Stress-dependent Diffusion Research Articles

Twofold Saddle-Point Formulation of Biot Poroelasticity with Stress-Dependent Diffusion

Twofold Saddle-Point Formulation of Biot Poroelasticity with Stress-Dependent Diffusion

Mechanics of electrochemical strain microscopy: Computational simulations and experimental validations

In the last decade, electrochemical strain microscopy (ESM) has emerged as a powerful tool to study electrochemical processes at the nanoscale, yet its quantitative analysis is quite challenging, involving complex electrochemo-mechanical coupling under highly concentrated electromechanical fields. In this work, we develop a theoretical framework of thermodynamics and kinetics for mobile ions in electrochemically-active solids, wherein full electrochemo-mechanical coupling is considered via concentration-dependent Vegard strain and stress-dependent diffusivity. The theory is applied to model electrochemical processes underneath a charged scanning probe tip, and implemented numerically to solve for the highly inhomogeneous electrochemo-mechanical field via combined fast Fourier transform and finite difference analysis. The simulations reveal that the ESM amplitude correlates linearly with both ionic concentration and diffusivity, while relaxation time constant depends only on diffusivity, making it possible to decouple these two material parameters. In order to validate our model analysis, ESM mapping and point-wise relaxation studies are carried out on solid state electrolyte ceria, and the experimental data agree with model predictions well. The analysis thus provides a powerful technique to analyze ESM experiments, and sheds deep insight into the nanoscale electrochemical process under a tip.

Effects of surface stress on lithium-ion diffusion kinetics in nanosphere electrodes of lithium-ion batteries

The experimental evidence suggests that the lithium ions tend to aggregate on the near-surface of nanoscale electrode particles in lithium-ion batteries. However, the underlying mechanism has not been well understood. In this work, based on the established chemo-mechanical coupled model featuring surface stress, stress-dependent chemical potential, and stress-mediated diffusivity, the size-dependence of diffusion kinetics in nanosphere electrodes is investigated. The results show that additional compressive stresses caused by the surface stress retard the attainable lithiation due to the reduced surface stress-dependent diffusivity, and the high lithiation region has a growing tendency to move on the near-surface region with decreasing the dimensions of nanospheres. The work indicates that the effects of surface stress on lithium-ion diffusion kinetics may result in the capacitor-like behavior of battery materials consisting of electrode nanoparticles.

High-fidelity multi-physics coupling for determination of hydride distribution in Zr-4 cladding

Hydride production in Zircaloy cladding continues to be one of the main limiting factors for extending the life of nuclear fuel rods in the core. The production of hydrides in the cladding comes as a direct result of corrosion with water during normal operation. Furthermore, the distribution of hydrogen in the cladding depends strongly on the temperature and temperature gradients inside the cladding. In order to accurately predict these temperature gradients, a high-fidelity multi-physics coupling is needed. The Department of Energy (DOE) recognized this need and sponsored a project at the Pennsylvania State University (PSU) in cooperation with North Carolina State University (NCSU) under the Nuclear Energy University Programs (NEUP). The overreaching goal of this project is to couple thermal-hydraulics, neutronics, and fuel performance codes together to predict the distribution of hydrogen and hydrides in the cladding as a function of time and space. This goal is attained through a two-step approach. The first step combines accurate high-fidelity thermal-hydraulic models for heat transfer, reactor physics models for neutron flux, and thermal-mechanics models for fuel performance calculations to acquire detailed temperature and stress distributions in the fuel rod. The second step develops a semi-analytical model and experimentally tests the temperature and/or stress dependent hydrogen pick-up, diffusion, and precipitation in the cladding. This paper aims to show the capabilities of the high-fidelity coupling, their effect on the power and temperature predictions, and subsequent effect on the distribution of hydrogen in the cladding, specifically in the inter-pellet gap region.

Using the material point method to model chemical/mechanical coupling in the deformation of a silicon anode

The lithiation and delithiation of a silicon battery anode is modeled using the material point method (MPM). The main challenges in modeling this process using the MPM is to simulate stress dependent diffusion coupled with concentration dependent stress within a material that undergoes large deformations. MPM is chosen as the numerical method of choice because of its ability to handle large deformations. A method for modeling diffusion within MPM is described. A stress dependent model for diffusivity and three different constitutive models that fully couple the equations for stress with the equations for diffusion are considered. Verifications tests for the accuracy of the numerical implementations of the models and validation tests with experimental results show the accuracy of the approach. The application of the fully coupled stress diffusion model implemented in MPM is applied to modeling the lithiation and delithiation of silicon nanopillars.

