text: The key to engineering a glass-ceramic material is controlling the nucleation and growth of crystals in the base glass. The amount of crystallinity will vary depending on the amount of nuclei present and the time and temperature at which the material is heated. It is important to understand the types of nucleation occurring in the material, whether it is homogeneous or heterogeneous.
  Homogeneous nucleation is a process resulting from the inherent thermodynamic instability of a glassy material. When enough thermal energy is applied to the system, the metastable glassy phase begins to return to the lower-energy, crystalline state. The term "homogeneous" is used here because the formation of nuclei comes from the base glass without any second phases or surfaces promoting their formation.
  The rate of homogenous nucleation in a condensed system can be described with the following equation, proposed by Becker in 1938.
  Where Q is the activation energy for diffusion across the phase boundary, A is a constant, and  is the maximum activation energy for formation of a stable nucleus, as given by the equation below.
  Where  is the change of free energy per unit volume resulting from the transformation from one phase to the other, and  can be equated with interfacial tension.
  Heterogeneous nucleation is a term used when a nucleating agent is introduced into the system to aid and control the crystallization process. The presence of this nucleating agent, in the form of an additional phase or surface, can act as a catalyst for nucleation and is particularly effective if there is epitaxy between the nucleus and the substrate. There are a number of metals that can act as nucleating agents in glass because they can exist in the glass in the form of particle dispersion of colloidal dimensions. Examples include copper, metallic silver, and platinum. It was suggested by Stookey in 1959 that the effectiveness of metallic nucleation catalysts relates to the similarities between the crystal structures of the metals and the phase being nucleated. 
  The most important feature of heterogenous nucleation is that the interfacial tension between the heterogeneity and the nucleated phase is minimized. This means that the influence that the catalyzing surface has on the rate of nucleation is determined by the contact angle at the interface. 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).