Single activation energy

Data for step-mobilities shown in Fig. 6 span an impressively large range a factor of 10 " separates step-mobilities measured by STM from the step-mobilities extracted from the relaxation of micron-sized gratings. Some discrepancies exist, but most of the step-mobilities are consistent with a single activation energy of 1.8 eV and an attempt rate given by the frequency of atomic vibrations. We hope that this initial comparison of step-mobility data will help motivate more detailed theoretical analysis and experiments on the coimections between step-mobility and the evolution of surface morphology. 

In all cases considered hitherto, we calculated, only one relaxation process coupled with one single activation energy AU. In reality, we have to consider different relaxation processes happening simultaneously. 

The defect density is non-zero at J = 0 K, and increases temperature, but is not described by a single activation energy. 

The conventional theory of thermal quenching by excitation of a carrier out of a shallow trap predicts a thermally activated process. No single activation energy is observed in a-Si H, but it is found that the luminescence efficiency, follows the relation (Collins, Paesler and Paul 1980),... 

Systems that are governed by reaction kinetics show well-defined behaviors as a function of temperature and potential. If the system can be described as being controlled by a single activation-energy-controlled process, graphical methods can be used to cause the data to superpose. 

The purpose o this work is to show that the values for temperatures o mold and storage bulb are important parameters in injection molding process o rubber. The study was performed by using two different thicknesses for rubber sheets and two values for the cure enthalpy. The problem was solved by applying an explicit numerical method with finite differences (6). Although rubber vulcanization consists of a complex series of reactions (8), the overall cure heat could be described by a first-order reaction with a single activation energy, as shown previously (6). 

That the reaction is described by a single activation energy. 

Measurements of the growth velocity, vg of the crystal-amorphous interface are shown in Fig. 10.6. The measured velocities extend over nearly ten orders of magnitude and can be characterized by a single-activation energy, EA = 2.76 eV, (Olson and Roth 1988) so that... 

In deriving this result, we assumed that the viscoelastic properties are determined by a single activation energy. In real-world polymers, this is usually not the case. Nevertheless, the equation can be used approximately as long as the same relaxation processes are involved. It is not possible, however, to extrapolate to temperatures so low that some relaxation processes do not occur, or to temperatures so high that additional mechanisms are activated. 

The obvious method of extrapolation is to assume that the rate determining step is characterized by a single activation energy and the Arrhenius equation can be applied (Cardamone and Brown, 1986). Unfortunately this method is normally invalid except for extrapolation over a short range of temperature and can only give a maximum lifetime (Gillen et al., 1996). 

The kinetics of vacancy elimination, measured by the time dependence of defect cluster density and size, shows either a simple (single activation energy) or a complex behavior, owing to its heterogeneous character or to competing mechanisms. Its analytical form depends on the existence of defect cluster nuclei in the quenched samples. 

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