Periodic Pattern Formation in Metal-Ceramic Reactions

2006 ◽  
Vol 46 ◽  
pp. 136-145 ◽  
Author(s):  
A.A. Kodentsov ◽  
F.J.J. van Loo
Keyword(s):  
Pattern Formation ◽  
Reaction Zone ◽  
Diffusion Zone ◽  
Kirkendall Effect ◽  
Periodic Pattern ◽  
Time And Space ◽  
Phase Layer ◽  
Diffusion Controlled ◽  
Metal Ceramic ◽  
Patterned Microstructure

Formation of diffusion zone morphologies periodic in time and space during metalceramic reactions is considered as a manifestation of the Kirkendall effect. In a diffusion-controlled interaction, the Kirkendall marker plane can bifurcate, which is attributed to diverging vacancies fluxes in the reaction zone. When the Kirkendall plane is present in a phase layer, it attracts in situproduced inclusions of “secondary-formed phase”, which, in turn, can result in a highly patterned microstructure.

Periodic pattern formation in solid state reactions related to the Kirkendall effect

1998 ◽  
Vol 46 (18) ◽  
pp. 6521-6528 ◽  
Author(s):  
A.A. Kodentsov ◽  
M.R. Rijnders ◽  
F.J.J. van Loo
Keyword(s):  
Solid State ◽  
Pattern Formation ◽  
Kirkendall Effect ◽  
Solid State Reactions ◽  
Periodic Pattern

scholarly journals Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xinze Lian ◽  
Shuling Yan ◽  
Hailing Wang
Keyword(s):  
Time Delay ◽  
Pattern Formation ◽  
Turing Instability ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Prey Model ◽  
Diffusion Controlled ◽  
The Stability ◽  
Self Replication

We consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns. One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication. The results indicate that time delay and cross diffusion play important roles in pattern formation.

The Kirkendall Plane in Binary Interdiffusion Systems

2004 ◽  
Vol 233-234 ◽  
pp. 61-76 ◽  
Author(s):  
A.A. Kodentsov ◽  
A. Paul ◽  
F.J.J. van Loo
Keyword(s):  
Experimental Evidence ◽  
Kirkendall Effect ◽  
Point Of View ◽  
Chemical Approach ◽  
Diffusion Controlled ◽  
Physico Chemical ◽  
Considerable Body

There is now a considerable body of experimental evidence to indicate that in a volumediffusion controlled interaction the Kirkendall plane need not be unique. The Kirkendall plane can microstructurally be stable as well as unstable (it does not exist!). Under predictable circumstances, it can also bifurcate and even trifurcate. This can be rationalised in terms of Kirkendall velocity construction as well as from a purely chemical point of view considering diffusion-controlled interactions at the interphase interfaces. The physico-chemical approach is also used to explain significance of the Kirkendall effect in the morphogenesis of interdiffusion systems.

Diffusionsuntersuchungen im System Palladium—Vanadium mit Hilfe der Mikrosonde / Diffusion In The System Pd—V Investigated By Means Of An Electron Microprobe

1972 ◽  
Vol 27 (6) ◽  
pp. 960-965 ◽  
Author(s):  
Peter Lamparter ◽  
Traudl Krabichler ◽  
Siegfried Steeb
Keyword(s):  
Diffusion Zone ◽  
Solid Solubility ◽  
Electron Probe ◽  
Diffusion Processes ◽  
Kirkendall Effect ◽  
Layer Growth ◽  
Arrhenius Law ◽  
Intrinsic Diffusion ◽  
Quantitative Electron Probe Microanalysis

Abstract Diffusion processes (600 to 1300 °C) were investigated by means of quantitative electron-probe-microanalysis. The composition of the diffusion zone corresponds quite well with the phase diagram. The following phases were observed: Pd-solid solubility, Pd3V, Pd2V, and V-solid solubility. Below 900 °C the growth of the diffusion zone is retarded; above 900 °C the layer grows according to d = k ·√t. For all phases observed, according to Matano's method the coefficients of the inter-diffusion were determined. The temperature dependency of these coefficients as well as that of the k-values follows an Arrhenius law. Thus the activation energies of the layer growth and of the interdiffusion were obtained. The determination of the intrinsic diffusion coefficients by the observation of the Kirkendall-effect is discussed.

