Statistical Approach to the Account of Metastable Phase Depletion in the Kinetics of Homogeneous Nucleation in the Vapor–Gas Medium at the Instantaneous Creation of Vapor Supersaturation

2004 ◽  
Vol 66 (3) ◽  
pp. 277-284 ◽  
Author(s):  
A. P. Grinin ◽  
I. A. Zhuvikina ◽  
F. M. Kuni
Author(s):  
A. Leineweber ◽  
M. Löffler ◽  
S. Martin

Abstract Cu6Sn5 intermetallic occurs in the form of differently ordered phases η, η′ and η′′. In solder joints, this intermetallic can undergo changes in composition and the state of order without or while interacting with excess Cu and excess Sn in the system, potentially giving rise to detrimental changes in the mechanical properties of the solder. In order to study such processes in fundamental detail and to get more detailed information about the metastable and stable phase equilibria, model alloys consisting of Cu3Sn + Cu6Sn5 as well as Cu6Sn5 + Sn-rich melt were heat treated. Powder x-ray diffraction and scanning electron microscopy supplemented by electron backscatter diffraction were used to investigate the structural and microstructural changes. It was shown that Sn-poor η can increase its Sn content by Cu3Sn precipitation at grain boundaries or by uptake of Sn from the Sn-rich melt. From the kinetics of the former process at 513 K and the grain size of the η phase, we obtained an interdiffusion coefficient in η of (3 ± 1) × 10−16 m2 s−1. Comparison of this value with literature data implies that this value reflects pure volume (inter)diffusion, while Cu6Sn5 growth at low temperature is typically strongly influenced by grain-boundary diffusion. These investigations also confirm that η′′ forming below a composition-dependent transus temperature gradually enriches in Sn content, confirming that Sn-poor η′′ is metastable against decomposition into Cu3Sn and more Sn-rich η or (at lower temperatures) η′. Graphic Abstract


1997 ◽  
Vol 481 ◽  
Author(s):  
E. Pineda ◽  
T. Pradell ◽  
D. Crespo ◽  
N. Clavaguera ◽  
J. ZHU ◽  
...  

ABSTRACTThe microstructure developed in primary crystallizations is studied under realistic conditions. The primary crystallization of an amorphous alloy is modeled by considering the thermodynamics of a metastable phase transition and the kinetics of nucleation and crystal growth under isothermal annealing. A realistic growth rate, including an interface controlled growth at the beginning of the growth of each single grain and diffusion controlled growth process with soft impingement afterwards is considered. The reduction in the nucleation rate due to the compositional change in the remaining amorphous matrix is also taken into account. The microstructures developed during the transformation are obtained by using the Populational KJMA method, from the above thermodynamic and kinetic factors. Experimental data of transformed fraction, grain density, average grain size, grain size distribution and other related parameters obtained from annealed metallic glasses are modeled.


The model considered in part I is generalized to include growth mechanisms in which the chemical reaction which proceeds at the particle-atm osphere interface is reversible, so that molecules may evaporate from a particle as well as condense upon it. The Becker-Döring-Zeldovich-Frenkel theory of homogeneous nucleation kinetics is then reviewed in the light of the known statistical problem of the birth -and -death process, and an improved approximation is introduced which significantly alters the calculated results. Both steady-state nucleation kinetics and the time lag problem are discussed.


1956 ◽  
Vol 34 (5) ◽  
pp. 473-490 ◽  
Author(s):  
K. A. Jackson ◽  
Bruce Chalmers

The kinetic theory of melting and freezing is developed from consideration of atom movements at an interface between solid and liquid. The equations developed are shown to have the same form as the corresponding thermodynamic equations. The homogeneous nucleation of a solid phase in a liquid is then considered from the point of view of this theory. Agreement with experimental observation is obtained on the following points. (1) The supercooling at which homogeneous nucleation occurs is proportional to the absolute equilibrium temperature. (2) The surface free energy per atom used in the quasi-thermodynamic treatment of nucleation should be equal to one-half the latent heat per atom. (3) The amount of liquid supercooled has a very small effect on the temperature at which homogeneous nucleation occurs.


2016 ◽  
Vol 18 (5) ◽  
pp. 4102-4111 ◽  
Author(s):  
Melisa M. Gianetti ◽  
Amir Haji-Akbari ◽  
M. Paula Longinotti ◽  
Pablo G. Debenedetti

Critical nuclei for bulk homogeneous nucleation at ζ = 0.845 for different values of λ.


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