ABSTRACT
As discussed in Chapter 1, the high surface-to-bulk ratio in nano particles is behind many of their anomalous properties.3 When the surface-to-bulk ratio is large, the surface’s contribution to the energy of the system is no longer negligible and must be considered. is can be done within the framework of classical thermodynamics.4 We can express the work done, dw, during a reversible process in which the surface area of an interface changes by an innitesimal amount, dA, as
d dw A= a (6.1)
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
6.2 Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 6.2.1 Classical Nucleation Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 6.2.2 Simulating Nucleation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189 6.2.3 Other Theories of Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
6.3 Crystal Growth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198 6.3.1 Crystal Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 6.3.2 Kinetics and Thermodynamics of Attachment. . . . . . . . . . . . . . . . . . . . . 205 6.3.3 Understanding the Role of Additives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
where α is a quantity known as surface tension. is quantity must be positive as only then can an interface exist between two phases. If the surface tension were negative, the area of the interface would tend to increase without limit, the phases would coalesce, and the interface would cease to exist.