Numerical simulation of residual stress in low temperature colossal carburised layer on austenitic stainless steel

A numerical model is proposed to quantitatively characterise the residual stress evolutions in low temperature colossal carburised layer on austenitic stainless steel. In this model, on the basis of the consideration of concentration and stress dependent carbon diffusivity, prediction of the carbon concentration distribution and growth regularity of carburised layer is performed. The strain rate is discussed taking the compositive effects of residual stress and carbon concentration gradient. Based on the strain compatibility of carburised layer and substrate, the residual stress is calculated. Meanwhile, a low temperature colossal carburisation experiment is carried out on 316L austenitic stainless steel and the carbon concentration and residual stress are measured to verify the validity of the model. The numerical results of carbon concentration and residual stress distributions agree with the experimental data, indicating that the numerical model established in this paper can be used to investigate the process of low temperature colossal carburisation.

Quantitative law of diffusion induced fracture

Through dimension analysis, an almost analytical model for the maximum diffusion induced stress (DIS) and critical temperature (or concentration) difference at which cracks begin to initiate in the diffusion process is developed. It interestingly predicts that the spacing of diffusion-induced cracks is constant, independent of the thickness of specimen and the temperature difference. These conclusions are validated by our thermal shock experiments on alumina plates. Furthermore, the proposed model can interpret observed hierarchical crack patterns for high temperature jump cases, and a three-stage relation between the residual strength and the temperature difference. The prediction for crack spacing can guide the biomimetic thermal-shock-failure proof design, in which the hard platelets smaller than the predicted diffusion induced by constant crack-spacing are embedded in a soft matrix, and, therefore, no fracture will happen. This may guide the design of the thermal protection system and the lithium ion battery. Finally we present the maximum normalized DISes for various geometry and boundary conditions by single-variable curves for the stress-independent diffusion process and two-variable contour plots for the stress-dependent diffusion process, which can provide engineers and materialists a simple and easy way to quickly evaluate the reliability of related materials and devices.

High-temperature discrete dislocation plasticity

A framework for solving problems of dislocation-mediated plasticity coupled with point-defect diffusion is presented. The dislocations are modeled as line singularities embedded in a linear elastic medium while the point defects are represented by a concentration field as in continuum diffusion theory. Plastic flow arises due to the collective motion of a large number of dislocations. Both conservative (glide) and nonconservative (diffusion-mediated climb) motions are accounted for. Time scale separation is contingent upon the existence of quasi-equilibrium dislocation configurations. A variational principle is used to derive the coupled governing equations for point-defect diffusion and dislocation climb. Superposition is used to obtain the mechanical fields in terms of the infinite-medium discrete dislocation fields and an image field that enforces the boundary conditions while the point-defect concentration is obtained by solving the stress-dependent diffusion equations on the same finite-element grid. Core-level boundary conditions for the concentration field are avoided by invoking an approximate, yet robust kinetic law. Aspects of the formulation are general but its implementation in a simple plane strain model enables the modeling of high-temperature phenomena such as creep, recovery and relaxation in crystalline materials. With emphasis laid on lattice vacancies, the creep response of planar single crystals in simple tension emerges as a natural outcome in the simulations. A large number of boundary-value problem solutions are obtained which depict transitions from diffusional to power-law creep, in keeping with long-standing phenomenological theories of creep. In addition, some unique experimental aspects of creep in small scale specimens are also reproduced in the simulations.

Reflow of Phosphorous Silicate Glass Layer Formed on Textured Si Surface in Crystalline Si Solar Cells

We have investigated the reflow behavior of phosphorus silicate glass (PSG) layer formed on textured Si surface using transmission electron microscopy and simulation. For conventional wet oxidation process, stress-dependent surface reaction and stress-dependent oxidant diffusion led to the oxidation retardation in both convex and concave regions of the textured Si surface, respectively. However, PSG film formed by POCl3-diffusion underwent reflow, resulting in the formations of thinner and thicker PSG films in convex and concave regions, respectively. Simulation results showed that the reflow of PSG films causes lateral thermal mismatch stresses to increase and decrease in convex and concave regions, respectively.

