Two-dimensional nucleation according to an exponential law with diffusion-controlled growth in the adsorption of camphor-10-sulfonate at the mercury/electrolyte interface

1988 ◽  
Vol 250 (1) ◽  
pp. 159-164 ◽  
Author(s):  
R. Philipp ◽  
J. Dittrich ◽  
U. Retter ◽  
E. Müller
Keyword(s):  
Controlled Growth ◽  
Two Dimensional ◽  
Exponential Law ◽  
Electrolyte Interface ◽  
Diffusion Controlled

A linearity test for thick specimens imaged by HVEM over a 180° angular range

1991 ◽  
Vol 49 ◽  
pp. 552-553
Author(s):  
Yu Liu
Keyword(s):  
Phase Contrast ◽  
Three Dimensional ◽  
Angular Range ◽  
Two Dimensional ◽  
Back Projection ◽  
Line Integral ◽  
Exponential Law ◽  
Transmission Electron ◽  
Absorption Law ◽  
Linearity Test

The image obtained in a transmission electron microscope is the two-dimensional projection of a three-dimensional (3D) object. The 3D reconstruction of the object can be calculated from a series of projections by back-projection, but this algorithm assumes that the image is linearly related to a line integral of the object function. However, there are two kinds of contrast in electron microscopy, scattering and phase contrast, of which only the latter is linear with the optical density (OD) in the micrograph. Therefore the OD can be used as a measure of the projection only for thin specimens where phase contrast dominates the image. For thick specimens, where scattering contrast predominates, an exponential absorption law holds, and a logarithm of OD must be used. However, for large thicknesses, the simple exponential law might break down due to multiple and inelastic scattering.

Suppression of vigorous liquid Sn/Te reactions by Sn–Cu solder alloys

2008 ◽  
Vol 23 (12) ◽  
pp. 3303-3308 ◽  
Author(s):  
Chien-Neng Liao ◽  
Ching-Hua Lee
Keyword(s):  
Reaction Time ◽  
Layered Structure ◽  
Controlled Growth ◽  
Square Root ◽  
Solder Alloys ◽  
Cu Content ◽  
Cu Alloys ◽  
Diffusion Controlled ◽  
Morphology Changes

Reactions of molten Sn–xCu (x = 0.05 to 1.0) alloys with Te substrate at 250 °C were investigated. A dosage of 0.1 wt% Cu in Sn is found to be effective in suppressing the vigorous Sn/Te reaction by forming a thin CuTe at the solder/Te interface. The CuTe morphology changes from irregular clusters into a layered structure with increasing Cu content in Sn. With the same reaction time, the CuTe thickness increases proportionally to the square root of Cu content in Sn–Cu alloys, suggesting a diffusion-controlled growth for CuTe.

Modeling the Diffusion-Controlled Growth of Needle and Plate-Shaped Precipitates

2002 ◽  
Vol 731 ◽  
Author(s):  
Z. Guo ◽  
W. Sha
Keyword(s):  
Free Energy ◽  
Transformation Strain ◽  
Interfacial Free Energy ◽  
Growth Theory ◽  
Controlled Growth ◽  
Precipitate Morphology ◽  
Interface Kinetics ◽  
Diffusion Controlled ◽  
Precipitate Growth ◽  
Strain Stress

AbstractVarious theories have been developed to describe the diffusion-controlled growth of precipitates with shapes approximating needles or plates. The most comprehensive one is due to Ivantsov, Horvay and Cahn, and Trivedi (HIT theory), where all the factors that may influence the precipitate growth, i.e. diffusion, interface kinetics and capillarity, are accounted for within one equation. However, HIT theory was developed based on assumptions that transformation strain/stress and interfacial free energy are isotropic, which are not true in most of the real systems. An improved growth theory of precipitates of needle and plate shapes was developed in the present study. A new concept, the compression ratio, was introduced to account for influences from the anisotropy of transformation strain/stress and interfacial free energy on the precipitate morphology. Experimental evidence supports such compression effect. Precipitate growth kinetics were quantified using this concept. The improved HIT theory (IHIT theory) was then applied to study the growth of Widmanstatten austenite in ferrite in Fe-C-Mn steels. The calculated results agree well with the experimental observations.

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