A model for the longitudinal patterns shaped by water on erodible rocks

2020 ◽  
Author(s):  
Matteo Bernard Bertagni ◽  
Carlo Camporeale
Keyword(s):  
Mathematical Model ◽  
Pattern Formation ◽  
Laminar Flow ◽  
Spatial Scales ◽  
Concentration Field ◽  
Water Film ◽  
Time And Space ◽  
Longitudinal Patterns ◽  
Flow Intensity ◽  
Alpine Environments

<p>The interactions between water and rocks create an extensive variety of marvelous patterns, which span on several classes of time and space scales. In this work, we provide a mathematical model for the formation of longitudinal erosive patterns commonly found in karst and alpine environments. The model couples the hydrodynamics of a laminar flow of water (Orr-Somerfield equation) to the concentration field of the eroded-rock chemistry. Results show that an instability of the plane rock wetted by the water film leads to a longitudinal channelization responsible for the pattern formation. The spatial scales predicted by the model span over different orders of magnitude depending on the flow intensity and this may explain why similar patterns of different sizes are observed in nature (millimetric microrills, centimetric rillenkarren, decametric solution runnels).</p>

Cruciform pattern formation in Sn/Co couples

2007 ◽  
Vol 22 (12) ◽  
pp. 3404-3409 ◽  
Author(s):  
Chao-hong Wang ◽  
Sinn-wen Chen
Keyword(s):  
Pattern Formation ◽  
Reaction Layer ◽  
Phase Region ◽  
Solid Reaction ◽  
Phase Layer ◽  
Reaction Phase ◽  
Phase Layers ◽  
Continuous Reaction ◽  
First Time

CoSn3 phase is formed in Sn/Co couples reacted at 200 °C. The reaction phase shows a unique cruciform pattern that is observed for the first time in the solid/solid reaction. The reaction phase layers are thick and uniform along the edges of the Co substrate, and there are no reaction phases at the corners. A continuous reaction layer is formed in Sn/Co couples reacted at 180 °C. A metastable CoSn4 phase is formed at the corner, and the reaction phase along the edge of the Co substrate is the CoSn3 phase. The reaction CoSn3 phase region shows a cruciform pattern if the CoSn4 phase region is ignored. It is concluded that the Sn flux is much faster than the Co flux, and the cruciform pattern of the reaction CoSn3 phase layer is formed either by cracking or transformation to the CoSn4 phase at the corners where stresses are most intensified.

scholarly journals The Kinetics of Joined Action of Triplet-Triplet Annihilation and First-Order Decay of Molecules in T1State in the Case of Nondominant First-Order Process: The Kinetic Model in the Case of Spatially Periodic Excitation

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Paweł Borowicz ◽  
Bernhard Nickel
Keyword(s):  
Diffusion Coefficient ◽  
Kinetic Model ◽  
Periodic Pattern ◽  
Constructive Interference ◽  
First Order ◽  
Dependent Rate ◽  
Diffusion Controlled ◽  
Spatially Periodic ◽  
Kinetics Of ◽  
Triplet Triplet Annihilation

In this paper the model developed for estimation of the diffusion coefficient of the molecules in the triplet state is presented. The model is based on the intuitive modification of the Smoluchowski equation for the time-dependent rate parameter. Since the sample is irradiated with the spatially periodic pattern nonexponential effects can be expected in the areas of the constructive interference of the exciting laser beams. This nonexponential effects introduce changes in the observed kinetics of the diffusion-controlled triplet-triplet annihilation. Due to irradiation with so-called long excitation pulse these non-exponential effects are very weak, so they can be described with introducing very simple correction to the kinetic model described in the first paper of this series. The values of diffusion coefficient of anthracene are used to calculate the annihilation radius from the data for spatially homogeneous excitation.

Laser Ablation Modeling of Periodic Pattern Formation on Polymer Substrates

2008 ◽  
Vol 10 (5) ◽  
pp. 488-493 ◽  
Author(s):  
A. Lasagni ◽  
M. Cornejo ◽  
F. Lasagni ◽  
F. Muecklich
Keyword(s):  
Laser Ablation ◽  
Pattern Formation ◽  
Periodic Pattern ◽  
Polymer Substrates ◽  
Ablation Modeling
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