2425 応力依存異方拡散現象による耐熱合金劣化損傷機構の検討(S13-3 高温材料・構造の強度と破壊(3),S13 高温材料・構造の強度と破壊)

2425 応力依存異方拡散現象による耐熱合金劣化損傷機構の検討(S13-3 高温材料・構造の強度と破壊(3),S13 高温材料・構造の強度と破壊)

P55 応力依存異方性拡散現象によるNi基超合金微細分散組織の変化挙動解析(OS13)

P55 応力依存異方性拡散現象によるNi基超合金微細分散組織の変化挙動解析(OS13)

Flow properties of hard structured particle suspensions

A class of structured particles is developed such that the effects of particle interactions are adjusted enabling suspension mechanics to be studied without the influence of interparticle forces other than volume exclusion, Brownian and hydrodynamic interactions. Three grades of these near-hard structured particles are developed from fumed silica. These particles have the same structure as measured by the mass fractal dimension. Stress dependent viscosities and diffusivity measurements are reported as a function of particle concentration, providing an opportunity to determine the scaling behavior of these properties with the two characteristic sizes: the primary particle and aggregate sizes. Except at stresses exceeding the critical value demarking the onset of shear thickening, flow curves superimposed with each other and with hard sphere suspensions compared at the same effective packing fraction, φ/φm.

Modeling electromigration-induced stress evolution and drift kinetics with a stress-dependent diffusivity

Clement and Thompson have justified that it is necessary to take into account the stress dependence of atomic mobility when describing stress evolution in a metal conductor caused by electromigration [J. J. Clement and C. V. Thompson, J. Appl. Phys. 78, 900 (1995)]. In the present contribution the role of this dependence is considered in more detail, leading to qualitatively new results concerning stress evolution and drift kinetics. The stationary stress distribution over the length of the elastic zone of the conductor was shown to be nonlinear and asymmetrical at superthreshold conditions, with the zone of compressive stress being more extended than that of tensile stress. This also results in an asymmetrical pattern for plastic deformation, the hillocking zone being more extended than the voiding region at the cathode. The drift rate was shown to achieve its maximum value during the nonstationary stage of stress evolution and then to drop down to its stationary value. The duration of the nonstationary stage of stress evolution is proportional to the conductor length and inversely proportional to the current density. This is essentially different from the result obtained in all previous works. Our model also predicts that for conductors with a length much longer than the critical one, the nonstationary stage of stress evolution corresponds to a quasistationary stage for drift kinetics, during which a constant drift rate is observed. Finally, we will consider the consequences of taking into account the stress dependence of mobility when describing the effects of passivation and thermal stress on drift kinetics.

On the effects of microstress on macroscopic diffusion processes

Summary. The effects of internal microstress fields are neglected in a usual simulation of the diffusion of a small solute trough solid heterogeneous media. However, when a heterogeneous material is used in a structure undergoing external mechanical loading, highly nonuniform stress fields can arise locally due to the variable microstructure. In this paper a simple quasi-Fickian model is studied which employs a spatially variable stress-dependent diffusivity, D ~. The structure of D ~ stems from an assumption that the stresses nonuniformly open and close the pores of the material microstructure, thus providing preferential sites for accumulation of the diffusing solute. When o- 0, the usual stress-free Fickian diffusivity, D ~ is recovered. Because of the highly oscillatory stress fields on the micro level, when employing numerical methods, such as the finite element or finite difference method, the distance between discretization nodes must be far smaller than the microstructural oscillations to obtain accurate simulations. This fact makes direct numerical simulations involving D ~ virtually impossible without computationally intensive, and complicated, special techniques. In this paper upper bounds are developed for the difference between solutions produced when using D ~ and alternatively D o in the body under analysis. The general case, when D ~ ~ and consequently D ~, are spatially variable, is considered. The bounds are a function of only D O and (7 and do not require any knowledge of the stress-dependent solution, and can thus be used as an a-priori check to determine whether potentially expensive computations are necessary.

