Diffusion-limited kinetics of terrace growth on GaAs(110)

2005 ◽  
Vol 72 (11) ◽  
Author(s):  
P. Piercy ◽  
A. M.-J. Castonguay
Keyword(s):  
Diffusion Limited ◽  
Kinetics Of

The Formation of Cu3Si from Cu/a-Si Multilayers

1997 ◽  
Vol 481 ◽  
Author(s):  
R. R. Chromik ◽  
W. K. Neils ◽  
E. J. Cotts
Keyword(s):  
Diffusion Couples ◽  
X Ray Diffraction ◽  
Limited Growth ◽  
Scanning Calorimetry ◽  
Individual Layer ◽  
Diffusion Limited ◽  
Reaction Constant ◽  
Multilayered Composites ◽  
Reaction Constants ◽  
Kinetics Of

ABSTRACTThe kinetics of the formation of Cu3Si in Cu/a-Si diffusion couples have been investigated by means of differential scanning calorimetry and x-ray diffraction. Multilayered composites of average stoichiometry Cu3Si were prepared by sputter deposition with individual layer thicknesses varying in different samples between 2 and 100 nm. We observed diffusion limited growth of Cu3 Si upon annealing these diffusion couples below 500 K. Reaction constants were measured for a temperature range of 455 to 495 K for thicknesses of growing Cu3Si between 2.6 and 80 nm. The temperature dependence of the reaction constant, k2, was characterized as k2 = k0 exp(− Ea/kbT) with activation energy, Ea = 1.0 eV/atom and pre-factor, k0 = 1.9×10−3 cm2/s.

Experimental Investigations of the Kinetics of a Catalytic Trapping Reaction in Confined Spaces

1996 ◽  
Vol 464 ◽  
Author(s):  
Mark S. Feldman ◽  
Anna L. Lin ◽  
Raoul Kopelman
Keyword(s):  
Reaction Front ◽  
Rate Coefficient ◽  
Capillary Tube ◽  
One Dimension ◽  
Experimental Investigations ◽  
Confined Spaces ◽  
Diffusion Limited ◽  
Kinetics Of ◽  
Oxidation Of Glucose ◽  
Theoretical Results

AbstractWe investigate the anomalous kinetics in one dimension of a diffusion limited catalytic trapping reaction, A + T → T, by measuring the oxidation of glucose. The reaction is carried out in a thin capillary tube, and the depletion of oxygen in the vicinity of the reaction front is monitored by the fluorescence of a Ru(II) dye. Theoretical results and simulations have predicted an asymptotic t1/2 dependence for the rate coefficient. We observe a depedence on t0.56, with what appears to be an asymptotic behavior approaching t1/2.

Ostwald–Freundlich diffusion-limited dissolution kinetics of nanoparticles

2014 ◽  
Vol 257 ◽  
pp. 120-123 ◽  
Author(s):  
David R. Ely ◽  
R. Edwin García ◽  
Markus Thommes
Keyword(s):  
Dissolution Kinetics ◽  
Diffusion Limited ◽  
Kinetics Of

Precipitation

2015 ◽  
Author(s):  
Roger G. Harrison ◽  
Paul W. Todd ◽  
Scott R. Rudge ◽  
Demetri P. Petrides
Keyword(s):  
Coming Out ◽  
Batch Reactor ◽  
Protein Solubility ◽  
Tubular Reactor ◽  
Advantages And Disadvantages ◽  
Long Term Storage ◽  
Diffusion Limited ◽  
Simple Scaling ◽  
Separation Of Proteins ◽  
Kinetics Of

Precipitation, which is the process of coming out of solution as a solid, is an important method in the purification of proteins that usually comes early in the purification process. Precipitation is frequently used in the commercial separation of proteins. The primary advantages of precipitation are that it is relatively inexpensive, can be carried out with simple equipment, can be done continuously, and leads to a form of the protein that is often stable in long-term storage. Since precipitation is quite tolerant of various impurities, including nucleic acids and lipids, it is used early in many bioseparation processes. The goal of precipitation is often concentration to reduce volume, although significant purification can sometimes be achieved. For example, all the protein in a stream might be precipitated and redissolved in a smaller volume, or a fractional precipitation might be carried out to precipitate the protein of interest and leave many of the contaminating proteins in the mother liquor. In this chapter the focus is first upon protein solubility, which is the basis of separations by precipitation. Then we discuss the basic concepts of particle formation and breakage and the distribution of precipitate particle sizes. The specific methods that can be used to precipitate proteins are treated next. The chapter concludes with methodology to use for the design of precipitation systems. After completing this chapter, the reader should be able to do the following: • Explain the various factors that influence protein solubility. • Use the Cohn equation to predict solution equilibria (precipitation recoveries). • Identify the distinct steps in the development of a precipitate. • Calculate mixing times in an agitated precipitator, the kinetics of diffusion-limited growth of particles, and the kinetics of particle-particle aggregation. • Perform particle balances as a function of particle size in a continuous-flow stirred tank reactor (CSTR). • Explain the methods used to cause precipitation. • Outline the advantages and disadvantages of the three basic types of precipitation reactor: the batch reactor, the CSTR, and the tubular reactor. • Implement simple scaling rules for a precipitation reactor.

