Lattice growth

The data given in Table 15.7 indicate that, as the calcination temperature increases, the variation of crystalline form is accompanied by crystal lattice growth. In particular, the size of the product calcined at 800°C is significantly enlarged the average size is larger than that of the product calcined at 600°C by about 20 nm. 

Northby27 discussed in detail the foundations of the lattice-growth approach and applied it in determining the structures of clusters for which the atoms interact with each other via Lennard-Jones potentials. As core structures Northby used structures derived from an icosahedron. He argued that also for cluster sizes for which icosahedra cannot be constructed directly, the icosahedron forms an important structural motif. Based on a single icosahedron, there are various ways of adding additional atoms. One set of structures is formed by the MIC structures, i.e., multi-layer icosahedral structures. Here,... 

Cluster Growth. - The lattice-growth method assumes that, starting with a pre-defined core, for a given cluster there is only a finite set of lattice positions that can be filled with additional atoms. A generalization of this approach is to let additional atoms take any positions as they want. Thus, from one or more structures for the cluster with N atoms, atom number N + 1 is placed at various randomly chosen positions. Subsequently, each of those structures is allowed to relax, and the structures of the lowest total energy are kept for the addition of a further atom. 

Northby27 optimized the structures of these clusters for 13 < N < 147 using the lattice-growth method of Section 2.6. He presented first of all a discussion of how the structure evolves when atom after atom is added to the cluster. By studying iE(N) of Eq. (49) he identified a number of values for which the clusters were particularly stable. 

The electrode reaction may involve the formation of a new phase (e.g. the electrodeposition of metals in plating, refining and winning or bubble formation when the product is a gas) or the transformation of one solid phase to another (e.g. reaction (1.5)). The formation of a new phase is itself a multistep process requiring both nucleation and subsequent growth, and crystal growth may involve both surface diffusion and lattice growth. 

---