Nanopatterning of Thin Cobaltdisilicide Layers by Local Oxidation

ABSTRACTLocal oxidation of thin cobaltdisilicide layers (10–30 nm) allows patterning with distances between silicide pads as small as 70 nm. The epitaxial silicide layers were grown by molecular beam allotaxy (MBA) on Si(100) substrates. They were characterized by TEM, RBS and sheet resistance measurements showing good crystal quality and excellent thermal stability up to 1200°C. Similar to the well established technology for local oxidation of silicon (LOCOS), the silicide layer was caped by 20 nm SiO2 followed by 300 nm of Si3N4. The nitride was patterned by optical lithography and dry etching. During dry oxidation at temperatures ranging from 900°C to 1000°C SiO2 is formed on the unprotected areas of the silicide. The Co atoms diffuse from the SiO2/CoSi2 interface to the CoSi2/Si interface to form CoSi2. Near the edges of the nitride mask the silicide layer thins and finally separates. Two metallic pads electrically separated by Si and SiO2 with a gap of 70 nm were produced this way. Monte Carlo simulations of the process revealed that the reason for the separation is stress dependent diffusion due to the stress induced by the nitride mask. The stress dependence of the separation process was experimentally verified using different nitride thicknesses. SEM and TEM studies showed perfect lateral patterning. This patterning process could be used in the fabrication of MOSFET's with ultrashort gatelengths.

Models of Moisture Transport and Moisture-Induced Stresses in Epoxy Composites

Mathematical models are presented to describe moisture transport in epoxy composites using concentration and stress dependent diffusion coefficients. These models take into consideration the stresses induced due to moisture and their influence on the transport mechanism. All governing differential equations are solved with appropriate boundary conditions to obtain concentration and stress profiles. It is concluded that non- Fickian and anomalous transport of moisture in epoxy composites can occur under certain conditions, leading to stress accumulation close to the fibers of the composite.

A mathematical model of damage accumulation taking into account microstructural effects

It is shown that the influence of microstructure in the damage accumulation process leads to a nonlinear diffusion effect, with a strongly stress-dependent diffusion coefficient. A nonlinear parabolic equation with a source term is obtained for the damage parameter. This equation is relevant to blow-up and quenching problems well known to mathematicians with rupture corresponding to blow-up or quenching. However, the damage accumulation equation possesses an additional nonlinearity due to the non-healing of damage. Depending on the value of a dimensionless constant parameter (the ratio of a properly defined microstructural length-size to a characteristic length-size of the initial damage distribution), two essentially different types of damage accumulation process appear to be possible for a given initial damage distribution over the bar length. In processes of the first type, the damage accumulation remains non-homogeneous over the length of the bar, so that the lifetime for the whole specimen is determined by the maximal initial damage within the bar. For processes of the second type the damage distribution over the specimen at first becomes homogeneous (at least in a considerable part of specimen), and then the damage accumulation proceeds uniformly over all or part of the specimen. The lifetime for processes of the second type is essentially longer than the first. Results of a numerical experiment based on the proposed model are presented. In particular, the origin and development of damage propagation waves is demonstrated. Also, it is demonstrated that when there is substantial damage transfer, the ultimate value of the damage parameter in the life-time calculation is of no significance.

Modelling of silicon oxidation based on stress relaxation

Abstract This paper deals with the modelling of thermal oxidation of silicon based on stress relaxation by viscous flow. An analysis of the anomalously high rate of dry oxidation occurring at low thickness is given. This initial regime is attributed to a reduced diffusivity in the vicinity of the Si-SiO2, interface due to the presence of high compressive stress. A model of oxidation based on stress-dependent diffusivity, namely the stress-state model, is then described. The model makes it possible to obtain the oxidation kinetics over a wide range of temperature. Moreover, the influence of stress both on the parabolic and linear kinetic constants is discussed. Finally, the effects of intrinsic oxidation stress on the structural properties of thermal oxides are also described. In particular, the role of growth temperature on densification phenomena is emphasized.

Transient flow of fluids in reservoirs with stress sensitive rock and fluid properties

An analytical solution is developed for the problem of fluid flow in stress sensitive porous medium. The solution technique uses the Kirchhoff type of transformation to define a stress factor which facilitates the specification of a one-parameter stress-dependent diffusivity function. The function is capable of fitting most known diffusivity data empirically. The general analytical solution is easily reduceable to the more familar solution derivable for the constant property porous medium.