Crystal plasticity modeling of irradiation growth in Zircaloy-2

Abstract

A physically based reaction-diffusion model is implemented in the visco-plastic self-consistent (VPSC) crystal plasticity framework to simulate irradiation growth in hcp Zr and its alloys. The reaction-diffusion model accounts for the defects produced by the cascade of displaced atoms, their diffusion to lattice sinks and the contribution to crystallographic strain at the level of single crystals. The VPSC framework accounts for intergranular interactions and irradiation creep, and calculates the strain in the polycrystalline ensemble. A novel scheme is proposed to model the simultaneous evolution of both, number density and radius, of irradiation-induced dislocation loops directly from experimental data of dislocation density evolution during irradiation. This framework is used to predict the irradiation growth behaviour of cold-worked Zircaloy-2 and trends compared to available experimental data. The role of internal stresses in inducing irradiation creep is discussed. Effects of grain size, texture and external stress on the coupled irradiation growth and creep behaviour are also studied and compared with available experimental data.     

Discrete phase space II. Relativistic lattice wave equations and divergence-free green's functions

Therelativistic lattice Klein-Gordon equation, Dirac equation, electromagnetic equations, and gauge field equations are presented as partialdifference equations. Various lattice Green's functions are constructed (except for non-abelian gauge fields). It is proved that many of the lattice Green's functions are non-singular or divergence-free. Moreover, it is conjectured that all lattice Green's functions are non-singular.     

Evolution of a microstructure of materials under irradiation

The evolution of a microstructure of metals (or alloys) under irradiation resulting in swelling of the material is considered for the case with the formation of Frenkel pairs. A closed system of equations describing the evolution of the microstructure of the material exposed to irradiation is obtained, and relationships for the swelling rate are derived. It is shown that the swelling rate varies linearly with time for a stationary source of point defects (the number of Frenkel pairs per lattice site). An expression for the swelling rate is deduced for a radiation source operating in a more realistic pulsed mode.     

Defect-density switching wave in crystals under pulsed laser irradiation

A model is proposed for the ignition of a defect-density switching wave in a crystal by powerful laser pulses. It is shown that the switching wave arises as a result of the nonlinear dependence of the activation energy of the defect-formation process on the strain field due to defects. The conditions under which a switching wave arises and the profile, velocity, and propagation direction of the wave are discussed. Zh. Tekh. Fiz. 68, 73–77 (August 1998)     

Nonlinear longitudinal waves in the presence of the interaction between the strain and temperature fields and the field of nonequilibrium atomic defects

The propagation of nonlinear longitudinal waves in a plate is studied by taking into account the interaction of the longitudinal displacement component with the temperature field and the field of concentration of nonequilibrium atomic point defects. A nonlinear evolution equation is derived for describing the self-consistent thermoelastic longitudinal strain fields. It is shown that the thermoelastic effect on the strain waves manifests itself in the appearance of dissipative terms, which describe the heat transfer and the thermoelastic interaction caused by the strain-induced heat release due to the recombination of nonequilibrium atomic defects. The soliton solutions to the evolution equation are investigated, and the characteristic features of their damping are considered with allowance for the low-frequency and high-frequency losses.     

Effect of irradiation with Ne<Superscript>+</Superscript> ions on the transformations of domain structures of a uniaxial magnetic film in an AC magnetic field

Effects of irradiation with Ne⁺ ions on the transformations of domain structures (DSs) that occur in a uniaxial magnetic film under the action of an ac magnetic field are investigated. Transitions of a DS from an amorphous state into a hexagonal lattice and a labyrinthine structure are considered. The irradiation is found to lead to a change in the amplitudes of the ac field at which phase transformations of the DS occur. The effect of the magnitude of the ac field on the number of domains in a block with a hexagonal lattice has been studied. It is shown that the process of annealing of defects in a DS consisting of blocks with a hexagonal lattice can be described by the equation of a first-order reaction. The irradiation-induced change in the energy of activation for the annealing of defects in the DS has been found.     

