Nuclei, crystal boundaries

Three main constraints tend to decrease the rate of product formation through nucleus growth. These are coalesence of nuclei, ingestion of sites potentially capable of generating nuclei, and crystal boundaries, and are explained below. 

The existence of the phase boundary between the solid and liquid phase complicates matters, since a phase boundary is associated with an increase in free energy of the system which must be offset by the overall loss of free energy. For this reason the magnitudes of the activated barriers are dependent on the size (i.e. the surface to volume ratio of the new phase) of the supramolecular assembly (crystal nucleus). This was recognized in 1939 by Volmer in his development of the kinetic theory of nucleation from homogeneous solutions and remains our best model today (Volmer 1939). 

The formation of a new phase inside a solid phase is very difficult, because the transition generally implies a change in density, hence in volume. This leads to a change in pressure, and thereby to an additional, generally large and positive, term in free energy for nucleus formation. Except for some solid —> solid transitions where the change in density is small, this tends to prevent nucleation any formation of a new phase will occur at the boundary of the system. Sublimation then does not need nucleation the new phase (gas) is already present. The same holds for a solid phase (crystals) in a solution. When crystals in air tend to melt, a liquid... 

Bonding within the silicate layers is predominantly ionic. As a result, forces are undirected and ion size plays an important role in determining crystal structure. Table 5.1 shows the crystal radii of common ions in silicates. The distance between two adjacent ions in a crystal can be measured accurately by x-ray methods. From a series of such measurements between different ions, the effective contributing radius of each ion can be determined. An ion has no rigid boundary an ion s radius depends on the number of its orbital electrons and on their relative attraction to the ion s nucleus. The radius of Fe ions, for example, decreases from 0.074 to 0.064 ran... 

In both, layer and suspension crystallization solid material forms from the melt starting with a nucleus through which a solid/liquid interface is created. As crystallization proceeds the mass of solidified substance steadily increases which causes the interface to move. The impurity components remaining in the melt thereby enrich in front of the solid/liquid interface, forming a concentration boundary layer. The concentration profile in this boundary layer changes as the interface advances which is in literature referred to as moving boundary problem. ... 

The formation of the polycrystal nucleus with defects distributed among the crystal grains with low atomic density and change interatomic distances. In addition, the grain boundaries are non-equilibrium and contain a great number of grain-boundary defects. 

The thermodynamic model presented above only predicts when phase separation will occur. There are, however, two mechanisms by which phase separation can actually occur. The first mechanism is similar to that discussed in an earlier chapter for precipitation of crystals from a melt, where a nucleus is formed and then grows with time. By analogy, this mechanism is termed nucleation and growth. Many of the same factors which control crystal formation also affect phase separation by this mechanism. The second mechanism is termed spinodal decomposition. This mechanism involves a gradual change in composition of the two phases until they reach the immiscibility boundary. 

The emergence of a new phase due to local structural fluctuations in a lattice of the original solid phase Ag occurs most often at the boundaries and defect sites of the crystals. Thermodynamically stable nucleus of new phase has often a critical size close to unit cell volume, which differs from the normal one. This gives rise to mechanical stresses in the transformation zone, and even the destruction of the original crystal. Such effect leads to smaller quantity of a desired product. Thermal decomposition reaction, like all topochemical reactions, proceeds more rapidly... 

---