Precipitation of Oxygen and Mechanism of Stacking Fault Formation in Czochralski Silicon Bulk Crystals

1982 ◽  
Vol 14 ◽  
Author(s):  
Kazumi Wada ◽  
Naohisa Inoue ◽  
Jiro Osaka
Keyword(s):  
Growth Model ◽  
Growth Kinetics ◽  
Stacking Faults ◽  
Diffusional Growth ◽  
Czochralski Silicon ◽  
Self Diffusion ◽  
Diffusion Limited ◽  
Silicon Bulk ◽  
Precipitate Growth ◽  
Kinetics Of

ABSTRACTThis paper describes recent progress on nucleation and growth of oxide precipitates and stacking faults in Czochralski silicon. Conclusions on the growth kinetics of oxide precipitates are drawn from the experiments and analysis of growth kinetics of two-dimensional precipitates: The experimentally obtained growth kinetics, three-quarter power law is theoretically derived and the precipitate growth is demonstrated to be diffusion-limited by oxygen interstitials. The formation mechanism of stacking faults is the Bardeen-Herring mechanism. Based on diffusional growth model, the growth kinetics of stacking faults are analyzed, assuming a coexistence of self-interstitial supersaturation and vacancy undersaturation. It is found that the growth is driven by vacancies in undersaturation. Vacancy component of self-diffusion has been determined and found to be predominant at low temperature. The possibility of growth model proposed for increase of oxide precipitate density during annealing has been excluded. Both processes, homogeneous and heterogeneous nucleation, have been taking place during annealing.

Role of Sedimentation and Buoyancy on the Kinetics of Diffusion Limited Colloidal Aggregation

Langmuir ◽  
2003 ◽  
Vol 19 (26) ◽  
pp. 10710-10718 ◽  
Author(s):  
Hua Wu ◽  
Marco Lattuada ◽  
Peter Sandkühler ◽  
Jan Sefcik ◽  
Massimo Morbidelli
Keyword(s):  
Colloidal Aggregation ◽  
Diffusion Limited ◽  
Kinetics Of

scholarly journals Diffusion-Limited Reaction Kinetics of a Reactant with Square Reactive Patches on a Plane

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1744
Author(s):  
Changsun Eun
Keyword(s):  
Reaction Kinetics ◽  
Rate Constant ◽  
Spatial Arrangement ◽  
Total Surface Area ◽  
Reaction Model ◽  
Discrete Models ◽  
Diffusion Limited ◽  
Size Number ◽  
Surface Reaction Kinetics ◽  
Kinetics Of

We present a simple reaction model to study the influence of the size, number, and spatial arrangement of reactive patches on a reactant placed on a plane. Specifically, we consider a reactant whose surface has an N × N square grid structure, with each square cell (or patch) being chemically reactive or inert for partner reactant molecules approaching the cell via diffusion. We calculate the rate constant for various cases with different reactive N × N square patterns using the finite element method. For N = 2, 3, we determine the reaction kinetics of all possible reactive patterns in the absence and presence of periodic boundary conditions, and from the analysis, we find that the dependences of the kinetics on the size, number, and spatial arrangement are similar to those observed in reactive patches on a sphere. Furthermore, using square reactant models, we present a method to significantly increase the rate constant by sequentially breaking the patches into smaller patches and arranging them symmetrically. Interestingly, we find that a reactant with a symmetric patch distribution has a power–law relation between the rate constant and the number of reactive patches and show that this works well when the total reactive area is much less than the total surface area of the reactant. Since our N × N discrete models enable us to examine all possible reactive cases completely, they provide a solid understanding of the surface reaction kinetics, which would be helpful for understanding the fundamental aspects of the competitions between reactive patches arising in real applications.

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