Electron microscopy of life-tested semiconductor laser diodes

Electron Microscopy on life-tested 980 nm SL SQW InGaAs/AlGaAs laser diodes is able to find and analyze lattice defects responsible for the detected failures. Anyway, the origin and evolution of those defects remains questionable. Only the comparative analysis of life-test measurements, EBIC-FIB/TEM images, and charge-transport physics is able to point out a coherent framework for complete decoding of the failure kinetics. Minority-carrier diffusion and their enhanced recombination at defective lattice points are indicated, as the energy supply required for defect reaction and growth. The rules of charge diffusion drive both the reaction model, the interpretation of EBIC images and the expected electrical and optical effects. Strain release at the ultimate propagation of defects into the strained InGaAs quantum layer is then easily related to the final state of the failed devices.     

Theoretical description of adatom migration in two-dimensional highly-ordered states

Analytical expressions for chemical, jump, and tracer diffusion coefficients are obtained for interacting lattice gases on a square lattice. Strongly repulsive nearest neighbor interactions cause the formation of a highly-ordered c() state in the vicinity of half coverage. It is shown that only strongly correlated successive adatom jumps contribute to the particle flow. This allows to describe the adatom kinetics by considering an almost ideal lattice gas of defects. Two types of defects are considered, adatoms in the empty sublattice and vacancies in the filled sublattice of the c() ordered state. The diffusion equations for these defects are developed considering the generation and recombination of defects. In addition we have considered adatom transport caused by the motion of defect pairs (dimers). Dimer transport mechanism prevails in the high coverage region. The characteristic features of the various diffusion coefficients near half coverage are analyzed and discussed. The theory is compared with the results of sophisticated Monte-Carlo simulations which have been executed with the use of a fully parallelized algorithm on a Cray T3E (LC784-128). The agreement between theoretical and MC results is excellent if the motion of dimers at is taken into account. Received 24 June 1998     

On diffusion-elastic instabilities in a solid half-space

A model of the diffusion-elastic instability that appears in an ensemble of non-equilibrium atomic defects in unbounded condensed media as well as on the free surface of a half-space is introduced and studied. The dynamical model developed here is based on coupled evolution equations for the elastic displacement of the medium and atomic defect density fields. The idea of an instability model is related to a drift of atomic defects under the influence of elastic fields. It is shown that the development of this instability creates ordered structures of coupled strain and defect-concentration fields. Dispersion relationships for the growth increment of these structures are derived and their characteristic scales are obtained.     

Dynamic modeling of total ionizing dose-induced threshold voltage shifts in MOS devices

The total ionizing dose (TID) effect is a key cause for the degradation/failure of semiconductor device performance under energetic-particle irradiation. We developed a dynamic model of mobile particles and defects by solving the rate equations and Poisson's equation simultaneously, to understand threshold voltage shifts induced by TID in silicon-based metal-oxide-semiconductor (MOS) devices. The calculated charged defect distribution and corresponding electric field under different TIDs are consistent with experiments. TID changes the electric field at the Si/SiO₂ interface by inducing the accumulation of oxide charged defects nearby, thus shifting the threshold voltage accordingly. With increasing TID, the oxide charged defects increase to saturation, and the electric field increases following the universal 2/3 power law. Through analyzing the influence of TID on the interfacial electric field by different factors, we recommend that the radiation-hardened performance of devices can be improved by choosing a thin oxide layer with high permittivity and under high gate voltages.     

