Bounds on the Nonlinear Diffusion Controlled Growth Rate of Spherical Precipitates

1960 ◽  
Vol 31 (9) ◽  
pp. 1621-1627 ◽  
Author(s):  
J. A. Morrison ◽  
H. L. Frisch
Keyword(s):  
Growth Rate ◽  
Nonlinear Diffusion ◽  
Controlled Growth ◽  
Diffusion Controlled

scholarly journals Mixed diffusion-controlled growth of pearlite in binary steel

2010 ◽  
Vol 467 (2126) ◽  
pp. 508-521 ◽  
Author(s):  
A. S. Pandit ◽  
H. K. D. H. Bhadeshia
Keyword(s):  
Experimental Data ◽  
Activation Energy ◽  
Growth Rate ◽  
Volume Diffusion ◽  
Controlled Growth ◽  
Mechanical Equilibrium ◽  
Interfacial Diffusion ◽  
Diffusion Controlled ◽  
Simplified Method ◽  
Transformation Front

A kinetic theory for the diffusion-controlled growth of pearlite is presented, which accounts simultaneously for diffusion through the austenite and via the transformation front. The simplified method abandons the need for mechanical equilibrium at the phase junctions and yet is able to explain experimental data on the growth rate of pearlite. Furthermore, unlike previous analyses, the deduced value for the activation energy for the interfacial diffusion of carbon is found to be realistic when compared with corresponding data for volume diffusion.

Diffusion-controlled growth

1989 ◽  
Vol 423 (1864) ◽  
pp. 123-132 ◽  
Keyword(s):  
Growth Rate ◽  
Cone Angle ◽  
High Growth ◽  
High Growth Rate ◽  
Two Dimensions ◽  
Flow Diagram ◽  
Equivalent Model ◽  
Controlled Growth ◽  
Diffusion Controlled ◽  
Tip Radius

The conditions of diffusion-controlled growth are outlined and the observed importance of anisotropy is discussed through a tentative flow diagram. A crucial role is played by the forwardmost tips, which lead to growth. The nature of the singularity in their growth rate determines the overall fractal dimension. This has been estimated in two dimensions from effective cone-angle models, which work well for the most extreme anisotropic growth and can be augmented into a self-consistent approximation for the isotropic fractal case. The way in which the tip growth rate singularity is limited by finite tip radius is also a key ingredient. For diffusion-limited solidification where it is set by competition with surface tension, this significantly changes the form of the equivalent model with a fixed (e. g. lattice spacing) imposed tip scale. The full distribution of growth rates everywhere provides a much richer problem. We show new data and examine the consistency of how sites can evolve from the regions of high growth rate where they are born, into well-screened regions devoid of further growth.

Polymer-Controlled Growth Rate of an Amorphous Mineral Film Nucleated at a Fatty Acid Monolayer

Langmuir ◽  
2002 ◽  
Vol 18 (23) ◽  
pp. 8902-8909 ◽  
Author(s):  
E. DiMasi ◽  
V. M. Patel ◽  
M. Sivakumar ◽  
M. J. Olszta ◽  
Y. P. Yang ◽  
...  
Keyword(s):  
Growth Rate ◽  
Fatty Acid ◽  
Controlled Growth

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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