Unified Kinetic Model Research Articles

Strain relaxation kinetics in Si1−xGex/Si heterostructures

A semiempirical kinetic model is presented which maps out the thermal budget for processing of strained layer devices through epitaxial growth and postgrowth anneals. Misfit strain relaxation in Si1−xGex/Si heterostructures by the injection and propagation of a/2 〈110〉 60°-type misfit dislocations has been studied for a range of geometries and dimensions. Strained layer superlattices, Si1−xGex alloy layers, 0<x<0.3, and alloy layers with unstrained Si capping layers of thickness 0 to 400 nm were grown by molecular-beam epitaxy on (100) Si substrates and subjected to post-growth thermal cycles. Velocity and nucleation rate data from Nomarski interference microscopy of defect-etched surfaces were correlated with electron beam induced current microscopy transmission electron microscopy and x-ray diffraction results to define Arrhenius relationships for misfit dislocation injection rates and propagation velocities. A unified kinetic model for misfit strain relaxation that incorporates both nucleation and propagation is then developed, which is applicable for all heterostructures and thermal cycles in the low dislocation density regime <103 mm−1. Nonuniform strain distribution in graded device heterostructures is considered by defining the effective stress acting on misfit dislocations for an arbitrary geometry. The effective stress was varied from 0 to 750 MPa in Si1−xGex/Si heterostructures by varying both layer dimensions and Ge concentration. Misfit dislocation nucleation rates varied from 10−3 to 103 mm−2 s−1 and misfit extension velocities of 25 nm s−1 to 2 mm s−1 were obtained over the temperature range 450–1000 °C for anneals of duration 5–2000 s. Activation energies, stress exponents, and prefactors in the Arrhenius relations were found to be independent of Ge concentration, effective stress, and heterostructure geometry allowing a comprehensive model to be developed. The onset of strain relaxation during epitaxial growth cycles (the ‘‘apparent critical thickness’’ or metastability limit) characteristic of molecular-beam epitaxy and chemical vapor deposition was measured and correlated with the simulation of misfit dislocation injection and propagation in typical growth sequences. The kinetic model is also used to define the maximum time-temperature envelope, or thermal budget (t, T), for the misfit dislocation-free processing of Si1−xGex/Si heterostructures subjected to post-growth thermal treatme

Enzymic hydrolysis of biopolymers via single-scission attack pathways: a unified kinetic model

A unified analytical model is suggested for describing single-scission attack pathways for enzymic hydrolysis of polymers. This model encompasses the preferred attack degradation, as well as the endo- and exo-type ones. The model is based on kinetic and statistic considerations. It was developed to account for a variety of reaction characteristics, including cases in which the kinetic constants depend upon the chain length of the polymeric substrate. The analytical model provides a dynamic description of the enzymic degradation process, including the overall reaction rate, the time course of the reaction and the array of products obtained throughout the process. These characteristics are shown to be affected, to a large extent, by even minor changes in the probabilities for bond cleavage. The model developed also provides the quantitative evidence for the view that the endo- and exo-type degradation pathways are but particular cases of the general, preferred attack one.

Performance Analysis of the Aeration Tanks in the Activated Sludge System

The performance of large scale aeration tanks was evaluated from the mutual relationship between the flow characteristics snd the substrate removal patterns. The results of the tracer studies indicated that the flow conditions in the aeration tanks were too complicated to describe satisfactorily with the mathematical models. In the light of the transient nature of physical, chemical, and biological factors controlling the mechanism of the activated sludge process, it would seem most unlikely to provide a unified kinetics model. As regards the load distribution, the empirical equation C/C0 = u/(u + Kx) well described the BOD distribution in the aeration tanks whatever the flow characteristics and tank geometry. The equation of C/C0 = u/(u + Kx) or C/C0 = 1/(1 + Kt) is definitely valid in field installations operating under conventional conditions.

A unified kinetic model of the tangential magnetopause structure

A self‐consistent model of the tangential magnetopause is formulated on the basis of the Vlasov‐Maxwell equations. In this model the plasmas on both sides are magnetized; the magnetic field is assumed everywhere parallel to the magnetopause (i.e., the normal component Bn=0) and is allowed to rotate through an arbitrary angle across the magnetopause. It is shown that the thickness of the magnetopause is greater than the gyroradius of the hotter species of the plasmas (the ions). The presence of a trapped particle population inside the magnetopause is shown to be required in order to allow the magnetic field to rotate more than a certain critical angle (∼90°). The observed ‘bulge‐out’ feature in B vector hodograms is found to be due to lack of overlap between plasmas from the two sides of the magnetopause. An electric field normal to the magnetopause is present in our model, with magnitudes from 0.1 to 10 mV/m, depending primarily on the relative flow speed parallel to the magnetopause between plasmas on the two sides. The magnetopause current in our model is carried predominantly by the ions and has a significant field‐aligned component. The magnetopause current is a possible source of field‐aligned currents on cusp as well as auroral oval field lines. The proposed model can reproduce the observed features of the tangential magnetopause structure by specifying boundary conditions on both sides of the magnetopause. It also provides a basis for understanding the electric and magnetic fields, the current, and the stability of the tangential magnetopause in terms of the collective particle dynamics.

The theory of branching processes applied to milk proteins: I. Heat-induced coagulation of whole milk

SummaryThe theory of branching processes is used to present a unified kinetic model for the heat induced coagulation of milk. Nitrogen depletion curves for the overall reaction are fitted to a theoretical curve to demonstrate that the reaction is a single process and that the idea of a lag phase up to the coagulation time, followed by the aggregation reaction proper, is an unnecessary complication. Coagulation times as a function of temperature are then used to determine the activation energy of the reaction; the average value of 126 kJ/mol agrees with that found from analysis of the post-coagulation reaction.