外延压应变对BaTiO$lt;sub$gt;3$lt;/sub$gt;铁电体抗辐射性能影响的分子动力学研究

采用基于壳模型的分子动力学模拟方法, 研究了存在外延压应变时BaTiO₃铁电体的辐射位移效应, 以O原子作为初冲原子(primary knock-on atom, PKA), 能量为1 keV, 方向为[001], 分别计算了外延压应变为0, 0.4%, 0.8%, 1.2%, 1.6%, 2.0%时体系的缺陷数量、分布, 以及辐射前后的极化强度, 比较了压应变为2%以及无应变下损伤区域、缺陷离位距离和反向外电场下PKA的迁移距离. 结果表明, 随外延压应变增加体系极化近似线性增加, 辐射后极化降低幅度降低、缺陷产生的数量有所减小, 2% 压应变存在时缺陷原子的离位距离、PKA在反向外电场作用下的迁移距离和损伤区域都小于无应变的情况, 说明外延压应变的存在对辐射造成的晶格损伤具有抑制作用, 对辐射损伤具有改善作用, 可以通过引入外延压应变来调控BaTiO₃的辐射损伤. 关键词： 应变 3')" href="#">BaTiO₃ 辐射损伤 分子动力学模拟     

Stochastic models for lattice gauge theories

Stochastic equations are derived which describe the (Euclidean) time evolution of lattice field configurations, with and without fermions, on a three-dimensional space lattice. It is indicated how the drifts and transition functions may be obtained as asymptotic solutions of a differential equation or from a ground state ansatz. For non-Abelian gauge fields (without fermions) a ground state is constructed which is an exact eigenstate of a Hamiltonian with the same (naive) continuum limit as the Kogut-Susskind Hamiltonian. It is described how Euclidean correlations (like the Wilson loop) are obtained from the stochastic equations and how mass gaps may be obtained from the technique of exit times.     

A model for the propagation of nonlinear dispersive strain waves in a solid with defect clusters

A model for the propagation of nonlinear dispersive one-dimensional longitudinal strain waves in an isotropic solid with quadratic nonlinearity of elastic continuum is developed with taking into account the interaction with atomic defect clusters. The governing nonlinear dispersive-dissipative equation describing the evolution of longitudinal strain waves is derived. An approximate solution of the model equation was derived which describes asymmetrical distortion of geometry of the solitary strain wave due to the interaction between the strain field and the field of clusters. The contributions of the finiteness of the relaxation times of cluster-induced atomic defects to the linear elastic modulus and the lattice dissipation and dispersion parameters are determined. The amplitudes and width of the nonlinear waves depend on the elastic constants and on the properties of the defect subsystem (atomic defects, clusters) in the medium. The explicit expression is received for the sound velocity dependence upon the fractional cluster volume, which is in good agreement with experiment. The critical value of cluster volume fraction for the influence on the strain wave propagation is determined.     

Analysis of a spray diffusion flame and its extinction in a shear layer

A new semi-analytical solution for a laminar spray diffusion flame in the shear layer between fuel and oxidant streams is developed. The Stokes number is identified as a small spray droplet-related parameter to be used in a perturbation analysis of the liquid phase governing equations. Appropriate specification of an additional parameter ensures that similarity is achieved so that the concentration field of the liquid in the spray can be readily found. The coupled gas-phase equations are treated using the usual inverse of the large Zeldovitch number for the asymptotic analysis. Numerical results demonstrate how the distribution of the liquid phase in the developing shear layer between two unidirectional gas streams flowing over one another with (the possibility of) dissimilar velocities in their respective free-streams influences the flame shape, location, fuel vapour and temperature fields. An extinction analysis enables a parametric mapping of conditions for extinguishment of the spray diffusion flames to be drawn.     

The non-Arrhenius migration of interstitial defects in bcc transition metals

Thermally activated migration of defects drives microstructural evolution of materials under irradiation. In the case of vacancies, the activation energy for migration is many times the absolute temperature, and the dependence of the diffusion coefficient on temperature is well approximated by the Arrhenius law. On the other hand the activation energy for the migration of self-interstitial defects, and particularly self-interstitial atom clusters, is very low. In this case a trajectory of a defect performing Brownian motion at or above room temperature does not follow the Arrhenius-like pattern of migration involving infrequent hops separated by the relatively long intervals of time during which a defect resides at a certain point in the crystal lattice. This article reviews recent atomistic simulations of migration of individual interstitial defects, as well as clusters of interstitial defects, and rationalizes the results of simulations on the basis of solutions of the multistring Frenkel–Kontorova model. The treatment developed in the paper shows that the origin of the non-Arrhenius migration of interstitial defects and interstitial defect clusters is associated with the interaction between a defect and the classical field of thermal phonons. To cite this article: S.L. Dudarev, C. R. Physique 9 (2008).     

