Nucleus shape

Fi gure 19.2 Calculated nucleus shapes for homogeneous nucleation of an f.c.c. phase in... 

F.K. LeGoues, H.I. Aaronson, Y.W. Lee, and G.J. Fix. Influence of crystallography upon critical nucleus shapes and kinetics of homogeneous f.c.c.-f.c.c. nucleation. I. The classical theory regime. In International Conference on Solid—>Solid Phase Transformations, pages 427-431, Warrendale, PA, 1982. The Minerals, Metals and Materials Society. 

The first term in the curved inner bracket is the energy of either the upper or lower half of the a/0 interface in Fig. 19.27, while the second represents half the energy of the area A. Their sum is therefore the total interfacial energy of the half-nucleus shape containing the fictitious boundary shown in Fig. 19.28. Using these results ... 

Figure 19.28 Cross section of half-nucleus shape.

McBride SH, Knothe ML (2008) Tate. Modulation of stem cell shape and fate A the role of density and seeding protocol on nucleus shape and gene expression. Tissue Eng A 14(9) 1561-1572... 

Calculating Minimum Viable Nucleus Size (r ) and Nucleation Activation Energy ( G ) Since a spherical nucleus minimizes the amount of interfacial area per unit volume, it represents the most likely nucleus shape. The total free-energy change, AG t, involved in forming a spherical nucleus of radius r is therefore... 

The problem of the surface shape of each phase, while still present to some extent, especially in considering the precursors of size below instrumental resolving power, is much reduced in the ferroelectric case because phase (domain) boundaries can be observed and the shape obtained quite directly. Furthermore, different ferroelectrics provide essentially different nucleus shapes which provide further tests of the theories. 

It would appear then that the reversal of 180° domains in a ferroelectric might be a simple system to use as a test of solid-solid nucleation theories without so many of the complexities of nucleus shape, transport mechanism, surface energy, and volume change found within most other systems. It is therefore intended to outline the current state of knowledge of ferroelectric domains and their nucleation and kinetics, with particular reference to ionic materials. 

---