Crystal morphology surface energy

Population balances and crystallization kinetics may be used to relate process variables to the crystal size distribution produced by the crystallizer. Such balances are coupled to the more familiar balances on mass and energy. It is assumed that the population distribution is a continuous function and that crystal size, surface area, and volume can be described by a characteristic dimension T. Area and volume shape factors are assumed to be constant, which is to say that the morphology of the crystal does not change with size. 

The equilibrium shape of a crystal is, as described above, a polyhedron where the size of the crystal facets is inversely proportional to their surface energy, ysg. In the present section we will consider other types of interfaces as well and we will show that the interface energies determine the equilibrium morphology of interfaces in general. 

Surface relaxation thus has several effects. It modifies and reconstructs the surface atomic structure. Surface energies are reduced (possibly by as much as a factor of three in the above example - from 6.0 to 2.0 J m-2). More generally, it can reorder the relative stability of different surfaces and thus have a profound effect on the crystal morphology. 

Crystals grow by addition of molecules from the surroundings to the exposed faces of the crystal. When there are present in the surroundings not only substrate molecules but also impurity molecules that are stereochemically similar to the substrate, these latter molecules may also add to the surfaces. The result will be a retardation of crystal growth (267). Furthermore, since the energy of the attachment of the impurity will differ from face to face, a modification of the crystal morphology may also result (268,269). 

The CVD reactor must be designed and operated in such a manner that changes in film thickness, crystal structure, surface morphology, and interface composition can be accurately controlled. The overall process performance depends on the reactor design and process variables such as reactant concentrations, flow rates, energy input, pressure, and substrate conditions. 

The systems described above are by deLnition metastable and are affected by temperature Luc-tuations. Two other factors inLuencing solubility are the effect of change in crystal morphology and the creation of a higher-energy surface on particles by mechanical stress (grinding). 

Vyas et investigated an extensive set of ceria surfaces using four different interatomic potential models they hnd that while there are differences in the absolute surface energies the relative energies do not vary, producing an ociahedral-type crystal morphology. 

---