The homology of defective crystal lattices and the continuum limit

The problem of extending fields that are defined on lattices to fields defined on the continua that they become in the continuum limit is basically one of continuous extension from the 0‐skeleton of a simplicial complex to its higher‐dimensional skeletons. If the lattice in question has defects, as well as the order parameter space of the field, then this process might be obstructed by characteristic cohomology classes on the lattice with values in the homotopy groups of the order parameter space. The examples from solid‐state physics that are discussed are quantum spin fields on planar lattices with point defects or orientable space lattices, vorticial flows or director fields on lattices with dislocations or disclinations, and monopole fields on lattices with point defects.     

基于流体动力学模型的2维砷化镓金属半导体场效应管数值模拟

 介绍了用于描述工作在高频强电场条件下的亚微米半导体器件的流体动力学模型,并讨论了为求解流体动力学模型所采用的算子分裂方法和有限体积法。使用流体动力学模型,对亚微米GaAs金属半导体场效应管器件进行了2维数值模拟,得到了该器件的I-V曲线、电子密度分布和电子温度分布。数值模拟结果表明,器件栅极电压越负,肖特基结的耗尽层越厚,源漏电流越小;在耗尽层内电场最强处,电子温度达到4 000 K;在强电场下,电子温度将严重偏离晶格温度,形成所谓热电子。     

A three-dimensional time-dependent theory for helix traveling wave tubes in beam-wave interaction

This paper presents a three-dimensional time-dependent nonlinear theory of helix traveling wave tubes for beamwave interaction.The radio frequency electromagnetic fields are represented as the superposition of azimuthally symmetric waves in a vacuum sheath helix.Coupling impedance is introduced to the electromagnetic field equations’ stimulating sources,which makes the theory easier and more flexible to realize.The space charge fields are calculated by electron beam space-charge waves expressed as the superposition solutions of Helmholtz equations.The focusing forces due to either a solenoidal field or a periodic permanent magnetic field is also included.The dynamical equations of electrons are Lorentz equations associating with electromagnetic fields,focusing fields and space-charge fields.The numerically simulated results of a tube are presented.     

Fe-Cr合金辐照空洞微结构演化的相场法模拟

Fe-Cr合金作为包壳材料在高温高辐照强度等极端环境下服役,产生空位和间隙原子等辐照缺陷,辐照缺陷簇聚诱发空洞、位错环等缺陷团簇,引起辐照肿胀、晶格畸变,导致辐照硬化或软化致使材料失效.理解辐照缺陷簇聚和长大过程的组织演化,能更有效调控组织获得稳定服役性能.本文采用相场法研究Fe-Cr合金中空洞的演化,模型考虑了温度效应对点缺陷的影响以及空位和间隙的产生和复合.选择400—800 K温度区间、0—16 dpa辐照剂量范围的Fe-Cr体系为对象,研究在不同服役温度和辐照剂量下的空位扩散、复合和簇聚形成空洞的过程.在400—800 K温度区间,随着温度的升高,Fe-Cr合金空洞团簇形核率呈现出先升高后下降的趋势.考虑空位与间隙的重新组合受温度的影响可以很好地解释空洞率随温度变化时出现先升高后降低的现象.由于温度的变化将影响Fe-Cr合金中原子离位阀能,从而影响产生空位和间隙原子.同一温度下,空洞半径和空洞的体积分数随辐照剂量的增大而增大.辐照剂量的增大,级联碰撞反应加强,空位与间隙原子大量产生,高温下空位迅速的扩散聚集在Fe-Cr合金中将形成更多数量以及更大尺寸的空洞.