Based on this, Turnbull and Vonnegut (1952) modified the equation for homogenous nucleation rate to give an expression for heterogenous nucleation rate. If activation energy for diffusion is included, as suggested by Stokey (1959a), the equation then becomes: From these equations, heterogeneous nucleation can be described in terms of the same parameters as homogeneous nucleation with a shape factor, which is a function of θ (contact angle). The term is given by: if the nucleus has the form of a spherical cap. In addition to nucleation, crystal growth is also required for the formation of glass ceramics. The crystal growth process is of considerable importance in determining the morphology of the produced glass ceramic composite material. Crystal growth is primarily dependent on two factors. First, it is dependent upon the rate at which the disordered structure can be re-arranged into a periodic lattice with longer-range order. Second, it is dependent upon the rate at which energy is released in the phase transformation (essentially the rate of cooling at the interface). Glass Ceramics in Medical Applications Glass-ceramics are used in medical applications due to their unique interaction, or lack thereof, with human body tissue. Bioceramics are typically placed into the following groups based on their biocompatibility: biopassive (bioinert), bioactive, or resorbable ceramics. Biopassive (bioinert) ceramics are, as the name suggests, characterized by the limited interaction the material has with the surrounding biological tissue. Historically, these were the "first generation" biomaterials used as replacements for missing or damaged tissues. One problem resulting from using inert biomaterials was the body's reaction to the foreign object; it was found that a phenomenon known as "fibrous encapsulation" would occur, where tissues would grow around the implant in an attempt to isolate the object from the rest of the body. This occasionally caused a variety of problems such as necrosis or sequestration of the implant. Two commonly used bioinert materials are alumina (Al2O3) and zirconia (ZrO2). Bioactive materials have the ability to form bonds and interfaces with natural tissues. In the case of bone implants, two properties known as osteoconduction and osteoinduction play an important role in the success and longevity of the implant. Osteoconduction refers to a material's ability to permit bone growth on the surface and into the pores and channels of the material. Osteoinduction is a term used when a material stimulates existing cells to proliferate, causing new bone to grow independently of