Grain size distribution in the Kolmogorov model for nucleation and growth: Heterogeneous versus homogeneous nucleation

1987 ◽  
Vol 22 (7) ◽  
pp. 869-875 ◽  
Author(s):  
B. Lorenz
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Homogeneous Nucleation ◽  
Nucleation And Growth ◽  
Kolmogorov Model

Development of the Grain Size Distribution During the Crystallization of an Amorphous Solid

2011 ◽  
Vol 1308 ◽  
Author(s):  
Andreas Bill ◽  
Ralf B. Bergmann
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Growth Rates ◽  
Amorphous Solid ◽  
Amorphous Solids ◽  
Nucleation And Growth ◽  
Analytic Description ◽  
Silicon Thin Films ◽  
Random Nucleation

ABSTRACTWe present an overview of the theory developed over the last few years to describe the crystallization of amorphous solids. The microstructure of the crystallizing solid is described in terms of the grain size distribution (GSD). We propose a partial differential equation that captures the physics of crystallization in random nucleation and growth processes. The analytic description is derived for isotropic and anisotropic growth rates and allows for the analysis of different stages of crystallization, from early to full crystallization. We show how the timedependence of effective nucleation and growth rates affect the final distribution. In particular, we demonstrate that for cases described by the Kolmogorov-Avrami-Mehl-Johnson (KAMJ) model applicable to a large class of crystallization processes a lognormal type distribution is obtained at full crystallization. The application of the theory to the crystallization of silicon thin films is discussed.

Modeling the Grain Size Distribution during Solid Phase Crystallization of Silicon

2009 ◽  
Vol 1153 ◽  
Author(s):  
Andreas Bill ◽  
Anthony V Teran ◽  
Ralf B Bergmann
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution ◽  
Solid Phase ◽  
Good Description ◽  
Nucleation And Growth ◽  
Solid Phase Crystallization ◽  
Silicon Thin Films ◽  
Analytical Expressions ◽  
Physical Principles

AbstractWe analyze the grain size distribution during solid phase crystallization of Silicon thin films. We use a model developed recently that offers analytical expressions for the time-evolution of the grain size distribution during crystallization of a d-dimensional solid. Contrary to the usual fit of the experimental results with a lognormal distribution, the theory describes the data from basic physical principles such as nucleation and growth processes. The theory allows for a good description of the grain size distribution except for early stages of crystallization. The latter case is expected and discussed. An important outcome of the model is that the distribution at full crystallization is determined by the time-dependence of the nucleation and growth rates of grains. In the case under consideration, the theory leads to an analytical expression that has the form of a lognormal-type distribution for the fully crystallized sample.

Grain size distribution in evaporated permalloy films

1970 ◽  
Vol 2 (2) ◽  
pp. K69-K73 ◽  
Author(s):  
M. Reinbold ◽  
H. Hoffmann
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Size Distribution

scholarly journals The Domain and Microstructure of Resin-Bonded Magnets

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 2849
Author(s):  
Marcin Jan Dośpiał
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Grain Size ◽  
Size Distribution ◽  
Domain Structure ◽  
Grain Size Distribution ◽  
Exchange Interactions ◽  
Force Microscopy ◽  
Transmission Electron ◽  
Scanning Electron

This paper presents domain and structure studies of bonded magnets made from nanocrystalline Nd-(Fe, Co)-B powder. The structure studies were investigated using scanning electron microscopy (SEM), high-resolution transmission electron microscopy (HRTEM), Mössbauer spectroscopy and X-ray diffractometry. On the basis of performed qualitative and quantitative phase composition studies, it was found that investigated alloy was mainly composed of Nd2(Fe-Co)14B hard magnetic phase (98 vol%) and a small amount of Nd1.1Fe4B4 paramagnetic phase (2 vol%). The best fit of grain size distribution was achieved for the lognormal function. The mean grain size determined from transmission electron microscopy (TEM) images on the basis of grain size distribution and diffraction pattern using the Bragg equation was about ≈130 nm. HRTEM images showed that over-stoichiometric Nd was mainly distributed on the grain boundaries as a thin amorphous border of 2 nm in width. The domain structure was investigated using a scanning electron microscope and metallographic light microscope, respectively, by Bitter and Kerr methods, and by magnetic force microscopy. Domain structure studies revealed that the observed domain structure had a labyrinth shape, which is typically observed in magnets, where strong exchange interactions between grains are present. The analysis of the domain structure in different states of magnetization revealed the dynamics of the reversal magnetization process.

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