coupled HJB equations. A numerical analysis, approximating the solution of the HJB equations through an associated Markov game, enables us to show that there exist cooperative equilibria which dominate the classical feedback Nash equilibrium of the original diffusion game model.This research was supported by FNRS-Switzerland, NSERC-Canada, FCAR-Quebec.     

A simple formula for mean multiplexing delay for independent regenerative sources

Simple expressions are given for the mean delay, mean waiting time, and mean busy period length in a multiplexer. Data streams with active periods having a general distribution are permitted, and the data rate during the active periods can be random. Data can also arrive in batches. The key restrictions of the model are that the sources are independent, idle periods are exponentially distributed, and a source generates at least enough data during an active period to keep the server busy throughout the period. The exact formulas allow evaluation of the error in approximations such as a heavy traffic diffusion approximation.Both continuous and discrete time models are considered. The discrete-time model includes that studied by Viterbi and subsequently generalized by Neuts. The Pollaczek-Khinchine formula for the mean amount of work in anM/GI/1 queue is retrieved as a limiting case.Preliminary version presented at IEEE INFOCOM, San Francisco, April 1993.     

一个反应扩散方程的门槛结果

本文讨论反应扩散方程Ｃａｕｃｈｙ问题解的整体存在性，渐近性质和Ｂｌｏｗｕｐ问题．其中或者１＜ｑ＜ｐ＜＋∞，ｎ＝２．得到门槛结果．     

中国聚变工程实验堆水冷包层钢构件流道成形控制研究

针对CFETR水冷包层流道钢构件热等静压制备时易变形压塌问题,利用单轴扩散焊设备开展了焊接工艺参数优化试验。在此基础上,重新设计了流道焊接界面位置和尺寸,用两步热等静压扩散焊法制备出了流道变形可控的平板型第一壁钢构件模块。优化试验表明,低活化钢试样的固相扩散焊温度需高于950℃,焊后经过760℃/60min回火热处理试样力学性能可以得到有效回复。     

基于局部加密纯无网格法非线性Cahn-Hilliard方程的模拟

为数值求解描述不同物质间相位分离现象的高阶非线性Cahn-Hilliard(C-H)方程,发展了一种基于局部加密纯无网格有限点集法(local refinement finite pointset method,LR-FPM).其构造过程为:1)将C-H方程中四阶导数降阶为两个二阶导数,连续应用基于Taylor展开和加权最小二乘法的FPM离散空间导数;2)对区域进行局部加密和采用五次样条核函数以提高数值精度;3)局部线性方程组求解中准确施加含高阶导数Neumann边值条件.随后,运用LR-FPM求解有解析解的一维/二维C-H方程,分析粒子均匀分布/非均匀分布以及局部粒子加密情况的误差和收敛阶,展示了LR-FPM较网格类算法在非均匀布点情况下的优点.最后,采用LR-FPM对无解析解的一维/二维C-H方程进行了数值预测,并与有限差分结果相比较.数值结果表明,LR-FPM方法具有较高的数值精度和收敛阶,比有限差分法更易数值实现,能够准确展现不同类型材料间相位分离非线性扩散现象随时间的演化过程.